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Characterizing debris discs in the late stages of planet formation White, Jacob Aaron 2018

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Characterizing Debris Discs in theLate Stages of Planet FormationbyJacob Aaron WhiteB.A., Texas Tech University, 2010B.Sc., The University of Texas at Dallas, 2014A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Astronomy)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)June 2018c© Jacob Aaron White 2018Committee PageThe following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the dis-sertation entitled:Characterizing Debris Discs in the Late Stages of Planet Formationsubmitted by Jacob White in partial fulfillment for the requirements forthe degree of Doctor of Philosophyin AstronomyExamining Committee:Aaron Boley, Physics and AstronomySupervisorIngrid Stairs, Physics and AstronomySupervisory Committee MemberHarvey Richer, Physics and AstronomyUniversity ExaminerMark Jellinek, Earth, Ocean and Atmospheric SciencesUniversity ExaminerAdditional Supervisory Committee Members:Brett Gladman, Physics and AstronomySupervisory Committee MemberPaul Hickson, Physics and AstronomySupervisory Committee MemberAllison Lister, Physics and AstronomySupervisory Committee MemberiiAbstractDebris discs are systems of dynamically evolved byproducts of the planetformation process. They can be used to test various planet formation the-ories. In my thesis I use submm-cm observations to characterize the debrisin HD 141569 and Fomalhaut, as well as to investigate how stellar emissioncan serve as a confounding parameter in disc studies.HD 141569 is a unique system hosting a large B9.5 star, a complexcircumstellar disc of gas and dust, and two M dwarf companions. UsingALMA data, I inferred the total gas mass of the system and directly imagedthe inner and outer edge of the gas disc. Using ALMA and VLA data,I placed constraints on the morphology, mass, and dynamical state of theinner and outer dust discs. I used the properties of the gas and dust to arguethat the system may be more accurately characterized as a young debris discas opposed to a transitional disc.Fomalhaut is a commonly studied nearby debris system. I used ALMAobservations to place tight constraints on the morphology, mass, and grainsize distribution of the outer debris ring. In addition, I used ALMA and IRdata to cast doubt on the existence of an asteroid belt in the inner system.To separate the emission from discs and their host stars, high angularresolution observations are necessary. When the resolution is still not suffi-cient to spatially separate the two, an accurate model of the stellar emissionis required. I am the PI on an observational campaign entitled Measuringthe Emission from Stellar Atmospheres at Submillimeter/millimeter wave-lengths (MESAS). This project seeks to observe stars with no known debrisat wavelengths commonly used for studying discs, build a spectral profileof the sub-millimetre to centimetre emission, and use these profiles as tem-plates for the stellar emission in unresolved debris features.iiiLay SummaryCircumstellar discs are the nurseries in which planets are born. Thick cloudsof gas and dust flatten out into a disc as a young star begins its life. Asthese discs evolve, the material sticks together making larger objects untilthey eventually form planets. During this planet formation process, therewill be leftovers in the form of asteroids and comets. These leftovers cangrind down over time into a broad ring of material, referred to as a debrisdisc. These debris discs are similar to the asteroid and Kuiper belts in ourown Solar System.Studying these debris discs can give insight into the planet formationprocess. As our Solar System is very evolved at an age 4.5 billion years,these debris discs can serve as an astrophysical lab to test various planetformation theories. My thesis focuses on ways to study the properties ofthese discs using radio telescopes.ivPrefaceChapter 2 presents ALMA observations of the HD 141569 system. Thischapter was published in The Astrophysical Journal (White et al., 2016a).Aaron Boley was the PI of the observations; Stuartt Corder and Mered-ith Hughes assisted in the reduction of the data; Eric Ford assisted in theMCMC analysis; all co-authors provided valuable feedback on the manuscript.Chapter 3 presents ALMA and VLA observations of the HD 141569system. This chapter was published in the Monthly Notices of the RoyalAstronomical Society (White et al., 2017). Aaron Boley was the PI of theVLA observations; Meredith MacGregor assisted in setting up the VLAobservations; all co-authors provided valuable feedback on the manuscript.Chapter 4 presents ALMA observations and analysis on the extendeddisc in HD 141569. The chapter was published in The Astrophysical JournalLetters (White and Boley, 2018). Aaron Boley provided valuable feedbackon the manuscript.Chapter 5 presents ALMA observations of the Fomalhaut system. Thischapter was published in the Monthly Notices of the Royal AstronomicalSociety (White et al., 2016b). Aaron Boley was the PI of the observations;Eric Ford provided assistance on the MCMC modelling; private communi-cation with Mark Booth was helpful for the image plane analysis; and allco-authors provided valuable feedback on the manuscript.Chapter 6 presents JCMT, SMA, and VLA observations of Sirius A.This chapter was published in The Astrophysical Journal (White et al.,2018). Jason Aufdenberg and Peter Hauschildt provided the PHOENIXmodel of the stellar atmosphere; private communication with Mark Gurwelland Chunhua Qi was helpful for the reduction of the SMA data; all co-authors provided valuable feedback on the manuscript.Chapter 7 presents an ongoing project to thoroughly analyze the cen-tral emission in the Fomalhaut system. The chapter makes use of resultsfrom chapters 5 and 6, and additional observations have been proposed (dis-position not known at the time of this writing) to extend the work into apublishable manuscript.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . xxivAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . xxviDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxvii1 Introduction to Circumstellar Discs: Theory, Observations,and Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Planet Formation . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Circumstellar Discs . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 Protoplanetary discs . . . . . . . . . . . . . . . . . . 21.2.2 Debris Discs . . . . . . . . . . . . . . . . . . . . . . . 41.3 How to Study Debris Discs . . . . . . . . . . . . . . . . . . . 71.3.1 Morphology . . . . . . . . . . . . . . . . . . . . . . . 71.3.2 Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3.3 Grain Distribution . . . . . . . . . . . . . . . . . . . . 101.4 Observational Studies of Debris Discs . . . . . . . . . . . . . 171.5 Observing and Modelling Discs . . . . . . . . . . . . . . . . . 211.5.1 Data Reduction . . . . . . . . . . . . . . . . . . . . . 21viTable of Contents1.5.2 Data Modelling Techniques . . . . . . . . . . . . . . . 241.5.3 MCMC Approach to Model fitting . . . . . . . . . . . 252 ALMA Observations of HD 141569’s Circumstellar Disc . 282.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.3.1 Continuum . . . . . . . . . . . . . . . . . . . . . . . . 332.3.2 Gas Disc . . . . . . . . . . . . . . . . . . . . . . . . . 352.3.3 MCMC Modelling . . . . . . . . . . . . . . . . . . . . 382.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.4.1 Disc Asymmetry . . . . . . . . . . . . . . . . . . . . . 442.4.2 Debris/Dust Mass . . . . . . . . . . . . . . . . . . . 452.4.3 Gas Mass . . . . . . . . . . . . . . . . . . . . . . . . . 472.4.4 What can HD 141569 tell us about grain growth, planetformation, and disc evolution? . . . . . . . . . . . . . 492.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 ALMA and VLA Observations of the HD 141569 System 533.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.2.1 Archival Data . . . . . . . . . . . . . . . . . . . . . . 553.3 UV Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 593.3.1 VLA Data . . . . . . . . . . . . . . . . . . . . . . . . 593.3.2 ALMA Data . . . . . . . . . . . . . . . . . . . . . . . 593.4 The Warm Dust Disc . . . . . . . . . . . . . . . . . . . . . . 613.4.1 The VLA 16A Null Detection of the Disc . . . . . . . 613.4.2 Millimetre Spectral Index of the Disc . . . . . . . . . 613.5 Origin of the 9 mm Emission . . . . . . . . . . . . . . . . . . 653.5.1 HD 141569A . . . . . . . . . . . . . . . . . . . . . . . 653.5.2 M Dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . 673.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704 Extended Millimetre Emission in the HD 141569 Circum-stellar Disc Detected with ALMA . . . . . . . . . . . . . . . 714.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.2 Observational Data . . . . . . . . . . . . . . . . . . . . . . . 724.3 Visibility Fitting . . . . . . . . . . . . . . . . . . . . . . . . . 724.3.1 Single-Component Model . . . . . . . . . . . . . . . . 734.3.2 Two-Component Model . . . . . . . . . . . . . . . . . 74viiTable of Contents4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835 1.3 mm ALMA Observations of the Fomalhaut Debris Sys-tem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.3 Debris Disc Modelling . . . . . . . . . . . . . . . . . . . . . . 885.3.1 Image Plane . . . . . . . . . . . . . . . . . . . . . . . 895.3.2 Visibility Plane . . . . . . . . . . . . . . . . . . . . . 905.3.3 Comparison between approaches . . . . . . . . . . . . 935.3.4 Additional Properties of the Debris System . . . . . . 965.4 SED Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 985.4.1 What can the observations tell us about a possibleclose in warm debris system? . . . . . . . . . . . . . . 1005.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046 MESAS: Measuring the Emission of Stellar Atmospheres atSubmm-mm Wavelengths . . . . . . . . . . . . . . . . . . . . . 1066.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1066.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 1086.2.1 JCMT . . . . . . . . . . . . . . . . . . . . . . . . . . 1086.2.2 SMA . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096.2.3 VLA . . . . . . . . . . . . . . . . . . . . . . . . . . . 1106.3 Visibility Model Fitting . . . . . . . . . . . . . . . . . . . . . 1116.4 PHOENIX Model . . . . . . . . . . . . . . . . . . . . . . . . 1126.5 Implications for Circumstellar Disc Studies . . . . . . . . . . 1166.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1177 No Evidence for an Asteroid Belt in the Fomalhaut DebrisSystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1197.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1197.2 Observational Data . . . . . . . . . . . . . . . . . . . . . . . 1217.3 Disc Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 1217.3.1 Stellar Model . . . . . . . . . . . . . . . . . . . . . . 1237.3.2 Asteroid Belt Models . . . . . . . . . . . . . . . . . . 1257.3.3 Small Grain Disc Model . . . . . . . . . . . . . . . . 1277.4 Model Comparison and Discussion . . . . . . . . . . . . . . . 1307.4.1 A Poynting-Robertson Disc . . . . . . . . . . . . . . . 1347.4.2 Followup Analysis . . . . . . . . . . . . . . . . . . . . 136viiiTable of Contents7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1368 Summary and Ongoing Work . . . . . . . . . . . . . . . . . . 1388.0.1 HD 141569 . . . . . . . . . . . . . . . . . . . . . . . . 1388.0.2 MESAS . . . . . . . . . . . . . . . . . . . . . . . . . . 1398.0.3 Fomalhaut . . . . . . . . . . . . . . . . . . . . . . . . 1408.1 Followup Work and Future Observations . . . . . . . . . . . 1408.1.1 HD 141569 . . . . . . . . . . . . . . . . . . . . . . . . 1408.1.2 Fomalhaut . . . . . . . . . . . . . . . . . . . . . . . . 1418.1.3 MESAS . . . . . . . . . . . . . . . . . . . . . . . . . . 141Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143ixList of Tables2.1 Summary of select previous HD 141569 debris disc obser-vations. Uncertainties provided when available. Referenceslisted are: (1) Fisher et al. (2000); (2) Walker and Wols-tencroft (1988); (3) Marsh et al. (2002), (4) Mouillet et al.(2001); (5) Augereau et al. (2001); (6) Nilsson et al. (2010);(7); Sylvester et al. (2001) . . . . . . . . . . . . . . . . . . . . 302.2 Summary of observed values for both gas and dust. The fluxdensities are determined by fitting the visibilities by a discmodel (see Sec. 5.1). The peak intensity and angular size arederived from the CLEANed images. Linear sizes assume adistance of 116 pc and are measured across the semimajoraxis of the continuum and gas. The uncertainties for the fluxdensities and the line fluxes include the σRMS of the observa-tions and an absolute flux calibration uncertainty of ∼ 10%added in quadrature. The uncertainties in the intensities onlyinclude the σRMS. . . . . . . . . . . . . . . . . . . . . . . . . . 322.3 Summary of CASA’s uvmodelfit results for the debris disc.The data were fit by comparing a simple, uniform disc modelto the data visibilities. The position angle is measured in de-grees East of North. The fitting uncertainties for parametersother than flux are not included here, but are addressed forthe gaseous disc in section 2.5. . . . . . . . . . . . . . . . . . 352.4 Ranges for the flat prior distributions of each parameter. TheGaussian widths are also given for the proposal distributions.The prior is based on the UV model fitting results given inTable 2.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.5 Summary of MCMC Results with 95% Credible Range. . . . 42xList of Tables3.1 Summary of CASA’s uvmodelfit results. The algorithm con-verges on the minimum χ2 iteratively. The solution is sen-sitive to the starting position and flux values, which weretaken from the CLEANed images. The sensitivity to the ini-tial starting position allows us to fit point source models tocomponents A and B separately. A point source model wasused for HD 141569A and HD 141569B in the VLA data. Adisc model was used for the ALMA data. The uncertaintiesgiven by uvmodelfit are not used throughout the analysis asthey can be underestimated up to a factor of√χ2reduced. Thelocation of the model is given as an offset from the phase cen-tre of the observations. The uncertainty in the location is thestatistical uncertainty in the model fitting procedure. . . . . . 603.2 Summary of best fit flux, peak intensity, and beam size ateach wavelength used in the analysis of the emission centredaround HD 141569A. References are given for data taken fromliterature. The best fit flux from VLA 14A presented hereis consistent with the 85 ± 5 µJy reported by MacGregoret al. (2016). The references for the various observations aredenoted by the superscripts on the observatory name and are:a) Flaherty et al. (2016), b) White et al. (2016a), c) This work. 644.1 Summary of best fit parameters for the single-component andtwo-component models. The most probable values (MP),95% credible regions (CR), and reduced χ2 are given for eachmodel along with the average for each model (assuming equalweighting). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.1 Summary of visibility and image plane MCMC results withthe most probable (MP) parameter values and 95% CredibleRange (CR). The “width” is the FWHM of the ring. . . . . . 93xiList of Tables5.2 List of select, previous observations of Fomalhaut from theliterature. The uncertainties, when not listed, are assumedto be 10%. The (*) denotes the ALMA 870 µm observationsby Boley et al. (2012). The central emission was located nearthe edge of the primary beam and as such the flux estimateis not as reliable as the flux from Su et al. (2016), where thecentral emission was at the phase centre of the observations.The 870 µm flux value from Su et al. (2016) was used in allanalysis. The references are: a) Ricci et al. (2015), b) ThisWork, c) Boley et al. (2012), d) Su et al. (2016), e) Hollandet al. (2003), f) Holland et al. (1998), g) Acke et al. (2012),h) Ishihara et al. (2010), i) Pickles and Depagne (2010), andj) Boyajian et al. (2012). . . . . . . . . . . . . . . . . . . . . . 1015.3 List of data sets selected for SED fitting. A black body wasfit to each data subset through a Bayesian approach thatincludes the uncertainties. For data from the literature, whenthe uncertainty is not given, a 10% uncertainty is used. Thebest fit brightness temperature and 95% credible region aregiven. The (*) denotes the range of data in the Herschelobservations. As these are inferred values, and not directmeasurements, for the star, they may not accurately representthe stellar flux at these wavelengths. . . . . . . . . . . . . . . 1056.1 Summary of flux values for Sirius A. The JCMT flux valueswere taken as the peak of the emission from the images. Theflux uncertainties are the σRMS of the images and the abso-lute flux calibration uncertainties added in quadrature. ForJCMT, a 5% flux calibration uncertainty is used for the 0.85mm data and a 10% flux calibration uncertainty is used forthe 0.45 mm data. For the SMA and VLA observations, theflux values were calculated using CASA’s uvmodelfit. A 10%flux calibration uncertainty is used for the SMA data and a5% flux calibration uncertainty is used for the VLA data. Theuncertainties from uvmodelfit are not used for these flux den-sity measurements because they can be underestimated up toa factor of√χ2reduced. Moreover, the uncertainty in the pointsource flux densities should be comparable to the sensitivityof the observations, motivating the use of σRMS. . . . . . . . 113xiiList of Tables7.1 Summary of the Fomalhaut observations from IR to mm wave-lengths used in this analysis. References denoted in the tableare: a) Ishihara et al. (2010), b) Stapelfeldt et al. (2004), c)Acke et al. (2012), d) Su et al. (2016), e) White et al. (2016b),f) MacGregor et al. (2017), g) Ricci et al. (2015). ∗ The pointof distinction for the two 1300 µm observations is noted be-cause of the difference in the synthesized beam (and thus theresolution) of the two observations. . . . . . . . . . . . . . . 1227.2 Summary of the best fit parameters for the two asteroid belt(AB) models (with and without the mm observation includedin the fitting procedure) and the small grain (SG) model. Themost probable values (MP), 95% credible regions (CR), andreduced χ2 are given for each model. . . . . . . . . . . . . . 132xiiiList of Figures1.1 Pictorial representation of a protoplanetary disc. This log-radial profile plot illustrates various ongoing processes as afunction of stellar separation. Republished with permission ofAnnual Reviews in Astronomy and Astrophysics from Dulle-mond and Monnier (2010); permission conveyed through Copy-right Clearance Center, Inc. . . . . . . . . . . . . . . . . . . 41.2 ALMA 230 GHz continuum image of the HL Tau protoplan-etary disc. A large series of concentric rings and gaps can beseen that may be due in part to young protoplanets activelysweeping up material in the disc (ALMA Partnership et al.,2015). Credit: ALMA (NRAO/ESO/NAOJ); C. Brogan, B.Saxton (NRAO/AUI/NSF). . . . . . . . . . . . . . . . . . . . 51.3 Resolved coronographic images of various debris discs. Fromleft to right: Fomalahut, HD 141941, HD 191089, HD 181327,β Pic. Image credits: Fomalhaut - (Kalas et al., 2005) NASA,ESA, P. Kalas, J. Graham, E. Chiang, E. Kite (University ofCalifornia, Berkeley), M. Clampin (NASA Goddard SpaceFlight Center), M. Fitzgerald (Lawrence Livermore NationalLaboratory), and K. Stapelfeldt and J. Krist (NASA JetPropulsion Laboratory); HD 141943 and HD 191089 - (Soum-mer et al., 2014) NASA, ESA, and R. Soummer and A. Feild(STScI); HD 181327 - (Schneider et al., 2006) NASA, ESA,G. Schneider (University of Arizona), and the HST/GO 12228Team; β Pic - (Apai et al., 2015) NASA, ESA, and D. Apaiand G. Schneider (University of Arizona). . . . . . . . . . . . 9xivList of Figures1.4 Illustration of how the spectra of a star can show evidencefor unresolved debris structures. The light from a star (toppanel) is approximately a black body at the stellar photo-sphere temperature. If the star was embedded in an opticallythick disc (middle panel), then this flattens the spectral in-dex, or “tail”, of the spectra at longer wavelengths. If thestar is surrounded by a ring of material that does not extenddown to the star (bottom panel), like the Kuiper Belt aroundthe Sun, then it looks like a second cooler black body addedto the stellar emission. Excess over stellar emission is takenas evidence for an unresolved debris structure. Modellingthe spectra can place constraints on the location and compo-sition of the debris. Image Credit: NASA/JPL-Caltech/T.Pyle, SSC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.5 A pictorial representation of a power law size distributionof grains in a disc. The bulk of the disc’s mass will be inthe largest of grains, with sizes up to 10s of km in diameter,similar to a large comet or asteroid. Conversely, the bulk ofthe disc’s surface area will be in µm - cm sized grains. Thelatter are the most easily observed and are used to probe thefull size distribution, and therefore mass, of a debris disc. . . 141.6 Cumulative size (diameter) distribution of objects in the KuiperBelt. The top panel shows the effective area surveyed as afunction of magnitude, which is related to the size of the ob-jects on the top axis. Due to the knee in the distributionaround radii of ∼ 50 km, a second power law is needed to ad-equately explain the total distribution. The different shadedareas correspond to the 1σ confidence regions for various pop-ulations of hot and cold Kuiper belt objects. c©AAS. Repro-duced with permission, the figure was originally published inThe Astrophysical Journal Fuentes et al. (2010). . . . . . . . 161.7 HST scattered light image of the HD 141569 circumstellar disc(Clampin et al., 2003). Spiral structure can be seen extendingout to several hundred au. The host star and inner warm discare masked out in the centre of the image. The two brightsource on the top left are bound M dwarf companions. Im-age Credit: NASA, M. Clampin (STScI), H. Ford (JHU), G.Illingworth (UCO/Lick), J. Krist (STScI), D. Ardila (JHU),D. Golimowski (JHU), the ACS Science Team and ESA . . . 18xvList of Figures1.8 Multi-wavelength view of the Fomalhaut debris system. Clock-wise from the upper left, the images show the HST scat-tered light (Kalas et al., 2008), Spitzer 24 µm data thatdo not clearly spatially separate the star and the outer disc(Stapelfeldt et al., 2004), ALMA 870 µm observations of theNW ring ansae (Boley et al., 2012), and 70 µm with Herschel(Acke et al., 2012). Image Credit: HST: NASA, ESA, P.Kalas, J. Graham, E. Chiang, E. Kite (University of Califor-nia, Berkeley), M. Clampin (GSFC), M. Fitzgerald (LLNL),and K. Stapelfeldt and J. Krist (JPL); Spitzer: NASA, JPL,K. Stapelfeldt (JPL); Herschel: ESA/PACS/Bram Acke, K.U.Leuven, Belgium; ALMA: A.C. Boley (University of Florida),M.J. Payne, E.B. Ford, M. Shabran (University of Florida), S.Corder (North American ALMA Science Center, National Ra-dio Astronomy Observatory), and W. Dent (ALMA, Chile),NRAO/AUI/NSF. . . . . . . . . . . . . . . . . . . . . . . . . 202.1 CLEANed 870 µm continuum image of HD 141569. Thecontours represent 3, 6, 12 and 21 × σRMS noise (σRMS =0.070 mJy beam−1). The dashed contour represents −1σ.The solid ellipse in the bottom left represents the beam size.A 50 au scale (assuming a system distance of 116 pc) is givenin the bottom right. The peak intensity is 1.74 ± 0.24 mJybeam−1. Coordinates are given as offset from the phase cen-tre. North is up and East is to the left. . . . . . . . . . . . . 342.2 Continuum subtracted CO(3-2) spectrum as a function ofLSRK velocity. The dashed line represents the system ve-locity of 6 km s−1. The σRMS of the individual channels is∼ 6 mJy meaning that the dominant source of uncertaintywill come from the absolute flux calibration, which I take tobe ∼ 10%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36xviList of Figures2.3 Left: CO zeroth moment map. The contours represent 3, 6, 9and 12 × σRMS noise of the continuum (σRMS = 0.070 mJybeam−1). The solid ellipse in the bottom left represents thebeam size with properties as given in Table 2.2. A 50 auscale (assuming a system distance of 116 pc) is given in thebottom right. Right: CO first moment map (velocity field).The contours represent 3, 6, 12 and 24×σRMS noise (σRMS =0.028 mJy beam−1). Coordinates are given as offset from thephase centre, as indicated on the left plot. North is up andEast is to the left. . . . . . . . . . . . . . . . . . . . . . . . . 382.4 Channel map of CO(3-2). The 25 subplots step forward in0.5 km s−1 intervals from −0.5 km s−1 to 11.5 km s−1 LSRK.The contours represent 3, 9, and 24 times the RMS noise ofthe intensity weighted map (as seen in Fig.2.3). Coordinatesare given as offset from the phase centre, as indicated on thebottom left plot. North is up and East is to the left. . . . . 392.5 Posterior probability distribution from MCMC modelling ofthe CO velocity field for 300 thousand links minus the burn-in.The blue points represent the most probable model parame-ter. The contours show 0.5, 1, 1.5, and 2×σ. . . . . . . . . . 422.6 Top: The left panel shows the first moment map of the data(same as RHS in Fig. 2.3), while the right shows the velocityfield of the model. Bottom: The panel shows the residu-als presented as a percent difference in the model from thedata. All images are shifted to the system centred velocity of6.04 km s−1. The model is consistent with the data to about10% or better throughout most of the disc. The largest de-viations occur along the minor axis. The black ellipse in thebottom corresponds to the beam with properties given in Ta-ble 2.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.7 The 4.5 km s−1, 6.0 km s−1, and 7.5 km s−1 velocity channelsof CO. The localized flux enhancement can be seen on thewest and northwest components of the gas disc. The velocitiesgiven are LSRK and are centred around a system velocity of6 km s−1. The contours represent 3, 6, 12 and 21×σRMS noise(σRMS = 0.070 mJy beam−1) fo the continuum. North is upand East is to the left. . . . . . . . . . . . . . . . . . . . . . 45xviiList of Figures3.1 CLEANed VLA 16A data of the HD 141569 system. Theemission from HD 141569A and HD 141569B are marked bythe letters “A” and “B”. HD 141569C was not detected, butits expected Gaia location is marked by “C”. The synthe-sized beam is given by the black ellipse in the bottom left ofthe image and a 150 au (∼ 1.35 arcsec) scale is given in thebottom right. Coordinates are given as offset from the phasecentre. North is up and East is to the left. . . . . . . . . . . 573.2 CLEANed ALMA 2.9 mm data of the HD 141569 system.Solid contours show 3, 6, and 12×σrms and the dashed contouris −σrms. The synthesized beam is given by the black ellipsein the bottom left of the image and a 50 au (∼ 0.45 arcsec)scale is given in the bottom right. Coordinates are given asoffset from the phase centre. North is up and East is to theleft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.3 Visibility plot of HD 141569A from VLA 16A. The top panelshows the real component of the visibilities and the bottomplanel shows the imaginary component. The red line is thebest fit point source model from uvmodelfit. The data wereannularly averaged with 40-kλ bins. The uncertainties shownare the standard deviation of each 40-kλ bin. The observa-tions are consistent with a point source centred on the loca-tion of HD 141569A. . . . . . . . . . . . . . . . . . . . . . . . 623.4 Spectrum of HD 141569, showing the range of spectral indicesbased on different values for the flux densities. The ALMAobservations are denoted by red stars. The VLA 9 mm ob-servations from semesters 14A and 16A are denoted as blackcircles. The SMA 870 µm flux observation is denoted by theblue triangle. The red shaded area represents the expectedflux values for a collisional cascade model (q = 3.5) with theflux anchored at the ALMA 870 µm and 2.9 mm observa-tions. The calculations for αmm are given in Section 4.2. Theuncertainties are for the total uncertainty of each observation(σrms and σabs in quadrature). . . . . . . . . . . . . . . . . . 63xviiiList of Figures3.5 Best fit 9 mm flux of HD 141569A as a function of on sourcetime divided into ∼ 5 min chunks. Left: Semester 14A ob-servations from June 2014 that found 82 ± 6 µJy. Right:Semester 16A observations from June 2016 that found 53 ±5 µJy. The CASA task uvmodelfit and a point source modelis used to fit the flux for each time chunk. Both observa-tions achieved roughly 1 hour on source and have uncertain-ties given by the σrms of the images of each individual timechunk. The mean values of σrms are 21 µJy beam−1 and16 µJy beam−1 for VLA 14A and VLA 16A, respectively.The solid lines represent the best fit flux for the entire lengthof each observation with the shaded region representing thetotal uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . 663.6 Best fit 9 mm flux of HD 141569B from VLA 16A as a func-tion of on source time divided into ∼ 5 min chunks. Theobservations found a total flux of 149± 8 µJy. The observa-tions achieved roughly 1 hour on source and have uncertain-ties given by the σrms of the images of each individual timechunk. The mean value of σrms is 16 µJy beam−1. The solidline represents the best fit flux for the entire length of eachobservation with the shaded region representing the total un-certainty. HD 141569C was not detected and has an upperlimit flux of ∼ 5 µJy. . . . . . . . . . . . . . . . . . . . . . . 684.1 Visibility plots of the three ALMA data sets. The real com-ponent is shown as a function of projected baseline. The cyancurves are the best fit single-component models for each fre-quency and the magenta curves are the best fit two-componentmodels for each frequency. The visibility data were annularlyaveraged with 10-kλ bins and the uncertainties shown are thestandard deviation of each bin. . . . . . . . . . . . . . . . . . 754.2 MCMC posterior distributions for the single-component model.The dashed lines indicate the most probable values and the95% Credible Region. . . . . . . . . . . . . . . . . . . . . . . 764.3 MCMC posterior distributions for the two-component model.The dashed lines indicate the most probable values and the95% Credible Region. . . . . . . . . . . . . . . . . . . . . . . 77xixList of Figures4.4 Azimuthally averaged radial profiles of HD 141569. The curveswere created by summing the total flux in elliptical aperturesof inclination 53.4◦ and PA 357◦ (White et al., 2016a). Theblack, red, and blue curves are from the ALMA data. Theywere created from the dirty images at each frequency. Theblack dashed curve is from the HST scattered light imagesfrom Konishi et al. (2016). The inner disc portion was maskeddue to artifacts as a byproduct of the PSF subtraction. Themost probable locations of the inner and outer discs as foundthrough fitting the visibilities are marked by the gray shadedareas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.1 CLEANed data of the Fomalhaut system. The syntheticbeam is given by the black ellipse in the bottom left of theimage. Coordinates are given as offset from the phase centre.North is up and East is to the left. 1′′ corresponds to ∼ 7.7au at the system distance of 7.66 pc. . . . . . . . . . . . . . 875.2 MCMC parameter posterior distributions from the image planefit. The blue points represent the most probable values. The“width” is the FWHM of the ring’s radial Gaussian profile. . 915.3 Left: Dirty Image of the Fomalhaut system used in imageplane model fitting. The synthetic beam is given by the blackellipse in the bottom left of the image. Middle: MCMC con-strained best fit model of the system. Image is convolved withthe synthetic beam and attenuated with the primary beam ofthe observations. Right: The data minus model residualsfrom the best fit model. The residuals are consistent with∼ σRMS of the observations. In all images, North is up andEast is to the left. The apparent excess in the centre of theimage is an artefact due to gridding effects in generating theimage. There is also a slight residual feature in the locationof the ring due to the image-plane fit not recovering the totalflux of the disc. . . . . . . . . . . . . . . . . . . . . . . . . . 925.4 MCMC parameter posterior distributions from the visibilityplane fit. The blue points represent the most probable values.As before, the width is the FWHM of the ring’s radial profile. 94xxList of Figures5.5 Left: CLEANed data of the Fomalhaut system. The syn-thetic beam is given by the black ellipse in the bottom leftof the image. Middle: MCMC constrained best fit model ofthe system and simulated in CASA by predicting onto the datavisibilities. Resulting image is CLEANed with the same maskas the actual data. Right: The data minus model residualsfrom the best fit model. The residuals are consistent with∼ 1.5 σRMS of the observations. In all images, North is upand East is to the left. The apparent excess in the centre ofthe image is an artifact due to gridding effects in generatingthe image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 955.6 Brightness temperature of the star from the recovered fluxat a given wavelength. The horizontal dashed line repre-sents a brightness temperature equal the stellar photosphereof TB = 8600 ± 200 K with the grey region representing theuncertainty. The blue circle is the 24 µm data, the black dia-monds are ALMA data, and the green square is ATCA data.The Herschel data are denoted as X’s since they are not directmeasurements of the star. For flux values and uncertaintiessee Table 5.2. . . . . . . . . . . . . . . . . . . . . . . . . . . 1035.7 Data from the literature and the corresponding fits to a blackbody. The blue dots represents a PHOENIX stellar atmo-sphere similar to Fomalhaut (Husser et al., 2013). The blackdashed line is the best fit black body for all data points withTB = 8647 K. The green dashed line is the 870 µm - 6600µm data with TB = 5540 K. The Herschel data are denotedas red X’s because they are not direct measurements of thestar. The vertical lines represent different regions measuredby different observatories. . . . . . . . . . . . . . . . . . . . . 1046.1 Submm-cm observations of Sirius A. The two blue curves rep-resent models of the Sun at maximum activity (solid line) andminimum activity (dashed line) from Loukitcheva et al. (2004)and are included for illustrative purposes. The observationsof Sirius A are denoted as black stars for the JCMT data,black diamonds for the SMA data, and black circles for theVLA data. The two black curves are PHOENIX models ofSirius A’s atmosphere with a non-LTE model (solid line) anda LTE model (dashed line). . . . . . . . . . . . . . . . . . . . 115xxiList of Figures7.1 Submm-cm observations of Sirius A from White et al. (2018).The two blue curves represent models of the Sun at maximumactivity (solid line) and minimum activity (dashed line) fromLoukitcheva et al. (2004) and are included for illustrative pur-poses. The observations of Sirius A are denoted as black starsfor the JCMT data, black diamonds for the SMA data, andblack circles for the VLA data. The two black curves arePHOENIX models of Sirius A’s atmosphere with a non-LTEmodel (solid line) and a LTE model (dashed line). The reddiamonds are observations of Fomalhaut’s central emission. . 1247.2 Spectral profile of Fomalhaut with the best fit models. Thered dot-dashed curve is the asteroid belt (AB) model that waswithout only 8.6 - 500 µm data (no ALMA data). The greendotted curve is an asteroid belt model that was fit with 8.6 -1300 µm data (now including ALMA data). The blue dashedcurve is the “small grain” (SG) disc model that considered 8.6- 1300 µm data. The black solid line is the stellar emissionprofile. The ATCA data is the point furthest to the right andis represented by a black X. It is not included in any modelfitting and is shown for illustrative purposes only. . . . . . . 1267.3 Posterior distributions from the MCMC model fitting of anasteroid belt without the mm data for Fomalhaut’s centralemission. The blue lines represent the most probable param-eter values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1287.4 Posterior distributions from the MCMC model fitting of anasteroid belt including the mm data for Fomalhaut’s centralemission. The blue lines represent the most probable param-eter values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1297.5 Posterior distributions from the MCMC model fitting of a“small grain disc model” (SG) for Fomalhaut’s central emis-sion. The blue lines represent the most probable parametervalues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317.6 Zoomed-in plot of Fig. 7.2. The two asteroid belt (AB) modelsclearly overpredict the flux at mm wavelengths. The greendotted curve is an asteroid belt model that was fit with allthe data up to 1300 µm. The red dot-dashed curve is theasteroid belt model that was without the mm data. Theblue dashed curve is the “small grain” (SG) disc model thatconsidered all the data. The black solid line is the Fomalhautstellar emission profile. . . . . . . . . . . . . . . . . . . . . . 133xxiiList of Symbols′ arcminute′′ arcsecondau astronomical unitδ DeclinationJy JanskyL Solar LuminosityM⊕ Earth MassMX Jupiter MassM Solar MassM∗ Stellar Masspc parsecRX Jupiter RadiusR Solar RadiusR∗ Stellar RadiusxxiiiList of AbbreviationsAB Asteroid BeltACF autocorrelation functionALMA Atacama Large Millimeter ArrayATCA Australian Telescope Compact ArrayCARMA Combined Array for Research in Millimeter-wave Astron-omyCASA Common Astronomy Software ApplicationsCHARA Center for High Angular Resolution AstronomyCO carbon monoxideCR credible regionEB execution blockESA European Space AgencyFDM frequency division modeFWHM full width half maximumGBT Green Bank TelescopeH2 molecular hydrogenHST Hubble space Telescopeinc inclinationIR infraredIRAS Infrared Astronomical SatelliteISM interstellar mediumJCMT James Clerk Maxwell TelescopeJPL Jet Propulsion LabKB Kuiper BeltLSRK local standard-of-rest kinetic velocityLSB lower side bandLTE local thermal equilibriumMESAS Measuring the Emission of Stellar Atmosphere at Sub-millimeter/millimeter wavelengthsMCMC Markov Chain Monte CarloMP most probableMS main sequencexxivList of AbbreviationsNASA National Aeronautic and Space AgencyngVLA Next Generation Very Large ArrayNOEMA Northern Extended Millimeter ArrayNIR near infraredNRAO National Radio Astronomy ObservatoryPA Position AnglePI principle investigatorPR Poynting-RobertsonPSF point spread functionPWV precipitable water vaporQA quality assuranceRA right ascensionRFI radio frequency interferenceRMS root-mean-squaredSB scheduling blockSED spectral energy distributionSMA Submillimeter ArraySNR signal-to-noise ratioSPW spectral windowSTScI Space Telescope Science InstituteTDM time division modeUSB upper side bandVLA Very Large ArrayVLT Very Large TelescopeVLTI Very Large Telescope InterferometerWVR water vapor radiometerxxvAcknowledgmentsI would like to acknowledge that all of the work done in fulfillment of thisthesis was completed on land which is the traditional, ancestral, and uncededterritory of the xwm eΘkw ey´ em (Musqueam) People.xxviDedicationThis thesis is dedicated to my parents, Loy White (TTU>UT) and MarshaSpohrer, for all of the support they have provided throughout my time as aPh.D. student.xxviiChapter 1Introduction toCircumstellar Discs: Theory,Observations, and ModellingThe Solar System is a ∼ 4.6 billion year old planetary system around a classG21 star (Bouvier and Wadhwa, 2010). As it is a single isolated system,it cannot be used to constrain the frequency of planets around other stars,nor can it be used to constrain how typical the Solar System’s configura-tion, multiplicity, and composition are in planet formation. Using the SolarSystem as a testbed for planet formation theories is also a challenge due toits age and because many of the main formation processes occur within thefirst few million years.Therefore, to understand our origins and how the Solar System formed,we turn to exoplanetary systems at different stages of evolution. Thousandsof planets have been discovered in the Milky Way galaxy and many systemsin the early to middle stages of planet formation have been identified throughthe presence of circumstellar discs. By studying the gas and debris in thesesystems, we can learn how planets may be forming in those systems andtest planet formation theories. Further still, the architecture of the disccan be used to study the dynamical history and location of planets in thosesystems.This thesis involves radio observations of two circumstellar discs: HD141569 and Fomalhaut. The former is a young system at ∼ 5 Myr and thelatter is a more evolved system at ∼ 440 Myr.HD 141569’s current stage of planet formation and disc evolution is notimmediately clear. In particular, there are a few outstanding questions thatthis thesis seeks to answer through radio observations and modelling: Whatis the source of the gas in the disc? What causes the observed morphologyof the dust? Is this disc consistent with second generation gas and dust1Throughout this thesis, spectral types are referred to by the Harvard Classificationscheme of OBAFGKM that ranges from hottest to coolest (e.g., Gray et al., 2009).11.1. Planet Formationproduction?Fomalhaut hosts two separate debris discs, similar to the Solar System.While Fomalhaut has been widely studied, this thesis uses radio observationsto answer: What is the grain size distribution, and thus the dynamical state,of the outer disc? What are the properties of the inner disc? How are theouter and inner discs related to each other?1.1 Planet FormationThe precise physical mechanisms that lead to the formation of planets arenot known, although many theories and simulations can reproduce the plan-ets in the Solar System under various assumptions (e.g., Johansen et al.,2014; Chabrier et al., 2014). The process ultimately begins with formationof stars. Stars are born out of the collapse of a large molecular cloud, con-sisting predominately of hydrogen, that can initially span over the order of0.1 pc to ∼ 200 pc and contain 100s - 1000s M of gas and dust (Williamsand Cieza, 2011). A small over-density in the cloud can disrupt the equilib-rium and lead to one or more cores collapsing. Protostars will begin to format the locations of these cores. Through the conservation of angular mo-mentum, additional material falling towards the star will eventually flattenout into a disc-like structure (Williams and Cieza, 2011). As this materialcontinues to fall into the disc and the evolution of the protostar increasesits temperature and thus radiation field, disc chemistry can begin creatinglarger and more complex solids in the disc (D’Alessio et al., 2001). Thesesolids, along with the gas in the disc, become the building blocks from whichplanets are formed.1.2 Circumstellar DiscsCircumstellar discs can be very broadly categorized as either protoplanetaryor debris discs. Although the evolutionary process may not be universal orlinear between the two, they are typically separated by at least a few millionyears in age. Studying both types of discs can give different insights intothe planet formation process.1.2.1 Protoplanetary discsA protoplanetary disc can form concurrently with or shortly after the col-lapse of a molecular cloud. This disc will be largely dominated by gas21.2. Circumstellar Discsand likely follow an Insterstellar Medium (ISM) abundance ratio of vari-ous molecular species. The grains in the disc will mostly be comprised ofsilicates of order ∼ 0.1 µm and polycyclic aromatic hydrocarbons (Draine,2003). As is the case with the local ISM, a protoplanetary disc is expectedto have a dust-to-gas mass ratio of ∼ 10−2. The dominant gas species will bemolecular hydrogen (H2), although many massive molecules will be presentat detectable abundances (e.g., CO, CO2, HCN, H2O2, CH2O) and can beused as tracers of the total gas mass of the disc. For example, the variousrotational transitions of CO are detectable with millimetre (mm) wavelengthtelescopes and their abundance ratios relative to H2 are known from studiesof the ISM (e.g., CO/H2 ∼ 10−4; Williams and Cieza, 2011).The structure of a protoplanetary disc varies with radius. Within ∼1 au of the star, the disc can be strongly influenced by stellar magneticfields. The temperatures at these distances are large enough that solids willnot be able to condense, making this section of the disc mostly comprisedof gas (Dullemond and Monnier, 2010). The stellar magnetic fields canguide accretion onto the star. Rapid accretion events likely trigger outburstsand increased periods of stellar luminosity (e.g., FU Orionis type stars;Herbig, 1977; Hartmann and Kenyon, 1996). Moving further out in thedisc, small solids can from dust that has accredited to the disc via thecollapsing envelope. The composition depends on the local disc temperatureand pressure. Condensation fronts will occur at the freeze-out points forvarious molecular species of gas, causing the surfaces of solids to changeand potentially show sudden increases in the local mass of solid material.The outer component of the protoplanetary disc will be much cooler and canserve as a “reservoir” for additional gases and small grains to be transportedthroughout the disc as clearing mechanisms begin to occur. Figure 1.1 showsa 2-D illustrative example of a protoplanetary disc (Dullemond and Monnier,2010). The broad characteristics of each region can be seen along with whichregions of the disc are observed at various wavelengths. There is also anoticeable increase in the vertical extent of the disc due to a flaring profile.This profile stems from the longer times required for dust to settle into themid-plane at larger separations from the host star.Regardless of whether or not planets actually form in a protoplanetarydisc, the disc material will eventually start to clear out. The small dustgrains in the disc will clump together and can build many “planetesimals”throughout the disc that will be of order the size of the asteroids and cometsobserved in the Solar System (Williams and Cieza, 2011; Dullemond andMonnier, 2010). As the gas freezes out of the disc and condenses on to thesolids, the disc will become increasingly optically thin. This evolution allows31.2. Circumstellar DiscsFigure 1.1: Pictorial representation of a protoplanetary disc. This log-radialprofile plot illustrates various ongoing processes as a function of stellar sep-aration. Republished with permission of Annual Reviews in Astronomyand Astrophysics from Dullemond and Monnier (2010); permission conveyedthrough Copyright Clearance Center, Inc.radiation from the host star to penetrate deeper into the disc. Processes suchas photoevaporation (e.g., Alexander et al., 2014) and photodissociation(e.g., van Dishoeck and Black, 1988; Visser et al., 2009) can then clear outthe remaining gas.The structure of protoplanetary discs can be seen with telescopes suchas the Atacama Large Millimeter Array (ALMA). Figure 1.2 shows an imageof the HL Tau protoplanetary disc (ALMA Partnership et al., 2015). Thissystem is < 1 Myr old and is located in the Taurus molecular cloud, aregion of active star formation (Welch et al., 2000; Anglada et al., 2007).As planets form, they will sweep up gas and dust making concentric “gaps”in the disc. These gaps can be difficult to observe directly due to the highangular resolution requirements. Figure 1.2 unambiguously shows multiplegaps in a protoplanetary disc for the first time.1.2.2 Debris DiscsThe planet formation process can yield a significant amount of leftover large,> km debris (Matthews et al., 2014). Most of the small µm-cm solids have41.2. Circumstellar DiscsFigure 1.2: ALMA 230 GHz continuum image of the HL Tau protoplanetarydisc. A large series of concentric rings and gaps can be seen that may bedue in part to young protoplanets actively sweeping up material in the disc(ALMA Partnership et al., 2015). Credit: ALMA (NRAO/ESO/NAOJ); C.Brogan, B. Saxton (NRAO/AUI/NSF).51.2. Circumstellar Discsrelatively short lifetimes compared to the age of the system and are expectedto be swept up into larger bodies or migrate inwards or outwards in thedisc. Hence, the bulk of leftover solid mass will be primarily in asteroid andcomet-sized material. Over a planetary system’s lifetime, these leftoverswill collisionally and dynamically evolve. This evolution is a destructiveprocess, repopulating the system with small µm-cm debris. This new systemof debris, which is referred to as a debris disc, can be taken as a signaturethat the planet formation process was at least partially successful (Wyatt,2008).Debris discs are broadly categorized into two groups: cold debris andwarm/hot debris. Cold debris discs are analogous to the Kuiper Belt in theSolar System. Most of their mass will likely be in comets and minor planetsat distances much beyond the water-ice line (the point in the disc where thetemperature is cool enough that water can freeze out and exists as ice). Asopposed to being broad and extended like a protoplanetary disc, debris discstypically have a narrower structure with well defined inner and outer edgesdue to the clearing mechanisms that created them. The location of the disccould potentially be dynamically influenced by planets in the system. In theSolar System, for example, the Kuiper Belt’s dust distribution is influencedby Neptune’s position and resonances (Moro-Mart´ın and Malhotra, 2002).Warm/hot debris discs are analogous to the asteroid belt and zodiacaldust in our Solar System. The asteroid belt overlaps the region of the SolarSystem in which the water-ice line likely existed during planet formation.These asteroids are primarily rocky, but do have varying compositions andwater content. as inferred from meteorites and asteroid taxonomy (e.g.,DeMeo and Carry, 2014). The belt’s structure and substructure is influencedby orbital resonances with the outer planets (e.g., Jupiter; Murray, 1986).Warm discs may have similar bulk properties to cold discs, but their warmertemperatures make them more likely to be primarily composed of heavierelements, such as iron and silicates, as opposed to water ice and CO.The formation of warm and cold discs likely happens concurrently withthe early clearing stages of planet formation. Warm discs could also formthrough the transport of material from the outer disc to the inner disc (e.g.,Chen et al., 2014). The transport of comets from the outer to inner SolarSystem may be a source of water on Earth (e.g., Morbidelli et al., 2000).By establishing a firm connection between the properties of and correlationbetween cold and warm debris, we can develop a virtual laboratory to testplanet formation theories.Debris discs tend to be evolved circumstellar systems and therefore donot typically have any detectable amounts of gas, as gas dispersal timescales61.3. How to Study Debris Discsare only a few million years (Haisch Jr et al., 2001). There is, however, asmall group of debris discs that contain non-negligible amounts of gas (Zuck-erman et al., 1995; Moo´r et al., 2015; Hughes et al., 2008). The total amountof gas is typically < 1 M⊕, small enough that basic clearing mechanisms,such as photoevaporation, are expected to clear them in 100s of years (e.g.,Alexander et al., 2014). Given that these system are millions of years old,there must be some source of continuous replenishment to offset the clear-ing mechanisms and molecular dissociation. The most common assumptionis that a system of dynamically evolving comets in a cold debris disc canexplain the observed gas abundances (Dent et al., 2005). As these cometscollide, they release gas such as CO. This gas should have a short lifetime,requiring a large number of cometary collisions to continuously replenish thedisc (Wyatt and Dent, 2002).β Pic is an example of a well studied gas-rich debris system. This ∼ 20Myr disc, is hosted by a bright A6 star (Binks and Jeffries, 2013). Its ageimplies that any gas leftover from the protoplanetary disc phase should havebeen cleared out. ALMA observations, however, found ∼ 4 × 10−4 M⊕ ofCO in the outer disc, the origin of which is thought to be due to a largesystem of comets (Dent et al., 2014).1.3 How to Study Debris DiscsThere are several key ways in which debris discs (and circumstellar discs ingeneral) can be studied. These include looking at the morphology of thedisc, modelling the spectral profile from a set of observations, and usingboth of these approaches to constrain the size distribution of the grains inthe disc.1.3.1 MorphologyWhen debris systems are resolved, their morphological structures can beused to constrain the locations of putative planets (e.g., Quillen, 2006) andthe dynamical history of the system (Raymond et al., 2011). Cold discsare the most commonly resolved debris discs as they have a larger angularseparation from their host star than their warm disc counterparts. Cold discscan be imaged and completely resolved through scattered light observations,thermal IR imaging, and sub-millimetre/radio observations (see Sec. 1.4).Figure 1.3 shows examples of various resolved debris discs detected withHubble Space Telescope (HST) scattered light observations.71.3. How to Study Debris DiscsEven though most of the mass in cold debris discs is in cometary objects,the small collisionally produced mm-cm sized grains can trace the locationof the parent body material. The smaller ∼ µm sized dust grains, however,will quickly migrate away from where they were produced due to processessuch as radiation pressure and Poynting-Robertson drag (Burns et al., 1979).Therefore, the grains seen in scattered light observations and the grains seenfrom thermal emission images may not necessarily be co-located with eachother.The gravitational interactions between planets in the system and thedisc itself (referred to as planet-disc interactions) can affect the location,orientation, and profile of a disc (as is the case with the Kuiper Belt andNeptune, Moro-Mart´ın and Malhotra, 2002). For example, the β Pic debrisdisc (seen in the bottom of Fig. 1.3) has an inner disc that is offset from theextended cold disc, an apparent “warping” in the cold disc, and an innerregion that is relatively debris-poor. The morphological features in the discwere thought to be due to an unobserved (at the time) planet dynamicallysculpting the disc (e.g., Burrows et al., 1995; Beust and Morbidelli, 2000;Augereau et al., 2001; Freistetter et al., 2007). This planet was later directlyimaged using the Very Large Telescope (VLT) and constrained to have amass of ∼ 8 MX and a projected semimajor axis of ∼ 8 au (Lagrange et al.,2010), well within the predicted parameters.Another example of planets sculpting the disc is in the HR 8799 system.This system hosts a large disc extending outward from 145 au (Booth et al.,2016) and four directly imaged gas giant planets with semi-major axes be-tween 15 au and 70 au (Marois et al., 2008). If the outermost planet wereto have an eccentricity of ∼ 0.3 (Moro-Mart´ın et al., 2010), then it couldbe dynamically sculpting the debris disc. Another possibility would be anas-of-yet undetected fifth planet located located near to the inner edge ofthe disc. Booth et al. (2016) find that a ∼ 1.25 MX planet located at ∼ 110au could explain the inner edge of the disc. The size of the proposed planetputs it just under the direct imaging sensitivity limits of that which wasused to detect the other planets (Zurlo et al., 2016).Warm discs are located at much smaller angular separations from theirhost stars. As such, resolving these discs is not possible unless the system issufficiently nearby. To study this unresolved debris, the excess flux over thestellar emission is taken as the flux contribution of the disc. The morphologyof the warm disc can be studied by looking at the spectral energy distribution(SED) of the system, as is discussed below.81.3. How to Study Debris Discs                            Soummer et al. 2014Schneider et al. 2014HD 181327Fomalhaut                      Kalas et al. 2005β Pic                                                                     Apai et al. 2015Figure 1.3: Resolved coronographic images of various debris discs. Fromleft to right: Fomalahut, HD 141941, HD 191089, HD 181327, β Pic. Imagecredits: Fomalhaut - (Kalas et al., 2005) NASA, ESA, P. Kalas, J. Graham,E. Chiang, E. Kite (University of California, Berkeley), M. Clampin (NASAGoddard Space Flight Center), M. Fitzgerald (Lawrence Livermore NationalLaboratory), and K. Stapelfeldt and J. Krist (NASA Jet Propulsion Labo-ratory); HD 141943 and HD 191089 - (Soummer et al., 2014) NASA, ESA,and R. Soummer and A. Feild (STScI); HD 181327 - (Schneider et al., 2006)NASA, ESA, G. Schneider (University of Arizona), and the HST/GO 12228Team; β Pic - (Apai et al., 2015) NASA, ESA, and D. Apai and G. Schneider(University of Arizona).91.3. How to Study Debris Discs1.3.2 SpectraPrior to the new age of high-resolution IR-mm facilities that exist today,most debris discs were unresolved. This situation is still the case for mostof the known warm discs, which are located at very small angular separa-tions from their host stars. Nevertheless, many properties of these warmdebris systems can still be inferred, so long as there is an accurate modelof the host star’s emission. A broad range of observations from NIR to mmwavelengths, with the stellar emission subtracted, will yield a set of “stellarexcess” flux values. These fluxes can be attributed to a warm debris discand can be studied by modelling their spectra. Figure. 1.4 is an illustrativeexample of how an unresolved disc can be studied. This image shows howthe spectra of a star, which is assumed to be approximately a black body,and the spectra of a disc can be separated. Modelling the spectral profilecan place constraints on the properties of the material in the disc, such asthe location and composition of the grains (e.g., Raymond et al., 2011). Thepeak wavelength of a ring of material’s emission, λpeak, will correspond toits temperature, TD, through Wien’s Lawλpeak =bTD, (1.1)where b is Wien’s displacement constant 2.8977×10−3 m K. Assuming thatthe disc is thin and the inner edge of the disc is in thermal equilibrium withthe host star, then the temperature of the disc, TD, can be found by settingthe power received by the star to be equal to the power emitted by the disc.The location of the disc, D, is then given byD =12R∗√(1−A)(T∗TD)2, (1.2)where R∗ is the stellar radius, T∗ is the stellar temperature, and A is thegrain’s albedo. The spectral index (the slope of the spectral profile) at longerwavelengths can also be related to the grain size distribution of the materialin the disc (e.g., MacGregor et al., 2016; Ga´spa´r et al., 2012). If this sizedistribution is known, then it can be used to obtain a mass estimate of thedisc for objects of a given size range.1.3.3 Grain DistributionResolved images that clearly map out the distribution of material are aninvaluable tool for studying debris discs. Even if such maps are not available,101.3. How to Study Debris DiscsFigure 1.4: Illustration of how the spectra of a star can show evidence forunresolved debris structures. The light from a star (top panel) is approxi-mately a black body at the stellar photosphere temperature. If the star wasembedded in an optically thick disc (middle panel), then this flattens thespectral index, or “tail”, of the spectra at longer wavelengths. If the staris surrounded by a ring of material that does not extend down to the star(bottom panel), like the Kuiper Belt around the Sun, then it looks like asecond cooler black body added to the stellar emission. Excess over stellaremission is taken as evidence for an unresolved debris structure. Modellingthe spectra can place constraints on the location and composition of thedebris. Image Credit: NASA/JPL-Caltech/T. Pyle, SSC.111.3. How to Study Debris Discsmany parameters of a disc can be constrained through studying its grain sizedistribution. The grain size distribution at any given radial location in adisc can depend on many factors, including properties of the host star, thesize and composition of the grains, and the current dynamical state of thedisc.While disc-disc and disc-planet interactions can influence the location ofdisc grains, radiation forces of the host star in a disc can lead to significantgain migration. These forces will not affect all grain sizes uniformly. Thus,the spatial distribution of grains relative to the parent bodies will be differentbased on given grain sizes and properties. One of these effects is radiationpressure from the star (Burns et al., 1979), which is given as~Frad =LAQpr4picr2rˆ, (1.3)where L is the stellar luminosity, A is the cross sectional area of a givengrain, r is the distance from the grain to the star, rˆ is the radial unit vector,c is the speed of light, and Qpr is a dimensionless efficiency parameter thatranges from 0 to 2. The ratio, β, of ~Frad to the gravitational force from thestar isβ =3LQpr16picGsMρ, (1.4)where s is the grains radius, M is the mass of the host star, G is the gravi-tational constant, and ρ is the density of the grains. This parameter can beused to write down an effective gravitational force a given grain feels fromthe host star~Feff = −GMmr2(1− β)rˆ. (1.5)Relating the potential energy of the effective force to the kinetic energy ofa grain, there exist values of β > 0.5 for which the grains are no longergravitationally bound to the disc for an initially circular orbit. The cor-responding size at which grains are no longer bound is referred to as the“blowout” size and is typically on the order of 1-10 µm, depending on thestellar environment. All collisionally produced grains smaller than this sizewill be blown out of the disc. This limit implies that any grains of this sizeobserved in a disc must have been collisionally produced recently.Conversely, radiation effects from the star can serve as a drag force onlarger grains. This Poynting-Robertson drag (PR) causes an inward migra-121.3. How to Study Debris Discstion of grains that, given enough time, will eventually accrete onto the staror be destroyed (Burns et al., 1979). This force can be expressed as~FPR = −GMmr2β[(1− 2vrc)rˆ − vθcθˆ], (1.6)where vr and vθ correspond to the grain velocity components in polar coordi-nates and β is the radiation pressure ratio calculated above. The associatedtimescale for infall onto the star istpr ∼ cr24GMβ. (1.7)Since these processes effectively clear out grains in a disc, the observedabundances of small grains require relatively frequent collisions to be occur-ring. Assuming that there is little to no gas present in a disc, and thereforenegligible gas-dust coupling, the collisional timescale of debris will be dic-tated by the surface density of material in the disc and the cross-sectionalarea of the grains. In the simplest of scenarios, the collisional timescale fora given grain size can be written astcol ∼ 1NσΩ, (1.8)where N is the vertical column number density, σ is a grain’s cross-sectionalarea, and Ω is the Keplerian orbital frequency. This collision rate can beenhanced further through processes such as mutual gravity between densepatches of grains or planetesimals, radiation driven migration of grains, orinteractions between grains and residual gas, if present (e.g., Wyatt et al.,2015). The collisional process will eventually lead to a steady-state sizedistribution in ∼ 10− 20 Myr (Wyatt, 2008).The collisional processes that repopulate the small grains in a disc yieldtheoretical size distributions of solid material (Pan and Schlichting, 2012).They typically follow a power law distributiondNds∝ s−q, (1.9)where N is the number of grains, s is a given grain size, and q is the index ofthe size distribution (q is often directly referred to as the grain size distri-bution). Figure 1.5 shows an illustrative example of a power law grain sizedistribution.The classic steady-state distribution given by Dohnanyi (1969) predictsq ∼ 3.5. Observational constraints on the µm-cm sized objects in debris131.3. How to Study Debris DiscsFigure 1.5: A pictorial representation of a power law size distribution ofgrains in a disc. The bulk of the disc’s mass will be in the largest of grains,with sizes up to 10s of km in diameter, similar to a large comet or asteroid.Conversely, the bulk of the disc’s surface area will be in µm - cm sized grains.The latter are the most easily observed and are used to probe the full sizedistribution, and therefore mass, of a debris disc.141.3. How to Study Debris Discsdiscs find 3 < q < 4 (e.g., MacGregor et al., 2016) In practice, as thecollisional process continues for Myr - Gyr, a collisional “grinding” will leadto deviations from a pure power law. This means there could be a “divot”or a “knee” in the size distribution that will lead to the total distributionbeing better explained by multiple power laws (e.g., Shankman et al., 2016).For example, in the Kuiper Belt there is a clear change in the slope ofthe size distribution. This occurrence is highlighted in Fig. 1.6 in which aturnover to a steeper power law is seen for objects with radii > 50 km. Asthe Kuiper Belt is much older than most observed debris discs, there hasbeen plenty of time for collisional grinding and the migration of small solidsthrough radiation pressure. Nevertheless, observations of the Kuiper beltcan provide constraints on the size distribution of large >km sized objectsin debris discs, as these large objects are not observable in other systems.A constraint on the grain size distribution of a given disc can allowfor estimates of the debris mass. For a single observation (and therefore asingle flux value), the conservative approach to infer the debris mass is toassume the disc is only populated by grains of a size, s. If the grains emitat a wavelength comparable to the wavelength of the observations, then thetotal debris mass is given byM =43ρpis3FνBν(r)Ωs, (1.10)where ρ is the grain density, Fν is the observed flux density, Bν(r) is theblack body intensity for a single grain placed at a distance r from the star,and Ωs = pi(rd)2 is the solid angle of a single grain for a system distance of d.In this relation, the grains are further assumed to be in thermal equilibriumwith the host star’s radiation and to be perfect absorbers and radiators(albedo of 0, emissivity of 1). For a cold disc, ρ ∼ 1 g cc−1 can typically beassumed to be representative of cometary-type material. For a warm disc,ρ ∼ 2.0− 3.0 g cc−1 would be more representative of asteroid-type material.This mass estimate assumes that no grains of any other size are present inthe disc and all the debris is located in a thin ring of material.A much more detailed calculation can be made with some straightfor-ward assumptions. A full distribution of grain sizes can be assumed witha minimum size equal to the blowout size and the maximum equal to thesize of a large asteroid/comet. The value for q can be assumed (e.g., 3.5 fora steady-state collisional cascade; Dohnanyi, 1969) or constrained from ob-servations (as is discussed in Section 1.4). The observationally constrainedsurface brightness profile can also be incorporated into the calculation. Thequantities, including the local value of Bν(r) in the above calculation, can151.3. How to Study Debris DiscsFigure 1.6: Cumulative size (diameter) distribution of objects in the KuiperBelt. The top panel shows the effective area surveyed as a function ofmagnitude, which is related to the size of the objects on the top axis. Dueto the knee in the distribution around radii of ∼ 50 km, a second power lawis needed to adequately explain the total distribution. The different shadedareas correspond to the 1σ confidence regions for various populations ofhot and cold Kuiper belt objects. c©AAS. Reproduced with permission, thefigure was originally published in The Astrophysical Journal Fuentes et al.(2010).161.4. Observational Studies of Debris Discsbe integrated from the inner to outer edge of the disc. Since a given grainwill not emit efficiently at all wavelengths, an additional emission coefficientcan be introduced. The grains are only assumed to radiate efficiently iftheir circumference is equal to or larger than the absorbing/emitted pho-tons (Draine, 2006). This constraint is again integrated over a wide range offrequencies. The mass can then be calculated through an iterative approachto converge on a final total disc mass. This approach again has a caveat oflargely depending on the density assumed as well as the maximum size usedin the calculation. For a grain size distribution of q = 3.5 the mass will beM(< Dmax) ∝ ρ√Dmax (1.11)for total grains less than a diameter Dmax. This mass calculation is discussedin much more detail in Chapters 2, 4, and 5.Even with the limitations of these mass calculations, they are still valu-able tools in assessing the total abundance of material leftover from planetformation. When studying unique systems, such as gas-rich debris discs, thetotal mass calculations can provide a useful diagnostic to determine if thecometary reservoir in a disc is sufficient enough to replenish the gas observedin the disc.1.4 Observational Studies of Debris DiscsWhile debris discs can be full of solids ranging from µm to planet-sized ob-jects, the µm - cm grains are the easiest to study. The smallest of these grainsare typically probed through scattered light observations in the optical andnear infrared (NIR). As discs evolve from the optically thick protoplanetaryphase to the optically thin debris phase, light from the host star can pen-etrate deeper into the disc. This starlight can be scattered by the debriswithin the disc, in which grains most efficiently scatter light at wavelengthscomparable to their size. When studying the scattered light data of a disc,properties of the grains such as diameter, composition, and porosity, as welldisc morphology can be obtained. Figure 1.7 shows a scattered light imageof the HD 141569 circumstellar disc as seen with the Hubble Space Telescope(Clampin et al., 2003). The large-scale spiral features suggest a combina-tion of (1) dynamical interactions between the companion M dwarfs (seenin the upper left of the image) and the disc, (2) potentially strong couplingbetween the dust grains and remaining gas in the system, and (3) possibleperturbations from a planetary system (Clampin et al., 2003).171.4. Observational Studies of Debris DiscsFigure 1.7: HST scattered light image of the HD 141569 circumstellar disc(Clampin et al., 2003). Spiral structure can be seen extending out to severalhundred au. The host star and inner warm disc are masked out in thecentre of the image. The two bright source on the top left are bound Mdwarf companions. Image Credit: NASA, M. Clampin (STScI), H. Ford(JHU), G. Illingworth (UCO/Lick), J. Krist (STScI), D. Ardila (JHU), D.Golimowski (JHU), the ACS Science Team and ESA .181.4. Observational Studies of Debris DiscsInfrared (IR) and longer wavelength observations of discs can directlydetect the thermal emission from the grains themselves. IR facilities such asthe Infrared Astronomical Satellite (IRAS) and Herschel Space Observatory(Herschel) began detecting debris discs around stars through inferred excessover the expected stellar emission. IRAS serendipitously discovered thefirst debris disc around Vega through IR excess at 25 µm, 60 µm, and 100µm (Aumann et al., 1984). This excess was first attributed to a “shell” ofmaterial around the star and later confirmed to be due to a cold debris belt.As infrared telescopes are put into space to avoid the Earth’s atmosphere,they tend to have smaller apertures and thus worse angular resolution thanground-based optical telescopes. Current facilities such as Spitzer, however,still provide valuable information. When combined with higher and lowerfrequency data, IR observations can help constrain the spectral index (andthus the grain size distribution) of the material in the disc.Sub-millimetre to millimetre observations of discs can be made withfacilities such as ALMA, the Karl G. Jansky Very Large Array (VLA),the James Clerk Maxwell Telescope (JCMT), and the Submillimeter Ar-ray (SMA). These wavelengths target thermal emission and are often easierto separate from stellar emission than IR observations. Facilities such asALMA provide up to 16 km baselines, yielding resolutions of ∼ 0.′′02 (or∼ 2 au for a disc at a distance of 100 pc). This capability allows for moreprecise morphological constraints to be made on the disc in addition to thespectral index constraints that come with the longer wavelength data.Figure 1.8 shows a multi-wavelength view of the Fomalhaut debris disc.The image shows HST scattered light observations, which are dominated bysmall grains, and thermal emission at 24 µm, 70 µm, and 870 µm µm (Kalaset al., 2008; Stapelfeldt et al., 2004; Acke et al., 2012; Boley et al., 2012).The multi-wavelength data have a synergistic effect and together provide amore complete picture of the debris disc.As mentioned above, a multi-wavelength study of a disc also allows thegrain size distribution to be inferred. As grains emit light most efficientlyat wavelengths similar to their size, the total flux observed at a given wave-length can be related back to the emission from the grains of that size.By measuring the spectral index of the disc, α, and making some simpleassumptions about the grain’s emission properties, an approximation for qcan be obtained. At ∼mm wavelengths, the spectral index, αmm is foundby fitting a power law to the disc’s spectrum and assuming F ∝ λαmm .Assuming the spectral index follows a single power law profile (see e.g.191.4. Observational Studies of Debris DiscsFigure 1.8: Multi-wavelength view of the Fomalhaut debris system. Clock-wise from the upper left, the images show the HST scattered light (Kalaset al., 2008), Spitzer 24 µm data that do not clearly spatially separate thestar and the outer disc (Stapelfeldt et al., 2004), ALMA 870 µm observa-tions of the NW ring ansae (Boley et al., 2012), and 70 µm with Herschel(Acke et al., 2012). Image Credit: HST: NASA, ESA, P. Kalas, J. Gra-ham, E. Chiang, E. Kite (University of California, Berkeley), M. Clampin(GSFC), M. Fitzgerald (LLNL), and K. Stapelfeldt and J. Krist (JPL);Spitzer: NASA, JPL, K. Stapelfeldt (JPL); Herschel: ESA/PACS/BramAcke, K.U. Leuven, Belgium; ALMA: A.C. Boley (University of Florida),M.J. Payne, E.B. Ford, M. Shabran (University of Florida), S. Corder (NorthAmerican ALMA Science Center, National Radio Astronomy Observatory),and W. Dent (ALMA, Chile), NRAO/AUI/NSF.201.5. Observing and Modelling DiscsD’Alessio et al., 2001; Ricci et al., 2015; MacGregor et al., 2016):q =α− αplβs+ 3, (1.12)where αpl is the spectral index of the Planck function over the wavelengthsof interest, and βs is the dust opacity spectral index in the Rayleigh limitand is commonly estimated to be βs = 1.8± 0.2 (Ricci et al., 2015). In theRayleigh-Jeans limit, αpl approaches 2. A more physical value for αpl factorsin the temperature of the dust and the wavelengths of the observations beingconsidered (e.g., Holland et al., 2003). Specifically,αpl =∣∣∣∣∣∣log(Bν1Bν2)log(ν1ν2)∣∣∣∣∣∣ , (1.13)where Bν is the Planck Function and ν1 and ν2 are the respective frequen-cies over which the observations were taken. Draine (2006) found that forparticles larger than 100 µm, βs in discs is consistent with the grains in theISM, which means βs ≈ βism = 1.8 ± 0.2 (with 1 σ uncertainties), as longas 3 < q < 4. It is worth noting though that the value of βs could actuallyrange between 1.0 and 2.0. A βs ≈ 1.0 has been inferred in protoplanetarydiscs (Andrews and Williams, 2005) and βs = 2.0 is found in simple modelsof conductors/insulators (Draine, 2004). Relating the spectral index backto q for a given disc will lead to more accurate assessments of the dynamicalstate and total mass of solids in a disc.1.5 Observing and Modelling Discs1.5.1 Data ReductionThe data analyzed in Chapters 2-6 were obtained from ALMA, SMA, JCMT,and VLA. This section describes how the data from each telescope are re-duced.ALMA is a 66 antenna array located in the Atacama desert in NorthernChile. It observes in the submm-mm wavelength range and has baselinesextending up to 16 km. There are 10 receivers operating from 45 GHz to950 GHz, and the research presented in this thesis uses the Band 7, 6, and3 receivers that are centred around 345 , 230, and 100 GHz, respectively.Each receiver can obtain continuum through 4 × 2.0 GHz basebands andalso has a spectral line sensitivity of 3.8 kHz (or ∼ 3 m s−1 at 345 GHz).211.5. Observing and Modelling DiscsThe VLA is a 27 antenna array located in the Plains of San Agustinin Western New Mexico. It operates in the mm-cm wavelength range withbaselines extending up to 36 km. The 10 backend receivers operate from 45GHz down to 74 MHz, and the research presented in this thesis uses the Qand Ka band receivers that are centred at 45 GHz and 33 GHz, respectively.Both ALMA and VLA data use phase, gain, and flux calibrators for thedata reduction. In addition, ALMA uses watervapor radiometer (WVR)and system temperature corrections in the reduction process. The ALMAdata presented in Chapters 2-5 and the VLA data presented in Chapters 3and 6, were reduced using the Common Astronomy Software Applications(CASA) package (McMullin et al., 2007). CASA is specifically designed tocalibrate and reduce the interferometric data produced by the ALMA andVLA telescopes, in which a data set (called a measurement set or ms) hasan archived pipeline reduction script. The script will in principle provide afully calibrated data set that can be used for analysis. In practice, additionalinspection of the data is necessary and the data will need to be re-reduced toobtain an accurately calibrated final product. Inspection of the amplitudeand phase signal coming from each antenna and each baseline, and flagginganything anomalous for removal, will help achieve an accurately calibratedfinal data product.As ALMA and the VLA are interferometers, they directly measure aninterference pattern from the source. Therefore, the signal received at eachantenna will be slightly out of phase compared to the other antennas in thearray. Bright point sources close to the observing target are necessary toensure accurate phase calibration. A gain (or bandpass) calibrator is usedto correct for any variations in frequency of the observations. This objectwill typically be a very bright (> 1 Jy) quasar observed at the beginningof the observing run. A phase calibrator is also used to correct for anyphase variations in time. The calibrator does not have to be as bright as thebandpass calibrator, but needs to be located very close to the science target.The observing run will typically loop back and forth on the phase calibratorand the science target until the total time on source is reached. The absoluteflux of the observations is set by the amplitude (or flux) calibrator. Theobject used will be a well studied and modelled astrophysical source suchas a Solar System object (e.g., Titan or Callisto) in the case of ALMA or aquasar in the case of the VLA. This object must be a very bright source toensure a large signal-to-noise (SNR) ratio. The flux calibrator is typicallyobserved at the start of the observing run.For ALMA observations, atmospheric fluctuations can significantly im-pact the quality of the observations. This problem is primarily due to the221.5. Observing and Modelling Discswater content of the atmosphere. To minimize this, the telescope was builtin one of the driest deserts on Earth. The atmospheric fluctuations andwater vapor content in the column of atmosphere above each antenna cancause variations in the phase delays throughout the array. A WVR on eachantenna measures the precipitable water vapor (PWV) directly above eachantenna. The PWV corrections can be made to the raw data at the be-ginning of the calibration process. The atmospheric transmission at thefrequency range of the VLA receivers is high enough that PWV correctionsare not required to obtain good quality data over and therefore the VLAdoes not have a WVR. For the shortest wavelength capabilities of the VLA,PWV issues can indeed affect the quality of the observations, requiring ad-ditional phase calibration and flagging.ALMA observations also have an additional system temperature correc-tions that must be applied in the calibration process. This is a correctionthat accounts for additional noise that can be added to the data from sourcessuch as the ambient and receiver temperatures. Since this information is notknown a priori, continuous monitoring of the system temperature is neces-sary to apply during the calibration. There will be separate temperaturemonitoring for each antenna in the array.The final data product product can be inspected by plotting the ampli-tude of the data as a function of various parameters such as frequency, time,telescope baseline, antenna, etc. Visual inspection of the data can serve asan additional check that the calibration was completed correctly and thatthere is no radio frequency interference (RFI). Significant problems, such asa large amount of RFI or an antenna/baseline that is out of phase with therest of the data, can be flagged for removal from the data ensemble and thepipeline calibration can be applied again.Chapter 6 uses data from the SMA. This facility has the ability to ac-quire 345 GHz and 230 GHz continuum data. The array is made of 8 re-configurable antennas with receivers whose upper and lower sidebands (USBand LSB, respectively) can acquire data simultaneously. Each sideband has4 × 2048 MHz basebands, giving a ∼ 8 GHz bandwidth at each frequency.The data are calibrated using the Interactive Data Language (IDL) with theMIR package2. The bandpass calibration is done with well-studied quasarsthat are commonly used for ALMA and VLA calibration (e.g., 3C84). So-lar System objects, such as Uranus and Ganymede, are used as stable fluxcalibrators. Nearby well-studied quasars are used as phase calibrators. Sys-tem temperature corrections are applied in a fashion similar to the ALMA2https://www.cfa.harvard.edu/∼cqi/mircook.html231.5. Observing and Modelling Discsdata reduction process. The data, reduced in IDL, are then converted to aMIRIAD file format using the IDL task idl2miriad and then converted to aCASA MeasurementSet using importmiriad. This process allows for imagingto be undertaken straightforwardly in the CASA environment with the sameapproach as ALMA and VLA data.Chapter 6 also uses data from JCMT. As JCMT is a single-dish telescope(as opposed to an interferometer like the other facilities described), the datareduction process is more straightforward than with the data from other tele-scopes discussed here. The Submillimetre Common-User Bolometer Array2 (SCUBA-2) instrument on JCMT observes simultaneously at 450 µm and850 µm. SCUBA-2 is a bolometer camera with 10,000 pixels and is primar-ily used for large-scale map making. As the observations taken in Chapter6 were of a single point source (Sirius A), no map making was necessary.The data were reduced using the STARLINK data reduction pipeline ORAC-DR(Gibb et al., 2005). The REDUCE SCAN ISOLATED SOURCE recipefrom the pipeline was used to calibrate the data.1.5.2 Data Modelling TechniquesChapters 2-6 utilize observations from ALMA, VLA, and SMA. To achievethe resolution and sensitivity necessary for detailed disc studies, submm/mmtelescopes are sometimes built as large interferometers. An interferometricobservation, however, is not the same as directly taking an image. Interfer-ometric observations sample the brightness distribution of an astronomicalsource. The observed data, or visibilties, along with the sampling function(based on the array configuration) can be Fourier transformed to recoverthe brightness distribution and construct an image (as is done in Chapters2-6).In interferometry, it is common to fit a model to the source directlythrough the visibilities. The dirty image is then recovered through the rela-tionI(x, y) =∫S(u, v)V (u, v)ei2pi(ux+vy)dudv, (1.14)where V is the visibility function observed, S is the sampling function cor-responding to the antenna array configuration, and (u,v) are the points inFourier space. Any height variations between the antenna in an array (whichwould be w in uvw-space) are typically assumed to be negligible. The sam-pling function represents how well Fourier space is observed. A broaderrange of baselines in the antenna configuration and longer time on source241.5. Observing and Modelling Discswill result in a better sampling of Fourier space. The Fourier transform ofthe sampling function, referred to as the dirty beam, approximately resem-bles a 2D Gaussian for a well-sampled uv plane. The Full Width at HalfMaximum (FWHM) of this Gaussian corresponds to the angular resolutionof the observationsTo model observations in the visibility plane, a sample sky model imageof the system (i.e, disc(s) plus star) can be constructed at the representativefrequency of the observations. The sky model can then be loaded in toCASA with the importfits task. The model is then “predicted” on to thedata visibilities of each spectral window through the setvp and predict tasks.This procedure samples the full sky model of the system in the same waythat the actual image was observed.The simulated model can then be compared to the actual data througha model fitting approach (as is described in Section 1.5.3). Each positionin (u,v)-space has a real and imaginary component, and a correspondingweight. The weights for ALMA visibilties are defined in CASA to beWT = WEIGHTi,j =wiwjσ2i,j, (1.15)where wi and wj are antenna-based calibration factors derived by the CASAtask applycal during the data reduction process, andσ =1√2∆ν∆t, (1.16)where ∆ν and ∆t are the channel bandwidth and integration time. A χ2 isthen calculated for each visibility viaχ2 =∑i,j(RDi,j −RMi,j)2WT + (IDi,j − IMi,j )2WT, (1.17)where RD, RM are the real components of the data and model visibilities;ID, IM are the imaginary components of the data and model visibilities;and WT is the weights as given above.1.5.3 MCMC Approach to Model fittingChapters 2, 4, 5, and 7 use a Metropolis-Hastings Markov Chain MonteCarlo (MCMC) approach to fit various models to the different data sets. Iwrote the algorithm for the approach in the Julia 0.5.2 programming language,with a Python 2.7.6 wrapper to plot the data. The posterior distributions were251.5. Observing and Modelling Discsmade using the corner package3. An overview of the algorithm is detailedbelow.Modelling the visibility data sets described in the previous section canbe computationally expensive. Therefore, an MCMC approach is adoptedto converge efficiently on a most probable model. This modelling procedurewill explore parameter space through a random walk that selects parametersfrom a Metropolis-Hastings algorithm. Beginning with an “initial guess” forall of the parameters to be modelled, this approach makes trial models for agiven set of randomly selected parameters, compares them to the actual datato calculate a χ2, calculates a likelihood for the trial model, and then eitheraccepts or rejects the model. If the model is accepted, then it is recordedin a Markov chain and the results are used to inform the new model. Ifthe model is rejected, then the previous model is recorded again and a newmodel is tried.An MCMC trial model will generate new parameter values from a ran-dom subset of the total parameters (e.g. 3 randomly selected parametersfrom 9 total). For a given current parameter, xi, a randomly selected newparameter value, xi+1, is drawn from a Gaussian distribution centred on theprevious value and with a predetermined width. The width of the Gaussiandistribution will affect how far away in parameter space the new set of trialvalues are from the previous values (and indirectly whether a given valueof a parameter is accepted), and how correlated the resulting values in thechain are for a given lag. A prior distribution range can be imposed on theselected parameters, if information about a given parameter’s expected val-ues is known. If prior information is not well constrained, then conservativeprior distributions are used, such as a uniform distribution.For a given trial model, a χ2i can be calculated fromχ2i =∑ (D −Mi)2σ2. (1.18)where D is the observed data, Mi is a given model, and σ is the uncertainty.A different relation for χ2 (like in Eqn. 1.17) can also be used if it bettersuits the data being modelled. The likelihood for a given model is thencalculated by comparing the current model χ2i to the previous model and isgiven byL = e 12 (χ2i−χ2i+1). (1.19)3Python 2.7.6 http : //joss.theoj.org/papers/10.21105/joss.00024)261.5. Observing and Modelling DiscsThe acceptance parameter, α, is then calculated asα = min(L, 1). (1.20)If for a given model, α is greater than a random number drawn from auniform [0,1] distribution, then the new model is accepted and recordedin the Markov chain. If the model is rejected, then the previous model isre-recorded. The process starts again with the newly accepted parametervalues or the previous values if the current model was rejected.The MCMC algorithm can be run for a predetermined number of linksin the chain, with a longer chain being more likely to converge on the mostprobable parameter values. Since the MCMC will not start off with verylikely parameter values, the first ∼ 10% of the links in the chain are oftendiscarded and referred to as the “burn-in”. The chain can be further thinnedby only keeping every nth link in the chain to minimize the correlationbetween values. The posterior distributions for each parameter are thenfound by making a histogram of each parameter’s chain and normalizing suchthat the area under the curve is 1. The peak of the resulting distributionis equal to the most probable parameter value. A Bayesian 95% credibleinterval is found by integrating under the posterior distribution. Startingfrom the most probable value, the area under the posterior is incrementallycalculated by stepping outward until a total area of 0.95 is obtained (recallthat the area under total curve is normalized to 1). This will give an estimateof the uncertainty of the best fit parameters. If the resulting posteriordistribution were a perfect Gaussian, then the most probable value and 95%credible interval would correspond to the mean and ∼ 2σ.27Chapter 2ALMA Observations of HD141569’s Circumstellar DiscThis chapter is based on an ApJ publication (White et al., 2016a). It usesALMA observations of HD 141569 to constrain properties of the inner dustdisc and the gas disc. Co-authors on this paper include Aaron Boley, StuarttCorder, Kevin Flaherty, Eric Ford, Meredith Hughes, Matthew Payne, andDavid Wilner.2.1 IntroductionWhile many details of planet formation are not fully understood (Johansenet al., 2014; Raymond et al., 2014; Chabrier et al., 2014; Helled et al., 2014),significant debris is expected to be produced by the planet-building process.These leftovers, such as asteroids and comets, dynamically and collisionallyevolve over a planetary system’s lifetime, creating a steady source of dustand small grains, which would otherwise be depleted on short timescales(Matthews et al., 2014). Thus, the presence of circumstellar debris arounda star is taken as evidence that planet building was at least partially success-ful in that system. When debris structures are resolved, the morphologiescan be used to place constraints on the architecture of putative planets(Kuchner and Holman, 2003; Quillen, 2006; Moro-Mart´ın et al., 2007; Starkand Kuchner, 2009) and to potentially understand the dynamical history ofa system (Raymond et al., 2011). Multi-frequency observations can furtherbe used to constrain dust properties (Wyatt, 2008), giving a way to explorethe debris itself.Among known debris discs, a limited number contain gas, as detected inradio molecular line emission. This includes β Pic (Zuckerman et al., 1995;Dent et al., 2014), HD 131835 (Moo´r et al., 2015), HD21997 (Moo´r et al.,2011, 2013), and 49 Cet (Hughes et al., 2008) with estimated ages of 12Myr, 16 Myr, 30 Myr, and 40 Myr, respectively. These systems are olderthan the typical lifetimes of gaseous discs, as inferred from IR excess and282.1. Introductionaccretion (e.g., Mamajek, 2009). Furthermore, if the gas has a primordialorigin (i.e., from the formation of the disc itself), the gas abundances need tobe reconciled with photoevaporation rates (Alexander et al., 2014) and COphotodissociation timescales (van Dishoeck and Black, 1988; Visser et al.,2009). Photoevaporation rates may not be constant throughout the lifetimesof the disc, and the radial distribution of gas is influenced by both UV andX-ray sources (e.g., Gorti et al., 2016).Instead of being primordial, the gas could be second-generation, pro-duced by the early evolution of a comet reservoir (Dent et al., 2014) throughimpact vaporization or sublimation of impact-generated particulates. Itnonetheless remains unclear whether or not there is sufficient mass in cometsto explain the amount of gas detected in these systems (Matthews et al.,2014; Moo´r et al., 2013). Regardless of the reason, the existence of this gashas implications for planet building. For example, while the measured gasmasses are too small to contribute significantly to gas giant planet forma-tion, the gas could still contribute to planetary atmospheres and potentially,for high enough gas masses, continue to affect small-grain dust.If the gas does have a debris origin, then the relative debris and gas mor-phologies, along with dynamical models of the system, can be used to probethe clearing stages of planet formation and serve as a probe of disc massduring that evolutionary stage. As such, debris+gas systems can poten-tially offer significant constraints on planet formation theory (Ko´spa´l et al.,2013; Wyatt et al., 2015). To this end, HD 141569 is of particular interest.HD 141569 is a B9.5 Ve star at a distance4 of 116± 8 pc (van Leeuwen,2007). At an age of about 5 Myr, it is surrounded by a complex dust andgas disc (van Den Ancker et al., 1998; Weinberger et al., 2000; Fisher et al.,2000). At distances > 100 au from the star, large-scale spiral structure hasbeen detected in optical scattered light, revealing at least two well-definedring/spiral-like structures (Weinberger et al., 2000; Clampin et al., 2003).One spiral is between ∼ 175 au and 210 au, and the other between ∼ 300au and 400 au. The rings/spirals are bright, with an optical depth ∼ 0.01in the outer arm (Clampin et al., 2003) and a scattered light flux density of4.5± 0.5 mJy at 1.6 µm (Mouillet et al., 2001; Augereau et al., 2001).In addition to having a large extended disc, HD 141569 also hosts an4Perryman et al. (1997) find a distance of 99±8 pc, van Leeuwen (2007) find a distanceof 116± 8 pc through a re-analysis of the Hipparcos data, and Lindegren et al. (2016) finda distance of 111±5 pc through Gaia data. Throughout the literature, all three distancesare used for HD 141569. In this chapter, when reporting linear sizes from other work, Isimply use their reported values. For the stellar, dust, and gas masses that are derivedhere, I will discuss how the results are expected to scale with distance.292.1. Introductioninner dust system. This disc was first detected by excess emission in themid-infrared using IRAS (Walker and Wolstencroft, 1988; Andrillat et al.,1990). Observations at 12 µm, 25 µm, 60 µm, and 100 µm wavelengths(Walker and Wolstencroft, 1988) led to a calculated disc outer edge of 47-63au, based on modelling (see also; Fisher et al., 2000; Marsh et al., 2002).Thi et al. (2014) used archival VLT data at 8.6 µm to resolve the innersystem out to ∼ 50 au. SED modelling suggests that the inner edge of smallgrains must be at about 10 au with a likely peak at 15 au (Malfait et al.,1998; Maaskant et al., 2015). Select previous continuum observations aresummarized in Table 2.1.If the dust’s origin is debris, HD 141569 may be viewed as the youngestof the gas-rich debris systems. By “debris”, it is meant that the majorityof the (sub)millimetre emission from solids is associated with grains thathave already been incorporated into a parent body and re-released into thenebula. If the solids have not already been processed into parent bodies,then they reflect the initial growth stages of grains in planet-forming discs.Table 2.1: Summary of select previous HD 141569 debris disc observations.Uncertainties provided when available. References listed are: (1) Fisheret al. (2000); (2) Walker and Wolstencroft (1988); (3) Marsh et al. (2002),(4) Mouillet et al. (2001); (5) Augereau et al. (2001); (6) Nilsson et al.(2010); (7); Sylvester et al. (2001)Wavelength Flux Density Instrument Ref.(µm) (Jy)10.8 0.318± 0.016 Keck OSCIR (1)18.2 0.646± 0.035 Keck OSCIR (1)12, 25, 60, 100 0.66, 1.99, 5.37, 3.34 IRAS (2)12.5, 17.9, 20.8 0.333, 0.936, 1.19 KECK MIRLIN (3)±0.022,±, 0.094,±0.161.6 0.0045± 0.0005 HST (4,5)870 0.0126± 0.0046 APEX (6)1350 0.0054± 0.001 JCMT SCUBA (7)The total gas mass has been constrained to be roughly between 13 M⊕and 200 M⊕ (Zuckerman et al., 1995; Thi et al., 2014; Flaherty et al., 2016),depending on assumed abundance ratios and model fitting. Most of thismass is likely located in the outer system, where CO kinematics suggestthat the gas is non-uniformly distributed in radius. Tracers of hot gas such302.2. Observationsas ro-vibrational CO lines in the near-infrared (Brittain and Rettig, 2002;Goto et al., 2006) show that there is a region of tenuous CO gas distributedbetween 10 au and at least 50 au, seemingly co-located with the inner dustsystem.HD 141569 may be in a stage where the outer gas regions have, at leastin part, a primordial component, but the inner region associated with mil-limetre grains may arise from the collisional evolution of parent bodies. Wemust also consider the possibility that the outer gaseous disc is dominatedby second-generation gas, making the entire system an early-stage debrisdisc.In this chapter, I present ALMA Band 7 observations of the inner dustand outer gas systems. Section 2.2 is an overview of the observations anddata reduction. The 870 µm continuum and 12CO(J = 3-2) (hereafter CO(3-2)) spectral imaging and analysis of the gas disc are given in section 2.3. Idescribe mass calculations and discuss interpretations in Section 2.4. Section2.5 summarizes the results.2.2 ObservationsThe data were acquired on 21 May 2014 as part of the ALMA cycle 1 cam-paign (project ID 2012.1.00698.S). Observations were made in two executionblocks (EBs), but one EB could not be calibrated due to phase amplitudeand water vapor radiometer (WVR) problems. The total integration time forthe successful EB was 1.43 hr (0.79 hr on target). A compact configurationwas used with 32 antennas; the longest baseline was 650.3 m. Observationswere centred on HD 141569 using J2000 coordinates RA = 15 hr 49 min57.73 sec and δ = −3◦55′16.62′′.To acquire high signal-to-noise ratio (SNR) data in both continuum andCO(3-2) efficiently, observations were taken in Band 7 (at ∼ 345 GHz) withthe correlator setup using the Frequency Division Mode (FDM) and dualpolarization. Four different spectral windows were used with 1875 MHzbandpasses at rest frequency centres of 335 GHz, 337 GHz, 345 GHz, and347 GHz. These locations were chosen to maximize continuum sensitivitywhile also overlapping the CO(3-2) transition. The correlator in FDM gives3840 channels of width 488 kHz, which corresponds to a velocity resolutionof 0.85 km s−1. Atmospheric variations at each antenna were monitoredcontinuously using the WVRs. The estimated WVR thermal contributionto path fluctuations is 5.8 µm per antenna.Data were reduced using the Common Astronomy Software Applications312.3. Results(CASA) package (McMullin et al., 2007). Antenna 14 was flagged duringquality assurance (QA), leaving 31 antennas for the final data product. Inaddition, spectral windows 1 and 3 each exhibited 120 bad channels (1/32of the bandwidth), which were also flagged. Antenna 14 and the flaggedchannels were removed from the data prior to reduction and subsequentanalyses using the task split. The data reduction in CASA included WVRcalibration, system temperature corrections, and bandpass, flux, and phasecalibrations with Titan and quasar J1550+0527.2.3 ResultsTable 2.2 summarizes observed system properties for both the dust andgas. The continuum flux density is determined by fitting a disc model tovisibilities (see Sec. 2.3.1), while the gas flux density is taken from integratingwithin the 3 σ contours of the zeroth moment maps (see Sec. 2.3.2).The peak intensity and angular size are taken from the CLEANed im-ages, assuming a distance of 116 pc for linear scales. The uncertainties forthe flux densities and the line fluxes include the σRMS of the observationsand an absolute flux calibration uncertainty of ∼ 10% added in quadrature.The uncertainties in the intensities only include the σRMS.Table 2.2: Summary of observed values for both gas and dust. The flux den-sities are determined by fitting the visibilities by a disc model (see Sec. 5.1).The peak intensity and angular size are derived from the CLEANed images.Linear sizes assume a distance of 116 pc and are measured across the semi-major axis of the continuum and gas. The uncertainties for the flux densitiesand the line fluxes include the σRMS of the observations and an absolute fluxcalibration uncertainty of ∼ 10% added in quadrature. The uncertainties inthe intensities only include the σRMS.Parameter Debris Gas [CO 3-2]Flux Density 3.8± 0.4 mJy 15.7± 1.6 Jy km s−1Peak Intensity 1.74± 0.24 mJy beam−1 0.90± 0.16 Jy beam−1Angular Radius 0.′′49 (∼ 56 au) 1.8′′ (∼ 210 au)σRMS 0.070 mJy beam−1 0.028 Jy beam−1Beam Area 0.163 arcsec2 0.121 arcsec2Beam major FWHM 0.′′42 0.′′34Beam minor FWHM 0.′′34 0.′′31Beam PA −61.1◦ −77.1◦322.3. Results2.3.1 ContinuumThe dust emission is clearly resolved by the ALMA beam. The continuum(with the CO channels removed) is deconvolved and imaged using CASA’sCLEAN algorithm. The average wavelength across the frequency range is870 µm. A threshold of 12 × σRMS and a natural weighting are used toproduce the final cleaned product in Fig. 2.1 (with contours correspondingto 3, 6, 12 and 21×σRMS). The inner disc around HD 141569 is imaged outto 56 au (assuming a distance of 116 pc). The longest baseline is unableto resolve a central clearing of < 15 au, leading to a central peak near thepointing centre (the star and inner disc). The peak intensity in the cleaneddata is 1.74 mJy beam−1, corresponding to a SNR of ∼ 25. At 870 µm, thethermal emission from the host star’s photosphere contributes < 1% to thepeak flux per beam, assuming a blackbody with TEff = 10, 500 K, a radiusof 1.7 R, and a distance of 116 pc. The star’s flux is thus negligible, aslong as corona and chromospheric effects can be ignored.332.3. ResultsFigure 2.1: CLEANed 870 µm continuum image of HD 141569. The con-tours represent 3, 6, 12 and 21× σRMS noise (σRMS = 0.070 mJy beam−1).The dashed contour represents −1σ. The solid ellipse in the bottom leftrepresents the beam size. A 50 au scale (assuming a system distance of 116pc) is given in the bottom right. The peak intensity is 1.74 ± 0.24 mJybeam−1. Coordinates are given as offset from the phase centre. North is upand East is to the left.The dust distribution is constrained using CASA’s uvmodelfit, which fitssingle component models directly to the visibility data and selects the bestfit through χ2 minimization. I run this task to fit a uniform disc modelto the continuum data (the CO channels are split out) and list the best-fitmodel in Table 2.3. Discs with inclinations near i ∼ 55◦ are favored with amajor axis of about 0.”85, corresponding to ∼ 85 au at a distance of 116 pc(an inclination convention of 90◦ corresponding to edge-on is adopted). Thepreferred model has a total continuum flux density of 3.78±0.23 mJy. Thisvalue is within 15% of the flux density found by summing the total flux from342.3. Resultsthe cleaned image down to the 3σ contour. The uncertainty in the flux isdominated by the uncertainty in the absolute flux scale, which is taken to be10%. This sets our flux estimate of the inner dust disc to be 3.8± 0.4 mJy.Table 2.3: Summary of CASA’s uvmodelfit results for the debris disc. Thedata were fit by comparing a simple, uniform disc model to the data visibil-ities. The position angle is measured in degrees East of North. The fittinguncertainties for parameters other than flux are not included here, but areaddressed for the gaseous disc in section 2.5.Parameter Continuum [Debris]Flux Density 3.78± 0.23 mJyX Offset −0.”032Y Offset -0.”023Major Axis 0.”85Axis Ratio (inclination) 0.58 [55◦]Position Angle 351.2◦2.3.2 Gas DiscIn addition to the continuum, CO(3-2) emission is kinematically and spa-tially resolved using the FDM capabilities of the ALMA correlators, with aspectral resolution of 0.85 km s−1. The double-horned spectrum is shownas a function of the local standard-of-rest kinetic (LSRK) velocity in Figure2.2. The previously constrained system velocity of 6 km s−1 is shown, aswell as the asymmetric emission from the disc (Dent et al., 2005).352.3. ResultsFigure 2.2: Continuum subtracted CO(3-2) spectrum as a function of LSRKvelocity. The dashed line represents the system velocity of 6 km s−1. TheσRMS of the individual channels is ∼ 6 mJy meaning that the dominantsource of uncertainty will come from the absolute flux calibration, which Itake to be ∼ 10%.The CO is continuum subtracted using the CASA task uvcontsub. Figure2.3 (left panel) shows the brightness map for the CO line (zeroth moment),in which the 3σ CO contour extends out to 1.8” (∼ 210 au). This brightnessdistribution is compared directly with the continuum emission (contours),which is more centrally concentrated. The right panel shows the velocitymap (first moment), with the CO brightness contours overlaid. There aretwo brightness peaks, each at about ∼ 0.9 Jy km s−1. The peaks are sepa-rated by ∼ 0.”5 in a morphology that resembles ring ansae and is suggestiveof an inner gas cavity. There is only a tenuous CO detection within this∼ 0.”5 (∼ 50 au) diameter cavity which is broadly consistent with previous362.3. Resultsshorter wavelength observations that find only tenuous CO between about10 au and 50 au in radius (Brittain and Rettig, 2002; Goto et al., 2006).The velocity field map shows clear Keplerian rotation, with the gas southof the star approaching us. The brightness is skewed westward (right in theimage), relative to the velocity map, which is discussed in more detail belowbelow.Fig. 2.4 shows maps for 25 velocity channels between −0.5 km s−1 and11.5 km s−1. Contours represent 3, 6, 9, and 24 times the RMS noise ofthe zeroth moment. The spectral resolution of the velocity, 0.85 km s−1, isa factor of 2 larger than the channel width. For Fig. 2.4, velocity channelspacing is chosen to be 0.50 km s−1 to include a slight oversampling. Thetotal flux density of the CO given in Table 2.2 is determined by summing theflux in the zeroth moment map down to 3 × σRMS and multiplying by thenumber of beams. This value is consistent with integrating over all channelsof the CO map to within 10%. Note again that there is a clear asymmetryin the emission west of the star.The peak flux in the northwestern limb is significantly brighter than itscounterpart in the northeastern and southwestern limbs.372.3. ResultsFigure 2.3: Left: CO zeroth moment map. The contours represent 3, 6, 9and 12× σRMS noise of the continuum (σRMS = 0.070 mJy beam−1). Thesolid ellipse in the bottom left represents the beam size with properties asgiven in Table 2.2. A 50 au scale (assuming a system distance of 116 pc) isgiven in the bottom right. Right: CO first moment map (velocity field).The contours represent 3, 6, 12 and 24 × σRMS noise (σRMS = 0.028 mJybeam−1). Coordinates are given as offset from the phase centre, as indicatedon the left plot. North is up and East is to the left.2.3.3 MCMC ModellingAs shown in Figure 2.3, the high spatial and velocity resolution capabili-ties of ALMA yield a well-constrained velocity field. These data can thus becompared with a Keplerian disc model to infer system properties. Trial mod-els are generated by first assuming a uniform Keplerian disc. For simplicity,the inner cavity, temperature profile, and line broadening of CO (whichis expected to be small) are not factored in to the model. Each model isprojected to a given trial model’s disc geometry and the LSRK velocity issubtracted. The model is then convolved with a 2D Gaussian beam as givenin Table 2.2. Using Markov Chain Monte Carlo (MCMC) techniques (specif-ically, Metropolis-Hastings with Gibbs sampling), the posterior distributionsare calculated for the disc’s inclination, position angle, LSRK system veloc-ity, dynamical centre, and mass. I assume flat prior distributions over theranges given in Table 2.4. Model comparison is conducted in the imagedomain due to the high velocity resolution and SNR.382.3. ResultsFigure 2.4: Channel map of CO(3-2). The 25 subplots step forward in0.5 km s−1 intervals from −0.5 km s−1 to 11.5 km s−1 LSRK. The contoursrepresent 3, 9, and 24 times the RMS noise of the intensity weighted map(as seen in Fig.2.3). Coordinates are given as offset from the phase centre,as indicated on the bottom left plot. North is up and East is to the left.392.3. ResultsTable 2.4: Ranges for the flat prior distributions of each parameter. TheGaussian widths are also given for the proposal distributions. The prior isbased on the UV model fitting results given in Table 2.3.Parameter Prior Range σMass [M] [1.0, 4.0] 0.02Position Angle [◦] [−15.0, 5.0] 0.1Inclination [◦] [45.0, 65.0] 0.2System Velocity [km s−1] [5.0, 7.0] 0.01X Offset [”] [−0.2, 0.2] 0.06Y Offset [”] [−0.2, 0.2] 0.06Parameter space is then explored through a random walk directed bya Metropolis Hastings MCMC (e.g., Ford, 2005). For each new trial, twomodel parameters are randomly chosen and then updated by drawing aGaussian random parameter centred on the current model (state i). Theacceptance probability for the new trial model (state i+ 1) is given byα = min(e12(χ2i −χ2i+1), 1), (2.1)where I takeχ2i =∑ (D −Mi)2σ2. (2.2)Here, D are the data from the CO first moment map (see Fig. 2.2) and Miis the current model. The velocity channel width, 0.5 km s−1, is used for σas it is a more accurate representative of the uncertainty than the error inD. The summation is over all points on the moment map. If α is greaterthan a random number drawn from a uniform [0,1] distribution, then thenew model is accepted and recorded in the Markov chain. If the model isrejected, then the previous model is used again and re-recorded.The MCMC routine is run using 3 chains, each with randomly chosenstarting points in the flat prior parameter space. Each chain contains 100thousand links of which about 1000 are needed for burn-in. The 3 chainsconverge on similar parameters, and the distributions are combined to givethe resulting posterior distributions in Fig. 2.5. The blue points correspondto the values of highest probability. The most probable parameters (i.e.,the mode of the distributions) are given in Table 2.5. Uncertainties aregiven by a 95% credible interval unless otherwise stated. The most probablemass is 2.39 M, for a distance5 of 116 pc. Since there is a degeneracy in5The most probable mass scales directly with the assumed distance.402.3. Resultsinclination and mass, I give M sin(i) and M. Previously constrained stellarmass estimates are between 2.0 M and 3.1 M (e.g., Merin et al., 2004;Wyatt et al., 2007). The posterior distributions for both quantities aresampled independently by the MCMC. Ultimately, the uncertainty in thederived mass is dominated by the distance uncertainty. The re-analyzedHipparcos Catalog distance with 1-σ uncertainty is 116±8 pc (van Leeuwen,2007). Considering only this 1σ distance uncertainty with our most probablemass yields 2.39+.16−.16 M.The most probable parameters are used to construct a final disc model,which is shown in Figure 2.6. The residuals of the model are also shown aspercent deviation from the data. The most probable model typically showsagreement with the data to about 10%, but has larger deviations along theminor axis of the data/model.412.3. ResultsFigure 2.5: Posterior probability distribution from MCMC modelling of theCO velocity field for 300 thousand links minus the burn-in. The blue pointsrepresent the most probable model parameter. The contours show 0.5, 1,1.5, and 2×σ.Table 2.5: Summary of MCMC Results with 95% Credible Range.Parameter Most Probable 95% Credible RangeMass [M] 2.39 [2.34, 2.43]Mass [Msin(i)] 1.92 [1.89, 1.95]Position Angle [◦] -3.36 [−3.78,−2.71]Inclination [◦] 53.4 [52.5, 54.6]System Velocity [km s−1] 6.04 [6.01, 6.06]X Offset [”] −0.049 [−0.060,−0.038]Y Offset [”] −0.11 [−0.12,−0.10]422.3. ResultsFigure 2.6: Top: The left panel shows the first moment map of the data(same as RHS in Fig. 2.3), while the right shows the velocity field of themodel. Bottom: The panel shows the residuals presented as a percentdifference in the model from the data. All images are shifted to the systemcentred velocity of 6.04 km s−1. The model is consistent with the data toabout 10% or better throughout most of the disc. The largest deviationsoccur along the minor axis. The black ellipse in the bottom corresponds tothe beam with properties given in Table 2.2.432.4. Discussion2.4 Discussion2.4.1 Disc AsymmetryAn interesting asymmetry is observed in the CO channel map. Looking atthe “butterfly” features in the 4 − 8 km s−1 channels of Fig. 2.4, there is alocalized flux enhancement on the northwestern (top right) component ofthe gas. The east wing of the butterfly has a fairly symmetrical intensityabout the system velocity of 6 km s−1, while the west wing is asymmetrical.To explore this feature further, Figure 2.7 shows three of the channelmaps (4.5 km s−1, 6 km s−1, and 7.5 km s−1), along with the continuumusing 3, 6, 9 and 12×σrms contours. The southern components of both sidesappear to be approximately symmetric, but a strong asymmetry becomesobvious for the 6 km s−1 and 7.5 km s−1 maps, in which the western wingis brighter than the eastern wing by ∼ 40% in each channel. These channelmaps also suggest that there is indeed an inner cavity to the CO disc, asnoted in other studies (Goto et al., 2006; Flaherty et al., 2016).Since the asymmetry is present throughout multiple channels (see Fig. 2.4),the feature appears to be real in the data. While the exact source of theflux enhancement is unknown, it may be caused by asymmetries in the in-ner disc edge, such as vortex formation (e.g., Lyra et al., 2008b,a) or byperturbations from an unseen companion. For example, Dent et al. (2014)observe a large asymmetry in β-Pic that is attributed to localized collisionsof gas-rich comets. The asymmetry is also in the general direction of thetwo distant red dwarf companions that orbit at ∼ 1000 au. Follow-up ob-servations and detailed simulations are required to determine the cause ofthe CO disc morphology.442.4. DiscussionFigure 2.7: The 4.5 km s−1, 6.0 km s−1, and 7.5 km s−1 velocity channels ofCO. The localized flux enhancement can be seen on the west and northwestcomponents of the gas disc. The velocities given are LSRK and are centredaround a system velocity of 6 km s−1. The contours represent 3, 6, 12 and21 × σRMS noise (σRMS = 0.070 mJy beam−1) fo the continuum. North isup and East is to the left.2.4.2 Debris/Dust MassAn initial estimate for the dust mass is made by assuming that the emissionis optically thin, dominated by mm grains, and spatially concentrated in athin ring. In this case,M =43ρipis3 Fν(Obs)Bν(R)Ωs(2.3)where Fν(Obs) is observed flux density of the continuum, Bν(R) is the blackbody intensity for a single grain placed at a distance R from the star, andΩs is the solid angle of a single grain. The grains are further assumed tobe in thermal equilibrium with the host star, to have an internal densityρi = 2.5 g cm−3 and size s = 1 mm, and to be perfect absorbers andradiators (albedo of 0, emissivity of 1). It is noted that this mass estimate isequivalent to M = d2Fν(Obs)κνBν(R)with κν = 3 cm2 g−1, for the given assumptions.This opacity is within a factor of two of the mm opacity used by Flahertyet al. (2016).For an approximate lower limit, the ring can be envisaged to be at R =10 au, which represents the innermost location for large grains based onSED modelling (Malfait et al., 1998). At this distance and for the notedassumptions, the grains would be T ∼ 200 K, which yields a mm grain452.4. Discussionmass6 of 0.04 M⊕. Placing grains at larger stellar separations would requireadditional mass to explain the emission. For example, if all the grains wereplaced at R = 50 au (T ∼ 90 K), the mm grain mass would be ∼ 0.09 M⊕.This simple estimate may only correspond to the actual dust mass if theobserved mm grains are leftovers that were never incorporated into planets.Instead, if the grains are produced by the evolution of a nascent debris disc,the total mass can be significantly different. I explore this possibility nextusing a size distribution of grains spread throughout a disc.For simplicity, I assume that the surface density of material decreasesas r−1 over disc radii 10-50 au. The dust is assumed to be absent out-side of these boundaries. It is further assumed that the grains radiate ef-ficiently as long as their diameter (2s) is equal to or larger than the ab-sorbing/emitted photons (e.g., Wyatt and Dent, 2002). For wavelengthslarger than the grain’s diameter, the emission and absorption coefficients(Qν(em) = Qν(abs) = Qν) are inversely proportional to the photon wave-length. Specifically,Qν ={1 2s > λ2sλ otherwise.(2.4)The calculations only considers a “total” debris mass up to some maxi-mum parent body size, which is taken to be smax = 50 km. This does notmean that 50 km is envisaged to be the largest solids in the debris disc; itis only the maximum size we consider in a given size distribution. To get atotal debris mass for solids s < 50 km, a particle size distribution must beassumed. Lacking further constraints, I use a collisional cascade such thatthe mass per size increment Ms ∝ s−0.5 (e.g., Dohnanyi, 1969). The totalmass is then determined by requiring the model continuum flux density tomatch the observations. In practice, the debris disc is divided into a seriesof rings (here 100), placed evenly between 10 au and 50 au. If each ringhas the same mass, then the surface density profile follows r−1. A flux den-sity for each ring is then calculated by first deriving a grain temperature,assuming that the grains are dark (albedo∼ 0) and balancing the receivedand emitted powers using a black body model with the effects of Qν . Thegrain temperature (e.g., Wyatt and Dent, 2002) isTg = Tg,BB(Qabs(Tstar)Qabs(Tg))1/4, (2.5)where Tstar is the host star’s surface temperature (assuming it is a black6Adopting a different distance will scale the mass by ( d116 pc)2462.4. Discussionbody), Tg,BB is the equilibrium grain temperature if the grain were also aperfect black body, and Tg is the actual grain temperature. The equationmust be solved iteratively, but converges quickly. For HD 141569, Tg ≈Tg,BB except at grains less than 10s of microns. To calculate Qabs(T ), Qνis integrated over all frequencies and weighted by a black body of the giventemperature, i.e.,Qabs(T ) =∫Bν(T, ν)Qνdν∫Bν(T, ν)dν. (2.6)Taking Tstar = 10500 K and the above grain size and spatial distribution,I find that M(s < Dmax) ∼ 160 M⊕ ρi2.5 g cm−3√Dmax50 km for all solids under amaximum size of Dmax = 50 km.This result should be interpreted with caution. A steeper (shallower)solid size distribution can lead to significantly larger (smaller) masses. Theresult is also dependent on the internal density of the grains, as well astheir effective albedo and emissivity. Nonetheless, the results are illustrativethat significant debris may be distributed between 10 au and 50 au. Thetotal mass of solids would be much larger should debris (at a lower surfacebrightness) be present at disc radii r > 50 au, which would be consistentwith single dish measurements (see Table 2.1).2.4.3 Gas MassThe mass of an optically thin gas disc near LTE can be calculated fromthe integrated line intensity (e.g., Perez et al., 2014). Given a line flux ofFOBS = 15.7 Jy km s−1, the average line intensity over the source’s solidangle Ω isIˆ =FOBSλΩ, (2.7)where λ = 867 µm is the average wavelength of the observations. The uppertransition level column density of CO is given byN3 =4piIˆhνA32, (2.8)where ν = 345.79 GHz is the frequency of the molecular feature, and A32 =2.497× 10−6 Hz is the Einstein emission coefficient7 for the transition.In the following, J = 3 (the upper transition level) unless otherwisenoted (such as in the summation). Under the assumption that all J energy7The spectral information for the CO molecule was obtained from the Splataloguedatabase http://www.splatalogue.net, Remijan (2010).472.4. Discussionlevels are populated in LTE, the total column density is given byNTotal = NJZ2J + 1ehBeJ(J+1)kT , (2.9)and Z isZ =∞∑j=0(2j + 1)e−hBej(j+1)kT . (2.10)Here, Be = 57.635 s−1 is the rotational constant7, T is the gas temperature,Z is the canonical partition function. The gas mass is then given byMCO = mCONTotalΩd2, (2.11)=4pimCO d2 FOBS ZhνλA32(2J + 1)ehBeJ(J+1)kTfor a solid angle Ω and distance to the object d. Taking a gas temperatureof T = 33K, the minimum excitation temperature of the J = 3-2 line,gives MCO = 1.9 ± 0.2 × 10−3 M⊕, with the uncertainty propagated fromthe CO flux density uncertainty in Table 2.2. The corresponding spatiallyaveraged column density, NTotal, is 1.2 ± 0.1 × 1016 cm−2. This value iswithin the optically thin limit (Wyatt et al., 2015), but should not be takenas independent confirmation, as the gas was assumed to be thin for themass calculation. If the gas is partly optically thick, then the actual COgas mass could be larger by a factor of a few (Matra` et al., 2015). Assuch, the CO mass here could be interpreted as a lower limit. Due to theuncertainty in the appropriate amount of the gas, I only report the CO massas M(CO) ∼ 2 × 10−3 M⊕ to emphasize that the calculation has importantunknowns.Flaherty et al. (2016) find the HD 141569 gas disc to have a total mass of13+50−9 M⊕ as constrained by LTE models of gas temperature and density ofCO(1-0) and CO(3-2) with CARMA and SMA, respectively. If I assume the104 ISM number density abundance ratio for H2 to CO (as in Flaherty et al.,2016), along with a H2 to CO mass molecular mass ratio of 1/14, the inferredH2 gas mass from the ALMA observations is MH2 ∼ 1.4 M⊕. Includingadditional metals would increase the total inferred gas mass to be slightlyabove ∼ 1.5 M⊕, which is a factor of a few below the lower bound of theSMA and CARMA based model. The observations and models altogetherthus suggest that there is one to a few tens M⊕ of gas mass, assuming theISM scaling can be used, which is not obviously the case. Additional caveatsfor these gas-mass estimates are discussed below.482.4. Discussion2.4.4 What can HD 141569 tell us about grain growth,planet formation, and disc evolution?The morphology of HD 141569 shows a dust disc extending out to about56 au and an extended CO gas component between about 30 au and 210au. This structure alone suggests that the system is an evolved transitiondisc. However, as discussed below, HD 141569 may be better interpreted asa nascent debris system. The distinction is that the dust would be secondgeneration, and any associated size distribution would reflect the clearingstages of planet formation rather than grain growth outcomes.Primordial v. Second GenerationWhile most debris discs are expected to be extremely gas-poor, severalyounger debris systems (e.g., β Pic as discussed in Sec. 2.1) have been ob-served with CO masses MCO = 10−5 − 10−2 M⊕ (Pascucci et al., 2006;Hughes et al., 2008; Dent et al., 2014). HD 141569 has a CO gas mass∼ 2× 10−3 M⊕, which, while younger, is comparable to these more evolvedsystems. The total gas mass of ∼ 1.5 M⊕ (∼ 5 × 10−3 MX) assumes anISM H2 to CO abundance ratio. There is ultimately no reason to suspectthat this conversion is applicable to HD 141569 after 5 Myr of evolution. Ifthe gas disc is not optically thin, as assumed in the calculation above, thenusing CO as a tracer of total gas could underestimate the actual gas mass(Bergin et al., 2013).The current CO disc should be expected to be depleted by photodissoci-ation on timescales of ∼ 120 yr (Visser et al., 2009), unless significant self-shielding is present. While the derived column density of CO (∼ 1016 cm2)would contribute to some shielding, it is not obviously sufficient to preventrapid dissociation. Unless the gaseous disc is massive enough to promptCO formation in rough balance with photodissociation, the low inferredCO mass creates a potentially serious timing problem for a primordial gasinterpretation. Instead, if the gas is second-generation as produced by aplanetesimal population (e.g., Moo´r et al., 2011), then the short dissocia-tion timescale may not be problematic. Rather, the problem now becomeswhether sufficient mass is available to produce a low-mass gaseous disc, andif so, whether the planetesimal destruction rates would be consistent withthe dynamics and the radiation field of the system.First, I note that the debris interpretation is corroborated by recentscattered light imaging (Konishi et al., 2016). The images reveal very smallgrains present around 50 au, a region co-located with the mm grains ob-492.4. Discussionserved here. Such small grains should be removed by the system quickly byradiation pressure. The presence of the small dust grains in this region ofthe disc suggests that significant collisional evolution is indeed taking place.This finding by itself does not suggest that the gaseous disc is best describedby a debris disc, but it motivates its consideration.If the CO gas is depleted quickly through photodissociation on ∼ 120yr timescales, then for the estimate of the CO mass, the CO productionrate must be M˙CO ≈ 17 M⊕ Myr−1. If a typical comet’s mass is 10%CO ice (Mumma and Charnley, 2011), then about 170 M⊕ of cometarymaterial must be destroyed per Myr to balance photodissociation. Thisalso implies that the total gas mass is within an order of magnitude ofthe CO gas. Based on cometary compositions, CO can be accompanied byapproximately similar abundances of H2O and CO2 (Mumma and Charnley,2011). Ultimately, spectroscopic followup must be used to determine the gascomposition and compare that with cometary abundances to constrain thisscenario observationally.Is the required comet destruction rate plausible? As discussed in section2.4.2, the ALMA continuum emission of 3.8 mJy with a collisional cascademodel implies a total solid mass M ∼ 160 M⊕ for s < 50 km in the innerdisc. While the ALMA CO observations are consistent with single-dishobservations, the continuum flux measured here is lower than that foundin previous studies. For example, single-dish observations by Nilsson et al.(2010) find a continuum flux density of 12.6 ± 4.6 mJy at 870 µm, andthe SMA observations measure 8.2 ± 2.4 mJy (Flaherty et al., 2016). Themuch larger beams in these observations could be biasing the detected fluxthrough contamination, but at face value, this difference suggests that theremay still be considerable dust mass at larger radii whose emission is resolvedout by the interferometer or is too low surface brightness to be detected atthe sensitivity of these observations. As such, the true mass in solids maybe larger than estimated here. For example, if the collisional cascade modelis extended out to 210 au (the extent of the CO disc) and the mass isnormalized to the single dish flux value of 12.6 mJy, the total solid mass isover 360 ρi1 g cm−3√Dmax50 kmM⊕, where I have used ρi = 1 g cm−3 to representicy bodies and Dmax = 50 km. This estimate is very uncertain, as it dependson the assumed size distribution, planetesimal densities, grain albedos andemissivities, and distance to HD 141569. Provided that the estimated massreservoir is dynamically accessible (which is not explored here or obviouslymet), there is potentially sufficient cometary material to produce the currentCO gas, although the system would not maintain this gas abundance for a502.4. Discussionprotracted time without shielding. The estimated total mass ofM ∼ 160 M⊕is much larger than the mass of solids in, for example, the Solar System.Accounting for the mass of the cores of the giant planets, the mass of theKuiper belt, and estimated masses of the Oort Cloud would yield ∼ 50 M⊕.Considering that the HD 141569 star was constrained here to have a massof ∼ 2.4 M, it would be reasonable to assume that there could be 2.4× theamount of material in the HD 141569 system than the Solar System. Thismakes the M ∼ 160 M⊕ mass estimate of solids feasible.Why should significant CO gas only appear outside a radius of about30 au? As noted in the introduction, tenuous, warm CO has been detectedinterior to the 50 au diameter cavity, but there is a large change in CO abun-dance exterior to this distance, as revealed here. If the gas is indeed secondgeneration, then the change in CO abundance may reflect where significantCO was incorporated into planetesimals at the time of their formation. Inthis paradigm, the entire disc is collisionally evolving, but significant COgas is only released in planetesimals that harbor a large fraction of COice. Alternatively, the reduced abundance of CO interior to about 30 aumay simply reflect the CO photodissociation environment closer to the starand/or changes in self-shielding. The inner edge of the CO could also be setby a region with a higher rate of stirring by planets and embryos (Lissauer,1993).There is a potential contradiction with this approach. The CO mass wasderived assuming that it is optically thin and in LTE. If the gas is indeedsecond-generation, then it is not obvious whether there will be sufficient col-lisional partners to populate the rotational levels thermally. In this case, thetrue CO mass could be significantly different from the estimates calculatedhere, and potentially even orders of magnitude more massive if non-LTEeffects do dominate (Matra` et al., 2015). To check the degree to whichthe LTE assumption may be valid, I use the ALMA measured CO(3-2) in-tegrated line flux to estimate the CO(1-0) integrated line flux under LTEconditions, which is approximately ∼ 0.8 Jy km s−1. The Flaherty et al.(2016) CARMA observations found an integrated line flux for CO(1-0) of1.6±0.2 Jy km s−1, making the estimate good to about a factor of two. Ul-timately, observations of disc chemistry are needed to understand the gas’sorigin.512.5. Summary2.5 SummaryIn this chapter, I have presented ALMA continuum (870µm) and CO(3-2)observations of HD 141569. The continuum observations show a dust discthat extends out to 0.”49 with a total continuum flux density of 3.8±0.4 mJy(peak flux of 1.74± 0.24 mJy beam−1). A rough lower limit to the amountof dust mass needed to explain the emission is 0.04 M⊕. If the dust is dueto the collisional evolution of debris (rather than leftover millimetre grainsfrom planet-building), then the millimetre flux reflects a comet and asteroidreservoir of ∼ 160 M⊕ for sizes s < 50 km (assuming a collisional cascade).The continuum flux density found here is about a factor of three lowerthan that obtained with single-dish observations, suggesting that there isadditional dust on larger spatial scales or at a lower surface brightness.The CO disc observations reveal CO extending from roughly the outeredge of the inner dust disc to about 1.”8. The CO(3-2) integrated fluxdensity is 15.7±1.6 Jy km s−1 (peak flux of 0.90±0.16 Jy km s−1 beam−1),which is consistent with single-dish measurements. Assuming that the gasis in LTE and optically thin, the corresponding CO mass is ∼ 2× 10−3 M⊕for a distance of 116 pc.Based on modelling the velocity field, the disc is constrained to have aPosition Angle = −3.36◦+.65−.42 , an inclination = 53.4◦+1.2−.9 , and a system veloc-ity vsys = 6.04+.02−.03 km s−1. The gas velocities are consistent with orbiting astar of 2.39+.04−.05 M for the most probable inclination and a distance of 116pc. The uncertainties represent the 95% confidence region computed fromMCMC samples. Instead, considering only the 1-σ distance uncertainty withthe most probable mass yields 2.39+.16−.16 M.The channel maps show a localized flux enhancement of the disc to thewestern section of the disc. Further detailed modelling of the system andhigher resolution imaging are needed to properly constrain the full mor-phology. Because CO should photodissociate rapidly, the gas may require,in part, replenishment through collisions of comets, making the disc a debrissystem. While the required mass to do this may be high, it is potentiallywithin plausible limits of the inferred debris field. Observations probingthe gas composition can be used to further constrain the origin of the gas,particularly as LTE assumptions may not apply.52Chapter 3ALMA and VLAObservations of the HD141569 SystemThis chapter is based on a MNRAS publication (White et al., 2017). It usesnew VLA observations along with archival VLA and ALMA observations tomake further constraints on the HD 145169 system. Co-authors on this paperinclude Aaron Boley, Meredith Hughes, Meredith MacGregor, and DavidWilner.3.1 IntroductionHD 141569 is a multiple star system that contains an extensive circumstellardisc of dust and gas. A broad overview of the disc, including the gas, dust,and observed morphology, is given in Sec. 2.1.In addition to the large-scale morphological features discussed previouslyWhile the previously discussed morphological features seen in HD 141569’scircumstellar disc make it a noteworthy system, the disc also has a poten-tially unique grain size distribution among debris discs. Karl G. JanskyVery Large Array (VLA) 9 mm (33 GHz) observations from Semester 14A(MacGregor et al., 2016) measured an unresolved flux density of 85± 5 µJycentred on HD 141569A and its disc (the M dwarf subsystem was resolvedseparately). This emission was attributed mainly to the warm disc due tothe expectation that the flux density from HD 141569A would be negligible.When combined with shorter wavelength observations, the 9 mm flux densityimplies that the warm disc must have a spectral slope αmm = 1.63±0.06. Ifthe emission is indeed due to dust in the warm disc, the result implies thatthe corresponding grain size distribution is very shallow and a clear outliercompared with debris discs (MacGregor et al., 2016). If this interpretationis correct, then HD 141569’s disc may reflect a unique (or short lived) evo-lutionary state. There may be, however, other reasons for the large 9 mm533.1. Introductionflux density. The beam size for the semester 14A observations was 3.0× 2.4arcsec2 (∼ 300 au at the system distance), which may include diffuse emis-sion from the cold disc that was missed in some of the higher frequency,higher resolution observations. This observed flux, however, would still bedifficult to reconcile with typical spectral slopes.Another possible source of contamination is HD 141569A itself. HD141569A is a Herbig Ae/Be pre-main sequence star classified as B9.5Veby Jaschek and Jaschek (1992) and A2Ve, as well as a possible λ Boomember, by Murphy et al. (2015). The λ Boo features suggest that HD141569A is accreting dust-poor gas from its disc (Venn and Lambert, 1990).Mendigut´ıa et al. (2017) detect Hα emission coming from within ∼ 0.12au of HD 141569A, but were unable to constrain whether or not the emis-sion is from accretion. The atmospheres of Herbig Ae/Be stars are largelyunstudied observationally at millimetre/centimetre (mm/cm) wavelengthsand the corresponding emission may not be captured well in stellar mod-els. Moreover, the submm and cm emission from main sequence stars otherthan the Sun are just now being explored, e.g., α Cen (Liseau et al., 2016);AU Mic (MacGregor et al., 2012); Fomalhaut (White et al., 2016b); Vega(Hughes et al., 2012); Sirius A (White et al., 2018). If significant non-discemission is present in pre-MS and MS stars, then inferred dust properties incircumstellar discs may be biased by this emission.The possibility of significant mm/cm emission from stars is highlightedby HD 141569A’s M dwarf companions, HD 141569B and HD 141569C. Thestars were not detected by ALMA at 870 µm (345 GHz) (White et al., 2016a)or 2.9 mm (103 GHz) (as discussed here), but MacGregor et al. (2016) founda 9 mm total flux of 51±5 µJy for both stars (the beam size was larger thanthe separation between the two stars). This flux is significantly greater thanwhat would be expected from a blackbody at the photosphere temperatureand is indicative of significant coronal processes that dominate the mm/cmwavelength emission for M dwarfs, as appears to be occurring in AU Mic(e.g., MacGregor et al., 2012).To characterize circumstellar debris properly, the emission from the hoststar must be taken into account. The observations presented here contributeto the ongoing project entitled Measuring the Emission of Stellar Atmo-spheres at Submillimeter/millimeter wavelengths (MESAS). The MESASproject aims to assess the contributions of stellar atmospheres at submm-cm wavelengths and use the results to inform stellar atmosphere models(e.g., PHOENIX; Hauschildt et al., 1999).In this chapter, I present 9 mm observations of the HD 141569 triplesystem. Throughout this chapter, I adopt the Gaia parallactic distance of543.2. Observations111± 5 pc (Lindegren et al., 2016). In Section 3.2 I give an overview of theobservations including: new VLA observations presented here, archival VLA(semester 14A) observations, and ALMA 2.9 mm measurements taken fromthe ALMA archive. In Section 3.3, I describe the model fitting proceduresused to derive flux values. In Section 3.4, I discuss properties of the warmdisc. In Section 3.5, I discuss the stellar atmospheres, and summarize theresults in Section 3.6.3.2 ObservationsObservations were taken during the VLA Semester 16A (project ID VLA/2015-06-140) using the Ka band (9 mm) in the B antenna configuration with 27antennas. The longest baseline was 11.1 km. The observations were centredon HD 141569A using J2000 coordinates RA = 15 h 49 min 57.73 s andδ = −03◦55′16.62′′. Three scheduling blocks (SBs) were requested startingon 2016 June 19, but only one SB was obtained, yielding a total on-sourceintegration time of 1.15 hr.The correlator setup used 4× 2048 MHz basebands with rest frequencycentres at 30 GHz, 32 GHz, 34 GHz, and 36 GHz. Quasars J1256-0547(3C279), J1246-0730, and J1557-0001 were used for bandpass and phasecalibration. J1331+305 (3C286) was used as a flux calibration source. Datawere reduced using the Common Astronomy Software Applications (CASA4.5.0) pipeline (McMullin et al., 2007), which included bandpass, flux, andphase calibrations. The size of the synthesized beam is 0.29 × 0.21 arcsec2at a position angle of 21.6◦. The beam size corresponds to ∼ 28 au at thesystem distance of 111 pc.Fig. 3.1 shows the resulting 9 mm continuum image using natural weight-ing and cleaned using CASA’s CLEAN algorithm down to a threshold of12 σrms. The observations achieve a 0.25 arcsec resolution and a sensitivityof 4.7 µJy beam−1. The average wavelength across the frequency range is9.06 mm. HD 141569A and the companion HD 141569B were clearly de-tected. The disc around HD 141569A, as well the second companion, werenot detected. The positions of all three stars are based on Gaia astrometryand are denoted by A, B, and C in Fig. 3.1.3.2.1 Archival DataIn addition to the new VLA 16A 9 mm observations presented here (hence-forth referred to as VLA 16A), three other data sets are used in this study.These data include VLA 9 mm observations from semester 14A (henceforth553.2. ObservationsVLA 14A), which measured an unresolved flux density of 85±5 µJy centredon HD 141569A and its disc (MacGregor et al., 2016). As described below,this data is taken from the VLA archive so that I can perform additionalanalysis of the observations. I take ALMA and SMA 870 µm flux and beamsize values from literature (White et al., 2016a; Flaherty et al., 2016). I alsopresent archival ALMA 2.9 mm observations are not yet published. All ofthe newly incorporated data and values from literature are summarized inTable 3.2.The VLA 14A data were taken from the VLA archive and calibrated withthe CASA 4.5.0 pipeline (McMullin et al., 2007) in the procedure described inMacGregor et al. (2016). The observations took place on 2014 June 6 in theD configuration with 25 antennas and a longest baseline of 1.31 km. Theon-source integration time was 1.03 hr. Quasars J1256-0547, J1557-0001,and 3C286 were used as bandpass, phase, and flux calibrators, respectively.The size of the synthesized beam is 3.0 × 2.4 arcsec2 at a position angle of338.6◦. The beam size corresponds to ∼ 300 au at the system distance of111 pc. These data achieve a sensitivity of 4.9 µJy beam−1.The 2.9 mm ALMA data were retrieved from the ALMA archive (ID2013.1.00883.S). These observations were made in two execution blocks(EBs) on 2015 August 8, but one EB was not used due to phase amplitudeand water vapor radiometer (WVR) problems. The total integration timefor the successful EB was 1.24 hr. Data were taken with 44 antennas withbaselines ranging from 15 m to 1547 m. Three different spectral windowswere used with 2000 MHz bandpasses at rest frequencies centred at 98.24GHz, 100.04 GHz, and 108.14 GHz. The correlator in FDM yielded 128channels with widths of 15625 kHz. Data were reduced using the CASA 4.5.0(McMullin et al., 2007) pipeline, which included WVR calibration; systemtemperature corrections; and bandpass, flux, and phase calibrations withquasars J1517-2422, J1550+054, and J1550+0527, respectively. Ceres wasoriginally selected as a flux calibrator but the ALMA Pipeline quality as-surance (QA) suggested use of the quasar J1550+05, as it is a more reliablecalibrator for Band 3 wavelengths.Figure 3.2 shows the ALMA 2.9 mm continuum image of HD 141569.The companions HD 141569B and HD 141569C were not detected. The im-age was generated using natural weighting and cleaned using CASA’s CLEANalgorithm down to a threshold of 12 σrms. The observations achieve a sen-sitivity of 24 µJy beam−1. The size of the resulting synthesized beam is0.69 × 0.52 arcsec2 at a position angle of 56◦, corresponding to ∼ 67 au atthe system distance of 111 pc.563.2. ObservationsFigure 3.1: CLEANed VLA 16A data of the HD 141569 system. The emis-sion from HD 141569A and HD 141569B are marked by the letters “A”and “B”. HD 141569C was not detected, but its expected Gaia location ismarked by “C”. The synthesized beam is given by the black ellipse in thebottom left of the image and a 150 au (∼ 1.35 arcsec) scale is given in thebottom right. Coordinates are given as offset from the phase centre. Northis up and East is to the left.573.2. ObservationsFigure 3.2: CLEANed ALMA 2.9 mm data of the HD 141569 system. Solidcontours show 3, 6, and 12 × σrms and the dashed contour is −σrms. Thesynthesized beam is given by the black ellipse in the bottom left of the imageand a 50 au (∼ 0.45 arcsec) scale is given in the bottom right. Coordinatesare given as offset from the phase centre. North is up and East is to the left.583.3. UV Modelling3.3 UV Modelling3.3.1 VLA DataThe CASA task uvmodelfit was used to recover the best fit flux density andposition of HD 141569A and HD 141569B. The task fits a given componenttype to the visibilities of the data, which in this case is a single point source.The algorithm converges on the minimum χ2 iteratively. The solution issensitive to the starting position and flux values, which were taken from theCLEANed images. The sensitivity to the initial starting position allows usto fit point source models to components A and B separately. The results areconsistent with the peak flux densities per beam as measured directly fromthe dirty image, which for true point sources, should be the same value forthe flux densities. Table 3.1 summarizes the best fit values for HD 141569A.I find a flux of 82 ± 6 µJy and 53 ± 5 µJy for VLA 14A and VLA 16A,respectively. The uncertainties represent the σrms and a 5% flux calibrationuncertainty, added in quadrature. The best fit value of 82± 6 µJy for VLA14A agrees well with the 85 ± 5 µJy found by MacGregor et al. (2016). Inthe analysis, I use the value derived here.HD 141569B was also fit with a point source model in the VLA 16Aobservations. The best fit flux is 149 ± 9 µJy and model results are sum-marized in Table 3.1. The uncertainties represent the σrms and a 5% fluxcalibration uncertainty8, added in quadrature. As the separation betweenHD 141569B and HD 141569C is not resolved in the VLA 14A observations,I use 51 ± 5 µJy reported by MacGregor et al. (2016) and assume the fluxis equally distributed over the two companions.3.3.2 ALMA DataThe archival ALMA 2.9 mm observations have a synthesized beam that isonly slightly smaller than the warm disc. For this reason, I use a disc witha flat intensity profile (instead of point source) to model the visibilties withthe CASA task uvmodelfit. The best fit flux density is 420 µJy. Includingan absolute flux uncertainty of 10% and the σrms = 24 µJy beam−1 I finda total flux of 420 ± 50 µJy. The uvmodelfit best fit parameters are alsosummarized in Table 3.1.8The 5% flux calibration uncertainty was added in accordance with the VLA documen-tation detailed on https://science.nrao.edu/. If the absolute flux uncertainty is assumedto be negligible, then the uncertainties are characterized by σrms which is 4.9 µJy beam−1for VLA 14A and 4.9 µJy beam−1 for VLA 16A.593.3. UV ModellingTable 3.1: Summary of CASA’s uvmodelfit results. The algorithm convergeson the minimum χ2 iteratively. The solution is sensitive to the startingposition and flux values, which were taken from the CLEANed images. Thesensitivity to the initial starting position allows us to fit point source modelsto components A and B separately. A point source model was used for HD141569A and HD 141569B in the VLA data. A disc model was used for theALMA data. The uncertainties given by uvmodelfit are not used throughoutthe analysis as they can be underestimated up to a factor of√χ2reduced. Thelocation of the model is given as an offset from the phase centre of theobservations. The uncertainty in the location is the statistical uncertaintyin the model fitting procedure.HD 141569A HD 141569BParameter VLA 16A VLA 14A ALMA VLA 16AWavelength [mm] 9 9 2.9 9Flux [µJy] 53± 3 82± 6 419± 18 149± 9X Location [mas] −21± 5 91± 37 13± 19 5670± 2Y Location [mas] −22± 6 −51± 47 12± 10 4975± 2Major Axis [arcsec] - - 0.64± 0.10 -Axis Ratio - - 1.00± 0.21 -Position Angle [◦] - - 19.7± 57.3 -Reduced χ2 3.88616 5.67236 1.47999 3.88616603.4. The Warm Dust Disc3.4 The Warm Dust Disc3.4.1 The VLA 16A Null Detection of the DiscThe warm disc is predicted by SED modelling to have an inner radius some-where around 11-17 au (Malfait et al., 1998; Maaskant et al., 2015) at theGaia distance of 111±5 pc (Lindegren et al., 2016). The synthesized beamsof the ALMA observations at 870 µm and 2.9 mm were too large to spatiallyresolve this central cavity (42 au and 67 au, respectively). The synthesizedbeam for the VLA 14A observations was larger than the full extent of thewarm disc, and thus also could not resolve the central clearing.The VLA 16A observations presented here have a synthesized beamwidth of 0.25 arcsec, which is sufficient for spatially resolving the warmdisc’s inner edge for radii > 14 au. The 870 µm ALMA observations founda peak intensity of 1740 µJy beam−1, which is presumed to be solely due todust emission in the warm disc. If this intensity is scaled to the frequencyand beam size of the 9 mm observations using the spectral index of αmm =1.63 (MacGregor et al., 2016), then the disc should have had a peak intensityof ∼ 22 µJy beam−1.Fig. 3.3 shows the visibilities of the VLA 16A observations. The pro-jected visibilities shown are annularly averaged with 40-kλ bins. Both thevisibilities of the 16A observations and the reconstructed image are consis-tent with a point source centred within the SED predicted central clearingof the warm disc. With no detection of a warm dust disc, the observa-tions place a 3σ upper limit on the intensity of the disc’s inner edge to be< 15 µJy beam−1 at 9 mm.3.4.2 Millimetre Spectral Index of the DiscFig. 3.4 shows the flux densities as measured by ALMA (red), VLA (black),and SMA (blue). Using the ALMA 870 µm and VLA 14A 9 mm observa-tions, MacGregor et al. (2016) found a mm spectral index of αmm = 1.63(black line), assuming the flux density at these frequencies is characterizedby Fν ∝ ναmm . Constraining the spectral index is key as it is related to thedistribution of grain sizes over the given wavelength range (e.g., Wyatt andDent, 2002). Adopting the methods of D’Alessio et al. (2001), Ricci et al.(2015), MacGregor et al. (2016), and White et al. (2016b), the slope of thegrain size distribution, q, can be determined as follows. If the number ofgrains per size interval is given by dn/dD ∝ D−q for grain diameter D, thenthe slope of the size distribution is related to the flux density spectral index613.4. The Warm Dust DiscFigure 3.3: Visibility plot of HD 141569A from VLA 16A. The top panelshows the real component of the visibilities and the bottom planel showsthe imaginary component. The red line is the best fit point source modelfrom uvmodelfit. The data were annularly averaged with 40-kλ bins. Theuncertainties shown are the standard deviation of each 40-kλ bin. Theobservations are consistent with a point source centred on the location ofHD 141569A.623.4. The Warm Dust DiscFigure 3.4: Spectrum of HD 141569, showing the range of spectral indicesbased on different values for the flux densities. The ALMA observationsare denoted by red stars. The VLA 9 mm observations from semesters 14Aand 16A are denoted as black circles. The SMA 870 µm flux observation isdenoted by the blue triangle. The red shaded area represents the expectedflux values for a collisional cascade model (q = 3.5) with the flux anchoredat the ALMA 870 µm and 2.9 mm observations. The calculations for αmmare given in Section 4.2. The uncertainties are for the total uncertainty ofeach observation (σrms and σabs in quadrature).633.4. The Warm Dust DiscTable 3.2: Summary of best fit flux, peak intensity, and beam size at eachwavelength used in the analysis of the emission centred around HD 141569A.References are given for data taken from literature. The best fit flux fromVLA 14A presented here is consistent with the 85 ± 5 µJy reported byMacGregor et al. (2016). The references for the various observations aredenoted by the superscripts on the observatory name and are: a) Flahertyet al. (2016), b) White et al. (2016a), c) This work.Observatory λ Flux Peak Beam Size Resolved[mm] [µJy] [Jy beam−1] [arcsec2]SMAa 0.87 8200± 2400 4100 1.66× 1.16 NALMAb 0.87 3800± 500 1740 0.42× 0.34 YALMAc 2.9 420± 50 350 0.69× 0.52 YVLA 14Ac 9 82± 6 75 3.0× 2.4 NVLA 16Ac 9 53± 5 43 0.29× 0.21 Nbyq =αmm − αplβs+ 3, (3.1)where βs = 1.8±0.2 is a power law index for the dust opacity (Draine, 2006)and αpl is a power law index for the Planck function that depends on thetemperature of the dust and the wavelengths of interest (e.g, Holland et al.,2003). Specifically,αpl =∣∣∣∣∣∣log(Bν1Bν2)log(ν1ν2)∣∣∣∣∣∣ , (3.2)where Bν is the Planck Function and ν is the frequency. As a reference, aDohnanyi (1969) collisional cascade will have q ≈ 3.5, although other sizedistributions are possible depending on assumptions for the internal strengthof the grains and other dynamical processes (see MacGregor et al., 2016, fora summary).Using this formalism and the flux from VLA 14A, I calculate αmm = 1.63(consistent with MacGregor et al., 2016) and a grain size distribution q =2.83 ± 0.08, which would make HD 141569 a clear outlier from other discswith values > 3.0. As discussed in MacGregor et al. (2016), such a value forq is inconsistent with proposed models for debris size distributions, whereq typically ranges from 3− 4. Fig. 3.4, however, highlights that deriving anappropriate αmm is non-trivial for HD 141569.The ALMA 2.9 mm observations are not consistent with αmm = 1.63643.5. Origin of the 9 mm Emissionat > 2σ (where σ is the total measurement uncertainty). Furthermore,with the VLA 16A data, I find a 9 mm flux that is ∼ 60% lower than theVLA 14A observations, meaning the 9 mm flux density between semestersis inconsistent at > 2σ. Because of this, I argue that the additional ALMAand VLA observations support a steeper αmm than that found by MacGregoret al. (2016).If only the two ALMA measurements at 870 µm and 2.9 mm are consid-ered, then I find αmm = 1.81±0.20 (Fig. 3.4, dotted line). This value wouldcorrespond to a q = 2.95 ± 0.11, which while still shallow, is marginallyconsistent with some models for the grain size distributions in collisionalcascades (e.g., Pan and Schlichting, 2012).Without a clear detection of any disc emission in the VLA datasets, itis difficult to make firm conclusions regarding the true spectral index of thewarm disc at cm wavelengths. I show in Fig. 3.4 the spectral slope that wouldbe consistent with a Dohnanyi (1969) collisional cascade. The red region isshown instead of a single line to highlight the range bounded between thetwo ALMA observations. This representation is not intended to suggestthat the spectra index must lie within this region; rather, it is intended toillustrate the range of possibilities with the current data set.3.5 Origin of the 9 mm Emission3.5.1 HD 141569AFig. 3.5 shows a time series analysis of the HD 141569A 9 mm flux forboth VLA 14A and VLA 16A. These points were generated by splittingout the data into ∼ 5 min chunks. Each time chunk was fit with a pointsource model using uvmodelfit similar to the procedure in Section 3. Theuncertainties are the σrms of the reconstructed image of each chunk. Themean values of σrms are 21 µJy beam−1 and 16 µJy beam−1 for VLA 14A andVLA 16A, respectively. While there is potential variability between the twoyears between observations, there is also potentially some low amplitudevariability within each on ∼ 1 hr on source. There is some correlation,however, between the perceived variability in HD 141569A and HD 141569B,suggesting an additional systematic effect (Pearson correlation coefficient of∼ 0.69).The VLA 16A observations presented here measure a flux density of53 ± 5 µJy centred at the location of HD 141569A. If this flux is entirelydue to stellar emission (i.e. no dust emission), and taking a stellar radiusof ∼ 1.5 R, then it would imply a brightness temperature of ∼ 5 ×653.5. Origin of the 9 mm EmissionFigure 3.5: Best fit 9 mm flux of HD 141569A as a function of on sourcetime divided into ∼ 5 min chunks. Left: Semester 14A observations fromJune 2014 that found 82± 6 µJy. Right: Semester 16A observations fromJune 2016 that found 53 ± 5 µJy. The CASA task uvmodelfit and a pointsource model is used to fit the flux for each time chunk. Both observationsachieved roughly 1 hour on source and have uncertainties given by the σrmsof the images of each individual time chunk. The mean values of σrms are21 µJy beam−1 and 16 µJy beam−1 for VLA 14A and VLA 16A, respec-tively. The solid lines represent the best fit flux for the entire length of eachobservation with the shaded region representing the total uncertainty.663.5. Origin of the 9 mm Emission106 K. This value is nearly 500 times the photosphere temperature of HD141569A (10500 K). While the photosphere temperature is not expectedto be representative of the mm/cm brightness temperature of stars, themm/cm temperature profile of A type stars is only just now being testedwith observations (White et al., 2018). The only star thoroughly studied andmodelled at these wavelengths is the Sun, which at 1 cm has an observedbrightness temperature that is 2 - 3 times larger than the Solar photospheretemperature (Loukitcheva et al., 2004). Another example is TW Hydrae, apre-MS K6 star that hosts an intricate circumstellar disc. VLA observationsof TW Hydrae at 3.6 cm found more emission than expected from a simpleextrapolation of the disc dust spectrum at shorter wavelengths (Wilner et al.,2000). Subsequent VLA observations showed no significant time variabilityand resolved this emission, ruling out a gyrosynchrotron origin in stellaractivity and implicating a population of pebbles (Wilner et al., 2005) andpossibly also an ionized wind (Pascucci et al., 2006).Thermal bremsstrahlung is a dominant emission mechanism in stars with> 20× 106 K (Gu¨del, 2002). While the derived temperature is a factor of afew less than this, it could contribute to HD 141569A’s emission. Magneticfields can provide a strong, variable source of emission through synchrotronemission in stellar atmospheres, but, the magnetic field properties of HerbigAe/Be stars (such as HD 141569A) are not very well constrained. Radioflaring has been observed in pre-MS stars of all spectral types and may becorrelated to X-ray variability (Forbrich et al., 2017). Stellar winds are an-other possible source of radio emission, although the mass loss rate for A/Bstars is thought not to be appreciable enough to contribute to significantradio emission (Drake et al., 1989). If HD 141569A is in fact a λ Boo typestar (Murphy et al., 2015), then accretion may be driving the observed radiovariability. Ultimately, the stellar emission in the mm and cm from moremassive stars, and particularly pre-MS stars, is poorly understood (see e.g.Gu¨del, 2002; Cauley and Johns-Krull, 2016).3.5.2 M DwarfsThere are two candidate M dwarf companions to HD 141569A (Weinbergeret al., 2000). Their positions are denoted in Fig.3.1. The peak of HD141569B is at the Gaia predicted location and is consistent with a pointsource. There is a non-detection for the expected location of HD 141569Cand the surrounding area. The effective temperatures of the stars are 3500±85 K and 3200± 85 K for B and C, respectively (Weinberger et al., 2000).Fig. 3.6 shows a time series analysis of the HD 141569B 9 mm flux673.5. Origin of the 9 mm EmissionFigure 3.6: Best fit 9 mm flux of HD 141569B from VLA 16A as a function ofon source time divided into ∼ 5 min chunks. The observations found a totalflux of 149±8 µJy. The observations achieved roughly 1 hour on source andhave uncertainties given by the σrms of the images of each individual timechunk. The mean value of σrms is 16 µJy beam−1. The solid line representsthe best fit flux for the entire length of each observation with the shadedregion representing the total uncertainty. HD 141569C was not detectedand has an upper limit flux of ∼ 5 µJy.683.5. Origin of the 9 mm Emissionfrom VLA 16A. This plot was generated by the same procedure as Fig. 3.5.The uncertainty of each data point is characterized by the σrms of thereconstructed image of each time chunk. The mean σrms for all pointsis 16 µJy beam−1. The flux density for HD 141569B is measured to be149± 9 µJy. This value is roughly 300% of the 50 µJy flux recovered fromVLA 14A (MacGregor et al., 2016), although they were not able to clearlydistinguish between B and C due to the large beam size. The values fromboth semesters, nonetheless, imply very large brightness temperatures. Ifthe two companion stars are indeed bound to HD 141569A, then they likelyhave the same approximate age of ∼ 5 Myr (Clampin et al., 2003). Thesepre-MS M dwarfs would be expected to have variable radio emission (For-brich et al., 2017), as is observed. The emission at these wavelengths maylikely be dominated by magnetic effects, which will extend out to ∼ 3 timesR∗ with R∗ ≈ RX (Burrows et al., 2001). Using the VLA 16A flux densityfor HD 141569B and using the σrms as an upper level limit of HD 141569C, Ifind brightness temperatures of 6×108 K and < 2×107 K, respectively. Thederived temperatures are in line with the temperatures of other magneticallyactive M dwarfs (Burgasser and Putman, 2005).If the emission reported by MacGregor et al. (2016) for the VLA 14Aobservations is equally distributed between HD 141569B and HD 141569C,then a flux of ∼ 25 µJy is expected for each M dwarf. This would correspondto a > 75% drop in flux for HD 141569C and a ∼ 500% flux increase forHD 141569B. The flux of HD 141569B, however, is not constant throughoutthe 1.15 hr observations (see Fig. 3.6) and ranges from about 90 µJy to 220µJy. This variability of > 200% is similar to what MacGregor et al. (2016)observed in AU Mic. I note again that there is some correlation betweenthe perceived variability in HD 141569A and HD 141569B, likely due tosystematic effects.The quiescent emission at these temperatures could be dominated bythermal bremsstrahlung (Gu¨del, 2002). Possible flaring features have beenobserved in other M dwarfs with durations of less than 10 minutes (Bur-gasser and Putman, 2005). Accurately characterizing the expected emissionof these types of stars can also play an important role in debris disc stud-ies. As HD 141569B and C were not detected in the either of the ALMAobservations, it is likely they do not have significant, detectable debris andall the observed flux is stellar emission (White et al., 2016a).693.6. Summary3.6 SummaryIn this chapter, I have presented VLA Ka Band 9 mm (33 GHz) observationsof the HD 141569 system. These 0.25 arcsec resolution observations targetedboth the circumstellar disc around HD 141569A as well as the two M dwarfcompanions, HD 141569B and HD 141569C. The 4.7 µJy beam−1 sensitiv-ity was insufficient for detecting the disc. I conclude that the previouslyconstrained spectral index of αmm = 1.63 is too shallow. Using ALMA 870µm (345 GHz) and archival ALMA 2.9 mm (102 GHz) data, I place a lowerlevel limit of αmm = 1.81 ± 0.20, corresponding to a grain size distributionof q = 2.95± 0.11.The recovered 9 mm emissions of 52± 5 µJy for HD 141569A and 149±9 µJy for HD 141569B are both consistent with point sources (HD 141569Cwas not detected). The brightness temperatures of HD 141569A and B are∼ 5× 106 K and ∼ 6× 108 K, respectively. While there is clearly significantvariability in the emission from HD 141569B, there is also non-negligiblevariability in HD 141569A.70Chapter 4Extended MillimetreEmission in the HD 141569Circumstellar Disc Detectedwith ALMAThis chapter is based on an article published in the Astrophysical Jour-nal White and Boley (2018). The paper uses archival ALMA observationsto make constraints on the mm structure of the extended structure in HD141569’s circumstellar disc. The co-author on this paper is Aaron Boley.4.1 IntroductionHD 141569 is a widely studied system that hosts an intricate circumstellardisc of gas and dust centred around a Herbig Ae/Be star. A broad overviewof the disc, including the gas, dust, and observed morphology, is given inSec. 2.1.The current stage of disc evolution in HD 141569 is debated in the lit-erature. The outer disc may be consistent with a thinning protoplanetarydisc that is still largely dominated by small grains, while the inner disc maybe consistent with a debris disc origin (White et al., 2016a, 2017). As yet,no planets have been detected in the system, but they could contribute tothe observed morphology in the outer disc (Augereau et al., 2001). If thedisc is in a debris-like state, then dynamical interaction should also producemm grains in both the inner and outer discs. The grain size distribution, q,as traced by the spectral index, is expected to be much steeper for a debrisdisc than for a protoplanetary or transitional disc (Wyatt and Dent, 2002;MacGregor et al., 2016). VLA 33 GHz observations sought to constrainthe dynamical state of HD 141569’s disc, but were potentially biased byunconstrained stellar emission (MacGregor et al., 2016; White et al., 2017).In this chapter, I present evidence for the presence of mm grains exterior714.2. Observational Datato the inner disc in the HD 141569 system. In Section 4.2, I describe the dataand observations. The model fitting and their implications are discussed inSections 4.3 and 4.4, respectively. The results are summarized in section4.5.4.2 Observational DataThe analysis in this chapter uses three archival ALMA data sets and aPSF subtracted HST scattered light image from Konishi et al. (2016). TheALMA observations are at 345 GHz (ID 2012.1.00698.S), 230 GHz (ID2015.1.01600.S), and 100 GHz (ID 2013.1.00883). The 345 GHz and 100GHz data were published previously by White et al. (2016a) and Whiteet al. (2017), respectively. The 230 GHz ALMA data were retrieved fromthe ALMA archive.The ALMA 230 GHz observations were taken on 2016 May 16th. Thetotal integration time was 20.5 minutes, with about 2.25 minutes on source.Four different spectral windows (SPWs) were used. One SPW had a band-pass of 468.75 MHz centred at 219.565 GHz, one SPW had a bandpass of117.18 MHz centred at 220.40 GHz, and two SPWs had 2000 MHz band-passes centred at rest frequencies of 231.02 and 233.02 GHz. The datawere reduced using the Common Astronomy Software Applications (CASA4.5.3) pipeline (McMullin et al., 2007), which included WVR calibration, sys-tem temperature corrections, bandpass and phase calibration with quasarsJ1517-2422 and J1549+0237, respectively, and flux calibration with Titan.The 230 GHz observations achieve a sensitivity of 130 µJy beam−1. Thesize of the resulting synthesized beam is 1.03 × 0.99 arcsec2 at a positionangle of 70.8◦, corresponding to ∼ 112 au at the system distance of 111 pc.4.3 Visibility FittingVisual inspection of the continuum images of HD 141569 at 345 GHz and100 GHz did not show any obvious structure outside of the inner disc (Whiteet al., 2016a, 2017). Continuum observations at ∼ 350 GHz, however, havefound a range of flux densities for the system including 3.8± 0.5 mJy withALMA (White et al., 2016a), 8.2±2.4 mJy with SMA (Flaherty et al., 2016),and 12.6±4.6 mJy with APEX (Nilsson et al., 2010). These observations allhave significantly different beam sizes (42 au, 156 au, and 2000 au, respec-tively), and the diffuse flux may not have been fully recovered in previousanalyses.724.3. Visibility FittingALMA should in principle be sensitive to mm emission beyond the innerdisc, if present. Such emission however may not be apparent in the images,requiring analysis of the visibilities. While previous visibility modelling useda single component model with a uniformly illuminated disc (White et al.,2016a, 2017), the analysis here fits single and two-component power lawmodels to all three ALMA visibility data sets simultaneously.The visibility data for each frequency is annularly averaged in 10-kλ bins(see Fig. 4.1). The uncertainties represent the standard deviation of each bin.The 230 GHz data have the largest uncertainties due to the relatively shorton-source integration time. I adopt a Metropolis-Hastings MCMC modellingapproach to explore parameter space using the framework laid out in Whiteet al. (2016b). For a given set of parameters, I calculate the visibilities andproject them to the disc geometry (PA = 356.6◦ and inc = 53.4◦, Whiteet al., 2016a). Each model is compared to the data and a χ2 is calculatedfor each frequency. The three are averaged together with equal weightingto get a representative χ2. I note that since each ALMA data set has adifferent beam size and sensitivity, an equal weighting of each frequencymay not directly reflect the contribution from each set of visibilities.4.3.1 Single-Component ModelThe single-component model assumes that the system is best characterizedby a single disc. Previous modelling of the disc at 345 GHz and 100 GHzused the uvmodelfit task in CASA to fit a uniform surface brightness disc tothe visibilities. If the disc has a varying surface brightness, does not extendall the way to the star, or has multiple components, then this previoussimple model could underpredict the total flux. I confirm that the MCMCmodelling approach recovers results consistent with those of uvmodelfit whenadopting a uniform surface brightness disc model.The single-component model used here adopts a surface brightness profile∝ r−1 and assumes the disc has an inner and outer edge. The 345 GHzflux, spectral index, disc centre, and disc width are free parameters (theinner/outer edge of the disc can be found by subtracting/adding half thedisc width from the disc centre). By fitting the spectral index, the fluxesat 230 GHz and 100 GHz can be obtained without fitting them directly(and assuming the flux is well defined by a single power law in frequency),reducing the number of free parameters in the modelling process. A uniformprior distribution is chosen for the flux to range from .01 mJy to 50 mJy, thedisc from 0.1 au to 300 au, and the spectral index from 0 to 4. While theuniform priors span orders of magnitude, and are therefore biased against734.3. Visibility Fittingsmall parameter values, the flux is expected to be greater than 1 mJy and theinner disc edge is expected to be greater than 1 au (from SED modelling).Therefore, using very low values for the lower bounds of the flux and the discis not expected to affect the results. To check this assumption, I ran MCMCmodelling for the single component using Jeffreys priors, which resulted innegligible differences. The best fit model is given by the cyan curves inFig. 4.1 and the posteriors are shown in Fig. 4.2. A summary of the mostprobable model parameters, 95% Credible Region, and reduced χ2 at eachfrequency are given in Table 4.1.The resulting best fit disc extends from about 3 au to 53 au with aspectral index of 1.87. The outer edge of the disc is consistent with previousALMA models of the inner disc and the spectral index is consistent withinthe uncertainties of the value reported in White et al. (2017). The inner edgeof the disc (which is not resolved in the images) is inconsistent with the SEDpredicted central clearing of 11 au to 17 au (Malfait et al., 1998; Maaskantet al., 2015). The best fit 345 GHz flux is 4.5 mJy and the spectral indexgives fluxes of 2.1 mJy and 0.45 mJy at 230 GHz and 100 GHz, respectively.4.3.2 Two-Component ModelThe two-component model assumes that the system can be characterizedby two separate discs. The model again assumes a surface brightness profile∝ r−1. The model sets the 345 GHz flux, inner disc spectral index, innerdisc centre, inner disc width, outer disc centre, outer disc width, and outerdisc spectral index as free parameters. The flux and spectral index priorsare the same as for the single-component model. The inner disc prior rangeis from 0.1 au to 100 au and the outer disc prior range is from 50 au to 500au, and models are not accepted if the two discs overlap. The best fit modelis given by the magenta curve in Fig. 4.1 and the posteriors are shown inFig. 4.3. A summary of the most probable model parameters, 95% CredibleRegion, and reduced χ2 at each frequency are given in Table 4.1.The resulting inner disc extends from 16 au to 45 au with a spectral indexof 1.81. The disc morphology is consistent with both SED models, somescattered light observations (Currie et al., 2016), and ALMA observations(White et al., 2016a). The spectral index is also consistent with the single-component model and previous estimates (White et al., 2017). The outerdisc extends from 95 au to 300 au with a spectral index of 2.28+0.43−0.29. Thiscomponent was not detected previously with ALMA or the VLA (MacGregoret al., 2016; White et al., 2017), but is consistent with the location of thespiral features seen in multiple scattered light observations. The spectral744.3. Visibility FittingFigure 4.1: Visibility plots of the three ALMA data sets. The real compo-nent is shown as a function of projected baseline. The cyan curves are thebest fit single-component models for each frequency and the magenta curvesare the best fit two-component models for each frequency. The visibilitydata were annularly averaged with 10-kλ bins and the uncertainties shownare the standard deviation of each bin.754.3. Visibility FittingFigure 4.2: MCMC posterior distributions for the single-component model.The dashed lines indicate the most probable values and the 95% CredibleRegion.764.4. DiscussionFigure 4.3: MCMC posterior distributions for the two-component model.The dashed lines indicate the most probable values and the 95% CredibleRegion.index of the outer disc is notably steeper than that of the inner disc. Forthe inner disc, the best fit 345 GHz flux is 5.8 mJy and the spectral indexgives fluxes of 2.8 mJy and 0.62 mJy at 230 GHz and 100 GHz, respectively.For the outer disc, the best fit 345 GHz flux is 11 mJy and the spectral indexgives fluxes of 4.2 mJy and 0.63 mJy at 230 GHz and 100 GHz, respectively(the uncertainties as characterized by a 95% Credible Region are given inTable 4.1).4.4 DiscussionThese observations provide the first morphological constraints on mm-sizedmaterial outside the inner disc in HD 141569. When comparing the reducedχ2 values for each of the models, the two-component model is preferred(1.74 versus 1.08 averaged reduced χ2). The low χ2 values for both of the230 GHz models are due to the very large uncertainties on the data points(which are in turn due to the short on source integration time). While the774.4. DiscussionTable 4.1: Summary of best fit parameters for the single-component and two-component models. The most probable values (MP), 95% credible regions(CR), and reduced χ2 are given for each model along with the average foreach model (assuming equal weighting).Single-Component Two-ComponentParameter MP 95% CR MP 95% CR345 GHz Din Flux [mJy] 4.5 [3.8, 5.3] 5.8 [4.8, 6.8]345 GHz Dout Flux [mJy] - - 11 [8.4, 13]Din Centre [au] 28 [24, 34] 31 [25, 38]Din Width [au] 50 [39, 65] 30 [3.7, 65]Dout Centre [au] - - 195 [170, 230]Dout Width [au] - - 200 [140, 250]αin 1.87 [1.75, 1.99] 1.81 [1.66, 1.96]αout - - 2.28 [1.99, 2.71]345 GHz χ2red 2.78 1.34230 GHz χ2red 0.77 0.80100 GHz χ2red 1.60 1.10Average χ2red 1.72 1.08784.4. DiscussionFigure 4.4: Azimuthally averaged radial profiles of HD 141569. The curveswere created by summing the total flux in elliptical apertures of inclination53.4◦ and PA 357◦ (White et al., 2016a). The black, red, and blue curvesare from the ALMA data. They were created from the dirty images ateach frequency. The black dashed curve is from the HST scattered lightimages from Konishi et al. (2016). The inner disc portion was masked dueto artifacts as a byproduct of the PSF subtraction. The most probablelocations of the inner and outer discs as found through fitting the visibilitiesare marked by the gray shaded areas.794.4. Discussion230 GHz data alone do not strongly prefer one model over the other, allthe frequency data together show that a two-component model is at leastslightly preferred.The inner disc morphology in the two-component model is consistentwith SED, scattered light, and the ALMA inferred disc properties. Themost probable flux of the 345 GHz and 100 GHz inner disc is larger thanpreviously reported at these frequencies (White et al., 2017). Prior analysesonly fit a single disc to the visibilities with a uniform brightness profile andno central clearing. When inspecting the visibilities in Fig. 4.1, however,it is clear that a single-component model can under predict the total flux.The spectral index fit to the inner disc is still consistent with the previousestimates.The outer disc morphology is broadly consistent with the location ofthe spiral features seen in scattered light observations. Figure 4.4 showsazimuthally averaged radial profiles for each ALMA data set image and theHST scattered light images from Konishi et al. (2016). (Note that for thescattered light image, the region of the inner disc is unreliable in this plotdue to the PSF subtraction creating many image artifacts.) These curveswere generated by summing up the total flux in elliptical apertures withthe inclination and position angle previously constrained in the disc (Whiteet al., 2016a). The data are then normalized and plotted together in Fig. 4.4.The image plane alone does not show a convincing detection of the outerdisc material at the location of the spiral arms. Nonetheless, the slight peakin flux is also broadly consistent with the 95 - 300 au outer disc locationdetected in the visibility data. The radial profile in Fig. 4.4 together with thevisibility modelling make a stronger case for the detection of mm structure.The best fit spectral indicies of 1.81 ± 0.15 and 2.28+0.43−0.29 for the innerand outer discs, respectively, are not inconsistent with those observed inprotoplanetary discs. As a protoplanetary disc will likely be optically thick,the spectral index in the Rayleigh Jeans limit will be α ∼ 2. Observed valuesof α range from α = 2.0±0.5 (Andrews and Williams, 2005) to 1.5-3.2 Ricciet al. (2011), but are typically less than 3 (Natta et al., 2007). There is,however, a large overlap with the spectral indicies observed in debris discsof ∼ 2 − 3 (e.g., MacGregor et al., 2016). To determine whether or notHD 141569 is consistent with a debris origin, properties of the disc otherthan the spectral index must be considered. It is possible that the grains inHD 141569 also have a debris origin or represent a mixture of evolutionarystages.To approximate the grain size distribution from the spectral index, Iadopt the methods of D’Alessio et al. (2001), Ricci et al. (2015), MacGre-804.4. Discussiongor et al. (2016), and White et al. (2016b), in which the slope of the sizedistribution is given byq =αmm − αplβs+ 3, (4.1)where βs = 1.8±0.2 is a power law index for the dust opacity (Draine, 2006)and αpl is a power law index for the Planck function that depends on thetemperature of the dust and the wavelengths of interest (e.g, Holland et al.,2003). Specifically,αpl =∣∣∣∣∣∣log(Bν1Bν2)log(ν1ν2)∣∣∣∣∣∣ , (4.2)where Bν is the Planck Function and ν is the frequency.The inner disc has a spectral index of 1.81±0.15, which corresponds to agrain size distribution of 2.95±0.10 (with uncertainties propagated from the95% credible region on the spectral index). The outer disc, with a spectralindex of 2.28+0.43−0.29, has a grain size distribution of 3.21+0.30−0.16. Both of thesevalues of q, and especially the outer disc, are at least marginally consistentof collisional models of debris production (e.g., Pan and Schlichting, 2012).As a reference, a Dohnanyi (1969) collisional cascade will have q ≈ 3.5.As the inferred grain size distribution is consistent with other debrisdiscs, then it is possible that the grains in HD 141569 also have a debrisorigin or represent a mixture of evolutionary stages. The presence of a non-negligible amount of gas in the disc and with the new detection of largermm grains indicates that the disc could be at least partially replenished bya dynamically evolving system of asteroids and comets (Matthews et al.,2014). This situation is also thought to apply to other gas-rich debris discsaround A stars (e.g., β Pic; Dent et al., 2014). A debris origin also meansthat the planet formation process was at least partially successful in the discand that there has been significant evolution of solids by 5 Myr. A strictdebris interpretation of the disc would suggest that, at an age of ∼ 5 Myr,HD 141569 is the youngest known debris disc. The only potentially youngerdebris disc would be HD 36546, which has an estimated age range of 3-10Myr if it is indeed located in the Taurus-Auriga star-forming region (Currieet al., 2017).A simple mass estimate for the debris in each component can be calcu-lated by assuming the emission is optically thin, is dominated by densityρ = 1.0 g cm−3 grains, the grains are perfect radiators (i.e., albedo ∼ 0),and the disc is populated from the inner to outer edge of each disc. The814.4. Discussionadopted stellar parameters are T∗ = 10500 K, L∗ = 24.2 L, and d = 111 pc.The total mass of grains of size s is given by Ms =43pis3ρNs, with Ns beingthe total number of grains of a given size. The number of grains within anannulus at distance r isdNsdr=dFs/drBν(TG)Ωs(4.3)where Ωs is the solid angle of a single grain, Bν is the black body intensityof a grain at temperature TG = T∗√R∗2r . The disc flux at a single frequencyisFs =∫ RoutRin2piσ0r0rrdrd2(4.4)where r0 is a characteristic radius for the surface brightness profile (equalto the inner disc edge in this case), σ0 is the disc surface density, and Rinand Rout are the inner and outer edges of the disc. Integrating Eqn. 4.3 andsolving for the total mass givesMs =4√29sc2d2ρFsν2kBT∗√R∗R3/2out −R3/2inRout −Rin . (4.5)For the inner disc, the mass estimates are 0.034 M⊕, 0.053 M⊕, and 0.14 M⊕at 345 GHz, 230 GHz, and 100 GHz, respectively. For the outer disc, themass estimates are 0.17 M⊕, 0.22 M⊕, and 0.37 M⊕. However, this relationassumes that only a single grain size contributes to a given flux density. Thegrain radius is set equal to the wavelength of the observations. In practice,multiple grain sizes contribute to emission at a given frequency.A more comprehensive mass estimate can be made by assuming a fullgrain size distribution with a given q for each disc and that the grains onlyradiate efficiently if their circumference is equal to or larger than the ab-sorbed/emitted photons (see, Wyatt and Dent, 2002; Draine, 2006). For thismass calculation, I adopt the methods laid out in White et al. (2016a, 2017)and assume the disc is populated only by grains that have been observed(i.e ∼ 10 µm to ∼ 3 mm). Integrating from the inner to outer edge of eachdisc gives roughly 0.041 M⊕ of small solids in the inner disc and 0.18 M⊕of small solids in the outer disc. For a strict debris interpretation, the discshould be populated by much larger solids up to the size of asteroids/comets(the limiting size depends on the collision timescales). In reality, the grainsize distribution may not follow a single power all the way to these sizes.Extending the current values of q will give unphysically large values for the824.5. Summarytotal mass of the disc. For example, I find a MTotal(D < 50 km) of 75,000M⊕ and 25,000 M⊕ for the inner and outer discs, respectively.4.5 SummaryIn this chapter I presented a multi-wavelength analysis of archival ALMAdata that shows evidence of mm structure in HD 141569’s outer disc. Theinner disc is constrained to be within 16 au to 45 au and has a spectralindex of 1.81. The outer disc is constrained to be within 95 au to 300 auand has a spectral index of 2.28. The location of the two disc componentsis consistent with scattered light images. The total disc mass in 10 µm - 3mm sized solids is estimated to be 0.041 M⊕ for the inner disc and 0.18 M⊕for the outer disc. The newly constrained properties of the system makeHD 141569 at least marginally consistent with a debris origin for the smallgrains.HD 141569 SummaryChapters 2-4 have detailed the work I have done on the HD 141569 system.I have used ALMA 345 GHz, 230 GHz, and 100 GHz observations alongwith VLA 33 GHz observations to place constraints on the gas and debrisin the system. Using ALMA, I found 2×10−3 M⊕ of CO in the system, andinferred a total gas mass of ∼ 1.5 M⊕. This amount of gas could be clearedout of the system within hundreds of years due to various mechanisms suchas photoevaporation. The gas, however, could be produced by a collisionallyevolving system of comets, making HD 141569 a debris disc.If HD 141569 is in fact a debris disc, then the size distribution of itsgrains needs to be reconciled with those of typical debris systems. VLAobservations, which aimed to measure the spectral index of the disc, didnot detect the disc and instead found that the emission is likely comingentirely from the host star in the system. Using archival ALMA observa-tions, I found that a two-component disc model is marginally preferred overa single component model. The constrained properties of the system makeHD 141569 at least marginally consistent with a debris origin for the smallgrains.A summary of my work on HD 141569, along with future work andproposed observations, is given in Chapter 8.83Chapter 51.3 mm ALMA Observationsof the Fomalhaut DebrisSystemThis chapter is based on a publication in the Monthly Notices of the RoyalAstronomical Society (White et al., 2016b). It uses ALMA observationsof Fomalhaut to make constraints on the disc’s morphology and grain sizedistribution. Co-authors on this paper include Aaron Boley, Stuartt Corder,Bill Dent, and Eric Ford.5.1 IntroductionFomalhaut is one of the Sun’s closest stellar neighbors and has been thetarget of numerous studies at multiple wavelengths. Located at a distanceof 7.66 ± 0.04 pc (van Leeuwen, 2007), this 200 − 440 Myr old A3V star(Di Folco et al., 2004; Mamajek, 2012) has a bright, eccentric debris ring atstellar separation of about 140 au, which can serve as an important testbedfor debris disc evolution models and potentially planet-disc interactions.Despite extensive study, outstanding issues remain in characterizing Fo-malhaut’s debris system at millimetre (mm) wavelengths. Two such issuesare (1) determining whether or not there is a debris component interior tothe 140 au main ring, and (2) constraining millimetre flux densities of theouter ring, thus determining the millimetre spectral index. Both of these aredirectly related to understanding the evolution of the debris system itself, aswell as using the debris to constrain the structure of Fomalhaut’s putativeplanetary system.The possible presence of a warm, inner debris disc was first identified byStapelfeldt et al. (2004) after unresolved excess, compared with the expectedstellar emission, was found at 24 µm using Spitzer data. To better improvethe flux uncertainty, a re-reduction of the Spitzer data by Su et al. (2016)finds an excess of 0.64± 0.13 Jy (∼ 20% over a Kurucz model atmosphere).845.1. IntroductionUsing archival VLTI data, Absil et al. (2009) report an excess of 0.88% ±0.12% over the stellar photosphere in the K band, although they are unableto distinguish between a point source and an extended source for the centralemission. Acke et al. (2012) fit a three-component model consisting of apoint source, an inner disc, and an outer disc to Herschel data and find anunresolved excess of 0.17± 0.02 Jy, or about 50% over the expected stellarflux. In contrast, ALMA 870 µm observations (Su et al., 2016) find a totalflux about 35% lower than what is expected from the stellar photosphereand detect no extended structures within 0.2 arcsec (∼ 15 au) of the centralemission.For the main ring, the grain size distribution index, q, can be used as atracer of the collisional processes that are present in the late stages of planetformation (Dohnanyi, 1969). The size distribution can be further influencedby gravitational interactions with a nearby massive planet or by self-stirringwithin the disc (Wyatt, 2008; Mustill and Wyatt, 2009). Smaller µm sizedgrains are subject to strong interactions with radiation pressure, while thelarger mm grains will be better tracers of the parent body distribution. Thedistribution of mm grains in Fomalhaut’s outer disc can therefore be used totest the collisional models of planetesimals and the dynamical state of thesystem (Vandenbussche et al., 2010; Ricci et al., 2015). Previous constraintsfind q in Fomalhaut’s ring to be between 3.4 and 4 at ∼mm wavelengths(Ricci et al., 2015). A more precise measurement is needed to describe thedynamical state of the Fomalhaut debris disc.There is also a well-known scattered light feature located NW of thestar, just inside the outer debris ring (Kalas et al., 2008). While the na-ture of the source is debated, it could be directly related to the putativeplanet Fomalhaut b, or it could also be a byproduct of collisional processes(Lawler et al., 2015). The orbital parameters of this putative planet putit on a disc crossing orbit, casting additional doubt on whether or not itis actually a planet. Observations at infrared wavelengths have failed todetect a planet (Marengo et al., 2009; Janson et al., 2012) in the system.Regardless, the significant eccentricity of the debris ring would be consistentwith perturbations from planets (Kalas et al., 2005; Quillen, 2006), althoughhydrodynamic processes could also play a role if there is sufficient gas (Lyraand Kuchner, 2013). If the feature or the ring’s eccentricity are related toa planetary system, then Fomalhaut would be an ideal system for studyingplanet disc-interactions.In this chapter, I present 1.3 mm ALMA data that provide the highestresolution (0.28 arcsec) observations to date of the outer mm-debris discand allow for resolving the regions immediately around the star to within855.2. Observationsabout 2 au. The observations are thus able to address whether or not thereis indeed excess over the stellar emission, constraining the presence of aninner debris disc or ring. Section 5.2 is an overview of the observations anddata reduction. Section 5.3 details the image-plane and visibility modellingof the debris disc and central emission. Section 5.4 shows a fit to the SED ofthe host star, explores the grain size distribution, and discusses the centralemission. Section 5.5 summarizes the results.5.2 ObservationsThe data presented in this chapter were acquired as part of the ALMAcycle 2 campaign (project ID 2013.1.00486.S). Observations were made inthree execution blocks (EBs) taking place between 2015 June 11 and 2015September 21. The average integration time was 1.08 hr. A 34-antennaconfiguration was used and the longest baseline was 1.1 km. Each of thethree observations were centred on Fomalhaut using J2000 coordinates RA= 22 h 57 min 39.44 s and δ = −29◦37′22.64′′. The observations were takenin Band 6 at ∼ 233 GHz with the correlator setup using the Time DivisionMode (TDM) and dual polarization. Four different spectral windows wereused with 2 GHz bandpasses at rest frequency centres of 224 GHz, 226GHz, 240 GHz, and 242 GHz. Each spectral window had 128 channels witha corresponding channel width of 15.625 MHz.Ceres and quasar J2258-2758 were used for absolute flux and bandpasscalibration, respectively. Atmospheric variations at each antenna were mon-itored continuously using the water vapor radiometer (WVR). Data werereduced using the Common Astronomy Software Applications (CASA) pack-age (McMullin et al., 2007). The data reduction in CASA included WVRcalibration; system temperature corrections; and bandpass, flux, and phasecalibrations with Ceres and quasar J2258-2758. The size of the syntheticbeam is 0.329 × 0.234 arcsec at a position angle of 83.6◦. The beam corre-sponds to ∼ 2.1 au at the system distance of 7.66 pc. The FWHM of theprimary beam is 27.3 arcsec at the wavelength of the observations.The CLEANed image is shown in Fig. 5.1. This 233 GHz continuumimage was produced by CASA’s CLEAN algorithm using threshold of 12 σRMSand natural weighting. The average wavelength across the frequency range is1296 µm. The central emission and the main debris ring are clearly detected,but no extended structure is found interior to the main ring. To analyze thesystem further, I fit the data with multi-component models.865.2. ObservationsFigure 5.1: CLEANed data of the Fomalhaut system. The synthetic beamis given by the black ellipse in the bottom left of the image. Coordinates aregiven as offset from the phase centre. North is up and East is to the left. 1′′corresponds to ∼ 7.7 au at the system distance of 7.66 pc.875.3. Debris Disc Modelling5.3 Debris Disc ModellingI constrain the morphology of the Fomalhaut debris system by conductinga search through model parameters using a Markov Chain Monte Carlo(MCMC) approach. For any given model, I represent the system using apoint source and a circular ring that has a Gaussian radial profile for thedebris. The ring’s centre is allowed to be offset from the star’s position,approximating a low-eccentricity ellipse. I do not include an additionalinner debris disc/ring here. The choice of a Gaussian profile for the debris’sspatial distribution is motivated in part by the system’s similarities to theSolar System’s Kuiper Belt (Kavelaars et al., 2008; Boley et al., 2012).In the analysis, I fit the following parameters: debris disc centre, discradial width (of the Gaussian profile), system inclination relative to theobserver, disc position angle, X-offset and Y-offset, disc flux, and centralemission flux. The X and Y-offsets are the projected angular distances(measured in arcsec) of the central emission relative to the geometric centreof the ring. Models are generated using the same approach as in Whiteet al. (2016a) and assume a flat prior distribution. In generating a model,particles are randomly distributed within the debris ring, according to thegiven profile. The local grain temperature is derived assuming thermal equi-librium with the star and is azimuthally symmetric around the centre of thedisc. I assume that all the grains in the disc are perfect radiators in radiativeequilibrium with the star. The model is then rotated to a trial sky positionand projected onto a grid to get the unscaled brightness distribution. Thefinal brightness distribution of the ring is then set by demanding that thesystem have a total flux density that is consistent with the given MCMClink. The central emission of the system (i.e., star and any stellar excess) ismodelled as a point source at the phase centre of the observations, consistentwith the lack of extended emission seen in Fig. 5.1.For each model, I assume that the vertical profile of the debris is Gaussianwith a width of 1◦, as viewed from ring’s centre (see, e.g., Boley et al.,2012). In principle, the ring opening angle can be constrained, albeit veryapproximately, by effectively comparing the width of the ring at the ansaewith the width of the ring close to quadrature. In the 1300 µm observationspresented here, however, the ring ansae are too close to the edges of theprimary beam to produce meaningful, independent results.I use two different approaches in fitting models to the data. In the firstmethod, following Booth et al. (2016), I fit the data in the image planeby producing dirty images for each model (discussed more below). For thesecond and more standard method, I use each model to predict visibilities885.3. Debris Disc Modellingand then compare those results with the actual visibility data. In both cases,parameter space is explored using a random walk directed by a Metropolis-Hastings MCMC (for a review of MCMC see Ford, 2005). For each new trial,two model parameters are randomly chosen and then updated by drawinga Gaussian random parameter centred on the current model (state i). Theacceptance probability for the new trial model (state i+ 1) is given byα = min(e12(χ2i −χ2i+1), 1). (5.1)The χ2 is different depending on whether the fit is done in the image orvisibility plane; the corresponding forms are described below in Sections5.3.1 and 5.3.2. If for a given χ2, α is greater than a random numberdrawn from a uniform [0,1] distribution, then the new model is accepted andrecorded in the Markov chain. If the model is rejected, then the previousmodel is used again and re-recorded. The resulting chains are thinned by afactor of 10 (i.e. every 10th link is used) and used to determine the posteriordistributions. The thinned chains are also checked for convergence using ak-lag autocorrelation function (ACF). The ACF tests how well the sampleis mixed by comparing a given parameter xi to a parameter further in thechain, xi+k. The less the chain is autocorrelated, the lower the lag, k, neededfor the ACF to drop to near 0.5.3.1 Image PlaneGiven the high dynamic range of ALMA images, accurate modelling of in-terferometric data in the image plane is becoming more plausible. Thisapproach has some advantages over visibility modelling, since it can be con-siderably faster and less complex to model in the image plane. Visibilitiesdo not need to be calculated for each model, and the number of calls to,e.g., CASA is greatly reduced.I carry out the MCMC modelling in the image plane based on the methoddescribed in Booth et al. (2016). A trial two-component model is constructedusing a debris ring and central emission (as described above). The modelis attenuated by the primary beam and then convolved with the syntheticbeam (the sampling function). The primary and synthetic beams are ob-tained from creating a “dirty” image in CASA using the CLEAN task (withzero iterations) and then exporting to a more manageable format via theexportfits task. The resulting model dirty image is then compared with theactual dirty image from the observations by using a χ2 statistic of the formχ2i =∑ (I −Mi)2σ2(5.2)895.3. Debris Disc Modellingwhere I are the data from the dirty image, Mi is the current model, andσ = 374 µJy is the σRMS of the dirty image multiplied by the beam sizein pixels (see Booth et al., 2016). The summation is over all pixels in theimage.The MCMC routine is run with three separate chains for a total of 100000links (minus about 1000 each for burn-in). The acceptance rate for the chainis ∼ 23%. The ACF becomes negligible for lags of 50 or less for all thinnedchains. The 3 chains converge on similar parameters, and the distributionsare combined to give the resulting posterior distributions in Fig. 5.2.The blue points correspond to the values of highest probability. Themost probable parameters (i.e., the mode of the distributions) are given inTable 5.1. Uncertainties are given by a 95% credible interval around themost probable value.5.3.2 Visibility PlaneTo model the ALMA observations of Fomalhaut using the visibility plane,I first construct a trial, two-component sky model image of the debris ringand central emission (as already discussed) for the representative frequencyof each spectral window. The sky model is then loaded into CASA andused to “predict” the visibilities that the model would have for the actualarray configuration and (u,v) coordinates using the tasks setvp and predict.Each position in (u,v)-space has a real and imaginary component, and acorresponding weight. The weights for ALMA visibilties areWT = WEIGHTi,j =wiwjσ2i,j, (5.3)where wi and wj are antenna-based calibration factors derived by the CASAtask applycal during the data reduction process, andσ =1√2∆ν∆t, (5.4)where ∆ν and ∆t are the channel bandwidth and integration time. A χ2 isthen calculated for each model visibility viaχ2 =∑i,j(RDi,j −RMi,j)2WT + (IDi,j − IMi,j )2WT, (5.5)where RD, RM are the real components of the data and model visibilities;ID, IM are the imaginary components of the data and model visibilities;and WT is the weights as given above.905.3. Debris Disc ModellingFigure 5.2: MCMC parameter posterior distributions from the image planefit. The blue points represent the most probable values. The “width” is theFWHM of the ring’s radial Gaussian profile.915.3. Debris Disc ModellingFigure 5.3: Left: Dirty Image of the Fomalhaut system used in imageplane model fitting. The synthetic beam is given by the black ellipse in thebottom left of the image. Middle: MCMC constrained best fit model ofthe system. Image is convolved with the synthetic beam and attenuatedwith the primary beam of the observations. Right: The data minus modelresiduals from the best fit model. The residuals are consistent with ∼ σRMSof the observations. In all images, North is up and East is to the left. Theapparent excess in the centre of the image is an artefact due to griddingeffects in generating the image. There is also a slight residual feature in thelocation of the ring due to the image-plane fit not recovering the total fluxof the disc.925.3. Debris Disc ModellingTable 5.1: Summary of visibility and image plane MCMC results with themost probable (MP) parameter values and 95% Credible Range (CR). The“width” is the FWHM of the ring.Image Plane VisibilityParameter MP 95% CR MP 95% CRCentre [au] 139 [136, 141] 139 [135, 144]Width [au] 13 [10, 16] 15 [9, 22]Inclination [◦] 66.7 [66.0, 67.2] 66.5 [65.7, 67.8]Position Angle [◦] 336.5 [337.1, 335.9] 337.0 [338.0, 335.8]X Offset [arcsec] −0.23 [−0.35,−0.10] −0.12 [−0.36, 0.06]Y Offset [arcsec] −1.87 [−2.08,−1.64] −1.74 [−2.16,−1.32]Disc Flux [mJy] 30.8 [27.8, 34.2] 26.3 [21.6, 30.8]Central Emission [mJy] 0.90 [0.83, 0.95] 0.89 [0.78, 0.98]The MCMC routine is run with ten separate chains for a total of 100000links (minus about 1000 each for burn-in). The acceptance rate for thechain is ∼ 26%. The ACF becomes negligible for lags of 50 or less forall thinned chains. The chains converge on similar parameters, and thedistributions are combined to give the resulting posterior distributions inFig. 5.4. The blue points correspond to the values of highest probability.The most probable parameters (i.e., the mode of the distributions) are givenin Table 5.1. Uncertainties are given by a 95% credible interval around themost probable value.The data and best fit model are then deconvolved and imaged using theCASA CLEAN algorithm. The data, model, and residuals are shown in Fig.5.5.5.3.3 Comparison between approachesThe image-plane and visibility fitting methods are both very consistent witheach other in describing the disc geometry. The biggest discrepancy amongthe results of the two methods is the most probable flux for the debris ring,which has a difference of about 15%. In contrast, the flux for the centralemission is only ∼ 1% different and well within the uncertainties at the 95%confidence level. If observations are simulated in CASA using the best fitimage-plane model, the resulting residuals reveal a small amount of leftoverflux in the location of the ring. Furthermore, I cautiously note that the fluxderived by fitting the visibilities is the most consistent with expectationsbased on extrapolating the 870 µm results. Visibility fitting appears to be935.3. Debris Disc ModellingFigure 5.4: MCMC parameter posterior distributions from the visibilityplane fit. The blue points represent the most probable values. As before,the width is the FWHM of the ring’s radial profile.945.3. Debris Disc ModellingFigure 5.5: Left: CLEANed data of the Fomalhaut system. The syntheticbeam is given by the black ellipse in the bottom left of the image. Middle:MCMC constrained best fit model of the system and simulated in CASA bypredicting onto the data visibilities. Resulting image is CLEANed with thesame mask as the actual data. Right: The data minus model residualsfrom the best fit model. The residuals are consistent with ∼ 1.5 σRMS ofthe observations. In all images, North is up and East is to the left. Theapparent excess in the centre of the image is an artifact due to griddingeffects in generating the image.955.3. Debris Disc Modellingthe most accurate approach.Nonetheless, fitting in the image plane can still be advantageous. Inparticular, the MCMC quickly converged on the debris disc morphology.Most of the best fit geometrical parameters are well within the 1σ resultsof those derived from fitting to the visibilities. If only the disc geometry isneeded, then image-plane fitting could be a reasonable approach, as advo-cated by Booth et al. (2016). Furthermore, a preliminary best model couldbe selected by fitting in the image-plane, particularly as using poor startingconditions can have a major impact on the required links for an MCMCto converge and fitting visibilities can be time-consuming. In some cases,fitting first in the image plane and then refining the fit using the visibilitiesmay improve model selection.5.3.4 Additional Properties of the Debris SystemThe Gaussian profile of the chosen model accurately recovers the geometry ofthe disc, as can be seen in the residuals in Fig. 5.5. Power law disc modelswere considered, but were not well constrained in the model fitting. Asnoted above, the ring ansae are close to the edges of the primary beam. Assuch, any potential North/South asymmetries are not reliable. Furthermore,there are no noted deviations from an azimuthally smooth ring to withinthe noise level of the measurements. The “fading out” of the ring and thenbrightening at the ansae is an artefact of the primary and synthetic beamsand is reproduced with the azimuthally symmetric models (see middle panelsof Fig. 5.3 and Fig. 5.5).Other than the unresolved central emission, there is no detection of anystructure or emission interior or exterior to the debris ring. Assuming thatthe debris ring has only a small eccentricity with the star at one of thefoci, the ring’s eccentricity can be calculated from the best fit semi-majoraxis and the X and Y-offsets of the ellipse centre, as derived from the mostprobable model values listed in Table 5.1. Thus,e =(X′2 + Y′2)1/2a, (5.6)which yields an eccentricity of 0.12 ± 0.03 with uncertainties propagatedfrom the 95% Credible Ranges listed in Table 5.1. X’ and Y’ are the de-projected offsets, i.e., they represent the offsets if the system were viewedface-on, before the disc is inclined and rotated by the PA. The eccentricityresult is in agreement with the e = 0.11 ± 0.01 from HST scattered lightobservations (Kalas et al., 2005).965.3. Debris Disc ModellingThis measured eccentricity is relatively high and has implications forpotential disc-planet interactions within the Fomalhaut system. One likelyscenario is that the ring has a forced eccentricity due to an interior massiveplanet (e.g., see Wyatt et al., 1999; Kalas et al., 2005). An inner planetarysystem could also give rise to a sharp inner edge, but additional dynamicsmay be required to explain the abrupt outer edge as well (Boley et al., 2012).While the main Fomalhaut ring has a large forced eccentricity, the millimetregrains are narrowly located within a radial region that has a FWHM of 13 au.Because the millimetre grains are not strongly affected by radiation pressure,these grains further suggest that the collisional parent body population isalso narrowly located. The putative Fomalhaut b observed previously doesnot have an orbit capable of producing the observed debris morphology andtherefore additional, as yet unseen planets would be required.A rough mass estimate can also be made by making a few simplifyingapproximations for the disc. I assume that the debris is comprised of 1.3mm grains, i.e., the wavelength of the observations, and that they are perfectradiators in thermal equilibrium with the host star. All of the grains areplaced at a distance 139 au from the star. Adopting an average densityof 2.5 g cc−1, this approach yields a mass of M1.3 mm ∼ 0.017 M⊕. Thisresult is in agreement with the simple mass Boley et al. (2012) derived forthe ALMA 345 GHz observations and can be interpreted as a lower limit towithin the assumed density of the grains.The above simple mass calculation is incomplete in that it does notconsider how a distribution of grain sizes, up to some parent body size,can affect the total debris mass. To illustrate this, I use the method laidout in White et al. (2016a) to estimate the debris mass contained withinobjects of a given grain size distribution. The grains are assumed to radiateefficiently as long as the their circumference is equal to or larger than theabsorbing/emitted photons (Draine, 2006). For wavelengths larger than thegrain’s circumference9, the emission and absorption coefficients are inverselyproportional to the photon wavelength. The flux density for any given grainis calculated by assuming that the albedo A ∼ 0 and that the receivedand emitted powers balance, using a black body model modified to takeinto account the emission and absorption coefficients. The relative fluxdensity for each bin of grain sizes is then evaluated. The total mass isthen determined by requiring that the flux density of the model match the9If the gain’s diameter is used instead (e.g., see Wyatt and Dent, 2002), then thisremoves a factor of pi from the absorption coefficient. This will affect the total mass by afactor ∼ 2, yielding ∼ 11 M⊕ instead of ∼ 6 M⊕ as given in Eqn. 5.7.975.4. SED Modellingflux density derived from the observations (30.8 mJy in this case). I onlyconsider a power law size distribution characterized by q = 3.5 for dNdD ∝D−q, where D is the grain or planetesimal diameter. The chosen value forq is consistent with a collisional cascade, and as will be shown below, is areasonable estimate for the millimetre grains in Fomalhaut’s debris ring (seeSection 4).The total estimated mass will be heavily influenced by the maximumgrain size. In our own Solar System, the Kuiper Belt has a significantchange in q, or “knee”, for objects with a diameter of 50 km (Gladmanet al., 2001). If a Kuiper Belt like grain density of 1 g cc−1 is adopted,which is more appropriate for cometary-like material, I find a total massof M(D < 50 km) ∼ 6 M⊕. This result assumes that the timescale forcollisions with D ∼ 50 km-sized objects is short enough for these objects tocontribute to the cascade. While it is unclear whether or not this assumptionthis applies to Fomalhaut, it is a working assumption for comparisons withthe Kuiper Belt. A more general mass relation for the collisional cascadecan be written asM(< D) ≈ 6(ρ1 g cc−1) (D50 km) 12M⊕ (5.7)for a given maximum diameter, D, and density, ρ.The Kuiper Belt has a total inferred mass for D < 50 km of ∼ 0.1 M⊕(Gladman et al., 2001). This mass means that there is potentially 60 timesmore collisional material in the Fomalhaut debris ring than in the currentKuiper Belt, assuming the size cutoffs are appropriate. It should be cau-tioned though that the current mass of the Kuiper Belt is likely smaller thanit was when our Solar System was the same age as Fomalhaut. Estimatingthe amount of mass that the Kuiper Belt has lost due to collisional erosionover its lifetime is model dependent. In the Kuiper Belt, the main massloss mechanism is the dynamical “erosion” of the scattering population dueto gravitational interactions with planets (e.g., see Lawler et al., 2015, andreferences therein).5.4 SED ModellingAs noted above, the estimate for the debris ring’s mass is dependent onthe size distribution of grains. The grain size distribution can be inferredfrom the slope of the flux density, assuming Fν ∝ ναmm , where αmm is thespectral index at millimetre wavelengths. WI calculate αmm by combining985.4. SED Modellingthe ring’s 1.3 mm flux density (30.8 mJy, as derived from the visibility fittinghere) with literature values for flux densities at different wavelengths (seeTable 5.2). The posterior distribution for the spectral index is determinedby performing a Bayesian parameter estimation for Fν . I use an MCMCapproach similar to that used for the disc model fitting, incorporating thelisted flux uncertainties, and assume a flat prior distribution. I fit the dataover the wavelength ranges of 350 - 1300 µm and 350 - 6600 µm separately,yielding most probable values of αmm = 2.62± 0.12 and αmm = 2.73± 0.13,respectively. The 1σ uncertainties are also given.The slope of the grain size distribution, q, for dnds ∝ s−q, is given by thefollowing (see e.g. D’Alessio et al., 2001; Ricci et al., 2015; MacGregor et al.,2016):q =αmm − αplβs+ 3, (5.8)where αpl is the spectral index of the Planck function over the wavelengthsof interest, and βs is the dust opacity spectral index in the Rayleigh limit.Following Ricci et al. (2015), I adopt αpl = 1.84± 0.02 and βs = 1.8± 0.2.The adopted value of αpl would normally be 2 in the Rayleigh-Jeanslimit. The actual value of αpl, however, depends on the temperature of thedust and the wavelengths of interest (e.g., Holland et al., 2003). Specifically,αpl =∣∣∣∣∣∣log(Bν1Bν2)log(ν1ν2)∣∣∣∣∣∣ , (5.9)where Bν is the Planck Function and ν1 and ν2 are, e.g., the respectivefrequencies for the 350 µm and 6600 µm observations. The derived tem-perature range for Fomalhaut’s ring is approximately between 40 - 50 K.Assuming a dust temperature of 45±5 K yields αpl = 1.84±0.02, as used inRicci et al. (2015). Finally, Draine (2006) find that for particles larger than100 µm, βs in discs is consistent with the grains in the ISM, which meansβs ≈ βism = 1.8± 0.2, as long as 3 < q < 4. It is worth noting though thatthe value of βs could range between 1.0 and 2.0. βs ≈ 1.0 has been found inprotoplanetary discs (Andrews and Williams, 2005) and βs = 2.0 is found insimple models of conductors/insulators (Draine, 2004). Adopting differentvalues of βs can lead to significantly different values of q.Using βs = βism, the calculated grain size distribution with the additionof the ALMA Band 6 observations is q = 3.50 ± 0.14, consistent with thepreviously calculated values of q = 3.48 ± 0.14 (Ricci et al., 2015). If a βsrange of 1.0 - 2.0 is considered, with the other parameters held fixed, then q995.4. SED Modellingcan range from ∼ 3.45− 3.89. Using only the 350 - 1300 µm data set givesq = 3.43± 0.15, which is a bit shallower, but still consistent within the 1σuncertainties. Both of these results are also consistent with the predictedq = 3.51, which would be expected for a steady-state collisional cascademodel (Dohnanyi, 1969), similar to that used in the mass estimates forthe ring. Strictly, this value reflects the size distribution for approximatelymillimetre grains, and does not necessarily extend to other size regimes.5.4.1 What can the observations tell us about a possibleclose in warm debris system?There is a clear detection of the central emission at the phase centre of theimages (see Figs. 5.3, 5.5). The best fit flux from the MCMC visibilitymodelling is 0.90±0.15 mJy. The photosphere temperature of the star isconstrained to be TB = 8600 ± 200 K from Herschel observations (Ackeet al., 2012). Assuming that this brightness temperature also reflects theflux density at longer wavelengths, the expected 1300 µm flux density wouldbe 1.3 mJy. The ALMA 1300 µm observations recover < 70% of this fluxestimate. The recovered percentage is consistent with the 870 µm observa-tions, where Su et al. (2016) recover 1.8 mJy while ∼ 2.8 mJy is expectedbased on a black body with the stellar photosphere temperature. Even ifthe measured flux density in the far-infrared were to be extrapolated tomillimetre wavelengths, the measured millimetre flux density would still belower than expected.To determine the presence of an inner debris component, there first needsto be an accurate characterization of the flux contribution of the host star.Because the observed flux is already lower than expected, this means thatthe brightness temperature of the Fomalhaut star at these wavelengths ismuch less than that of the photosphere and even less than in the far-infrared(although consistent within the uncertainties). As such, the degree of unre-solved excess emission in the inner system cannot be easily determined.If we assume that there is no inner debris component and all the observedflux is intrinsic to the star, then processes in the stellar atmosphere (e.g.,chromospheric opacity effects) must be causing significant changes to thebrightness temperature of the star at millimetre wavelengths. Fig. 5.6 showsthe 24 µm and the 350-6600 µm recovered fluxes along with the brightnesstemperatures that the star would need to have to produce each measurement.The horizontal dashed line represents a brightness temperature equal to thestellar photosphere of TB = 8600±200 K. Around wavelengths of 1 mm, thebrightness temperature drops below 65% of the photosphere temperature.1005.4. SED ModellingTable 5.2: List of select, previous observations of Fomalhaut from the liter-ature. The uncertainties, when not listed, are assumed to be 10%. The (*)denotes the ALMA 870 µm observations by Boley et al. (2012). The centralemission was located near the edge of the primary beam and as such the fluxestimate is not as reliable as the flux from Su et al. (2016), where the cen-tral emission was at the phase centre of the observations. The 870 µm fluxvalue from Su et al. (2016) was used in all analysis. The references are: a)Ricci et al. (2015), b) This Work, c) Boley et al. (2012), d) Su et al. (2016),e) Holland et al. (2003), f) Holland et al. (1998), g) Acke et al. (2012), h)Ishihara et al. (2010), i) Pickles and Depagne (2010), and j) Boyajian et al.(2012).Wavelength Disc Flux Uncertainty Star Flux Uncertainty Ref.(µm) (mJy) (mJy) (mJy) (mJy)6600 0.308 - 0.092 ±0.015 a1300 30.8 ±4.1 0.89 ±0.149 b870 85 ±8.5 3.4∗ ±0.34 c870 - - 1.79 ±0.216 d850 97 - - - e850 81 - - - f500 345 ±35 10 - g450 595 ±35 - - f350 595 ±35 22 - g250 1970 ±220 54 - g160 4650 ±450 124 - g70 7990 ±666 540 - gWavelength Disc Flux Uncertainty Star Flux Uncertainty Ref.(µm) (Jy) (Jy) (Jy) (Jy)24 - - 2.96 ±0.29 d18.4 - - 5.34 ±0.08 h8.6 - - 23.0 ±0.04 h2.16 - - 257 - i1.65 - - 399 - i1.24 - - 594 - i0.554 - - 1250 - j1015.4. SED ModellingAt larger wavelengths, the brightness temperature increases to nearly doublethat of the photosphere temperature. This behaviour is very similar to thatobserved in the Sun at mm/submm wavelengths (e.g., Fig. 1 in Loukitchevaet al. (2004)), in which the observed solar flux drops down to ∼ 80% of theSun’s photosphere brightness temperature before increasing with increasingwavelength. This profile for the millimetre flux densities ultimately reflectsdifferent layers in the chromosphere, with longer wavelengths probing higheratmosphere altitudes (e.g., see Wedemeyer et al., 2016). ALMA 440-3100µm observations of the α Centauri system (Liseau et al., 2016) also find Solarchromosphere-like behaviour in the binary. The G2V and K1V stars’ stellaratmospheres indicate that the observed trends in the brightness temperatureare not exclusive to the Sun. The Fomalhaut observations allow us to beginto explore such behaviour in an A star, assuming any inner dust is negligible.Using the stellar fluxes given in Table 5.2, black body models were fit tosubsets of the flux density data using a Bayesian approach. In the ALMA870 µm observations by Boley et al. (2012), the central emission was locatednear the edge of the primary beam. As such, that flux estimate is not asreliable as the one from Su et al. (2016), where the central emission was atthe phase centre of the observations. The 870 µm flux value from Su et al.(2016) was used in all further analysis.The corresponding brightness temperatures for specific wavelength rangesare given in Table 5.3. Fitting to all the stellar data, 0.554 - 6600 µm, aswell as the wavelengths 0.554 - 24 µm, yields TB = 8650 K. This value isvery much in line with the previously constrained photosphere temperatureof TB = 8600± 200 K (Acke et al., 2012). If instead only the 870-6600 µmdata are used, then the expected brightness temperature is TB = 5540 K.This value is less than 65% of what can be “expected” from assuming thebrightness temperature is the same as the stellar photosphere temperature.Fig. 5.7 shows all of the stellar flux data from Table 5.2, along with twoblack bodies with TB = 8600 K (the photosphere) and TB = 5540 K (frommillimetre data). A PHOENIX Stellar atmosphere model similar to thatof Fomalhaut (Husser et al., 2013) is also shown. The Herschel data from70-500 µm are not a direct measurement of the stellar emission, but insteadare the estimated stellar contribution to the unresolved central emission ateach corresponding wavelength. Thus, these data points may not accuratelyrepresent the stellar emission at far-infrared/submm wavelengths. Overall,the emission centred on the star Fomalhaut does not show clear evidence foran inner debris system. Precise limits on any excess emission over the stellaremission, should it exist, can only be obtained if the stellar emission of Astars is properly characterized at submillimetre and millimetre wavelengths.1025.4. SED ModellingFigure 5.6: Brightness temperature of the star from the recovered flux at agiven wavelength. The horizontal dashed line represents a brightness tem-perature equal the stellar photosphere of TB = 8600± 200 K with the greyregion representing the uncertainty. The blue circle is the 24 µm data, theblack diamonds are ALMA data, and the green square is ATCA data. TheHerschel data are denoted as X’s since they are not direct measurements ofthe star. For flux values and uncertainties see Table 5.2.1035.5. SummaryFigure 5.7: Data from the literature and the corresponding fits to a blackbody. The blue dots represents a PHOENIX stellar atmosphere similar toFomalhaut (Husser et al., 2013). The black dashed line is the best fit blackbody for all data points with TB = 8647 K. The green dashed line is the 870µm - 6600 µm data with TB = 5540 K. The Herschel data are denoted asred X’s because they are not direct measurements of the star. The verticallines represent different regions measured by different observatories.Dynamical processes in the stellar atmosphere may further be a source ofsignificant deviations in brightness temperature at submm/mm wavelengths(Wedemeyer et al., 2016), further confounding the problem.5.5 SummaryIn this chapter, I have presented ALMA Band 6 observations of the Fo-malhaut debris system. These 0.28 arcsec resolution observations targetedboth the outer debris ring as well as the central emission around the hoststar. A two component model was fit to the data, consisting of a ring witha Gaussian radial width and a point source for the central emission. Thebest fit model recovered a flux of 30.8 mJy for a ring centred at 139 au anda FWHM of 13 au. The system inclination was found to be 66.7◦ with aposition angle of 336.5◦. The best fit model’s ring has a projected X, Yoffset of -0.23 arcsec and -1.87 arcsec from the central emission, which wasfound to have a flux density of 0.90 mJy. Model fitting was conducted usingthe visibilities and the image-plane separately, and while the image-planewas able to consistently recover the geometry and central emission, I findthat there is a ∼ 15% discrepancy in the amount of recovered ring flux.I conclude that visibility fitting remains necessary, but image-plane fittingcan be used to determine preliminary models.1045.5. SummaryTable 5.3: List of data sets selected for SED fitting. A black body was fit toeach data subset through a Bayesian approach that includes the uncertain-ties. For data from the literature, when the uncertainty is not given, a 10%uncertainty is used. The best fit brightness temperature and 95% credibleregion are given. The (*) denotes the range of data in the Herschel obser-vations. As these are inferred values, and not direct measurements, for thestar, they may not accurately represent the stellar flux at these wavelengths.Data Range [µm] Brightness Temp [K] Uncertainty [K]0.554 - 6600 8647 8645-86490.554 - 2.16 8651 8650-86522.16 - 24 7611 7605-761770 - 6600 10,750∗ 10,500-11,020870 - 6600 5540 3570-7860870 - 1300 5550 3530-7910The spectral index of the mm grains within Fomalhaut’s debris ring wasconstrained to be αmm = 2.64 ± 0.12 for wavelengths from 350 - 1300 µm,and αmm = 2.73± 0.13 for 350 - 6600 µm. This corresponds to a grain sizedistribution of q = 3.43± 0.15 and q = 3.50± 0.14, respectively, consistentwith a steady state collisional cascade model.The 0.28“ resolution of the observations is about 2.1 au at the distanceof the system. There is no detected extended structure or any obviousexcess emission over the intrinsic stellar flux. Instead, I find that the fitted0.90 mJy of flux density corresponds to a stellar brightness temperature of5540 K, less than 70% of what can be expected by assuming the millimetrebrightness temperature is the same as the stellar photosphere temperature.This difference is likely due to the star’s chromosphere, analogous to theSun. The ALMA observations of the Fomalhaut star presented here arepart of an ongoing project in measuring the emission of stellar atmospheresat submm/mm wavelengths.105Chapter 6MESAS: Measuring theEmission of StellarAtmospheres at Submm-mmWavelengthsThis chapter is based on a publication that has been published in the Astro-physical Journal (White et al., 2018). It combines JCMT, SMA, and VLAobservations of Sirius A with aims to build an stellar model of a debris-poor A star. Collaborators on this project include Jason Aufdenberg, AaronBoley, Peter Hauschildt, Meredith Hughes, Brenda Matthews, and DavidWilner.6.1 IntroductionStellar emission at sub-millimetre (submm) to centimetre (cm) wavelengthsis nontrivial and is generally not well-constrained (Cranmer et al., 2013).As the Sun is the most well studied star at submm-cm wavelengths, it canbe used as an illustrative example for the complexity of stellar emission. Inthe atmosphere of a “quiet” Sun, the submm-cm continuum radiation is dueprimarily to free-free emission (Dulk, 1985; Loukitcheva et al., 2004). QuietSun models predict a 1 mm brightness temperature10 (TB) of ∼ 4700 K,or ∼ 80% of the Sun’s photosphere TB (Wedemeyer et al., 2016). The “ac-tive” Sun, with strong magnetic fields, is difficult to model because of manycontributing emission mechanisms, such as umbral oscillations and explosiveevents (Wang, 2011; Wedemeyer et al., 2016). The TB spectrum of the Sunvaries significantly, with a minimum in the far-infrared/submm that is wellbelow the optical TB(phot) of 5800 K, followed by a pronounced increase in10The brightness temperature adopted in this chapter is the thermal temperature ex-pected for black body emission.1066.1. Introductionflux at mm wavelengths, and then a very high TB at cm wavelengths (seeblue curves in Fig.6.1).The brightness temperature spectrum of the Sun is largely due to itschromosphere and corona. Massive A-type stars, on the other hand, arethought to not have coronal processes and thus should have a flat mm spec-trum. The details of the brightness temperature spectra, however, are poorlyunderstood, including the expected deviation from the photospheric bright-ness temperature at a given wavelength. Moreover, the submm-cm emissionfrom main sequence stars other than the Sun is just now being explored, e.g.α Cen (Liseau et al., 2015); AU Mic (MacGregor et al., 2012); Fomalhaut(White et al., 2016b); Vega (Hughes et al., 2012); Sirius A (this work).This lack of understanding of submm-cm fluxes has direct implicationsfor studying debris discs. IRAS and Spitzer surveys at 70 µm and 100µm find a high occurrence rate of debris systems around A-type stars (Suet al., 2006; Thureau et al., 2014). This high occurrence rate, however,could be an age-selection effect due to A stars being hotter and youngerthan their F/G/K counterparts (Thureau et al., 2014). Regardless, the highoccurrence rate of debris makes A stars common targets in studies thatseek to characterize debris. Debris discs are commonly detected throughthe presence of excess over the expected stellar emission (e.g., Matthewset al., 2014). Demonstrating excess, however, requires an accurate model ofthe star’s spectrum. Therefore, understanding stellar emission is not justimportant for modelling stellar atmospheric processes, it is also critical fordebris disc studies.During the early stages of planet formation, small dust grains grow tobecome mm-sized particles, and then eventually form asteroids, comets, andplanets (e.g., Johansen et al., 2014; Raymond et al., 2011). These minor bod-ies act as a reservoir of new dust, collisionally replenishing µm to cm-sizeddebris, which would otherwise be cleared on short timescales (Matthewset al., 2014). The presence of heated dust leads to detectable radiation fromthe grains. Observed emission in excess over stellar emission in the IR to mmcan be used as evidence for such debris, and multi-frequency observationscan be used to probe grain size distributions through the dust emission’sspectral index. Both the occurrence of stellar excess and the dust’s spectralindex, however, can only be determined with properly calibrated and char-acterized stellar models that extend to submm-cm wavelengths. Submm-cmobservations of debris systems can allow us to infer grain properties, whichin turn can be used to constrain material properties of the planetesimalsthemselves (e.g., MacGregor et al., 2016).Our ability to study the abundance and architecture of extrasolar plan-1076.2. Observationsetary systems from circumstellar debris relies on an accurate understandingof the stellar emission in these systems. When a debris system is unre-solved, such as a distant system or a close-in asteroid belt analogue, it isoften difficult to spatially separate the emission from the disc and the emis-sion from the host star. Since observations of debris-poor stars are largelynon-existent, to approximate the flux contribution from the star itself it iscommon to extend the far-infrared brightness temperature to larger wave-lengths (e.g., Su et al., 2013). This assumption may over-predict the flux atsubmm wavelengths and under-predict the flux at submm-cm wavelengths.A poor estimate of the submm-cm flux from a debris system’s host star hassignificant consequences for the characterization of the disc.Sirius A is a nearby 225 - 250 Myr A1Vm star (Liebert et al., 2005) withno known debris. At a distance of 2.64± 0.01 pc (van Leeuwen, 2007), it isone of our Solar System’s closest neighbors and a logical starting point tostudy the submm-cm stellar emission of A stars. Previous observations ofSirius A at 0.8-1.3 mm by Zuckerman and Becklin (1993) and Chini et al.(1990) find very inconsistent flux values and large uncertainties that varysignificantly over the few years between observations. As such, they are notreliable for studying the ∼mm emission of Sirius A.The data presented in this chapter are part of an ongoing observa-tional campaign entitled Measuring the Emission of Stellar Atmospheresat Submm/mm wavelengths (MESAS). The MESAS campaign seeks to ob-tain a broad spectral submm-cm coverage of a range of spectral types tobuild a more complete catalog of stellar submm/mm/cm emission. In thischapter, I present JCMT, SMA, and VLA observations of Sirius A. Sec-tion 6.2 describes the details of the observations. Section 6.3 discusses themodelling procedure to obtain flux densities. Section 6.4 presents a detailedPHOENIX model of Sirius A’s stellar photosphere. Section 6.5 discusses theimplications for circumstellar discs.6.2 Observations6.2.1 JCMTThe data from the James Clerk Maxwell Telescope (JCMT) were acquired on2017 October 17 and 20 (project ID M17BP008; PI White). The SCUBA-2instrument (Holland et al., 2013) was used which provides continuum obser-vations at 0.45 mm and 0.85 mm (666GHz and 353 GHz, respectively). Theprimary beam is 7.9′′ and 13.0′′ at the two wavelengths, respectively, mak-ing Sirius A effectively a point source for these observations. The weather1086.2. Observationsconditions were good with a 225 GHz opacity τ225 ranging from 0.032 to0.033 on the first day of observing and 0.027 to 0.020 on the second day ofobserving. The total on source time was 2110 seconds on each day.The data were reduced using the STARLINK data reduction pipeline ORAC-DR (Gibb et al., 2005). The REDUCE SCAN ISOLATED SOURCErecipe from the pipeline was used for calibration. This recipe is ideal forbright isolated point sources, such as Sirius A. The calibrated images ateach wavelength were then co-added together using the STARLINK packagePICARD (Gibb et al., 2013) and MOSAIC JCMT IMAGES. The peakflux at the location of Sirius A was taken from the resulting calibratedimages (see Table 6.3). The σRMS of the map was measured using the PI-CARD package and the SCUBA2 MAPSTATS command and is 1.81 mJybeam−1 and 17.8 mJy beam−1 for the 0.85 mm and 0.45 mm observations,respectively.6.2.2 SMAThe data from the Submillimeter Array (SMA) were acquired on 2017 Jan-uary 28 and 2017 March 04 (project ID 2016B-S017; PI White). The ob-servations were requested to be taken approximately a month apart to testfor short term variability. A third observation was accepted as filler timeand observed on 2018 January 04 (PI Wilner). The observations were cen-tered on Sirius A using J2000 coordinates RA = 06 hr 45 min 08.30 sec andδ = −16◦ 43′ 18.91′′. To acquire 0.88 mm and 1.3 mm (340 GHz and 225GHz) data simultaneously, the upper side band (USB) of the low frequencyreceiver was tuned to 345 GHz and the USB of the high frequency receiverwas tuned to 230 GHz. The USB of the low frequency tuner used 4 × 2.0GHz basebands with rest frequency centers at 351.013 GHz, 349.000 GHz,347.012 GHz, and 345.000 GHz. The lower side band (LSB) used 4× 2.048GHz basebands with rest frequency centers at 335.011 GHz, 332.998 GHz,331.010 GHz, and 328.998 GHz. This set-up gives an effective frequency of340 GHz (0.88 mm) for the low frequency receiver. The USB of the highfrequency receiver used 4× 2.0 GHz basebands with rest frequency centersat 236.011 GHz, 233.998 GHz, 232.020 GHz, and 229.998 GHz. The spectralwindows in the LSB used 4×2.0 GHz basebands with rest frequency centersat 220.009 GHz, 217.997 GHz, 216.009 GHz, and 213.996 GHz. This set-upgives an effective frequency of 225 GHz (1.33 mm) for the high frequencyreceiver. The 2018 January 04 observations only utilized the lower frequencyreceivers and have an effective frequency of 227 GHz (1.32 mm).The data were calibrated using Interactive Data Language (IDL) with the1096.2. ObservationsMIR package11. The 2017 January 28 observations used 7 antennas in thecompact configuration with baselines ranging over 9.5 - 68.4 m. There wasgood weather with a measured 225 GHz opacity of 0.075. Quasar 3C84 wasused as to calibrate the bandpass, Uranus was used to calibrate the flux,quasars 0725-009 and 0522-364 were used as phase calibrators, and systemtemperature corrections were applied. The 2017 March 04 observations used7 antennas in the extended configuration with baselines ranging over 50.0- 226.0 m. There was good weather with a measured 225 GHz opacity of0.06. Quasar 3C273 was used to calibrate the bandpass, Ganymede was usedto calibrate the flux, quasars 0725-009 and 0522-364 were used as phasecalibrators, and system temperature corrections were applied. The 2018January 04 observations were in the compact configuration. Quasar 3C273was used to calibrate the bandpass, Uranus was used to calibrate the flux,quasars 0725-009 and 0522-364 were used as gain calibrators, and systemtemperature corrections were applied.The SMA data, reduced in IDL, are converted to a UV-Fits file formatusing the IDL task autofits and then converted to a CASA MeasurementSetusing MIRFITStoCASA12. This conversion allows for imaging to be under-taken straightforwardly in the CASA environment. The data were imagedwith a natural weighting and cleaned using CASA’s CLEAN algorithm downto a threshold of 12 σRMS. The 2017 January 28 observations achieve a sen-sitivity of 0.85 mJy beam−1 and 3.30 mJy beam−1 for the 1.3 mm and 0.88mm data, respectively. The 2017 March 04 observations achieve a sensitivityof 0.85 mJy beam−1 and 1.48 mJy beam−1 for the 1.3 mm and 0.88 mmdata, respectively. The 2018 January 04 observations achieve a sensitivityof 0.32 mJy beam−1.6.2.3 VLAThe data from the Jansky Very Large Array (VLA) were acquired in Semester17A on 2017 March 02, 2017 August 21, and 2017 August 22 (project ID17A-239, PI White). The observations were centered on Sirius A using J2000coordinates RA = 06 hr 45 min 08.30 sec and δ = −16◦ 43′ 18.91′′. The2017 March 02 observations were taken in the D antenna configuration with26 antennas and baselines ranging over 0.035 - 1.03 km. The two 2017 Au-gust observations were taken in the C configuration with 28 antennas andbaseline ranging over 0.035 - 3.4 km.11https://www.cfa.harvard.edu/∼cqi/mircook.html12https://www.cfa.harvard.edu/rtdc/SMAdata/process/casa/convertcasa/1106.3. Visibility Model FittingThe observations were set up to include 6.7 mm and 9.0 mm (45 GHz and33 GHz) data in the same Scheduling Block (SB). The 33 GHz data used theKa Band correlator setup with 4× 2.048 GHz basebands and rest frequencycenters of 28.976 GHz, 31.024 GHz, 34.976 GHz, and 37.024 GHz. Thisset-up gives an effective frequency of 33 GHz (9.0 mm) for the Ka band.The 45 GHz data used the Q Band correlator setup with 4 × 2.048 GHzbasebands and rest frequency centers of 41.024 GHz, 43.072 GHz, 46.968GHz, and 48.976 GHz. This set-up gives an effective frequency of 45 GHz(6.7 mm) for the Q band. Quasar J0650-1637 was used for bandpass andphase calibration. 3C48 was used as a flux calibration source. Data werereduced using the CASA 4.5.0 pipeline (McMullin et al., 2007), which includedbandpass, flux, and phase calibrations.After consultation with the VLA HelpDesk, the Q band data from thetwo 2017 August observations had to be discarded due to poor weather andatmospheric conditions adversely effecting the high frequency observationsand in particular the reliability of the flux calibrator (3C48). The flux ofSirius A is too low for a reliable self-calibration.The data were imaged with a natural weighting and deconvolved usingCASA’s CLEAN algorithm down to a threshold of 12 σRMS. The 2017 March02 observations achieve a sensitivity of 7 µJy beam−1 and 24 µJy beam−1 forthe 9.0 mm and 6.7 mm data, respectively. The 2017 August 21 and 22 9.0mm observations achieve sensitivities of 13 µJy beam−1 and 14 µJy beam−1,respectively.The flux densities presented here rely on well modelled flux calibrators.Therefore, the accuracy of the observed flux of Sirius A in a given observationdepends on the absolute flux uncertainty of the flux calibrator. For allstated uncertainties in Table 6.3, I include the absolute flux uncertainty ofthe calibrator and the σRMS of the observations added in quadrature. ForJCMT, a 5% flux calibration uncertainty is used for the 0.85 mm data and a10% flux calibration uncertainty is used for the 0.45 mm data. For the SMAand VLA, a 10% and 5% flux calibration uncertainty is used, respectively.6.3 Visibility Model FittingThe small angular size of Sirius A compared to the synthetic beam of theVLA and SMA observations makes Sirius A effectively a point source. Assuch, the flux at a given wavelength would in principle be the peak fluxdensity in the reconstructed images. Nevertheless, I choose to take a morerobust approach by modelling the visibilites, which is the more standard1116.4. PHOENIX Modelmodelling procedure for interferometic observations.I use the CASA task uvmodelfit to recover the best-fit flux density ofSirius A at each wavelength. The task fits a point source to the visibilitiesof a given data set. A minimum χ2 is converged on through an iterativeprocedure. The best fit solution is sensitive to the starting parameters,which were taken from the CLEANed images. Although this algorithm canyield a large reduced χ2 (as was the case for the SMA 0.88 mm observationsfrom 2017 January 28), the results are consistent with the peak flux densitiesper beam as measured directly from the dirty image. Table 6.3 summarizesthe final values and reduced χ2 for Sirius A at each wavelength. For theJCMT observations, the peak flux and σRMS were taken from the calibratedimages. All of the listed uncertainties include absolute flux calibration addedin quadrature.6.4 PHOENIX ModelAs submm-cm observations of debris poor A stars are largely nonexistent,stellar atmosphere models have not been tested at submm-cm wavelengths.I use the SMA, JCMT, and VLA data presented to inform the PHOENIXstellar atmosphere (Hauschildt et al., 1999) and compare model photospherefluxes to the long wavelength observations.Fig. 6.1 shows fractional brightness temperature as a function of wave-length. The brightness temperature is normalized to the optical photospheretemperature so that different types of stars can be compared on the sameplot. In Fig. 6.1, the two blue curves are models of the “active” and “quiet”Sun from Loukitcheva et al. (2004) and are included as an illustrative exam-ple (normalized to Teff = 5750 K). The SMA observations of Sirius A aredenoted with black diamonds, the VLA observations are with black circles,and the JCMT observations with black stars.The two black curves represent spherical 1-D PHOENIX model syntheticspectra of Sirius A’s photosphere (version 17.1, see Hauschildt and Baron,2010, for an earlier code version). The modelling procedure is similar toHusser et al. (2013), but now includes the following updates. The atomicline list and the model atoms for the non-local thermodynamic equilibrium(non-LTE) models are based on the 2016 versions of the Kurucz data13. Forthe non-LTE models, new model atoms were generated from the same dataso that LTE and non-LTE models are internally consistent with each other.The temperature-pressure structure is computed from the conditions of ra-13(http://kurucz.harvard.edu/linelists.html)1126.4. PHOENIX ModelWave. Facility Date Calibrator Flux Reduced(mm) YY/MM/DD (mJy) χ20.45 JCMT 17/10/17 Uranus 61.6± 18.8 -0.85 JCMT 17/10/17 Uranus 15.2± 1.96 -0.88 SMA 17/01/28 Uranus 17.4± 3.74 6.720.88 SMA 17/03/04 Ganymede 15.7± 2.15 1.121.3 SMA 17/01/28 Uranus 8.52± 1.21 1.911.3 SMA 17/03/04 Ganymede 6.86± 0.85 1.601.3 SMA 18/01/04 Uranus 7.49± 0.87 0.9776.7 VLA 17/03/02 3C48 0.240± 0.027 1.099.0 VLA 17/03/02 3C48 0.137± 0.010 1.119.0 VLA 17/08/21 3C48 0.119± 0.014 3.859.0 VLA 17/08/22 3C48 0.145± 0.015 7.86Table 6.1: Summary of flux values for Sirius A. The JCMT flux values weretaken as the peak of the emission from the images. The flux uncertaintiesare the σRMS of the images and the absolute flux calibration uncertaintiesadded in quadrature. For JCMT, a 5% flux calibration uncertainty is usedfor the 0.85 mm data and a 10% flux calibration uncertainty is used for the0.45 mm data. For the SMA and VLA observations, the flux values werecalculated using CASA’s uvmodelfit. A 10% flux calibration uncertainty isused for the SMA data and a 5% flux calibration uncertainty is used for theVLA data. The uncertainties from uvmodelfit are not used for these fluxdensity measurements because they can be underestimated up to a factorof√χ2reduced. Moreover, the uncertainty in the point source flux densitiesshould be comparable to the sensitivity of the observations, motivating theuse of σRMS.1136.4. PHOENIX Modeldiative and convective equilibrium for both LTE and non-LTE models withthe assumption of a hydrostatic atmosphere. The non-LTE statistical equa-tions are solved with the 1-D mode of the method discussed in Hauschildtand Baron (2014), which includes the non-local operator splitting radia-tive transfer solver and the rate-operator setup as well as the mpack/gmp14based arbitrary precision solver that allows for large dynamic range withinthe statistical equations.Fundamental stellar parameters of Sirius A are taken from measuredconstraints on the angular diameter and bolometric flux (Davis et al., 2011)together with the trigonometric parallax and dynamical mass (Bond et al.,2017) from its orbit about Sirius B. For the model, an effective temperatureof Teff = 9843 K, a surface gravity of log(g)=4.28, and a radius of 1.71 Rare adopted. Elemental abundances are taken from recent detailed spectralanalyses (Landstreet, 2011; Cowley et al., 2016). The model fluxes can beconverted to the observed fluxes using the measured limb-darkened angulardiameter of 6.04 mas (Davis et al., 2011) and plotted in Fig.6.1 by dividingthe model fluxes by a Planck function with Teff = 9940 K.The solid black line is the synthetic spectrum from a non-LTE modelfor Sirius. The model temperature structure and level departure coefficientswere converged for 192 atom/ion species with 37,419 levels in statisticalequilibrium and a total of 467,982 spectral lines (bound-bound transitions)in non-LTE and 1,903,022 background “fuzz” lines from PHOENIX version17.01.02A. The dashed line is the synthetic spectrum from an LTE modelwith the same fundamental parameters and 1,283,018 spectral lines consid-ered in LTE only. The non-LTE temperature structure is flatter and warmer,by 500 K to 1000 K, at the formation depths of the submm-cm continuumrelative to the LTE temperature structure. This temperature structure dif-ference yields a brighter and flatter profile for the non-LTE model comparedto LTE model through the submm-cm band.Neither model appears to be ruled out given present uncertainties in theobserved submm-cm fluxes, however the two models diverge further beyond1 cm and flux measurements at longer wavelengths may more clearly favorone of the models. For a full spectral model of Sirius A’s stellar atmosphere,see Aufdenberg et al. (in prep).14(http://mplapack.sourceforge.net)1146.4. PHOENIX ModelFigure 6.1: Submm-cm observations of Sirius A. The two blue curvesrepresent models of the Sun at maximum activity (solid line) and minimumactivity (dashed line) from Loukitcheva et al. (2004) and are included forillustrative purposes. The observations of Sirius A are denoted as black starsfor the JCMT data, black diamonds for the SMA data, and black circles forthe VLA data. The two black curves are PHOENIX models of Sirius A’satmosphere with a non-LTE model (solid line) and a LTE model (dashedline).1156.5. Implications for Circumstellar Disc Studies6.5 Implications for Circumstellar Disc StudiesThe observations presented here are the first reliable submm-cm flux densi-ties of Sirius A and A stars in general. To further the detection and charac-terization of debris discs, it is imperative to understand potential sources ofbias in the submm/cm wavelength regime. For unresolved systems, where itis not possible to spatially separate the stellar and disc emission, an accuratemodel of the stellar emission is necessary to study the debris.In the literature, when estimating the flux contribution of a host starin a debris system, it is common to either assume black body emission atthe photosphere temperature or to extrapolate IR observations (also assum-ing a black body profile) to the observed wavelengths. As is shown in thePHOENIX models of Sirius A’s atmosphere, neither of the assumptions arevalid at the tens of percent level.To see how uncertainty in stellar emission can affect the study of debrissystems, consider the following example. Fomalhaut is a 200-440 Myr oldA3V star (Di Folco et al., 2004; Mamajek, 2012) with a well-known extendeddebris ring at 140 au (e.g., Kalas et al., 2005; Boley et al., 2012; White et al.,2016b; MacGregor et al., 2017). There is also additional potential IR excessat much closer orbital distances (e.g., an asteroid belt analogue, Su et al.,2013). Adopting different stellar models, however, significantly changes theamount of this inferred excess (Su et al., 2016; White et al., 2016b). Inparticular, ALMA observations at 0.87 mm and 1.3 mm (Boley et al., 2012;Su et al., 2016; White et al., 2016b) find a TB of ∼ 5500 K for the centralemission (which include both disc and stellar emission). This temperatureis much lower than the optical photosphere temperature of 8600 ± 200 K(Acke et al., 2012), and even lower than that surmised by extrapolating far-IR emission to mm wavelengths. Confusingly, ATCA 6.6 mm observationsfind a TB of > 16000 K (Ricci et al., 2015), nearly ∼ 200% of TB(phot),potentially showing a profile similar to the Sun. As Fomalhaut is an A3Vstar, it is not expected to have a corona, and thus should not have a solar-like submm-cm emission profile. No conclusions on unresolved mm debrisin the Fomalhaut system can be made until the emission of the host star isknown and subtracted from the observed disc flux.Fomalhaut and Sirius A are of a similar spectral type and age. There-fore it is reasonable to expect a similar brightness temperature structure forthe two stars. The SMA receivers at 0.87 mm and 1.3 mm (345 GHz and230 GHz) are complementary to ALMA Bands 7 and 6, which were used tostudy Fomalhaut. The mm brightness temperature of the central emissionin Fomalhaut (which should include the star and the putative inner disc) is1166.6. Summaryconsistent with the mm spectra of Sirius A. Taken at face value, the obser-vations and modelling of Sirius A imply that Fomalhaut has no detectablemm debris at close in separations. This inference would suggest that eitherthe IR observations of Fomalhaut are only detecting stellar emission, thatthe spectral index of the dust emission is anomalously steep, or that there isonly small µm dust in the inner disc (i.e., more like a Zodiacal Dust analoguethan an asteroid belt analogue). These possibilities are discussed further inCh. 7.The data and modelling presented here assume that there is no detectablevariability at any of the observed wavelengths in Sirius A’s atmosphere. A-type stars are not expected to have any significant magnetic field activity.A weak surface magnetic field of 0.2 ± 0.1 G, however, was detected onSirius A, although the source of the field is unknown (Petit et al., 2011).The submm-cm spectrum of Sirius A over the ∼yr timescale of all the ob-servations presented here is stable enough that if any variability is present,it would either occur only very quickly between observations or over largertimescales than observed. Significant radio variability, however, is observedin other stars. For example, the Herbig Ae/Be B9.5Ve star HD 141569 wasfound to have potentially significant variability at 9.0 mm (White et al.,2017) as seen with the VLA in 2014 (MacGregor et al., 2016) and 2016(White et al., 2017). Indeed, this variability is prohibiting an accurate char-acterization of the inner disc around HD 141569. Ongoing observations ofSirius A to determine its long-term stability, or variability, are necessary toensure consistency in the modelling.Utilizing the full potential of facilities such as ALMA and VLA as well asfuture facilities such as ngVLA (Murphy et al., 2018) to study debris discswill require increasingly accurate models of the stellar emission of the hoststars in those systems.6.6 SummaryIn this chapter, I presented SMA and VLA observations of Sirius A at 0.45mm, 0.85 mm, 0.88 mm, 1.3 mm, 6.7 mm, and 9.0 mm. The observationswe used to inform both an LTE and non-LTE PHOENIX model atmosphereof Sirius A. The resulting spectra provides a good match to the data andcan be used as a template for stellar emission for A stars at submm-cmwavelengths. An accurate stellar template at long wavelengths is necessaryto assess stellar excess due to unresolved features such as a debris disc.The observations are part of an ongoing observational campaign entitled1176.6. SummaryMeasuring the Emission of Stellar Atmospheres at Submm/mm wavelengths(MESAS).118Chapter 7No Evidence for an AsteroidBelt in the Fomalhaut DebrisSystemThis chapter is based on an ongoing project to study the central emissionfrom the Fomalhaut debris system. It combines the ALMA results fromChapter 5 and the stellar model from Chapter 6 in order to make constraintson the nature of a potential inner asteroid belt in the Fomalhaut system.7.1 IntroductionFomalhaut is a nearby ∼ 440 Myr old A3V star (Di Folco et al., 2004;Mamajek, 2012) that hosts one of the most well-studied circumstellar debrisdiscs. A bright and narrow ring of material is located ∼ 139 au from thestar and has been imaged in scattered scattered light (Kalas et al., 2005),IR (e.g., Acke et al., 2012), and mm wavelengths (e.g., White et al., 2016b).Its close proximity to the Sun (7.7 pc) allows for high spatial resolutionobservations of the disc, making Fomalhaut a valuable testbed for planetand circumstellar disc formation and evolution.Interior to the resolved debris ring is a possible warm disc, similar tothe asteroid belt in the Solar System. Studying multi-component discshelps to establish a firm connection between the properties and correla-tion between cold and warm debris discs. If Fomalhaut does indeed hosta multi-component disc, then it can be used to constrain debris transportmechanisms that were thought to have occurred in the young Solar System(e.g., Chen et al., 2014). The location of a debris disc can also be influencedby planets in the system. For example, the structure of the asteroid beltin the Solar System is influenced by both giant and terrestrial planets (e.g.,Murray, 1986; Dermott et al., 1994; Murray et al., 1998).Warm discs are located closer to their host stars than cold discs, meaningthey are generally very difficult to spatially resolve. As such, a warm disc1197.1. Introductioncan be indistinguishable from a point source centred at the location of thestar. The disc’s properties must therefore be inferred through excess overthe expected stellar emission. Modelling the spectrum of the disc throughits excess allows for constraints on the location, temperature, and grain sizedistribution of the disc.The inner debris disc in Fomalhaut was first inferred through unresolvedexcess at 24 µm with Spitzer (Stapelfeldt et al., 2004). Acke et al. (2012)used Herschel data to find an unresolved excess of about 50% over theexpected stellar flux from 70− 500 µm. SED modelling found the excess tobe consistent with an asteroid belt located at 11 au (Su et al., 2013). None ofthese IR observations, however, had sufficient resolution to separate spatiallythe star from the inner disc. The longer wavelength Herschel observations donot separate the central emission from the outer debris as well as the shorterwavelength data, adding additional uncertainty to the flux contribution ofthe various components of the Fomalhaut system. ATCA 45 GHz (6600µm) observations also found an excess over stellar emission of nearly 200%(Ricci et al., 2015). The observations again were not of sufficient resolutionto clearly distinguish the central emission from the outer debris ring, so itis again unclear if the inferred flux truly reflects the central emission alone.If a warm asteroid belt is indeed present in the Fomalhaut system, thenit would in principle be detectable at mm wavelengths with facilities suchas ALMA. Su et al. (2016) observed Fomalhaut at 870 µm with ALMA andreport a flux about 35% lower than what is expected from the stellar emissionalone and no extended structures within ∼ 15 au of the central emission.Similarly, ALMA 1300 µm observations (White et al., 2016b) detect a totalflux about 30% lower than the expected stellar emission and no extendedstructure outside of ∼ 2 au. Lower resolution ALMA 1300 µm observations(MacGregor et al., 2017) find a total flux about 40% lower than the expectedstellar emission. The ∼ 12 au synthesized beam of these observations wouldhave been able to detect an asteroid belt if were indeed at the SED inferredlocation of 11 au.Modelling an unresolved disc through its excess over stellar emissionrequires assumptions about the stellar emission profile. As was seen withALMA observations of Fomalhaut, the observed flux of the central emissionwas less than what might be expected from simple estimates. For example,in the literature it is common to assume a black body emission profile for thestar following either the photosphere temperature or the brightness temper-ature from the longest wavelength IR observations with no detectable debris(e.g., Boley et al., 2012; Su et al., 2016), as observations of stars with nodebris at longer than IR wavelengths are largely nonexistent (White et al.,1207.2. Observational Data2016b, 2018). Most stellar emission models of A-type stars also do not ex-tend past ∼ 10 µm (e.g., Kurucz, 1992), making long wavelength stellaremission profiles difficult to constrain. Sirius A is a nearby star that is ofa similar age and spectral type as Fomalhaut and has no known debris.The MESAS observational campaign (White et al., 2018) used submm-mmobservations of Sirius A to build a spectral profile of the star. The datawere used to inform a PHOENIX model (Hauschildt et al., 1999) of SiriusA’s stellar atmosphere incorporating observations from the UV to the Radio(Aufdenberg et al. in prep). The Sirius A profile is used in this chapter toprovide a more accurate stellar emission model for Fomalhaut.7.2 Observational DataTo accurately constrain the properties of the central emission, a broad spec-tral profile of the system is necessary. This analysis uses data from multiplefacilities, which are summarized in Table 7.1.The ATCA observations at 6600 µm are plotted in Fig. 7.1, but were notspecifically used in the model fitting process. The synthesized beam of theATCA observations is 14.3′′ × 10.7′′ (or 110au× 83 au at a system distanceof 7.7 pc) and it is difficult to clearly separate the central emission from theouter debris ring at 139 au (White et al., 2016b). Due to this difficulty, andthe larger than expected flux value reported in Ricci et al. (2015), the 6600µm flux value is only plotted for illustrative purposes.The two ALMA 1300 µm flux values (see Table 7.1) are consistent withintheir respective uncertainties. The observations from White et al. (2016b),however, have a synthesized beam of 0.329′′ × 0.234′′ (∼ 2 au at a systemdistance of 7.7 pc) and the observations from MacGregor et al. (2017) havea synthesized beam of 1.56′′×1.15′′ (∼ 12 au at a system distance of 7.7 pc).Since the latter covers a larger potential area for an inner belt to reside (andis consistent with the previously determined location of an asteroid belt), itis the value used for the 1300 µm flux in the model fitting.7.3 Disc ModellingTo best constrain the source of the stellar excess observed around Foma-lhaut, several different emission models are considered. For all models, aMetropolis-Hastings MCMC approach is undertaken to explore parameterspace. The approach follows the framework and model generation laid outin White et al. (2016a,b). For a given set of parameters, a spectral profile is1217.3. Disc ModellingWavelength [µm] Flux [mJy] Uncertainty [mJy] Facility Ref8.6 23010 690 AKARI a18.4 5338 230 AKARI a24 3600 130 Spitzer b70 540 45 Herschel c160 124 12 Herschel c250 54 6 Herschel c350 22 2 Herschel c500 10 1 Herschel c870 1.789 0.181 ALMA d1300∗ 0.89 0.12 ALMA e1300∗ 0.75 0.08 ALMA f6600 0.092 0.015 ATCA gTable 7.1: Summary of the Fomalhaut observations from IR to mm wave-lengths used in this analysis. References denoted in the table are: a) Ishiharaet al. (2010), b) Stapelfeldt et al. (2004), c) Acke et al. (2012), d) Su et al.(2016), e) White et al. (2016b), f) MacGregor et al. (2017), g) Ricci et al.(2015). ∗ The point of distinction for the two 1300 µm observations is notedbecause of the difference in the synthesized beam (and thus the resolution)of the two observations.1227.3. Disc Modellingcalculated over the wavelength range of the observations. The trial spectralprofile is then compared to the total observed flux at each wavelength anda χ2 is calculated to assess the likelihood of the trial model.7.3.1 Stellar ModelDue to the resolution of all the observations being considered, it is not pos-sible to spatially separate the stellar emission from any potential warm discemission. Therefore, all of the data listed in Table 7.1 also include the emis-sion from the star itself. To determine the appropriate excess over stellaremission, a “Sirius-like” stellar emission profile is used for Fomalhaut (Whiteet al., 2018). This profile is based on a PHOENIX modelled stellar atmo-sphere (Hauschildt et al., 1999) of Sirius A, which is of a similar spectraltype and age to Fomalhaut, scaled to the brightness temperature of Foma-lhaut (See Fig. 7.1). White et al. (2018) found that the 345 GHz and 230GHz ALMA observations of Fomalhaut, when compared to Sirius A, wereconsistent with no excess emission over the stellar atmosphere.The IR-mm spectral index of Fomalhaut’s stellar emission, α∗, can beestimated from the data with no reported excess, and will be given byα∗ =∣∣∣∣∣∣log(Bν1Bν2)log(ν1ν2)∣∣∣∣∣∣ , (7.1)where Bν is the Planck Function and ν1 and ν2 are the respective frequenciesover which the observations were taken. In the case of Fomalhaut, and usingthe 8.6 µm and 1300 µm data, I find a spectral index of α∗ = 2.05. A blackbody emission profile in the Rayleigh Jeans limit between the two pointswould correspond to a spectral index of 2.0. The stellar emission at any givenwavelength can thus be calculated assuming a black body emission profileextending from the 8.6 µm flux value multiplied by a factor of ∝ λ−0.05,which is the difference between a black body profile and the inferred stellarprofile. This formulation gives a total stellar fluxF∗(λ) = pi(R∗d)2B(T∗)(8.6µmλ)0.05, (7.2)where R∗ is the stellar radius, d is the distance to the system, B is thePlanck Function, and T∗ is the brightness temperature of the star at 8.6µm.1237.3. Disc ModellingFigure 7.1: Submm-cm observations of Sirius A from White et al. (2018).The two blue curves represent models of the Sun at maximum activity (solidline) and minimum activity (dashed line) from Loukitcheva et al. (2004)and are included for illustrative purposes. The observations of Sirius A aredenoted as black stars for the JCMT data, black diamonds for the SMA data,and black circles for the VLA data. The two black curves are PHOENIXmodels of Sirius A’s atmosphere with a non-LTE model (solid line) and aLTE model (dashed line). The red diamonds are observations of Fomalhaut’scentral emission.1247.3. Disc Modelling7.3.2 Asteroid Belt ModelsFor the asteroid belt models, it is assumed that the excess over stellar emis-sion is due to a system of dynamically evolving asteroids/comets close tothe star. The total flux then at a given wavelength is given byFT = F∗ + FD, (7.3)where F∗ is the flux of the star and FD is the flux of the disc. If a grain sizedistribution ofdNds∝ s−q (7.4)is assumed, then the total disc flux for a thin ring will be given asFD = NΩsB(Tr)(λ), (7.5)where N is the total number of grains, s is the grain size, B is the PlanckFunction for a disc at a distance r and temperature Tr = T∗√R∗2r , Ωs isthe solid angle of a given grain, and  is an efficiency factor for the grainemission at longer wavelengths. Here, it is assumed that the tail of the blackbody emission profile can vary has a function of wavelength such that(λ) ∼(sλmax)γ, (7.6)where λmax is the peak wavelength of the emission as found through Wien’slaw and γ is the modulation to the tail of the thermal emission profile. Thegrains are assumed to emit only photons at wavelength s ∼ λ.Integrating Eqn. 7.4 to get N and combining with the previous two re-lations, gives a disc flux ofFD = K0pis3−q(1− q)d2B(Tr)(sλmax)γ, (7.7)where K0 is a normalization factor, q is the grain size distribution, s isthe grain size, and Tr is the temperature at a stellar separation r assumingthermal equilibrium with the star. It is further assumed that the grains areconfined to a thin ring at a distance r. This makes q, r, and γ the only freeparameters that need to be constrained through model fitting.The asteroid belt models use Eqn. 7.7 to calculate the disc’s contributionto the spectrum of the central emission. This first model considers all thedata in Table 7.2 with wavelengths shorter than the ALMA observations1257.3. Disc ModellingFigure 7.2: Spectral profile of Fomalhaut with the best fit models. The reddot-dashed curve is the asteroid belt (AB) model that was without only 8.6- 500 µm data (no ALMA data). The green dotted curve is an asteroid beltmodel that was fit with 8.6 - 1300 µm data (now including ALMA data).The blue dashed curve is the “small grain” (SG) disc model that considered8.6 - 1300 µm data. The black solid line is the stellar emission profile. TheATCA data is the point furthest to the right and is represented by a black X.It is not included in any model fitting and is shown for illustrative purposesonly.1267.3. Disc Modelling(i.e., 8.6 - 500 µm). Excluding the ALMA data is done as a check to recoverthe previously constrained location of the asteroid belt from Su et al. (2016).A uniform prior range is set for the three free parameters with r allowed torange from 1 au to 50 au, q from 1 to 5, and γ from -5 to 5. This model findsa best fit disc with r = 11 au, q = 3.5, γ = 0.13, and a reduced χ2 = 2.18.The most probable values and 95% Credible Region are given in Table 7.2.The resulting disc radius is consistent with the 11 au asteroid belt found bySu et al. (2013) and the grain size distribution is consistent with a steady-state collisional cascade (Dohnanyi, 1969). The posterior distributions areshown in Fig. 7.3.A second asteroid belt model is tested, now including the data from theALMA observations (i.e. 8.6 - 1300 µm). This model again uses Eqn. 7.7and fits the same parameters as the previous model. The resulting mostprobable values are r = 17 au, q = 3.9, and γ = 0.280, and a reducedχ2 = 3.83. The most probable values and 95% Credible Region are againgiven in Table 7.2 and the best fit models are shown in Figs. 7.2 and 7.6. Theposterior distributions are shown in Fig. 7.4. The two asteroid belt modelsare compared and discussed further in Section 7.4.7.3.3 Small Grain Disc ModelThe IR observations of Fomalhaut, taken at face value, allow for the exis-tence of an inner asteroid belt. The mm observations of the central emission(the star and a potential disc) are consistent with no excess emission (Whiteet al., 2018). There is the possibility that the uncertainties on IR data aresignificantly underestimated, meaning that there is no detectable excess.The likelihood that every IR observation of Fomalhaut (with data frommultiple facilities taken over the course of several years) would all be biasedtowards excess emission, however, seems unlikely. Therefore, additional discmodels that explore the likelihood of an inner disc that has IR emission butno mm emission, must be considered. Such a disc would be possible if, forexample, the grain size distribution had a sharp cutoff in grains at some sizesmaller than ∼mm, or if the grain size distribution was anomalously steep.Both of these scenarios would lead to negligible mm emission compared tothe expected stellar emission, consistent with what is observed. This modelwould, however, conflict with the asteroid belt models as the small grainsobserved in an asteroid belt are thought to be collisionally produced from adynamically evolving system of asteroids and follow a grain size distributionof q ∼ 3 − 4. This should in theory produce grains much larger than mmsizes (e.g., Wyatt and Dent, 2002).1277.3. Disc ModellingFigure 7.3: Posterior distributions from the MCMC model fitting of anasteroid belt without the mm data for Fomalhaut’s central emission. Theblue lines represent the most probable parameter values.1287.3. Disc ModellingFigure 7.4: Posterior distributions from the MCMC model fitting of anasteroid belt including the mm data for Fomalhaut’s central emission. Theblue lines represent the most probable parameter values.1297.4. Model Comparison and DiscussionIf the inner disc were only populated by small grains, then a “smallgrain” disc model (SG) can be fit to the data through the same MCMCapproach as before (potential sources of the small grains are discussed inSection 7.4). The same stellar emission model from Eqn. 7.2 is assumed.The SG disc model now allows the minimum and maximum grains, sminand smax, respectively, to be free parameters. Similar to the asteroid beltmodels, the location of the belt and the grain size distribution are stillfree parameters. The grains now are assumed only to radiate efficiently iftheir circumference is equal to or larger than the absorbing/emitted photons(Draine, 2006). This is a more realistic expectation for the grain emissionthan s ∼ λ, as was assumed previously. Grains with a circumference smallerthan a given wavelength in the spectrum will have an emission efficiencyfactor of (2pisλ)γ, (7.8)where s is the grain size, λ is the wavelength of the emission, and γ is afree parameter similar to the black body emission modulating parameter forthe asteroid belt model. For a given trial model, the flux is numericallyintegrated over the size distribution from smin to smax as well as over abroad range of frequencies for incident photons on the disc.The resulting most probable values are r = 11 au, q = 4.1, γ = 3.2,smin = 32 µm, and smax = 110 µm corresponding to a reduced χ2 = 1.45.The most probable values and 95% Credible Region are again given in Ta-ble 7.2 and the best fit models are shown in Figs. 7.2 and 7.6. The posteriordistributions are shown in Fig. 7.5.7.4 Model Comparison and DiscussionThe three models can be compared by looking at their best fit parameters inTable 7.2 and the plots in Fig. 7.6. The first model (which did not considerthe mm observations) was done as a check to see if the previously constraineddisc parameters could be recovered (Su et al., 2016). The most probablelocation and grain size distribution are r = 11 au and q = 3.5, respectively.This is consistent with the values reported in Su et al. (2016). However, ascan be seen in Fig. 7.6, this model clearly overpredicts the mm flux. As theALMA observations have a synthesized beam larger than 11 au, any discemission at that distance would be within the central emission and thus theflux density should have been larger by nearly a factor of a few. Thereforethis disc model does not seem to accurately characterize the inner disc. The1307.4. Model Comparison and DiscussionFigure 7.5: Posterior distributions from the MCMC model fitting of a “smallgrain disc model” (SG) for Fomalhaut’s central emission. The blue linesrepresent the most probable parameter values.1317.4. Model Comparison and DiscussionTable 7.2: Summary of the best fit parameters for the two asteroid belt(AB) models (with and without the mm observation included in the fittingprocedure) and the small grain (SG) model. The most probable values (MP),95% credible regions (CR), and reduced χ2 are given for each model.AB µm AB mm SGParameter MP 95% CR MP 95% CR MP 95% CRr [au] 11 [5.6, 22] 17 [11, 25] 11 [7.1, 17]q 3.5 [3.0, 4.1] 3.9 [3.5, 4.4] 4.1 [2.0 5.5]γ 0.13 [-0.09, 0.40] 0.28 [0.03, 0.51] 3.2 [1.4, 5.8smin [µm] - - - - 32 [13, 55]smax [µm] - - - - 110 [70, 430]χ2red 2.18 3.83 1.4595% Credible Region of the disc location does include values outside of theALMA synthesized beam. If an asteroid belt in Fomalhaut does exist, but itat a location outside of the synthesized beam, then the ALMA observationswould not have observed it.The second model is identical to the first except now incorporates themm observations into the fitting procedure. Since the emission efficiency, astraced through γ, is a free parameter, having more data could allow for alarger γ and a better fit. The most probable values of q = 3.9 and γ = 0.28are still reasonable for an asteroid belt debris disc, but the new location ofr = 17 au is not consistent with the ALMA observation’s beam size. As the1300 µm observations had a synthesized beam of ∼ 12 au, a best fit discexterior to this location would be inconsistent with the spatial resolution ofthe ALMA observations. This model again overpredicts the mm flux as canbe seen in Fig. 7.6. The reduced χ2 of 3.83 compared to the previous modelof 2.18 also suggests that this is not a good fit to the data.The third model assumes the disc is only populated by small grains asopposed to a collisionally evolving system of asteroids. This model incorpo-rates a more realistic emission profile for the grains and sets the minimumand maximum grain sizes as free parameters. The r = 11 au radius of thedisc is within the ALMA synthesized beam and again consistent with theIR data alone. Fig. 7.6 shows that this model has the best fit to the dataand the reduced χ2 of 1.45 is the lowest for all three models as well. Tofurther assess how likely the SG model is, the source of the grains must beconsidered.1327.4. Model Comparison and DiscussionFigure 7.6: Zoomed-in plot of Fig. 7.2. The two asteroid belt (AB) modelsclearly overpredict the flux at mm wavelengths. The green dotted curve isan asteroid belt model that was fit with all the data up to 1300 µm. The reddot-dashed curve is the asteroid belt model that was without the mm data.The blue dashed curve is the “small grain” (SG) disc model that consideredall the data. The black solid line is the Fomalhaut stellar emission profile.1337.4. Model Comparison and Discussion7.4.1 A Poynting-Robertson DiscOne possible way to have only small grains in the inner disc would be if allthe grains had migrated inward from the small grain population producedin the outer debris ring at 139 au (White et al., 2016b). This type of discwould be similar to the zodiacal cloud in the Solar System. While the originof the zodiacal cloud is not clearly understood, it is thought to be dueto collisionally produced dust from further out in the Solar System (e.g.,from comets; Nesvorny` et al., 2010). In the case of Fomalhaut, the mostlikely place to produce this dust is from the outer debris ring where smallµm - mm grains have been observed (e.g., Kalas et al., 2005; Boley et al.,2012; Ricci et al., 2015; White et al., 2016b) and constrained to a grain sizedistribution of q ∼ 3.5 (Ricci et al., 2015; White et al., 2016b). As this grainsize distribution is consistent with a collisional cascade (Dohnanyi, 1969),the outer disc could in principle be continuously producing µm - mm grains.The small dust in the outer disc will be influenced by radiation pressurefrom the star. The force of this radiation pressure is given by~Frad =LAQpr4picr2rˆ, (7.9)where L is the stellar luminosity, A is the cross-sectional area of the grain,r is the distance from the grain to the star, c is the speed of light, and Qpris a dimensionless efficiency parameter that ranges from 0 to 2. The ratioof the radiation pressure and the gravitational force, denoted as β, isβ =3LQpr16picGsMρ, (7.10)where s is the grain size, M is the mass of the host star, G is the gravitationalconstant, and ρ is the density of the grains. This parameter can be used tofind an effective gravitational force a given grain feels from the host star~Feff = −GMmr2(1− β)rˆ. (7.11)When β > 0.5, the grains will no longer be gravitationally bound to thedisc and will be blown out of the system. For Fomalhaut, I adopt stellarproperties of L = 16.63 L and M = 1.92 M, and set Qpr = 1 andρ = 2.0 g cc−1. This set of parameters gives a blowout size of ∼ 5 µm,meaning no grains of this size or smaller will be able to migrate to the innerdisc.Due to an effect known as Poynting-Robertson Drag (PR), all objectslarger than the blowout size will feel a drag due to the radiation of the star1347.4. Model Comparison and Discussion(Burns et al., 1979). This effect will cause these larger grains to spiral slowlyinward, potentially making them a source of material to populate the innerdisc. The larger the grain, the longer it will take to fall into the star. Theassociated timescale for infall is given bytPR ∼ cr24GMβ. (7.12)The upper level limit to the size of grains that could migrate into thearea of an inner disc through PR drag is dictated by the age of the system.Fomalhaut is ∼ 440 Myr (Mamajek, 2012), meaning that the maximumpossible grain size that could migrate inward over the lifetime of the systemis ∼ 250 µm. The minimum and maximum grain sizes of smin = 32 µmand smax = 110 µm from the best fit SG model are well within the limits of∼ 5− 250 µm set by the blowout size and the age of the system.As the grain size distribution in the outer disc is ∼ 3.5 (Ricci et al., 2015;White et al., 2016b) then a PR disc should have q ≥ 3.5. This slope changeis expected as tPR is longer for larger grains (see Eqn. 7.12) and thereforethe size distribution would skew towards smaller grains. The most probablevalue of q = 4.1 is therefore not an unreasonable constraint.Taken at face value, the SG disc model with PR-driven grains is pre-ferred over both asteroid belt models for the Fomalhaut inner disc. If appli-cable here, this scenario implies there is no detectable asteroid belt in theFomalhaut system and the observed emission can be readily explained bymigrating grains from the outer, previously observed disc. There are, how-ever, a few issues with a PR driven inner disc. First, while the recovereddisc parameters make sense physically, the emission efficiency factor γ = 3.2is quite high. This high value would be related to the physical propertiesof the grains such as composition, albedo, porosity, etc. Since the grainsin this model would be produced in the outer ring, in order to accept thismodel the factor of γ needs to be reconciled with the emission efficiency ofthe outer ring. Second, the posterior distributions in Fig. 7.5 are not verywell constrained (especially when compared to the two asteroid belt mod-els). This behaviour could be due to the model not accurately reflecting thedata or an underlying issue with the fitting procedure (the same procedurehowever was successful for the previous two models).Regardless, the ability of this model to reproduce the data more accu-rately than the other two suggests that the central emission in Fomalhautis likely not well represented by a typical asteroid belt. The spectrum ofthe central emission could perhaps be explained by an anomalous grain sizedistribution that has a sharp cutoff in grains around sizes ∼ 100 − 200 µm1357.5. Summarybut then continues again for much larger than mm sizes. As the observationsare most sensitive to the µm - mm sized grains, such a gap in the grain sizedistribution cannot be confirmed through current data.7.4.2 Followup AnalysisOne important common feature in all three models is that they all predicta significantly smaller flux at 6600 µm than was observed with the ATCA.This disparity implies that the ATCA observations are either biased by fluxfrom the outer debris ring or have drastically underestimated uncertainties.Followup observations with the VLA at the same wavelength have been pro-posed (PI White, disposition not yet known). If the new data are consistentwith the ATCA data, it could signify unexpected stellar activity from theFomalhaut star or an anomalous gap in the grain size distribution of anasteroid belt.A PR populated disc would also have material spread out from the starto the outer ring. The PR model considered here assumed that the onlydetectable disc emission would be consolidated at a single radius. Suchconfinement would depend on the grains getting trapped at, e.g., a resonancewith a giant planet in the inner system. At the time of writing, there havebeen no confirmed planets in the Fomalhaut system. Should one be present,however, its gravitational influence could cause the grains to “pile up” at alocation of ∼ 11 au (e.g., Moro-Mart´ın and Malhotra, 2002).No extended emission was detected in the ALMA observations betweenthe central emission and the outer disc (Boley et al., 2012; Su et al., 2016;White et al., 2016b; MacGregor et al., 2017). The images can still provideupper level limits to any potential emission coming from the PR influencedgrains at various radii throughout the disc. Further modelling of the discin the image plane, in conjunction with the proposed VLA data, will yieldconstraints on the possibility of a PR driven disc.7.5 SummaryThis chapter presents spectral profile models of the central emission in Fo-malhaut. The models included 870 µm and 1300 µm data from ALMA, anda Sirius-like stellar emission profile. I find that an asteroid belt model isnot consistent with the observed ALMA data. The inner disc around Fo-malhaut, should it be present, must either have an anomalously steep grainsize distribution or only be populated by small 5 − 250 µm grains. Thisarrangement gives rise to the possibility of a disc populated by PR driven1367.5. Summarymigration of small grains coming from the outer, spatially resolved debrisring. This scenario would place the inner disc at a radius of 11 au and wouldbe populated by grains of smin = 32 µm and smax = 110 µm following a sizedistribution of q = 4.1.Future proposed observations of Fomalhaut will help build a more com-plete spectral profile of the central system. This chapter is an ongoingproject and will be published upon receiving and incorporating new datainto the model fitting procedure.137Chapter 8Summary and Ongoing WorkDuring my thesis, I have worked on ways to characterize debris discs obser-vationally. Chapters 2-4 presented a detailed look at the HD 141569 system.Using multiple ALMA and VLA observations, I was able to constrain themorphology, dynamical state, and mass of tits debris as well as the morphol-ogy and mass of CO gas in its disc. Chapter 5 presented an ALMA study ofthe Fomalhaut debris system. I constrained the mass and dynamical stateof its outer debris disc and cast doubt on the existence of an inner asteroidbelt. Chapter 6 presented the work of an observational campaign that tar-geted Sirius A, an A star with no known debris. Chapter 7 combined theresults of Chapters 5 and 6 to analyze the potential inner warm disc aroundFomalhaut.8.0.1 HD 141569In Chapter 2, I used ALMA 345 GHz observations to resolve HD 141569’sinner disc out to a radius of 56 au from the star. The continuum flux forthis material is 3.8±0.4 mJy, which corresponds to a mass of ∼ 0.04 M⊕. Ifthe millimetre grains are part of a collisional cascade, then I infer that theinner disc (< 50 au) has ∼ 160 M⊕ contained within objects less than 50km in radius, depending on the planetesimal size distribution and densityassumptions. The 12CO(3-2) gas is resolved kinematically and spatially fromabout 30 au to 210 au. The integrated line flux is 15.7 ± 1.6 Jy km s−1,which corresponds to a mass of ∼ 2 × 10−3 M⊕. MCMC modelling of thesystem reveals a disc morphology with an inclination of 53.4◦ centred arounda M = 2.39 M host star (Msin(i) = 1.92 M).In Chapter 3, I used new VLA observations, along with archival ALMAand VLA observations to constrain the inner disc as well as the stellar emis-sion of the host star. The VLA observations found (1) a 52 ± 5 µJy pointsource at the location of HD 141569A that shows potential variability, (2)the detected flux is contained within the SED-inferred central clearing of thedisc meaning the spectral index of the dust disc is steeper than previouslyinferred, and (3) the two M dwarf companions are also detected and vari-138Chapter 8. Summary and Ongoing Workable. When combined with ALMA observations, the VLA 14A observationssuggested the spectral index and grain size distribution of HD 141569’s discwas shallow and an outlier among debris systems. Using archival ALMAobservations of HD 141569 at 0.87 mm and 2.9 mm I found a dust spectralindex of αmm = 1.81± 0.20. The VLA 16A flux corresponds to a brightnesstemperature of ∼ 5 × 106 K, suggesting strong non-disc emission is affect-ing the inferred grain properties. The VLA 16A flux density of the M2Vcompanion HD 141569B is 149± 9 µJy, corresponding to a brightness tem-perature of ∼ 2 × 108 K and suggesting significant stellar variability whencompared to the VLA 14A observations, which are smaller by a factor of∼ 6.In Chapter 4, I used archival ALMA data to model the HD 141569circumstellar disc at 345 GHz, 230 GHz, and 100 GHz. These data detectextended millimetre emission coming from outside the inner disc for the firsttime. I constrained the disc properties through simultaneous fitting two-component models to all the ALMA data. By fitting a two-component discmodel to the visbilities of all three data sets simultaneously, I constrainedthe properties of the inner disc and part of the outer disc. The inner discranges from approximately 16 au to 45 au with a spectral index of 1.81(q = 2.95) and the outer disc ranges from 95 au to 300 au with a spectralindex of 2.28 (q = 3.21). The locations of the material is also marginallyseen in azimuthally averaged radial profiles of the continuum images at eachfrequency. These observations suggest that the disc, which is traditionallyviewed as a transitional disc, may be more consistent with a debris discorigin as traced by its small solids.8.0.2 MESASIn Chapter 6, I presented the first stages of my ongoing observational cam-paign Measuring the Emission of Stellar Atmospheres at Submm/mm wave-lengths (MESAS). I used JCMT, SMA, and VLA observations of Sirius Aat 33 GHz, 45 GHz, 225 GHz, 227 GHz, 340 GHz, 353 GHz, and 666 GHz.These data comprise the first reliable observations of an A-type star withno known debris at these frequencies. As such, these data probe only theemission from Sirius A. The observations were used to inform a PHOENIXmodel of Sirius A’s atmosphere, which can be used as a template for thesubmillimeter and millimeter emission of other early A-type stars whereunresolved debris may be present. The results of this Chapter are a valu-able tool in determining both the occurrence and abundance of debris inunresolved circumstellar discs.1398.1. Followup Work and Future Observations8.0.3 FomalhautIn Chapter 5, I used ALMA 230 GHz continuum observations to study theinner and outer disc components of the Fomalhaut system. The observationswere the highest resolution observations to date of the millimetre grains inFomalhaut’s main debris ring. Through an MCMC modelling approach, Iwas able to tightly constrain the outer ring to 139+2−3 au with a FWHM of13±3 au, following a Gaussian profile. The millimetre spectral index is alsoconstrained to αmm = 2.73±0.13. The detected central emission is indistin-guishable from a point source, with a most probable flux of 0.90±0.12 mJy.This emission level implies that any inner debris structure, as was inferredfrom far-Infrared observations, must contribute little to the total centralemission. Moreover, the stellar flux is less than 70% of that predicted byextrapolating a black body from the constrained stellar photosphere tem-perature. This result emphasizes that unresolved inner debris componentscannot be fully characterized until the behavior of the host star’s intrinsicstellar emission at millimetre wavelengths is properly understood.In Chapter 7, I used the results of Chapters 5 and 6 to make furtherconstraints on the nature of the central emission in the Fomalhaut debrissystem. As Fomalhaut is a very similar age and spectral type to Sirius A, theresulting stellar atmosphere model of Sirius A can be used as a template forFomalhaut. I tested three possible disc models and fit them to the spectralprofile through an MCMC approach. Asteroid belt models are difficult toreconcile with the observed mm emission. The disc is at least marginallyconsistent with small grains collisionally produced in the outer disc that havemigrated inward through PR drag. This scenario would place the inner discat a radius of 11 au and would be populated by grain sizes of smin = 32 µmto smax = 110 µm following a size distribution of q = 4.1.8.1 Followup Work and Future Observations8.1.1 HD 141569HD 141569 is a unique system in that, at a relatively young age of ∼ 5Myr, its circumstellar material may be consistent with a debris disc origin.I will submit future ALMA proposals to confirm or reject the debris originhypothesis for this disc.Future proposals include high sensitivity continuum observations thataim to directly image the mm emission in the outer disc at a high enoughresolution to reveal the SED-predicted central clearing in the inner disc.1408.1. Followup Work and Future ObservationsThese data will provide more precise morphological and spectral index (andthus grain size distribution) constraints on the small solids in the disc.Additionally, I will conduct a small “spectral survey” of the gas disc toconstrain the abundances of various molecular species. This survey will helpconstrain the origin of the gas in the disc. As a significant body of CO wasalready detected, by comparing the abundance of common cometary gasesto CO, I will be able to conclude whether or not the gas does indeed have acometary origin. If the gas instead follows a more ISM-like abundance ratio,then it is likely that the gas is left over from the planet formation stages ofthe disc and is not collisionally produced by a large cometary reservoir. Thespectral line sensitivity of ALMA allows for both of the models to be testedand easily distinguished from each other.8.1.2 FomalhautThe outer ring of debris was well characterized by the ALMA observationspresented in Chapter 5. The properties of the inner warm disc, however,remain unconstrained at submm-cm wavelengths. VLA observations of Fo-malhaut at 45 GHz have been proposed (disposition not known at the timeof writing) to re-assess the observed stellar excess from ATCA 45 GHz ob-servations. If there is indeed no excess, as is hypothesized in Chapters 5and 7, even stronger evidence will exist that there are no large solids in theinner warm disc.These results will be combined with the analysis presented in Chapter 7.A thorough multi-wavelength analysis of the possible location of material inthe inner disc will be undertaken and the results will be published in leadingjournals. The future work to be done on Fomalhaut is of key importance asit provides the strongest argument for the necessity of the MESAS project.8.1.3 MESASChapter 6 presented the first stages on an ongoing observational campaignentitled the MESAS project. To increase the impact of MESAS, a broadspectral coverage of a range of spectral types is necessary to build a morecomplete catalog of stellar submm-cm emission.Along with the rest of the MESAS collaboration, I have multiple upcom-ing observations of Sirius A. These include ALMA 100 GHz, 150 GHz, and200 GHz observations, GBT 90 GHz observations, and followup VLA 33GHz and 45 GHz observations (which should be acquired throughout 2018).Additional observations of Sirius A will be requested in the future to assess1418.1. Followup Work and Future Observationsthe long term variability or stability of the star’s submm-cm emission.In addition to the observations of Sirius A, proposals to observe fourfainter stars have been accepted. 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