Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Cassity, Alyssa
Master of Science - MSc
University of British Columbia
Pulsars are rapidly rotating, highly magnetized neutron starsâthe collapsed remnants of massive stars following a supernova explosion. They produce beams of radiation that reach our observatories on Earth at regular intervals. The precise timing of these radio pulses has many applications, including exploring fundamental physics, testing the predictions of general relativity, probing the interstellar medium, and even detecting gravitational waves. This work investigates variability in pulsar emission using the unprecedented observing cadence of the CHIME telescope. The Canadian Hydrogen Intensity Mapping Experiment (CHIME) is a radio telescope near Penticton, British Columbia, Canada. Although initially conceived as a cosmology experiment, it has proven to be an excellent instrument for discovering and studying radio transients. This thesis utilizes the CHIME/Pulsar science backend. First, for PSR B0540+23 we conduct an analysis to explore emission modulation during periods of low solar elongation, which occur once a year. Each year, the pulsar is occulted by the solar wind due to its position in the sky. We observe dispersion measure variations caused by excess solar wind electrons along the line of sight and infer a solar electron density based on these observations. Next, we study nulling and mode-changing behavior in PSRs B0809+74 and B0329+54. We employ a matched filtering pipeline to identify this behavior. We investigate links between these phenomena and an excess of outlier TOAs identified by the NANOGrav Collaborationâs outlier analysis. We find that the outlier analysis is sensitive to mode-changing in PSR B0329+54. These findings highlight the utility of CHIME/Pulsarâs daily observing cadence for studying pulsar emission. With the capabilities of CHIME/Pulsar, we are able to identify yearly occultations of PSR B0540+23 by the solar wind. We also provide a foundation for applying the NANOGrav outlier analysis to identify mode-changing in pulsars. The results of this work highlight the value of CHIME/Pulsar in studying a wide range of pulsar emission phenomena.
High Cadence Pulsar Timing withCHIME/PulsarbyAlyssa CassityB.A., Smith College, 2020A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Astronomy)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)February 2025© Alyssa Cassity 2025The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the thesisentitled:submitted by in partial fulfillment of the requirements forthe degree ofinExamining Committee:SupervisorSupervisory Committee MemberiiAlyssa CassityMaster of ScienceAstronomyHigh cadence pulsar timing with CHIME/PulsarIngrid Stairs, Professor, Physics and Astronomy, UBCJeremy Heyl, Professor, Physics and Astronomy, UBCAbstractPulsars are rapidly rotating, highly magnetized neutron starsâthe collapsedremnants of massive stars following a supernova explosion. They producebeams of radiation that reach our observatories on Earth at regular intervals.The precise timing of these radio pulses has many applications, includingexploring fundamental physics, testing the predictions of general relativity,probing the interstellar medium, and even detecting gravitational waves.This work investigates variability in pulsar emission using the unprecedentedobserving cadence of the CHIME telescope.The Canadian Hydrogen Intensity Mapping Experiment (CHIME) is aradio telescope near Penticton, British Columbia, Canada. Although ini-tially conceived as a cosmology experiment, it has proven to be an excellentinstrument for discovering and studying radio transients. This thesis utilizesthe CHIME/Pulsar science backend.First, for PSR B0540+23 we conduct an analysis to explore emissionmodulation during periods of low solar elongation, which occur once a year.Each year, the pulsar is occulted by the solar wind due to its position in thesky. We observe dispersion measure variations caused by excess solar windelectrons along the line of sight and infer a solar electron density based onthese observations.Next, we study nulling and mode-changing behavior in PSRs B0809+74and B0329+54. We employ a matched filtering pipeline to identify this be-havior. We investigate links between these phenomena and an excess ofoutlier TOAs identified by the NANOGrav Collaborationâs outlier analy-sis. We find that the outlier analysis is sensitive to mode-changing in PSRB0329+54.These findings highlight the utility of CHIME/Pulsarâs daily observingcadence for studying pulsar emission. With the capabilities of CHIME/Pulsar,we are able to identify yearly occultations of PSR B0540+23 by the solarwind. We also provide a foundation for applying the NANOGrav outlieranalysis to identify mode-changing in pulsars. The results of this workhighlight the value of CHIME/Pulsar in studying a wide range of pulsaremission phenomena.iiiLay SummaryPulsars are rapidly rotating neutron stars, the collapsed remnant cores ofmassive stars. By precisely timing the arrival of their pulses, we can studythe behavior of extreme matter and gain insight into the physical proper-ties of these systems. This thesis utilizes the Canadian Hydrogen IntensityMapping Experiment (CHIME) radio telescope to investigate temporal vari-ations in pulsar emission.First, we examine how pulsar radio emission enables the study of materialalong the line of sight. Finally, we leverage the high observing cadence ofCHIME/Pulsar to detect pulsars that temporarily stop emitting (nulling) orswitch between different states (mode-changing) for one or more rotations.ivPrefaceUnless otherwise noted, the work presented in this thesis is the original prod-uct of Alyssa Cassity, with invaluable support, guidance, and feedback fromProf. I. H. Stairs. Additionally, Prof. Stairs edited and provided feedbackon this text. The data were collected by the CHIME/Pulsar Collabora-tion, of which Alyssa Cassity is a member, and are used with permission.Members of the CHIME/Pulsar Collaboration have contributed to telescopeand software maintenance, enabling this work. This thesis presents timinganalyses of three pulsars, which were not discovered by the author.â¢ In Chapter 2, we discuss work within the CHIME/Pulsar and CHIME/FRBcollaborations that uses pulsars as VLBI calibrators. This effort is sup-ported by the contributions of Dr. Aaron Pearlman, Prof. EmmanuelFonseca, Alice Curtin, and Dr. Jane Kaczmarek.â¢ In Chapters 2, 3, and 4, analyses were conducted using the NANOGrav15-year dataset analysis framework, developed by the NANOGravTiming Working Group.â¢ In Chapter 3, we study PSR B0540+23, a pulsar discovered in 1972 byJ.G. Davies, A.G. Lyne, and J.H. Seiradakis using the Jodrell BankMark IA radio telescope.â¢ In Chapter 4, we examine PSRs B0809+74 and B0329+54, both dis-covered in 1968 by T.W. Cole and J.D.H. Pilkington at CambridgeUniversity. This chapter also utilizes a matched filtering pipeline, de-veloped by Ng et al. (2020) [52], to detect nulling and mode-changingbehavior.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . xiiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xviDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Dispersion Measure . . . . . . . . . . . . . . . . . . . 41.1.2 Pulsar Scintillation . . . . . . . . . . . . . . . . . . . 61.1.3 Nulling, Mode Changing, and Intermittent Pulsars . . 61.2 Fast Radio Bursts . . . . . . . . . . . . . . . . . . . . . . . . 72 The Canadian Hydrogen Intensity Mapping Experiment . 82.1 The Canadian Hydrogen Intensity Mapping Experiment . . . 82.2 CHIME System Overview . . . . . . . . . . . . . . . . . . . . 92.2.1 Telescope Structure . . . . . . . . . . . . . . . . . . . 92.2.2 CHIME FX Correlator . . . . . . . . . . . . . . . . . 102.3 CHIME/FRB . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.1 CHIME/FRB Outriggers . . . . . . . . . . . . . . . . 112.3.2 Pulsars as VLBI Calibrators . . . . . . . . . . . . . . 11viTable of Contents2.4 CHIME/Pulsar . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4.1 Fold Mode . . . . . . . . . . . . . . . . . . . . . . . . 132.4.2 Filterbank Mode . . . . . . . . . . . . . . . . . . . . . 132.5 Pulsar Timing . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5.1 PSRCHIVE . . . . . . . . . . . . . . . . . . . . . . . 142.5.2 Generating Standard Profiles . . . . . . . . . . . . . . 142.5.3 Generating TOAs . . . . . . . . . . . . . . . . . . . . 152.5.4 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . 152.5.5 Improving Data Quality . . . . . . . . . . . . . . . . 163 High-Cadence Pulsar Timing of PSR B0540+23 . . . . . . 183.1 PSR B0540+23 . . . . . . . . . . . . . . . . . . . . . . . . . 183.2 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . 183.2.1 TOA Outlier Analysis . . . . . . . . . . . . . . . . . . 193.3 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3.1 Dispersion Measure Variation . . . . . . . . . . . . . 193.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . 214 Identifying nulling and mode-changing behavior in PSRsB0809+74 and B0329+54 . . . . . . . . . . . . . . . . . . . . . 294.1 PSR B0809+74 . . . . . . . . . . . . . . . . . . . . . . . . . 294.2 PSR B0329+54 . . . . . . . . . . . . . . . . . . . . . . . . . 304.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.4 Nulling and Mode-changing Detection Pipeline . . . . . . . . 304.5 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.5.1 TOA Outlier Analysis . . . . . . . . . . . . . . . . . . 324.5.2 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . 324.6 Results and Discussion . . . . . . . . . . . . . . . . . . . . . 334.6.1 PSR B0809+74 . . . . . . . . . . . . . . . . . . . . . 334.6.2 PSR B0329+54 . . . . . . . . . . . . . . . . . . . . . 385 Conclusions and Future Work . . . . . . . . . . . . . . . . . . 45Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47viiList of Tables3.1 Post-fit parameters obtained with fitting procedure in PINTfor PSR B0540+23. Note the values in parentheses, whichdenote the uncertainty in the preceding digit(s). . . . . . . . 283.2 Estimated solar wind electron density ne at two occurrencesof low solar elongation angle. Uncertainties in DMX valueare given in parenthesis. . . . . . . . . . . . . . . . . . . . . . 284.1 Summary of parameters and TOAs for PSRs B0809+74 andB0329+54. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2 Post-fit parameters obtained with fitting procedure in PINTfor PSR B0809+74. Note the values in parentheses, whichdenote the uncertainty in the preceding digit(s). . . . . . . . 384.3 Post-fit parameters obtained with fitting procedure in PINTfor PSR B0329+54. Note the values in parentheses, whichdenote the uncertainty in the preceding digit(s). . . . . . . . 44viiiList of Figures1.1 The magnetic dipole model of a pulsar. Particles stream alongthe magnetic field lines and emit in radio wavelengths. Im-age credit: National Aeronautics and Space Administration(NASA). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Photo of the CHIME telescope at night, located at the Do-minion Radio Astrophysical Observatory. ©Andre Recnik2016, by permission. . . . . . . . . . . . . . . . . . . . . . . . 93.1 Standard Profile for B0540+23 generated following the pro-cess outlined in subsection 2.5.2. âFluxâ is in arbitrary units. 193.2 Profile of B0540+23 at 404 MHz and 797 MHz (the two endsof the CHIME band) on MJD 59017. The scattering tailis frequency-dependent, so the tail is broader at 502 MHz.âFluxâ is in arbitrary units. . . . . . . . . . . . . . . . . . . . 203.3 Post-fit timing residuals for B0540+23, with TOA outlieranalysis performed prior. Note that the fourth spike in TOAuncertainty, observed at the end of 2022 and the beginningof 2023 (MJD â¼59900), is not caused by the solar elongationangle but by reduced telescope sensitivity due to snow. . . . . 223.4 The average profile for B0540+23 at long (left) and short(right) solar elongation angles. At long solar elongation, thepulsar is at a great distance from the Sun in the sky. Atshort solar elongation angle, the profile is noisier. âFluxâ isin arbitrary units. . . . . . . . . . . . . . . . . . . . . . . . . 23ixList of Figures3.5 Signal-to-noise ratio (S/N), TOA uncertainty (us), and SolarElongation Angle (radians) over time for B0540+23. As thepulsar approaches the Sun in the sky, the S/N drops and theTOA error rises. These are consistent with the solar elonga-tion angle as it approaches zero. Note that the fourth spikein TOA uncertainty, observed at the end of 2022 and the be-ginning of 2023 (MJD â¼59900), is not caused by the solarelongation angle but by reduced telescope sensitivity due tosnow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.6 Zoom in on TOA uncertainty (us) and S/N over time at the3rd occultation by the Sun. MJD range 59350-59410. Solarelongation angle decreases from 0.45 to 0, and then rises againto 0.53. When solar elongation is zero, we have marked witha red dashed line. . . . . . . . . . . . . . . . . . . . . . . . . . 253.7 Zoom in on TOA uncertainty (us) and S/N over time at the4th occultation by the Sun. MJD range 59720-59780. Solarelongation angle decreases from 0.45 to 0, and then rises againto 0.53. When solar elongation is zero, we have marked witha red dashed line. . . . . . . . . . . . . . . . . . . . . . . . . . 263.8 DM variation over the MJD range 59718-59778, around thefourth yearly occultation by the Sun in our dataset. We adopta DMX bin of one day. . . . . . . . . . . . . . . . . . . . . . . 263.9 DMX variation over time for PSR B0540+23 assuming solarn0= 0. We allow for a DMX bin of one day. . . . . . . . . . . . 274.1 Averaged standard profile (flux vs. pulse phase) for B0809+74generated with process outlined in Subsection 2.5.2. âFluxâis in arbitrary units. . . . . . . . . . . . . . . . . . . . . . . . 314.2 Averaged standard profile (flux vs. pulse phase) for B0329+54generated with process outlined in Subsection 2.5.2. âFluxâis in arbitrary units. . . . . . . . . . . . . . . . . . . . . . . . 324.3 Results of the nulling detection pipeline for B0809+74. Eachobserved profile is fit to the template profile of the pulsar ateach subintegration, returning the signal-to-noise ratio (S/N)and phase for each of the fitted profiles. . . . . . . . . . . . . 344.4 A raw dynamic spectrum of B0809+74 taken on MJD 58605.Nulling behavior (no pulsar emission) can be seen around the22 and 23 minute marks. Note this dynamic spectrum isnot cleaned of RFI in order to confirm this is indeed nullingbehavior, and not time segments zeroed out due to zapped RFI. 34xList of Figures4.5 We plot the probability of being an outlier p out vs. S/Nof the TOA for 6 non-nulling ânormalâ pulsars: B0114+58,B0320+39, B0353+52, B0105+65, J2043+7045, J2241+6941.The âcleanâ TOAs that were not removed as outliers areshown in gray. Note the TOAs with p out = 1 but highS/N - after manual inspection, these are in general observa-tions with bright impulsive RFI. TOAs with p out > 0.1 areflagged as outlier10. If >8% of TOAs in an observationare flagged, the entire file is flagged as maxout. An entireepoch of TOAs are flagged as epochdrop based on an F-test.The F statistic compares the Ï2 of the timing residuals beforeand after TOAs from an entire observing epoch have been re-moved [58]. Since an epoch and an observation are the samefor the CHIME instrument, the maxout and epochdrop bothflag an entire observation if a large amount of the TOAs arepoor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.6 Results of the outlier analysis for B0809+74. We plot theprobability of being an outlier p out vs. S/N of the TOA.Note the blue and green outlier TOAs, which have similartrend in p out and S/N to âcleanâ non-outlier TOAs in nor-mal pulsars in Figure 4.5. TOAs with p out > 0.1 are flaggedas outlier10. If >8% of TOAs in an observation are flagged,the entire file is flagged as maxout. An entire epoch of TOAsare flagged as epochdrop based on an F-test. The F statis-tic compares the Ï2 of the timing residuals before and af-ter TOAs from an entire observing epoch have been removed[58]. Since an epoch and an observation are the same for theCHIME instrument, the maxout and epochdrop both flag anentire observation if a large amount of the TOAs are poor. . . 374.7 Post-fit timing residuals for B0809+74 after TOA outlier anal-ysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39xiList of Figures4.8 Results of the outlier analysis for B0329+54. We plot theprobability of being an outlier p out vs. S/N of the TOA.TOAs with p out > 0.1 are flagged as outlier10. If >8% ofTOAs in an observation are flagged, the entire file is flagged asmaxout. An entire epoch of TOAs are flagged as epochdropbased on an F-test. The F statistic compares the Ï2 of thetiming residuals before and after TOAs from an entire ob-serving epoch have been removed [58]. Since an epoch andan observation are the same for the CHIME instrument, themaxout and epochdrop both flag an entire observation if alarge amount of the TOAs are poor. . . . . . . . . . . . . . . 404.9 Results of the nulling detection pipeline for B0329+54. Eachobserved profile is fit to the template profile of the pulsar ateach subintegration, returning the signal-to-noise ratio (S/N)and phase for each of the fitted profiles. Note the subinte-grations with medium S/N, but apparently random phase.These points require further investigation to distinguish be-tween intermittent behavior and RFI. . . . . . . . . . . . . . 414.10 Pulse profile of B0329+54 created by co-adding observationsflagged by the outlier analysis. Note that the left outer com-ponent is higher intensity than the right outer, deviating fromthe typical average profile of the source. âFluxâ is in arbitraryunits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.11 Pre-fit timing residuals for B0329+54. Trailing componentshown with time delay in residuals. . . . . . . . . . . . . . . . 434.12 Post-fit timing residuals for B0329+54 after outlier excision.The offset TOAs due to the multi-component profile are notentirely cut in the automated excision. . . . . . . . . . . . . . 43xiiList of AbbreviationsATNF Australian Telescope National Facility.BAO Baryonic Acoustic Oscillation.BIPM Bureau International des Poids et Mesures.CHAMPSS CHIME All-Sky Multiday Pulsar Stacking Search.CHIME The Canadian Hydrogen Intensity Mapping Experiment.CHIME/FRB The Fast Radio Burst backend on CHIME.CHIME/Pulsar The pulsar timing instrument on CHIME.DM Dispersion Measure.DRAO The Dominion Radio Astrophysical Observatory.DSPSR Digital Signal Processing for Pulsars.FAST Five-hundred-meter Aperture Spherical Telescope.FDM Fourier Domain with Markov-Chain Monte Carlo.FFT Fast Fourier Transform.FOV Field of view.FPGA Field Programmable Gate Arrays.FRB Fast Radio Burst.GPS Global Positioning System.GPU Graphics Processing Unit.xiiiList of AbbreviationsHI Hydrogen Intensity.ISM The Interstellar Medium.J2000 The standard epoch used as a reference for celestial coordinate sys-tems. Defined as January 1, 2000 at 12:00 Terrestrial Time (TT)..MJD Modified Julian Date.MSP Millisecond pulsar.NANOGrav North American Nanohertz Observatory for GravitationalWaves.NF Null fraction.NG15 The NANOGrav Collaboration 15 year Dataset.PGS Phase Gradient Scheme.PINT PINT Is Not TEMPO3. PINT is a project to develop a new pulsartiming solution based on python and modern libraries.PSRCHIVE An Open Source C++ development library for the analysisof pulsar astronomical data.PTA Pulsar Timing Array.RFI Radio Frequency Interference.RRAT Rotating Radio Transient.S/N Signal-to-noise ratio.TEMPO TEMPO is a program for pulsar timing data analysis.TEMPO2 TEMPO2 is a software package for the analysis of pulsar pulsetimes of arrival.TOA Time of Arrival.TT Terrestrial Time.xivList of AbbreviationsUTC Universal Time.VLBA Very Long Baseline Array.VLBI Very Long Baseline Interferometry.xvAcknowledgementsI would like to begin by acknowledging the land on which I work and learn.The UBC campus is located on the traditional, ancestral, and unceded ter-ritory of the xwm@θkw@y´@m (Musqueam) People. I am deeply grateful forthe opportunity to grow as a scientist on this beautiful land. The CHIMEtelescope that enables this work is located on the traditional, ancestral, andunceded territory of the Syilx/Okanagan people. Additionally, the CHIMEKKO Outrigger is on the traditional and unceded territory of the SimilamixPeople.First and foremost, I want to thank my supervisor, Prof. I. H. Stairs,for her continued guidance and support, without which this work would nothave been possible. Her vast knowledge and insight in radio astronomy andpulsar science have been invaluable. It has been the greatest honor to workwith and learn from her, and I look forward to continuing this as a PhDstudent.I also want to extend my gratitude to the members of the CHIME/Pulsarand CHIME/FRB Collaborations, especially everyone in the UBC Pulsargroup. Your incredible expertise and guidance make my work possible. Ithas been such a joy to be part of this vibrant community of scientists.I am also endlessly grateful to all my fellow graduate students at UBC,particularly Maude Larivie`re and Jasmine Zhang. Thank you for alwayslending an ear and being a source of joy during difficult times. I feel sohonored to have your friendship!Lastly, thank you to my parents, my family, and my friends who havebecome like family. I am so lucky to have so many loved ones that I stay intouch with from afar. Your constant, unwavering love and support keep megoing. Thank you for everything!xviDedicationFor my niece, Rowyn.xviiChapter 1Introduction1.1 PulsarsThe existence of neutron stars was first speculated shortly after the discoveryof the neutron in 1932. In 1934, Baade and Zwicky proposed that extremelydense stars composed of neutrons could be formed during supernovae [6].For about 30 years following, the possibility of observing neutron stars wasall but ignored. Astronomers reasoned that given their small area, neutronstars would be too faint to be seen with optical telescopes. However, the 1962discovery of the first extrasolar X-ray source, Sco X-1, generated a burst ofexcitement about detecting neutron stars within interacting binary systems[73]. The astronomical community went to work, attempting to developa method for detecting emission from these theoretical objects. Finally in1967, Pacini showed that a rapidly rotating neutron star with a strong,dipolar magnetic field could accelerate particles to high energies, as well asconvert its rotational energy to electromagnetic radiation [55].The slow progress on the observation of neutron stars was quickly accel-erated in 1967, when Cambridge University graduate student Jocelyn Bellnoticed a strange bit of âscruffâ in her data from the Mullard Radio Astron-omy Observatory. The radio signal came in regular pulses every 1.3 seconds.This seemed too fast to be emanating from a normal star. Additionally, theâscruffâ was dissimilar from other sources of interference, and reappearedeach sidereal day - suggesting the source lie outside of our solar system. Sheand her supervisor Anthony Hewish for a brief period speculated that thesignal was coming from an extraterrestrial civilization. They jokingly namedthe source LGM-1 for âlittle green men.â When they found three more pul-sating sources from entirely different areas in the sky, they quickly realizedthat they had not found aliens, but the first pulsar. They announced theirdiscovery the following February 1968, while the actual nature of the sourcewas unknown [33].The connection of pulsars and neutron stars was not immediate. Pul-sations and variability were previously observed in stars, but these weretypically on the order of days, not seconds. The short pulse period sug-11.1. Pulsarsgested a compact source, such as a white dwarf, neutron star, or black hole.A few months after Bell and Hewish announced their discovery, ThomasGold proposed that pulsed radio emission could be created by a rotatingneutron star with a strong magnetic field on the order of B â¼ 1012 G [29].This strong field and rapid rotation would produce a beam of emission. Theneutron star would act like a lighthouse as it rotates; each time the beampoints toward Earth, a pulse is observed in the radio. Borner and Cohenshortly later concluded that the energy supply required to compensate forthe energy losses in the Crab Nebula could be explained by the energy out-put from a rotating neutron star [11].In 1968, these ideas were proven correct. The Crab Nebula, a knownsupernova remnant, was the laboratory for this important discovery. Ithad long been suspected that neutron stars were created as the result ofa supernova explosion at the end of a massive starâs lifetime. In 1968,Richard Lovelace and astronomers at the Arecibo Observatory detected aradio signal with a periodicity of about 33 milliseconds at the center ofthe Crab Nebula. Only a rotating neutron star could produce such rapidpulsations. This discovery made it clear that pulsars, or rapidly rotatingneutron stars, were created in supernovae [42].Astronomers speculate that there are on the order of 100 million neutronstars within the Milky Way Galaxy [17]. However, only about 4,200 neu-tron stars in our Galaxy have been discovered as pulsars, according to theAustralia Telescope National Facility (ATNF) Pulsar Catalogue1 and theFive-hundred-meter Aperture Spherical Telescope (FAST) Galactic PlanePulsar Snapshot survey [31, 46]. This is because neutron stars that are notpulsars are difficult to detect, although some emit thermal X-rays and non-pulsating radio emission [68]. Pulsations constitute the easiest method fordetecting neutron stars.We now know that neutron stars are the stellar remnants of massivestars in the â¼8-20 Mâ range. These compact objects are formed whenthe star runs out of nuclear fuel and can no longer produce the energyrequired to withstand gravity. This causes the gravitational collapse of thestellar core, which triggers a core-collapse supernova explosion of the outermaterial. The collapsed remnant of this explosion is about 1.4 times themass of our Sun, but squished into a body 20-30 km across. It is so dense,up to â¼ 1017 kgmâ3, that most of the protons and electrons merge intoneutrons. The only thing that prevents the core from further collapsing isthe strong nuclear force between nucleons and neutron degeneracy, which1http://www.atnf.csiro.au/research/pulsar/psrcat21.1. Pulsarsnow balances against gravity. Thus these remnants are called neutron stars.To get a sense for these extreme objects: a single tablespoon of NS weightsas much as Mt. Everest [1, 62]. Neutron stars that are rapidly rotating andhighly magnetized are known as pulsars. A schematic diagram of a pulsaris shown in Figure 1.1.Figure 1.1: The magnetic dipole model of a pulsar. Particles stream alongthe magnetic field lines and emit in radio wavelengths. Image credit: Na-tional Aeronautics and Space Administration (NASA).Stars, like our planet, are best modeled by a dipolar magnetic field. Theinteriors of stars are ionized, and thus are great electrical conductors. It isspeculated that the magnetic field of the progenitor star is responsible forthe resulting extreme magnetic fields in a neutron star [27]. When a core-collapse supernova occurs and the star collapses from â¼106 km to â¼10 kmin radius, the cross-sectional area is reduced by â¼1010. The starâs magneticflux Φ â¡ â® Bâ · nË da, however, is conserved. Thus the magnetic field strengthB of the newly collapse core must be multiplied by â¼1010. In other words,this amount of mass in such a small area creates an intense gravitationalfield at its surface. A massive star with B â¼ 100 G will create a youngneutron star with B â¼ 1012 G. In the most extreme cases, the dynamo effectduring the core-collapse process can power magnetic field strengths up toâ¼ 1015 G, as seen in magnetars. These are young pulsars with extremelyhigh magnetic fields.There are many kinds of pulsars that we know of today - those that emitin radio, X-ray, or gamma-ray wavelengths, millisecond pulsars (MSPs),those in interacting binaries, magnetars, those that emit pulses sporadi-cally, etc. [19]. This thesis will focus on pulsars that are visible in radiowavelengths.31.1. PulsarsPulsars will radiate their energy away via magnetic dipole radiation overtheir lifetime. This loss of energy causes the object to subtly slow down, orfor the spin period P to slowly increase, over time. Both the spin periodP and spin period derivative PË can be measured to high precision usingpulsar timing. With this in mind, we can use these timing properties ofpulsars to separate them into unique populations. A common usage is thePPË diagram, which is similar to a Hertzsprung-Russell diagram for mainsequence stars, as pulsars will inhabit particular regions of the plot overtheir lifetime.Although pulsars are interesting in their own right, high-precision pul-sar timing can also be used for many other applications. This is thanksto the incredible consistency of a pulsarâs spin parameters, particularly inMSPs. One application is the measurement of the neutron star mass inbinary systems, which is done by measuring the relativistic Shapiro delay[61]. Precise measurement of the objectâs mass aids in better constrain-ing the neutron star equation of state (e.g. [12, 21, 23]). Another majorapplication is the search for low-frequency gravitational waves with pulsartiming arrays (PTAs), such as the North American Nanohertz Observatoryfor Gravitational Waves (NANOGrav) [2, 3]. These searches use MSPs asdetectors for gravitational waves caused by supermassive black hole mergersthroughout cosmic time.1.1.1 Dispersion MeasureAlthough we often think of space as âempty,â radiation emitted by pulsarsencounters many obstacles on its way to our telescopes on Earth. The mostsignificant contribution to this effect is the Interstellar Medium (ISM). TheISM that these pulses travel through is a dynamic landscape: a cold, ionizedplasma full of gas and dust, replenished and disturbed by stellar winds andsupernovae. In order to properly understand our objects of interest, wemust understand how light propagates through the ISM. This section closelyfollows the derivation in Lorimer & Kramer (2005) [41].The cold plasma of the ISM has a refractive index nn =ckÏ=[1â(fpf)2]1/2(1.1)where f is the frequency of light, and fp is the plasma frequencyfp =(e2neÏme)1/2â 8.97 kHz( necmâ3)(1.2)41.1. Pulsarswhere ne is the electron number density and me is the mass of the electron.For radio waves propagating through a plasma, n < 1. The group velocityof the radio pulses in the plasmavg =dÏdk= c[1â(fpf)2]1/2(1.3)is less than the speed of light in a vacuum c. For most radio observatories,fp << f , and so the group velocity becomes:vg â c(1â f2p2f2)(1.4)A broadband pulse of radiation moves through the plasma more slowlyat lower frequencies compared to higher frequencies. This introduces afrequency-dependent time delay tt =â« d0dlvgâ dc(1.5)where dl is the infinitesimal length segment along the line of sight, and dthe distance to the source and path length along the line of sight. The timedelay t further simplifies:t =1câ« d0(1 +f2p2f2)dl â dc=(e22Ïmec)fâ2â« d0nedl (1.6)The time delay can be written as(tsec)â 4.149Ã 103(DMpc cmâ3)(fMHz)â2(1.7)whereDM â¡â« d0nedl (1.8)is called the dispersion measure in units of pc cmâ3, representing the inte-grated column density of electrons along the line of sight.The dispersion measure can thus be used to infer the distance to as-tronomical sources, for example, assuming an estimated electron numberdensity ne â¼ 0.3 cmâ3. However, more sophisticated estimates of electronnumber density ne now exist, such as NE2001 [20] and YMW16 [79].51.1. Pulsars1.1.2 Pulsar ScintillationIf the ISM were homogeneous, radio waves would propagate affected onlyby dispersion, but otherwise unperturbed across large distances. Instead,the ISM affects the light we receive from pulsars in many other ways besidesdispersion. A significant effect among these is scintillation. Scintillation is acommon effect in astronomy - for example, stars exhibiting a âtwinklingâ ef-fect due to their light scattering in the Earthâs turbulent atmosphere. Radiopulsars scintillate due to inhomogeneities and turbulence in the ISM. Thereare two kinds of scintillation: diffractive and refractive [19].These types of scintillation are differentiated by the size of the inhomo-geneities in relation to the Fresnel scale. The Fresnel scale can be definedas dF =â2Î»z, where λ is the wavelength of light, and z is the distancethe light waves travel to the detector. Diffractive scintillation is caused byirregularities smaller than the Fresnel scale. These cause rapid variationsin radio flux from sources on short timescales (minutes to hours), causingflux-density fluctuations greater than an order of magnitude. On the otherhand, refractive scintillation is caused by inhomogeneities larger than theFresnel scale. These cause variations on longer timescales (days to years),with flux-density fluctuations less than a factor of 2 in amplitude [50, 64].1.1.3 Nulling, Mode Changing, and Intermittent PulsarsAlthough we often think of pulsars as incredibly stable over long timescales,the observed flux of pulsars can fluctuate greatly on short timescales. Thereare several such variations that can characterize pulsar behavior. Pulsarnulling occurs when the pulsarâs emission drops to zero (or nearly zero) over1-2 pulse periods, before sharply increasing again [8]. It is characterized bythe null fraction, hereafter âNF,â which is the fraction of time the pulsar isin the null state. NFs can range from 0% in the case of ânormalâ pulsars,and can be as high as 95% [26, 76]. Rotating radio transients, or RRATs,can be viewed as the extreme end of pulsar nulling with a NF of nearly100%, except when emitting in single pulses [47]. Nulling is a somewhatcommon phenomenon, with â¼150 nulling pulsars observed with a publishedNF [52].Another short-term phenomenon observed in pulsars is mode changing.This mode changing is characterized by an average pulse profile with two ormore quasi-stable states that the emission abruptly switches between. Thisbehavior was first observed in PSR B1237+25, which has a profile with 5components [7]. There are now about a dozen or so pulsars that are known to61.2. Fast Radio Burstsmode change. Both nulling and mode changing are broadband events, and itis suggested that they are likely linked to the same underlying phenomenon[69, 76]. The unprecedented daily cadence of CHIME/Pulsar shows greatpromise for studies of these pulsars.1.2 Fast Radio BurstsFast Radio Bursts (FRBs) are short, cosmologically distant radio transients,lasting on the order of milliseconds. They are known to be extragalacticin origin due to their high DMs. The first FRB, the Lorimer Burst FRB010724, was discovered in 2007 when Lorimer and his student Narkevic weresearching through archival data from the Parkes Multibeam Pulsar Survey[40].Since their initial discovery, the number of FRBs has exploded - pri-marily due to the rapid discovery of hundreds of FRBs by CHIME [5, 14].As the population of FRBs grows, so do the number of mysteries. Therehave been many theories to explain this new class of radio transient, rangingfrom merging white dwarfs to magnetar bursts. However, no model thus farhas been sufficient to explain the wide range of FRB behavior. As such,the current field of FRB science is incredibly active. Among recent break-throughs are the discovery of repeating FRBs (the first being FRB 121102)[63], and the discovery of FRB-like emission from the Galactic magnetarSGR 1935+2154 [10, 15]. The localization of a large number of FRBs totheir host galaxies will shed light on the mysterious nature of FRBs.7Chapter 2The Canadian HydrogenIntensity MappingExperiment2.1 The Canadian Hydrogen Intensity MappingExperimentSince the time of Edwin Hubble, astronomers have known that the Universeis expanding. More recently, the rate of this expansion has been shown tobe accelerating. The unknown reason for this acceleration has been dubbedthe enigmatic âdark energy.â The Canadian Hydrogen Intensity MappingExperiment (CHIME) experiment was proposed in order to understand thenature of dark energy, and thus the expansion of the Universe2. Its primarygoal is to study dark energy by measuring the evolution of Baryonic AcousticOscillations (BAOs) across a wide redshift range. The BAOs are fluctuationsin baryonic matter, established by acoustic waves in the hot plasma of theearly Universe. These serve as a standard ruler for the expansion rate of theUniverse. CHIME maps the distribution of baryonic matter using the 21cmradio emission of intergalactic hydrogen, a technique known as HydrogenIntensity (HI) Mapping [13, 57].For the purposes of HI mapping, the CHIME instrument has a uniquesetup: it is a transit telescope, thus it has no moving parts, and insteadviews new portions of the sky as the Earth rotates. It observes the entireNorthern sky each day at 400-800 MHz, thanks to its massive field-of-view(FOV) of >200 deg2. The frequency range is targeted to view 21cm radioemission in redshift ranges 0.8 < z < 2.5, thus enabling CHIME to studythe expansion history of the Universe across a range of cosmic time [13].It was realized early on that CHIME would be a fantastic instrumentfor observing and detecting radio transients, due to its wide bandwidthand large field-of-view. First came the idea to perform high-cadence radio2https://chime-experiment.ca/82.2. CHIME System Overviewpulsar observations, which evolved into the CHIME/Pulsar project. Laterduring the development of CHIME, it was also realized that CHIME wouldserve as an excellent untargeted detector of Fast Radio Bursts (FRBs), alsospawning the CHIME/FRB project [13]. Since its construction, other newprojects have begun. These include the CHIME All-Sky Multiday PulsarStacking Search (CHAMPSS), originally named the Slow Pulsar Search, andthe construction of three outrigger telescopes to enable VLBI localization ofFRBs.Figure 2.1: Photo of the CHIME telescope at night, located at the DominionRadio Astrophysical Observatory. ©Andre Recnik 2016, by permission.2.2 CHIME System OverviewCHIME is a radio interferometer located at the Dominion Radio Astrophys-ical Observatory (DRAO) near Penticton, British Columbia, Canada. Afigure of the telescope and site is shown in Figure 2.1. The natural moun-tain landscape surrounding the site provides a natural shield against someradio frequency interference (RFI). A small radio quiet zone also encom-passes the site, although it is not nearly as extensive as that of the GreenBank Observatory. The CHIME signal path is detailed in the followingsections.2.2.1 Telescope StructureThe telescope consists of four cylindrical, parabolic reflectors, each 100 min the North-South direction, and 20 m in the East-West direction. The92.3. CHIME/FRBcylinders are composed of a mesh reflector surface constructed with steel.As the telescope is not steerable, the reflectors cannot be pointed to low-elevation angles in order to shed snow. Thus the mesh allows for snow anddebris to fall to the ground through the gaps. Each cylinder is outfitted with256 dual-polarized cloverleaf antennas in a linear feed-array, located alongthe focal line of the cylinder. With four cylinders, there are a total of 1024antennas, each spaced 30 cm apart along 80 m of the focal line. This analogsignal is fed into a hybrid FX correlator.2.2.2 CHIME FX CorrelatorCHIME utilizes an FX correlator, which is a hybrid of FPGAs and GPUs.The F-engine converts incoming data from the analog front-end to adigital signal. The digitized signal is fed to the FPGAs, where a frequencychannelization is performed. The F-engine is housed in two RF-shieldedshipping containers, each 20 ft in length, called the Receiver Huts. Eachhut services two cylinders, and thus they are placed halfway between eachpair. The F-Engine is discussed in greater detail in [9].The GPU-based X-engine is the second step in the FX Correlator, andperforms a spatial correlation of the entire signal. 256 optical cables trans-mit the data from the F-engine to the X-engine. It is composed of 256nodes, each equippied with 4 GPU chips. It also simultaneously performsthe FFT-based beamforming for the CHIME/FRB system and tracking volt-age beamforming for the CHIME/Pulsar system, discussed in Sections 2.3and 2.4, respectively. The X-engine is housed in two RF-shielded roomswithin 40-foot shipping containers adjacent to the CHIME telescope. Thetechnical details of the CHIME X-engine are discussed in [24]. The X-enginegenerates data products for the three major backends: CHIME/Cosmology,CHIME/FRB, and CHIME/Pulsar.2.3 CHIME/FRBThe primary goal of the CHIME/FRB backend is to search for FRBs inreal time. The backend must sift through a massive amount of data in or-der to identify FRBs. To accomplish this, it splits up the tasks into fourlevels, which together form the CHIME/FRB pipeline. A more detaileddiscussion of the backend can be found in [14]. In brief, the CHIME/FRBsoftware pipeline (L0) creates 1024 static beams, (L1) dedisperses the dataand identifies event candidates, (L2) groups multi-beam events, (L3) identi-fies extragalactic events based on DM and position, and finally (L4) triggers102.3. CHIME/FRBaction implementation and archives the event. A more detailed discussionof the static beamforming pipeline is discussed in [53]. The CHIME/FRBbackend instrument can also save baseband (i.e., voltage) data for brightFRBs. This will make it possible to perform very long baseline interfer-ometry (VLBI) with the upcoming CHIME/FRB Outriggers discussed in2.3.1.2.3.1 CHIME/FRB OutriggersIn order to understand the origin of FRBs, sources need to be localized totheir host galaxies and environments. Unfortunately, this effort is limitedby the angular resolution of CHIME/FRB, which has a theoretical limit ofabout an arcminute when taking baseband data [48]. This angular resolutionis insufficient for localizing FRBs at great distances. The CHIME/FRBOutriggers project seeks to add very long baseline interferometry (VLBI)capabilities to CHIME, in order to localize FRBs to tens of milliarcsecondprecision. This will be accomplished with the deployment of three CHIME-like outrigger telescopes across North America.The first outrigger telescope is located 66 km west of CHIME, namedkâniPatn kâlâ£stkâmasqt (KKO). The name was offered by the Upper Sim-ilkameen Indian Band and roughly translates to âlistening device for outerspace.â This is the shortest baseline of the outrigger network. The KKO out-rigger began full science operations in 2023. The second outrigger, whichbegan commissioning in 2023, is located in West Virginia at the Green BankObservatory. This site creates the longest baseline with CHIME of â¼3300km, mostly in the E-W direction. The third outrigger is located at the HatCreek Observatory in northern California, forming a baseline mostly in theN-S direction. The Hat Creek site began commissioning in early 2025 [38].2.3.2 Pulsars as VLBI CalibratorsDue to the nature of both the CHIME telescope and FRBs, traditionalVLBI calibration techniques prove to be a challenge. As CHIME is a transittelescope that performs untargeted searches of FRBs, we cannot predictwhen and where in the sky an FRB will occur. Additionally, there arefew compact sources used as traditional VLBI calibrators at the low radiofrequencies of the CHIME band. These two constraints create the needfor bright, compact radio sources evenly distributed across the sky to beavailable as VLBI calibrators. Pulsars offer an ideal solution, as they arecompact, bright, and sufficiently abundant across the sky. A novel VLBI112.4. CHIME/Pulsarcalibration technique using pulsars is discussed in greater detail in [56], andsummarized below.A sample of â¼100 pulsars evenly distributed across the CHIME FOVhave been selected to function as astrometric calibrators for the CHIME/FRBOutriggers project. These sources were selected based on their brightness,sky position, and timing properties. When an FRB occurs within theCHIME FOV, a calibration solution will be derived from the observationof pulsars nearby (in space and time) to the FRB target. Observationswith the Very Long Baseline Array (VLBA) have been conducted in orderto precisely measure positions and proper motions for each of these pulsars(VLBA/21A-314, PI: Kaczmarek; VLBA/22A-345, PI: Curtin; VLBA/23A-099, PI: Curtin).The CHIME/Pulsar system will perform high cadence observations ofthese calibrators in order to regularly update their timing solutions. Withthis information, the times at which the pulsar is âon-pulseâ will be deter-mined so that the data can be stored only during this time.2.4 CHIME/PulsarThe primary purpose of the CHIME/Pulsar backend is to continuously moni-tor radio pulsars. CHIME/Pulsar is motivated by several science goals. Mostnotable are high-precision pulsar timing for PTAs such as NANOGrav, andfollow-up observations of newly discovered pulsars. However, other effortsinclude: high-cadence timing of pulsars in binary systems, single pulse detec-tion of RRATs and nulling pulsars, the discovery of new pulsars, observationsof repeating FRBs, monitoring of pulsar glitching, etc. [25, 28, 30, 51, 52].As opposed to the static CHIME/FRB beam array, the CHIME/Pulsarbeamformer creates 10 independent tracking beams within the X-engine.Beamforming is a signal processing technique in which spatial inputs arecombined in weighted manner, in order to generate a digital beam at thedesired sky position. This is accomplished for CHIME/Pulsar by summingall 1024 inputs phased to the desired celestial coordinates. These are alsoreferred to as tied-array beams. The CHIME/Pulsar beamformer is furtherdescribed in [16]. Most notably, the 10 independent beams allow for theobservation and tracking of 10 distinct sources simultaneously. Each of the10 tracking beams has 1024 frequency channels, and a best time resolutionof 2.56 µs. These beamformed data are scaled down and packetized prior tobeing sent on to the CHIME/Pulsar backend.As CHIME observes the sky continuously, an automated scheduler is122.4. CHIME/Pulsarnecessary in order to maximize pulsar observations and decide which pul-sars to observe. Sources are observed according to a probabilistic schedulingalgorithm. The algorithm relies on user-defined weights in order to prioritizesome sources over others. There are five weights to select from, and highpriority NANOGrav MSPs are usually given the highest weight. The sched-uler also prioritizes sources that havenât been observed recently, in order toprevent repeatedly observing the same few sources.The CHIME/Pulsar backend is composed of 10 independent GPU nodes,one per tracking beam. The exact method of data processing depends on theobserving mode in which the data were collected, defined in the scheduler.CHIME/Pulsar has two modes of operation for collecting data: fold modeand filterbank/search mode.2.4.1 Fold ModeFold mode is the primary mode of operation for CHIME/Pulsar. Fold modedata are coherently dedispersed using the Digital Signal Processing for Pul-sars DSPSR suite [16, 70]. The system can coherently dedisperse up toâ¼2500 pc cmâ3 in real-time. The time series data are also folded based onthe provided source ephemeris and produce time-averaged full-Stokes pro-files with 1024 frequency channels. In most cases, a fold-mode observationis recorded with 256 profile phase bins, although this number can be alteredin the scheduling process. By default, the fold-mode data are taken in 10-ssubintegrations, although this can also be adjusted on a per-pulsar basis.The maximum scan length for a given observation is primarily determinedby the declination of the source. The fold mode data are written to disk inthe format of âarchiveâ structured files that are readable by PSRCHIVE3[35]. This work utilizes fold mode data exclusively.2.4.2 Filterbank ModeIn filterbank or search mode, time-series data are converted to a Stokes-Idata stream and are downsampled in time. The primary goal of filterbankmode in the CHIME/Pulsar backend is to conduct follow-up observationsof new and repeating FRBs, RRATs, and single pulses of sources. Thus theCHIME/Pulsar backend must be able to record coherently dedispersed, hightime resolution filterbank data. Given the extragalactic nature of FRBs,which can have DM values up to 1000 pc cmâ3, the backend must be ableto dedisperse to high DMs in real-time as well. Given constraints on the3http://psrchive.sourceforge.net132.5. Pulsar Timingavailable DSPSR filterbank module digifile, a new codebase able to dedis-perse up to 3300 pc cmâ3 in real-time was developed, based on [49]. Thefilterbank data are integrated to 327.68 µs and written out.2.5 Pulsar TimingThe basic premise of pulsar timing is to track the regular rotation of thepulsar through measuring the time of each pulseâs arrival (TOA, literallyTime of Arrival). Over long periods of observation, we can build up atiming model that details the pulse frequency, its derivative(s), and other keyproperties of the pulsar. The measured TOAs are compared to the expectedmodel of TOAs in a pulsar timing software such as TEMPO4 [54], TEMPO25[34], and PINT6 [43]. These programs perform a many-parameter leastsquares fitting, and return the fit parameters and residuals. The residualscan be simply understood as the data subtracted from the timing model.2.5.1 PSRCHIVEPSRCHIVE is an open-source software library for pulsar data manipulationand analysis [71]. Its uses include TOA generation, RFI mitigation, datavisualization and plotting, and many other utilities outside the scope ofthis work. This project primarily uses PSRCHIVE for producing templateprofiles and a set of TOAs from raw data. The routines described in sections2.5.2 and 2.5.3 are performed using PSRCHIVE commands.2.5.2 Generating Standard ProfilesIn order to obtain a timing solution for each pulsar, we first must generatea standard profile for a given source. The observations are âfoldedâ over thepredicted pulse period P prior to being written to disk, as described in Sec-tion 2.4.1. In order to mitigate RFI in the CHIME band, frequency channelsknown to be contaminated are removed using paz. Known contaminators inthese frequencies include, but are not limited to: TV stations, 5G and LTEnetworks, and a handful of known narrow-band emitters.The data are collapsed in frequency (usually to 16 channels, but variesby pulsar) and in time with pam, before being added together with psradd.4https://www.ascl.net/1509.0025https://bitbucket.org/psrsoft/tempo2/src/master/6https://github.com/nanograv/PINT142.5. Pulsar TimingPerforming this routine over many observations yields a standard (or tem-plate) pulse profile for the source. These are generally quite stable, despitevariation from pulse-to-pulse due to noise. The final profile is smoothedusing the wavelet smoothing algorithm implemented with psrsmooth.2.5.3 Generating TOAsOnce a standard profile has been generated, we can calculate a set of TOAsfrom our observations. The standard procedure, called the phase gradientscheme (PGS), was outlined by [65]. This routine cross-correlates each ob-served pulse profile with the standard profile, computing a difference in phasebetween the two. The phase shift is determined by a Ï2-fitting procedurein Fourier space. The resulting phase shift for each observed pulse profile isadded to the time-stamp in the midpoint of the integration, yielding a TOAfor each arriving pulse.It has been observed that the PGS algorithm tends to underestimateTOA uncertainties for low signal-to-noise (S/N) data [39]. A proposedmethod that has become increasingly popular is to still use the PGS methodto generate the TOAs, but measure the TOA uncertainties with a MonteCarlo analysis [72, 75]. This is called the Fourier Domain with Markov-Chain Monte Carlo (FDM) method. The pat command can be used witheither of these methods by specifying the desired shift algorithm with â-Aâ.This was used to generate TOAs from the observations in this work withthe FDM method. The final output is a set of TOAs known as a âtimâ filethat can be fit to a timing model contained in a âparâ file.2.5.4 TimingBefore we can fit our timing model to the data, we must first make timingcorrections to account for our non-inertial reference frame on Earth. We usePINT to perform these corrections. The solar system barycenter, or centerof mass, is approximately inertial or at rest. We can convert the time ofarrival on Earth (ttopo) to a barycentric time of arrival (tbary). The TOA atthe solar system barycenter can be calculated by the following equation:tbary = ttopo + tcorr â âDf2+âRâ +âSâ +âEâ (2.1)The first additional term tcorr is a clock correction to adjust the localtopocentric time measured at the observatory to an established terrestrialtime standard. Observatories usually measure time locally with a hydrogen152.5. Pulsar Timingmaser clock and convert this to Universal Time (UTC) with the help ofGPS. This is converted to Terrestrial Time (TT), which is based on atomicclocks and is regularly updated by the Bureau International des Poids etMesures (BIPM) each year. The next term is a frequency-dependent timedelay to due to dispersion by the ISM (DM).The last three terms are used to correct the topocentric time to barycen-tric time. These are the Ro¨mer delay âRâ, the Shapiro delay âSâ, and theEinstein delay âEâ. The Ro¨mer delay is the classical light travel-time acrossthe Earthâs orbit. The Shapiro delay is a relativistic correction that accountsfor the additional light travel-timed due to a curved spacetime in the solarsystem. Lastly, the Einstein delay accounts for time dilation due to themotion of the Earth and gravitational redshift due to masses in the solarsystem [19, 41].A basic timing model for a pulsar begins with the spin and astrometricparameters of the pulsar. The spin parameters typically include the spinfrequency, frequency derivative, and in some cases the second frequencyderivative. Astrometric parameters inform us about the pulsarâs locationin space, and typically include coordinates in two dimensions, proper mo-tion in two dimensions, and sometimes the parallax. More robust modelsmay include the dispersion measure (DM), binary parameters, frequency-dependence, and âjumpsâ to correct for phase offsets between data [2]. Weuse PINT via pint pal7 to fit the timing model to our data and obtainpost-fit parameters and residuals.2.5.5 Improving Data QualityPrior to timing analysis, a number of steps are taken to ensure a cleandataset. We follow the convention outlined by the NANOGrav Collaborationin the 15 year data set (NG15) [2]. These include a cut of TOAs with S/N< 8 and the removal of outlier TOAs. Outliers are broadly defined as datapoints arising from processes different from the majority of the data, suchas RFI from terrestrial sources. Outlier contamination prevents us fromobtaining precise timing solutions for pulsars.The NG15 outlier analysis uses a Gibbs sampler to identify outliers in anautomated fashion. In a Gibbs sampling scheme, one performs a Bayesiananalysis by sampling from a parameterâs conditional posterior distribution inan iterative manner [77]. Each TOA is assigned a probability p out of beingan outlier. By default, TOAs with p out > 0.1 are removed and flagged as7https://github.com/nanograv/pint pal162.5. Pulsar Timingoutlier10. If >8% of TOAs in an observation are flagged, the entire file isremoved and flagged as maxout. An entire epoch of TOAs are removed andflagged as epochdrop based on an F-test. The F statistic compares the Ï2 ofthe timing residuals before and after TOAs from an entire observing epochhave been removed [58]. Since an epoch and an observation are the samefor the CHIME instrument, the maxout and epochdrop both cut an entireobservation if a large amount of the TOAs are poor. The Gibbs samplingoutlier analysis is available in enterprise outliers 8.The NG15 automated outlier analysis was intended for use specificallyin the analysis of MSPs. We chose to test this automated outlier removal onCHIME TOAs from slow pulsars, with frequencies several orders of magni-tude smaller than MSPs. In this work we find that this analysis nonethelessperforms well at removing outliers in an automated fashion for slower pulsarsand the RFI environment of CHIME. This proves to be especially promisingfor ongoing efforts to integrate CHIME/Pulsar into future NANOGrav datareleases.8https://github.com/nanograv/enterprise outliers17Chapter 3High-Cadence Pulsar Timingof PSR B0540+233.1 PSR B0540+23PSR B0540+23 (J0543+2329) is a slow pulsar with a 0.245-s spin period,discovered in 1972 with the Jodrell Bank Mark IA radio telescope [22]. Itis associated with the IC 433 supernova remnant. This chapter presents atiming analysis of the source capable only with the quasi-daily observingcadence of CHIME/Pulsar.3.2 Data ProcessingAll observations for this source were obtained with CHIME/Pulsar andrecorded in fold mode with 256 profile bins. We utilize a data set span-ning MJD 58600-60027 (April 2019 to March 2023) in which the source wasobserved approximately daily. We only include data collected after MJD58600, a point at which our instrument time stamp is relatively stable. Eachobservation has a duration of approximately 912-s.The TOA generation from this data follows the process outlined Subsec-tion 2.5.2. Fold-mode observations for the pulsar are gathered, cleaned ofRFI, and scrunched in frequency and time as described. For B0540+23, wescrunch down to 16 frequency channels. Observations are added togetherand smoothed to form a standard profile, shown in Figure 3.1. To furtherinvestigate the observed scattering tail in the profile, we also plot the profileat two ends of the CHIME band in Figure 3.2. We observe a broader scat-tering tail at low frequencies, consistent with thin screen scattering alongthe line of sight by intervening ISM. We generate a set of TOAs from thedata with the standard profile and the FDM shift algorithm available in pat,as described in Section 2.5.4. This pipeline generates a total of 31,910 rawTOAs.183.3. TimingFigure 3.1: Standard Profile for B0540+23 generated following the processoutlined in subsection 2.5.2. âFluxâ is in arbitrary units.3.2.1 TOA Outlier AnalysisFollowing convention of the NANOGrav 15 year dataset mentioned in sub-section 2.5.5, we performed the Gibbs outlier analysis on the B0540+23TOAs prior to fitting to a timing model. 5,476 TOAs flagged as outlierswere removed from the data (17% cut). A further 2,948 TOAs with S/N< 8 were removed (9%). A set of 23,486 TOAs are maintained from thesedata quality cuts.3.3 TimingWe use PINT implemented in pint pal to perform solar system time cor-rections and fit a model to the cleaned TOAs.3.3.1 Dispersion Measure VariationAcross the â¼4 year dataset, we expect variation in DM due to shifting ISMmaterial along the line of sight between the pulsar and the observatory. Inadditional to ISM turbulence, DM variations can also arise from changes inthe solar wind along the line of sight [32, 80]. Given that B0540+23 liesclose to the ecliptic plane, we should expect regular DM variation due to193.3. TimingFigure 3.2: Profile of B0540+23 at 404 MHz and 797 MHz (the two endsof the CHIME band) on MJD 59017. The scattering tail is frequency-dependent, so the tail is broader at 502 MHz. âFluxâ is in arbitrary units.203.4. Results and Discussionsolar wind electrons. We use a DMX model in pint pal, which representsDMX as an offset from a fixed DM value using a piecewise constant function[2]. Given the position of this source and the high-cadence of observations,we adopt a DMX bin of one day, allowing DM variations to be quantifiedon a daily basis.3.4 Results and DiscussionWe fit a timing model to the B0540+23 data, obtaining residuals and post-fit parameters, which are reported in Table 3.1. Severe spikes in the TOAuncertainty on a yearly basis suggest that the pulsar is occulted by the Sun,as shown in the post-fit residuals in Figure 3.3. A detailed examination ofthe residuals reveals that the TOA uncertainty increases rapidly to â³2000µs once a year. The first such event occurs around MJD 58647, though atthat time, data for the pulsar was not collected daily. The subsequent threeoccultations occur one year apart, during which the pulsar was observed ona near-daily basis. It is important to note that the fourth spike in TOAuncertainty, observed at the end of 2022 and the beginning of 2023 (MJDâ¼59900), is not caused by the solar elongation angle but by reduced telescopesensitivity due to snow.213.4. Results and DiscussionFigure 3.3: Post-fit timing residuals for B0540+23, with TOA outlier analy-sis performed prior. Note that the fourth spike in TOA uncertainty, observedat the end of 2022 and the beginning of 2023 (MJD â¼59900), is not causedby the solar elongation angle but by reduced telescope sensitivity due tosnow.We further investigated this by tracking several TOA-related quantitiesover time. In the top two panels of Figure 3.5, we plot the TOA signal-to-noise ratio (S/N) and TOA uncertainty across the entire dataset. TheTOA uncertainty spikes to â³2000 µs as the pulsar approaches a low solarelongation angle, before returning to typical values. Concurrently, the S/Nof the TOAs drops to nearly zero as the pulsar approaches a low solarelongation angle. We attribute these variations to increased refraction bysolar wind electrons, as the pulsarâs emission traverses a larger volume ofthe solar wind (see 1.1.2).To illustrate this effect, we plot the TOA uncertainty and S/N aroundthe time of the third occultation (MJD â¼59385) in Figure 3.6 and the fourthoccultation (MJD â¼59748) in Figure 3.7. Finally, in the bottom panel ofFigure 3.5, we show the solar elongation angle over the dataset. As expected,the solar elongation angle decreases to zero each year, coinciding with thetimes when the pulsar is occulted by the Sun.Finally, we investigate DM variation across our entire dataset. Using aDMX model as described in 3.3.1, we adopt a bin width of one day, informedby the high observing cadence for this source. The magnitude of DM vari-ation is on the order of â¼ 10â3 pc cmâ3, with DMX reaching values as high223.4. Results and DiscussionFigure 3.4: The average profile for B0540+23 at long (left) and short (right)solar elongation angles. At long solar elongation, the pulsar is at a greatdistance from the Sun in the sky. At short solar elongation angle, the profileis noisier. âFluxâ is in arbitrary units.as +0.03 pc cmâ3. The DM variation observed in B0540+23 is consistentwith that found in other pulsars [36, 59].We observe annual spikes in DM at low solar elongation angles. TheDM variation over the entire dataset is shown in Figure 3.9, with a zoomed-in view of the DM variation around the fourth occultation (MJD 59735)provided in Figure 3.8.We can use the observed excess DM at zero solar elongation angle toestimate the solar wind electron density along the line of sight. Recall thedefinition of dispersion measure:DM =â«nedl (3.1)The DM represents the integrated column density of electrons along the lineof sight to the radio source. The solar wind is typically modeled as a time-independent spherical distribution of free electrons. Isolating the excess DMcaused by the solar wind, we write:âDMSW = neL = neÏresin(Ï)[1AU ]2 (3.2)where âDMSW is the excess DM due to the solar wind, L is effective thepath length through the solar wind, Ï is the solar elongation angle of thepulsar, and re is the distance from the observatory to the Sun [67]. At lowsolar elongation angles, we can use the DM contribution from the solar windand the path length to estimate the solar electron density.At solar elongation angles of Ï = 0, the path length simplifies to L =1 AU. During the second and fourth occultations, where the DM variation233.4. Results and DiscussionFigure 3.5: Signal-to-noise ratio (S/N), TOA uncertainty (us), and SolarElongation Angle (radians) over time for B0540+23. As the pulsar ap-proaches the Sun in the sky, the S/N drops and the TOA error rises. Theseare consistent with the solar elongation angle as it approaches zero. Notethat the fourth spike in TOA uncertainty, observed at the end of 2022 andthe beginning of 2023 (MJD â¼59900), is not caused by the solar elongationangle but by reduced telescope sensitivity due to snow.243.4. Results and DiscussionFigure 3.6: Zoom in on TOA uncertainty (us) and S/N over time at the3rd occultation by the Sun. MJD range 59350-59410. Solar elongationangle decreases from 0.45 to 0, and then rises again to 0.53. When solarelongation is zero, we have marked with a red dashed line.253.4. Results and DiscussionFigure 3.7: Zoom in on TOA uncertainty (us) and S/N over time at the4th occultation by the Sun. MJD range 59720-59780. Solar elongationangle decreases from 0.45 to 0, and then rises again to 0.53. When solarelongation is zero, we have marked with a red dashed line.Figure 3.8: DM variation over the MJD range 59718-59778, around thefourth yearly occultation by the Sun in our dataset. We adopt a DMX binof one day.263.4. Results and DiscussionFigure 3.9: DMX variation over time for PSR B0540+23 assuming solarn0= 0. We allow for a DMX bin of one day.is largest, we measure âDMSW and estimate ne, assuming this sphericalmodel. These estimates are presented in Table 3.2. These values are consis-tent with expected electron densities near the Sun reported in other studies[32, 45]. The proximity of B0540+23 to the ecliptic plane makes it an espe-cially interesting target for more robust solar wind modeling, such as a fullyBayesian approach similar to [32].273.4. Results and DiscussionPost-fit Model Parameters B0540+23Right Ascension (J2000) 05h43m09s.674(1)Declination (J2000) 23â¦29â²09â²â².6(6)Proper motion in R.A. (mas yrâ1) 44.(1)F0, Spin frequency (sâ1) 4.065228123072(2)F1, First frequency derivative (sâ2) -2.5480247(6) Ã 10â13F2, Second frequency derivative (sâ3) 2.94(6) Ã 10â25PEPOCH, Epoch of period determination(MJD)59315CORRECT TROPOSPHERE, Troposphericdelay correctionsYPLANET SHAPIRO, Planetary Shapiro de-laysYDILATEFREQ, Gravitational redshift andtime dilationNFixed parametersDM, Dispersion Measure (pc cmâ3) 77.6822(4.3)DMX, bin width (days) 1.0EPHEM, Solar system ephemeris DE440CLK, Clock correction TT(BIPM)UNITS, Relativistic coordinate time scale TDBTIMEEPH, Time ephemeris FB90SOLARN0, Solar wind constant (ne cmâ3) 0.00STAR, Start of data span (MJD) 58603FINISH, End of data span (MJD) 60027Table 3.1: Post-fit parameters obtained with fitting procedure in PINT forPSR B0540+23. Note the values in parentheses, which denote the uncer-tainty in the preceding digit(s).Estimated Solar Electron DensityMJD DMX (pc cmâ3) ne (cmâ3)59017 +0.02(±0.004) 4.1659748 +0.03(±0.025) 6.02Table 3.2: Estimated solar wind electron density ne at two occurrences of lowsolar elongation angle. Uncertainties in DMX value are given in parenthesis.28Chapter 4Identifying nulling andmode-changing behavior inPSRs B0809+74 andB0329+54We seek to leverage the unprecedented high cadence of CHIME/Pulsar todetect nulling and mode-changing behavior in two pulsars, B0809+74 andB0329+54. These sources have been observed on a quasi-daily basis since2019, providing a rich dataset for exploring temporal variation in pulsaremission. Additionally, we seek to identify nulling and mode-changing be-havior using the Gibbs outlier analysis scheme. We investigate whether suchpulsar behavior leads to an excess of outlier TOAs detectable in this analysiscompared to ânormalâ pulsars. If successful, this would offer an alternative,semi-automated method for flagging nulling and mode-changing behavior inpulsars.4.1 PSR B0809+74B0809+74 (J0814+7429) is a 1.29-s pulsar discovered in the early years ofpulsar science by astronomers at Cambridge University. It was discovered in1968 in a survey conducted at the Mullard Radio Astronomy Observatory[18]. In 1969 and 1970 the pulsar was shown to exhibit drifting subpulses[4, 74]. Subpulse drifting is identified by examining individual pulses, whichshows that their component subpulses shift regularly through the averagephase window. Finally in 1971 it was shown that a cessation of the pulsarâsemission, known as a null, preceded the subpulse drifting phenomenon [66].Since this time, B0809+74 has been studied as a leading example of regularsubpulse drifting [60, 69].294.2. PSR B0329+544.2 PSR B0329+54B0329+54 (J0332+5434) is a 0.72-s pulsar, discovered alongside B0809+74in the same 1968 Cambridge pulsar survey [18]. It was identified as a mode-changing source in 1971, when observations found the pulse profile includeda main component with two outer components. It was also observed that therelative intensities of the three components in the profile varied dramaticallyduring a mode change [44]. This pulsar is an excellent choice for studying themode-changing phenomenon due to its brightness and incredibly frequentmode changes.4.3 DataThe CHIME/Pulsar dataset for these pulsars spans MJD 58600-60012 (April2019 to March 2023). Observations were taken in fold-mode on a quasi-dailybasis for each pulsar. The B0809+74 and B0329+54 observations have aduration of approximately 3123-s and 1448-s, respectively. As mentionedpreviously, we only include data collected after MJD 58600, a point at whichour instrument time stamp is relatively stable.4.4 Nulling and Mode-changing DetectionPipelineFollowing previous work with CHIME/Pulsar data by Ng et al. 2020 [52],we utilized a matched filtering pipeline to detect nulling and mode-changingbehavior in the data. This pipeline is implemented in PSRCHIVE. First,a standard/template profile is made for each pulsar. All available fold-mode observations for a given pulsar are gathered, cleaned for RFI, andadded together to form a template profile. The template profile is scrunchedcompletely in frequency and time, and then smoothed.Next, individual observations are processed before being fit to the tem-plate profile. RFI is excised from observations using paz to remove badfrequency channels. The observations are then scrunched entirely to onefrequency channel. Each observed profile is fit to the template profile of thepulsar at each subintegration, returning the signal-to-noise ratio (S/N) andphase for each of the fitted profiles.Potential nulling behavior is identified by producing a scatter plot ofthe S/N versus phase values and visually inspecting the resulting plot. Forsubintegrations when the pulsar is âonâ or non-nulling, the S/N is high and304.5. TimingFigure 4.1: Averaged standard profile (flux vs. pulse phase) for B0809+74generated with process outlined in Subsection 2.5.2. âFluxâ is in arbitraryunits.the phase is consistent with that of the template profile. This creates avertical clustering with high S/N values and a common phase value. Forsubintegrations when the pulsar is âoffâ or nulling, the S/N is low and thephase will be random. This results in a horizontal clustering at low S/Nvalues. Together these create an inverted âT shapeâ scatter plot when thereis nulling activity within the data for a given pulsar (example in Figure 4.3).4.5 TimingWe generate a set of TOAs for each pulsar following the process outlinedin Subsection 2.5.2. Fold-mode observations for the pulsar are gathered,cleaned of RFI, and scrunched in frequency and time as described previ-ously. For both B0809+74 and B0329+54, we scrunch down to 16 frequencychannels. Observations are added together and smoothed to form a stan-dard profile for each pulsar, shown in Figures 4.1 and 4.2. We generate aset of TOAs from the data with the standard profile and the FDM (Fourierdomain with Markov chain Monte Carlo) shift algorithm available in pat,as described in Section 2.5.4. This pipeline generates a total of 20,002 rawTOAs for B0809+74, and 18,068 raw TOAs for B0329+54.314.5. TimingFigure 4.2: Averaged standard profile (flux vs. pulse phase) for B0329+54generated with process outlined in Subsection 2.5.2. âFluxâ is in arbitraryunits.4.5.1 TOA Outlier AnalysisFollowing the convention of the NANOGrav 15 year dataset mentioned insubsection 2.5.5, we performed the Gibbs outlier analysis on both B0809+74and B0329+54 prior to fitting to a timing model. For B0809+74, 2,936TOAs with S/N < 8 were removed (14.7%). 2,027 TOAs flagged as outlierswere removed from the data (10%). A set of 15,039 cleaned TOAs forB0809+74 remain after the quality cuts.For B0329+54, 1,967 TOAs with S/N < 8 were removed (11%). Anadditional 2,527 TOAs are flagged as outliers and removed from the data(14%). A set of 13,574 cleaned TOAs for B0329+54 remain after these cuts.A summary of the TOA removal process is shown in Table 4.1.For both pulsars, we keep the outlier TOAs separate from the cleanedTOAs for further analysis. We compare the TOAs flagged by the nullingand mode-changing detection pipeline with those flagged as outliers. Weseparate outliers based on the identified âcut reasonsâ outlier10, maxout,and epochdrop.4.5.2 TimingWe utilize PINT in pint pal to perform solar system time corrections andfit a timing model to the cleaned TOAs for B0809+74 and B0329+54. Weobtained post-fit parameters and residuals, presented in Tables 4.2, 4.3 and324.6. Results and DiscussionData SummaryPulsar Period (s) DM NTOAs Cut Outliers Cut Low S/NB0809+74 1.29 6.20677 20,002 2,027 2,936B0329+54 0.72 26.7996 15,039 2,527 1,967Table 4.1: Summary of parameters and TOAs for PSRs B0809+74 andB0329+54.Figures 4.7, 4.12.4.6 Results and DiscussionWe present the results of the nulling and mode-changing detection pipelinefor PSRs B0809+74 and B0329+54. We compare these with the resultsof the TOA outlier analysis, and identify any correlation between thesetemporal variations and increased outlier TOAs.4.6.1 PSR B0809+74We fed all available fold-mode observations for B0809+74 into the matchedfiltering pipeline to detect pulsar nulling (i.e. non-emission). The outputof the pipeline reveals an inverted âT shapeâ scatter plot, shown in Figure4.3, indicating subintegrations where the pulsar exhibits nulling behavior.After identifying potential nulling with the pipeline, we further investigatethese flagged observations. Specifically, we plot the time series over theseobservations and search for intensity modulations consistent with no pulsaremission. A dynamic spectrum for a flagged observation is shown in Figure4.4. We see two instances of non-emission around the 20-minute mark,consistent with nulling.We analyzed the properties of TOAs identified as outliers to evaluatewhether this approach could also flag nulling behavior. We compared theperformance of the outlier analysis on these sources with its performanceon ânormal,â or non-nulling, pulsars. In general, for normal pulsars, outlierTOAs have low S/N, high p out (>0.1), and are predominantly assigned thecut reason outlier10. Outliers with cut reasons maxout and epochdrop ac-count for only a small fraction of all outliers. A plot showing the distributionof outlier TOAs for normal pulsars is presented in Figure 4.5.In the case of B0809+74, we observed an excess of TOAs flagged asoutliers with high S/N (>200). Upon further investigation, most of these334.6. Results and DiscussionFigure 4.3: Results of the nulling detection pipeline for B0809+74. Eachobserved profile is fit to the template profile of the pulsar at each subinte-gration, returning the signal-to-noise ratio (S/N) and phase for each of thefitted profiles.Figure 4.4: A raw dynamic spectrum of B0809+74 taken on MJD 58605.Nulling behavior (no pulsar emission) can be seen around the 22 and 23minute marks. Note this dynamic spectrum is not cleaned of RFI in orderto confirm this is indeed nulling behavior, and not time segments zeroed outdue to zapped RFI.344.6. Results and DiscussionTOAs have low p out and were assigned cut reasons maxout or epochdrop.This behavior is atypical compared to ânormalâ pulsars, where high S/NTOAs are generally retained in the âcleanâ dataset. The flagged outliers forB0809+74 are visualized in Figure 4.6. Notably, the maxout and epochdropoutlier TOAs (green and blue) in Figure 4.6 exhibit similar S/N and p outto the âcleanâ TOAs (gray) seen in normal pulsars (Figure 4.5). Overall,we find that the outlier analysis flagged a significantly larger proportion oflow p out, high S/N TOAs for B0809+74 compared to normal pulsars.We also investigated any overlap between observations showing potentialnulling behavior and those with TOAs flagged as outliers. Of the 152 ob-servations identified as potential nulling candidates by the matched filteringpipeline, only 20 were also flagged as outliers. The observation shown inFigure 4.4, which exhibits nulling behavior, was initially identified by theoutlier analysis scheme.Given both the subpulse drifting and nulling observed in this source, theoutlier analysis scheme has to the potential to flag observations in which thisbehavior occurs. The excess of outliers flagged as maxout and epochdropcould indicate the presence of nulling occurring sometime within the ob-servation window. The Gibbs outlier analysis could be utilized to identifynulling candidates in an semi-automated fashion, which can subsequentlybe confirmed through manual inspection of the flagged TOAs. However,further work would be required to establish the effectiveness of the outlieranalysis in detecting nulling, as the results for this source are not entirelyconvincing of such a correlation.Finally, we fit a timing model to the cleaned TOAs for B0809+74, ob-taining post-fit residuals and model parameters. These are presented inFigure 4.7 and Table 4.2.354.6. Results and DiscussionFigure 4.5: We plot the probability of being an outlier p out vs. S/N of theTOA for 6 non-nulling ânormalâ pulsars: B0114+58, B0320+39, B0353+52,B0105+65, J2043+7045, J2241+6941. The âcleanâ TOAs that were notremoved as outliers are shown in gray. Note the TOAs with p out = 1 buthigh S/N - after manual inspection, these are in general observations withbright impulsive RFI. TOAs with p out > 0.1 are flagged as outlier10.If >8% of TOAs in an observation are flagged, the entire file is flagged asmaxout. An entire epoch of TOAs are flagged as epochdrop based on anF-test. The F statistic compares the Ï2 of the timing residuals before andafter TOAs from an entire observing epoch have been removed [58]. Sincean epoch and an observation are the same for the CHIME instrument, themaxout and epochdrop both flag an entire observation if a large amount ofthe TOAs are poor.364.6. Results and DiscussionFigure 4.6: Results of the outlier analysis for B0809+74. We plot the prob-ability of being an outlier p out vs. S/N of the TOA. Note the blue andgreen outlier TOAs, which have similar trend in p out and S/N to âcleanânon-outlier TOAs in normal pulsars in Figure 4.5. TOAs with p out > 0.1are flagged as outlier10. If >8% of TOAs in an observation are flagged,the entire file is flagged as maxout. An entire epoch of TOAs are flaggedas epochdrop based on an F-test. The F statistic compares the Ï2 of thetiming residuals before and after TOAs from an entire observing epoch havebeen removed [58]. Since an epoch and an observation are the same for theCHIME instrument, the maxout and epochdrop both flag an entire obser-vation if a large amount of the TOAs are poor.374.6. Results and DiscussionPost-fit Model Parameters B0809+74Right Ascension (J2000) 08h14m59s.670(1)Declination (J2000) 74â¦29â²04â²â².444(6)Proper motion in R.A. (mas yrâ1) 17.(4)Proper motion in Dec. (mas yrâ1) -54.(5)F0, Spin frequency (sâ1) 0.7738491040270(8)F1, First frequency derivative (sâ2) -1.0078(5.6) Ã 10â16PEPOCH, Epoch of period determination(MJD)59320CORRECT TROPOSPHERE, Troposphericdelay correctionsYPLANET SHAPIRO, Planetary Shapiro de-laysYDILATEFREQ, Gravitational redshift andtime dilationNFixed parametersDM, Dispersion Measure (pc cmâ3) 6.206(1.8)EPHEM, Solar system ephemeris DE440CLK, Clock correction TT(BIPM)UNITS, Relativistic coordinate time scale TDBTIMEEPH, Time ephemeris FB90START, Start of data span (MJD) 58601FINISH, End of data span (MJD) 60038Table 4.2: Post-fit parameters obtained with fitting procedure in PINT forPSR B0809+74. Note the values in parentheses, which denote the uncer-tainty in the preceding digit(s).4.6.2 PSR B0329+54We gathered all available fold-mode observations for B0329+54 and cleanedthe TOAs with the Gibbs outlier analysis. The outlier TOAs in the B0329+54dataset are shown in Figure 4.8. Upon investigating the properties of theseoutliers, we observed trends similar to those seen in B0809+74. Comparedto ânormalâ pulsars, a significant number of TOAs for B0329+54 with highS/N (>2000) were flagged as outliers. Most of these high S/N outliers wereassigned the cut reason epochdrop. However, unlike other pulsars in thiswork, we observed a notable number of high S/N outliers with varying p out,particularly the red and green data points in Figure 4.8. This deviates from384.6. Results and DiscussionFigure 4.7: Post-fit timing residuals for B0809+74 after TOA outlier anal-ysis.the typical behavior of outlier TOAs observed in other pulsars analyzed inthis work. These findings suggest that the outlier analysis is sensitive tomode-changing behavior in pulsars.All available fold-mode observations for B0329+54 were processed withthe matched filtering pipeline to pinpoint mode-changing behavior in ourdataset. We visualize the mode-changing detection pipeline in Figure 4.9.The scatter plot exhibits a âT shapeâ pattern, with a second vertical clus-tering to the left of the main component. The typical averaged profile ofB0329+54 has three components: a central, brightest component, and twodimmer outer components 4.2. The relative intensities of the two outer com-ponents vary across the dataset. Changes in these relative intensities havebeen frequently reported for this source. As noted by [37], this is could be anindication that each mode corresponds to a different magnetospheric state.As noted by [52], the matched filtering pipeline is particularly effectiveat detecting relative changes in the intensities of the profile components.Therefore, the secondary vertical clustering observed in the pipeline visu-alization likely corresponds to subintegrations where the relative intensitiesof the left and right outer components are modulating. Additionally, thehorizontal clustering at low S/N could also suggest some nulling or non-emission, warranting further follow-up. Previous studies have suggestedthat nulling and mode-changing are related phenomena. Coexisting nullingand mode-changing behavior has been observed in other pulsars, such as394.6. Results and DiscussionFigure 4.8: Results of the outlier analysis for B0329+54. We plot the prob-ability of being an outlier p out vs. S/N of the TOA. TOAs with p out> 0.1 are flagged as outlier10. If >8% of TOAs in an observation areflagged, the entire file is flagged as maxout. An entire epoch of TOAs areflagged as epochdrop based on an F-test. The F statistic compares the Ï2 ofthe timing residuals before and after TOAs from an entire observing epochhave been removed [58]. Since an epoch and an observation are the samefor the CHIME instrument, the maxout and epochdrop both flag an entireobservation if a large amount of the TOAs are poor.404.6. Results and DiscussionFigure 4.9: Results of the nulling detection pipeline for B0329+54. Eachobserved profile is fit to the template profile of the pulsar at each subinte-gration, returning the signal-to-noise ratio (S/N) and phase for each of thefitted profiles. Note the subintegrations with medium S/N, but apparentlyrandom phase. These points require further investigation to distinguish be-tween intermittent behavior and RFI.PSRs B0523+11 and B2323+63 [52, 78]. However, the subintegrations inthe horizontal clustering could also correspond to weak emission with in-herently low S/N. We encourage follow-up on this source with single-pulseobservations to confirm any nulling behavior.To further explore the relationship between the Gibbs outlier analysisand mode-changing behavior, we compare the averaged profile of the pulsarfor observations flagged as outliers (Figure 4.10) to the average profile in theâcleanâ data shown previously (Figure 4.2). The pulse profiles of the outlierTOAs frequently exhibit a left outer component that is brighter than theright outer component, deviating from the relative intensities observed in thetypical pulse profile. This behavior is also consistent with the visualizationof the nulling detection pipeline discussed earlier, which shows a secondaryvertical cluster to the left of the main component.After excising the outlier TOAs, we present the pre-fit timing residualsin Figure 4.11. The multiple components in the pulse profile are reflectedin TOAs offset from the main mode, resulting in higher residuals. We thenfit a timing model to the cleaned dataset, obtaining post-fit model param-eters and residuals, shown in Table 4.3 and Figure 4.12. The two outercomponents of the profile manifest as notably larger absolute residuals com-414.6. Results and DiscussionFigure 4.10: Pulse profile of B0329+54 created by co-adding observationsflagged by the outlier analysis. Note that the left outer component is higherintensity than the right outer, deviating from the typical average profile ofthe source. âFluxâ is in arbitrary units.pared to the main (central) component. This is consistent with a timingmodel best fit to the main mode of the profile, with residual offsets arisingfrom the outer components. The trailing (left) component is prominent inthe residuals, aligning with the second vertical clustering observed in thematched filtering pipeline, and the relative intensities of components in theoutlier-flagged pulse profiles.The NANOGrav outlier analysis is effective in identifying mode changesin PSR B0329+54. We observe this in its ability to flag TOAs correspond-ing to significant profile variations, i.e. changes in relative intensity betweencomponents. This demonstrates the ability of this analysis scheme in de-tecting mode-changing behavior, which would allow for the semi-automatedidentification of such phenomena in other radio pulsars. Future applicationto other pulsar datasets would further demonstrate the effectiveness of thismethod in identifying mode-changing.424.6. Results and DiscussionFigure 4.11: Pre-fit timing residuals for B0329+54. Trailing componentshown with time delay in residuals.Figure 4.12: Post-fit timing residuals for B0329+54 after outlier excision.The offset TOAs due to the multi-component profile are not entirely cut inthe automated excision.434.6. Results and DiscussionPost-fit Model Parameters B0329+54Right Ascension (J2000) 03h32m59s.42176(4)Declination (J2000) 54â¦34â²43â²â².2653(6)F0, Spin frequency (sâ1) 1.3995370952413(4)F1, First frequency derivative (sâ2) -4.00813(5) Ã 10â15F2, Second frequency derivative (sâ3) -1.47(3) Ã 10â25F3, Third frequency derivative (sâ4) 2.80(5) Ã 10â32F4, Fourth frequency derivative (sâ5) -1.99(1)Ã 10â40F5, Fifth frequency derivative (sâ6) -1.40(3) Ã 10â46PEPOCH, Epoch of period determination(MJD)59301CORRECT TROPOSPHERE, Troposphericdelay correctionsYPLANET SHAPIRO, Planetary Shapiro de-laysYDILATEFREQ, Gravitational redshift andtime dilationNFixed parametersDM, Dispersion Measure (pc cmâ3) 26.7996(1.3)EPHEM, Solar system ephemeris DE440CLK, Clock correction TT(BIPM)UNITS, Relativistic coordinate time scale TDBTIMEEPH, Time ephemeris FB90START, Start of data span (MJD) 58601FINISH, End of data span (MJD) 60002Table 4.3: Post-fit parameters obtained with fitting procedure in PINT forPSR B0329+54. Note the values in parentheses, which denote the uncer-tainty in the preceding digit(s).44Chapter 5Conclusions and FutureWorkIn this work we have utilized radio observations from CHIME/Pulsar toperform high-cadence pulsar timing of PSRs B0540+23, B0809+74, andB0329+54. Quasi-daily observations of these pulsars since 2019 provide arich dataset for studying temporal variation in pulsar emission.In the B0540+23 dataset, we characterized yearly variability as the pul-sar is occulted by our Sun. We observe a drop in signal-to-noise and a spikein both TOA uncertainty and DM at low solar elongation angles, consistentwith refraction of the pulsar emission due to excess solar wind electronsalong the line of sight. With the observed excess DM we estimated the solarelectron density, assuming a spherically-symmetric solar wind. This workdemonstrates the use of pulsars as sensitive probes of the ISM and the solarwind.A natural continuation of this project would be to conduct a more robustBayesian modeling of the solar electron density with astrophysical priors[32]. Other ongoing efforts of this research include characterizing scatteringand pulse broadening in this source, which we showed has a scattering tailin its profile. Polarization studies of B0540+23 would be another fruitfulcontinuation of this work, as polarization properties could provide insightinto the pulsar emission mechanism [41]. The ability to measure rotationmeasures with CHIME has been demonstrated previously [51].In the B0809+74 and B0329+54 datasets, we implemented a matched fil-tering pipeline to identify nulling and mode-changing behavior. We leveragethe NANOGrav collaborationâs TOA outlier analysis, and search for linksbetween its outlier flagging and nulling or mode-changing behavior. Wefind that the NANOGrav outlier analysis is effective in identifying mode-changing behavior. This is demonstrated its ability to flag TOAs corre-sponding to changes in relative intensity between components. The outlieranalysis could be applied to other pulsar datasets as an semi-automatedtechnique for flagging emission modulation for further follow-up.The CHIME/Pulsar instrument is well suited for identifying new nulling45Chapter 5. Conclusions and Future Workand mode-changing pulsars, adding to the sparse population of known sources.The work of this thesis could be applied to larger population of pulsars whichare observed daily by CHIME to identify new candidates. However, the10-second subintegration length of CHIME fold-mode data limits us fromdetecting modulations at shorter timescales, and thus from estimating anaccurate NF in nulling pulsars. Single-pulse observations of this class ofsources are necessary for the precise analysis of nulling and mode-changingmodulations. 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Thesis/Dissertation
eng
Astronomy
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Stairs, Ingrid Helen, 1972-
High cadence pulsar timing with CHIME/Pulsar
Text