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The nature of M33’s AGB stars Rowe, Jason F. 2003

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T H E N A T U R E O F M 3 3 ' S A G B S T A R S B y Jason F. Rowe H. B. Sc. University of Toronto, 2000 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF SCIENCE in T H E FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS AND ASTRONOMY We accept this thesis as conforming to the required standard T H E UNIVERSITY OF BRITISH COLUMBIA August 2003 © Jason F. Rowe, 2003 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of ^ R I ^ S H ' C A , CKST^A. A S V & V V S V V U - ^ The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract Using the C F H 1 2 k imager on the Canada-France-Hawaii Telescope, photometry of 1.3 mi l l ion stars is used to investigate stellar populations in the metal poor ([Fe/H]=-0.6) late type spir ial galaxy M33. M33 has a distance modulus of D=24.64 and A G B stars are highly luminous, allowing resolved population studies wi th 4 metre class telescopes. A G B stars are identified and classified in C (carbon) and M-type stars. Examin ing star counts and colour-magnitude selected stellar populations, the galactic structure of M33 is examined. Further, we search for evidence of galactic interactions as seen in other nearby galaxies, such as M31. We use the ratio of C-stars to M-stars to investigate the metal l ici ty distr ibution throughout the disk. The C / M - s t a r ratio is found to increase and flatten with galactocentric distance in agreement wi th viscous disk formation models. The C-star Luminosity function is found to be similar to the S M C and M31 making C-stars possible distance indicators. i i Table of Contents Abstract ii Table of Contents iii List of Tables v List of Figures vi 1 I N T R O D U C T I O N 1 1.1 Product ion of Carbon Stars 1 1.2 Interest in Carbon Stars 3 1.3 M33: Target of Study and A ims of Thesis 4 1.4 Photometr ic Identification of Carbon Stars 10 2 D A T A C O L L E C T I O N 12 2.1 Instrumentation and Fi l ters 12 2.2 Basic C C D Theory 13 2.2.1 Mosaic C C D s 14 2.3 Observations 15 3 D A T A ANALYSIS 18 3.1 Processing Mosaic Images 18 3.2 C C D Art i facts 20 3.3 Narrow-band data processing 21 i i i 3.4 Broad-band data processing 25 3.5 Photometry 27 3.6 Astrometr ic Registration 30 3.7 Photometr ic Cal ibrat ion 32 4 R E S U L T S 37 4.1 Stellarity Cuts 37 4.2 Duplicate Detections 40 4.3 Incompleteness Tests 40 4.4 Star Counts 44 4.5 Colour-Magnitude Diagrams 46 4.5.1 C M D selected Star Counts 50 4.6 Colour-Colour Diagrams 56 4.6.1 Colour-Colour Diagram Selected Star Counts 63 4.7 C-star Luminosi ty Funct ion 73 5 C O N C L U S I O N S A N D D I S C U S S I O N 81 5.1 Da ta reduction Improvements 81 5.2 S U M M A R Y A N D F U T U R E S T U D I E S 82 Bib l iography 84 iv List of Tables 2.1 List of Fi l ters 13 2.2 List of Targets 15 2.3 Observation Log 17 3.1 Object Catalog for M33 35 v Lis t of Figures 1.1 M33 mosaic V-band image from this data set 5 1.2 C-star luminosity functions 7 1.3 C-star luminosity functions 8 3.1 C C D 0 5 19 3.2 overscan 21 3.3 biashist 23 3.4 c a l F l F 2 34 3.5 ca l l 36 4.1 Sharp measurements versus I mag 38 4.2 x2 measurements versus I mag 39 4.3 Star M a p 41 4.4 Incompleteness M a p 45 4.5 C M D for I versus V - I 48 4.6 C M D for V versus V - I 49 4.7 Surface density map of Ma in Sequence stars 52 4.8 Binned Surface density map of Ma in Sequence stars 53 4.9 Surface density map of Super Giant stars 54 4.10 Surface density map of Super Giant stars 55 4.11 Surface density map of A G B stars 57 4.12 Binned surface density map of A G B stars 58 4.13 Colour-Colour diagram 60 v i 4.14 Colour-magnitude diagram of C-stars 61 4.15 Est imat ion of I band completeness l imit 62 4.16 Surface density map of C-stars 65 4.17 Binned surface density map of C-stars 66 4.18 Binned surface density map of M-stars 67 4.19 C-star density profile 68 4.20 M-star density profile 69 4.21 C / M - s t a r ratio radial profile 71 4.22 C / M - s t a r ratio map 73 4.23 C / M - s t a r error map 74 4.24 C / M - s t a r S / N map 75 4.25 C M D for V versus V - I for a region at the edge of the visible disk . . . . 76 4.26 V-Magn i tude distr ibut ion of C-stars 78 4.27 I-magnitude distr ibution of C-stars 79 4.28 Bolometr ic Luminosity Function for C-stars 80 vi i Chapter 1 I N T R O D U C T I O N In every man there is an eye of the soul which is purified and re-i l luminated, and is more precious by far than ten thousand bodi ly eyes, for it alone sees truth. Plato 1.1 Production of Carbon Stars Stars, for the most part, are giant spheres of gas consisting mostly of hydrogen and helium. The sheer size and amount of material in a star creates large central temperatures and pressures that allow fusion to occur wi th the final product of 4 hydrogen atoms being converted to 1 helium atom. After central hydrogen burning in a star, a hel ium core is left behind. The central core tends to become isothermal and energy generation continues with the fusion of hydrogen in a broad shell. Th is constitutes evolution from the M a i n Sequence (MS) to the Red Giant Branch ( R G B ) . The width of the shell decreases as hydrogen is consumed. The first abundance changes at the surface of the star occur when the convection zone extends inward to "dredge up" processed material wi th in the thermonuclear core. The first dredge-up brings up material that experienced hydrogen burning during the M S and turn-off on to the R G B . The relative surface abundances are changed significantly with a 30% reduction of 12C [1]. When the central temperature reaches approximately 10 8 K helium ignites in the core. The dominant reaction is 1 Chapter 1. INTRODUCTION 2 3a ^ 1 2 C W i t h this new energy source the star once again achieves hydrostatic equi l ibr ium. The star has now reached the Horizontal Branch (HB) . When the central hel ium supply runs out, fusion resumes with a helium-burning shell. The star now is on the Asymp-totic Giant Branch ( A G B ) . The A G B is a relatively short-lived phase for stars wi th masses of about 0.8 — 8 M© [2]. A n electron-degenerate core is formed as the second dredge-up phase occurs. As the radius of the star increases and the temperature drops in the expanding layers, and with extra energy generation from helium burning, the ra-diative transport gradient increases above the adiabatic gradient making convection the dominant transport mechanism [1]. The base of the convection zone moves inward, and upwards of 1 MQ of material is dredged-up. A G B stars are grouped into early ( E A G B ) and thermally pulsating (TP) classes. In E A G B stars the only energy source is helium burning in a shrinking shell. A th in hydrogen shell ignites below a deep convective shell and helium shell burning becomes repetitive and explosive in a series of He-shell flashes or thermal pulses (TPs) . The triple alpha reaction is the dominant energy source for T P s , located outside an electron-degenerate (C-O) core causing an expansion of the surrounding material. T P s repeat on t ime scales of 10 4 yr wi th luminosity peaks upwards of 10 8 LQ [3]. The expanding material cools and stops hydrogen shell burning, allowing the convective envelope to move inward. The most abundant element produced during a T P is 1 2 C from the triple alpha reaction. Double shell sources were shown to be thermally unstable by Schwarzchild and Harm [4]. Convection extends deep into the core and carbon and heavy s-process elements are dredged up [5],[1]. The convective mix ing of material during T P s is known as the th i rd dredge-up ( T D U ) . When the total luminosity produced by helium burning falls below Chapter 1. INTRODUCTION 3 the surface luminosity the star collapses, restarting hydrogen burning and start ing the thermal pulse cycle once again. A G B stars can also be subdivided into groups based on the surface composit ion of the star: M / S and C . The third dredge up can bring a significant amount of carbon towards the surface of the star, changing an oxygen dominant M-star ( C / O < 1) to an S-star ( C / O ~ 1) or C-star ( C / O > 1). This chemistry change wi l l alter which molecules can form. For instance, in M-stars T i O produces strong absorption bands in the infrared, whereas C-stars wi l l exhibit strong C N bands as the oxygen is captured in the production of C O inhibi t ing the formation of T i O . Thus the M / S and C categories refer to the spectral features of the A G B star. 1.2 Interest in Carbon Stars Whether a star is a C-star or M-star depends on the amount of oxygen at its surface. The surface abundances are a function of the in i t ia l mass and metal l ici ty of the star on the Z A M S , compared to the amount carbon dredged up towards the surface, which wi l l depend on the evolution of the star. If a star is formed from ini t ia l ly metal-poor material in the protostellar molecular cloud then not as much carbon wi l l be required to alter the surface chemistry from oxygen dominated ( C / O < 1) to carbon dominated ( C / O > 1). Atmospheric chemistry wi l l be dominated by the production of C O molecules. If there is an over-abundance of carbon or oxygen, then addit ion molecules such as C N and T i O can form. A star wi l l in i t ia l ly have an oxygen dominated atmosphere, inhibi t ing the formation of C N as the carbon pr imari ly forms C O . When a star undergoes dredge up, material , which is chemically different, mixes into the atmosphere because of convection. If there is low oxygen ini tal ly in the star which was formed from a low metall ici ty molecular cloud, then not as much carbon is need to transform it from an M-star into a C-star. Lower Chapter 1. INTRODUCTION 4 metall icit ies result in higher core masses when a star enters the T P - A G B phase causing eariler and more violent third dregdeup events[6]. Thus the ratio of the number of C-stars to M-stars wi l l depend on the metall icity of the system and observations support the idea that higher C / M ratios in lower metall icity systems.[7], [8], [9], [10], [11], [12], [13]. The observed correlation spans 4 dex in C / M and 1.5 dex in [Fe/H][14] and holds regardless of the galaxy morphology or star formation history. This provides a method to measure the metal l ici ty distr ibution wi th in a galaxy as only age and metal l ici ty appear to have a strong effect on the C / M - s t a r ratio. Stars on the A G B can also exhibit large pulsations with characteristically long periods and strong stellar winds producing mass loss rates between 10~ 8 and 10~ 4 M 0 y r _ 1 [2]. Stellar winds in turn lead to the formation of a cool circumstellar envelope where complex molecules and dust can form, to be returned to the interstellar medium ( ISM). As a large fraction of this material was processed by stellar nucleosynthesis, the high mass loss rates associated with A G B winds means these stars contribute substantially to the chemical evolution of galaxies [3], as they can account for the majority of material returned to the I S M [16]. 1.3 M33: Target of Study and Aims of Thesis A G B stars are very luminous and easy to identify in Local Group Galaxies wi th modest telescopes. Located in the Tr iangulum constellation, M33, also known as the Tr iangulum Galaxy 1.1, is a late type spiral located approximately 840 pc away. A V-band image using data from this thesis is shown in Figure 1.1. M33 is smaller than both M31 and our M i l ky Way and is an interesting target to study as it has no observed bulgeo f halo and we can resolve its A G B / R G B stellar content. Its lack of nearby dwarf companions provides it wi th an almost isolated environment. This is different from M31 which has Chapter 1. INTRODUCTION 5 Figure 1.1: M33 mosaic V-band image dwarf spherical galaxies, such as N G C 185 and N G C 205. Another of its companions, M32 is the probable cause of the observed plumes of R G B stars[17] wi th t idal interactions. A G B stars are members of intermediate aged (1-10 Gyr) stellar populations and due to their age represent a relaxed subsystem in galaxies [2]. Th is means that their field halo stars uniquely record their early history and minor mergers, as galaxies wi th substantial disks cannot have experienced recent major mergers [18]. B y observing M33 to large galactocentric distances we can examine the underlying stellar populat ion to see if there is evidence for any recent t idal interactions. F inding these interactions and remants is an observational constraint on galaxy formation models such as hierarachical formation and its variants [19]. Since we are able to resolve the luminous stellar populat ion of M33 and since our observations cover a large field of view, we can sample the galactic structure of M33 though its resolved stellar populations. For example the newly discovered t idal r ing that seems to surround the M i l kyWay was discovered by an overabundance of F-stars in particular directions [20], [21] and is easily identified in colour-magnitude diagrams. Chapter 1. INTRODUCTION 6 Using the C / M - s t a r ratio one can trace metallicity. Zaritsky's [22] star-forming vis-cous disk models predict a change in the slope of the metall icity gradient at the radius where the rotation curve flattens. Th is data set wi l l allow us to measure the metal l ici ty gradient of the galaxy as a function of galactocentric radius and the projected location in the galaxy. Direct tests of galaxy formation and evolution models can therefore be made. Metal l ic i ty distributions are observational tests of the details within for simulations of galaxy formation, where the metall icity distributions can be directly compared, testing the validity of star formation and chemically enrichment recipes. Probing the metal l ici ty distr ibut ion in a galaxy can also trace galactic mergers, as canibi l ized dwarf galaxies and t idal streams can be relatively metal poor or at least different than the host galaxy, providing another constaint on galaxy formation models. The C-star luminosity function ( C S L F ) has a narrow peak and thus could be a good distance indicator, for example, see Figures 1.2 and 1.3 which are reproduced from the review by Groenewegen[14]. The problem is disentangling the dependence of the peak of the C S L F on galactic properties such metall icity or star formation history. Figure 8 of Groenewegen[14] shows that the mean of the C S L F does not depend on [Fe/H], wi th most systems having a mean bolometric magnitude between -4 and -5. Discrepancies can be explained either through incompleteness of the C S L F at faint magnitudes causing the mean to be too bright, or the absence of an intermediate age populat ion leaving only faint C-stars. The C S L F is the only constraint on synthetic A G B evolution models that rely on the correlation of H-exhausted core mass with stellar luminosity. These models help constrain the efficiency of the T D U which is defined as A = (1.1) Chapter 1. INTRODUCTION 7 Figure 1.2: Reproduced from Groenewegen[14] this figure shows the C-star luminosity function of other galaxies where C-stars have been observed. Chapter!. INTRODUCTION ~k I j l i l I [ a t f I j $ I \—i—$—\—i—i—r SaeDIG i — i H -Leo I Andll 1 f ~ } 1 {—|—4 1—|—:{—j-Acpiari • LeoII •5 •6 -7 M,. T — i — | — ! — i — i — r — | — i — i — n q — i — m — | — I — I t i Sculp I 1 ! I | I I I I Carina UMinor-4-4-Draco •3 -4 - 5 - 6 M, , Figure 1.3: Reproduced from Groenewegen[14] is the continuation of Figure 1.2. Chapter 1. INTRODUCTION 9 where AMdr edge is the mass dredged up and AMC is the amount the core mass has changed because of H-burning during the thermal pulses [3]. The T P U efficiency is depen-dent on the treatment of convective overshooting, especially for low-mass stars where the base of the convection zone may not extend deep enough to produce effective dredge-up. The first complete luminosity function of C-stars in the L M C showed large discrepan-cies wi th theory[23]. Not unt i l major revisions in theories of stellar evolution for the formation of C-stars was a reasonable match made. Studying the A G B and luminosity function can also help understand mass loss effects in metal-rich stars where stars below 2 M 0 do not produce dredge-up in synthetic models. Th is may be inconsistent wi th the C S L F (for solar metallicities) where the low-mass end of the carbon star distr ibut ion has progenitor masses of 1 — 3 M© [24]. Models have also been unable to reproduce the C S L F of the L M C and S M C as determining the mass range of stars' that become C-stars and the dependence on metall icity is a constraint on A G B structure and evolution models as models must properly handle convection and mass loss; two physical phenomena that are usually unphysically parametrized (ie. mix ing length theory). Since the C-star phenomenon is relatively short-lived, C-stars make good dynamical and structural probes of the intermediate age population, giving a snapshot of the galaxy from the past. The metal l ici ty gradient provided by the C / M - s t a r ratio can be compared to measurements from other stellar types and remnants as a comparison for data sanity and also for evidence of evolution. In C D M simulations, galaxies appear to evolve inside out through accretion, with recent material settling down at the edge of the galactic disk[25]. The viscous disk models of Zaritsky[22] predict that the slope of the metal l ici ty gradient wi l l change over time as material moves radial ly through the influence of dark matter on the flat rotation curve. Chapter 1. INTRODUCTION 10 1.4 Photometric Identification of Carbon Stars In order to distinguish C and M type A G B stars, groups led by Richer[26], [8], [27], [28], [29], [30] and Aaronson [31], [9] developed a technique using four niters to classify A G B stars. Further, Brewer[12] obtained spectra of A G B stars in M31 to confirm that the technique works. The four-band photometric system ( F B P S ) uses two narrow-band filters to provide low-resolution spectral information and two broadband colours as temperature criteria. A C-star spectrum wi l l be dominated by C N and C O bands, whereas an M-star is dominated by oxide bands such as H 2 0 and T i O . The C N and T i O filters were developed to measure the C N and T i O molecular band strengths. Figure 2.1 of Brewer[12] shows spectra of a C-star, an M-star and an A-star and demonstrates how the filters can easily discriminate between the three. A C-star wi l l have strong absorption in the C N filter and when compared to the magnitude measured from wi l l produce a positive C N — T i O index. A n M-star wi l l produce a negative C N — T i O index, as it wi l l exhibit strong absorption from T i O , and an A-star wi l l produce a C N — T i O index of approximately zero. The benefit of the F B P S is that large areas can be quickly surveyed by direct imaging providing simultaneous measurements of al l stars in the field of view (eg. over 1 mi l l ion stars in this study), compared to spectroscopic observations which are l imi ted to a rel-atively narrow field of view, small numbers of potential targets and longer integration times. The F B P S is also advantageous as it w i l l work in fields too crowded for grisms. Survey strategies applied to the L M C [32], [7] would not work in this case due to the distance of M33 and the projected number density of stars. A spectroscopic survey of al l potential A G B stars in M33 for the purpose of classification would be unfeasible. Using the F B P S , stars can be quickly classified, and targeted for followup spectroscopy and supplemental studies, such as kinematics. For example, in the L M C , the kinematics of Chapter 1. INTRODUCTION 11 about 1000 C-stars were used to measure the velocity field and find that the L M C is embedded in a dark halo whose mass inside a radius of 8.9 kpc is 9 x 10 9 M 0 compared to 3.2 x 10 9 M 0 in stars and gas in the disk[33]. C-star candidates from surveys in the local group, such as this one, can then be used to study their kinematics and physical properties. Since M33 is the only nearby late-type spiral, kinematic studies are important and can be compared to early type spirals such as M31 . Chapter 2 D A T A C O L L E C T I O N 2.1 Instrumentation and Filters Mul t iband photometric data were collected on October 30 and 31, 1999 and Decem-ber 3 and 4, 2000, wi th the 3.58 m Canada-France-Hawaii Telescope ( C F H T ) located atop M a u n a K e a on the island of Hawai i (the B i g Island). C F H T is a joint facil i ty of the Nat ional Research Counci l of Canada, Centre Nat ional de la Recherche Scientifique (France) and the University of Hawaii . The telescope became operational in 1979 and provides some of the best images in the world. The weather and observing conditions are mainly dependent on the Northeast Pacific Ocean anticyclone that produce an easterly tradewind and an inversion layer in the atmosphere at a height of approximately 2000 m. The telescope is located above this layer at an altitude of 4204 m where the air is ex-tremely dry and stable providing excellent transparency and sharp seeing w i th a median F W H M of 0.7" for imaged stars [34]. The detector used was the C F H 1 2 k mosaic C C D camera which employes 12 M I T / L L C C I D 2 0 C C D s to provide an effective size of 12228x8192 pixels. The camera is positioned at the prime focus of the telescope and with a pixel size of 15 microns and a plate scale of 0.206"/pixel the field of view is 42x28 ' or approximately 1.5 times the size of the ful l moon. The wide field of view accessible by this camera is one of the largest in the world. Apar t from wide field optical imaging C F H T also provides adaptive optics, infrared and U V imaging and many modes of spectroscopy including multi-object spectroscopy, 12 Chapter 2. DATA COLLECTION 13 also known as M O S . Recently the CFH12k camera was replaced wi th a larger camera known as Megacam featuring 40 2048x4612 C C D detectors covering a l x l degree field of view. Table 2.1: filters Fi l ter Central Wavelenght (nm) Bandwidth (nm) Max . Trans. Mou ld V 537.4 97.4 94 Mou ld I 822.3 216.4 91 T i O 777.7 18.4 92 C N 812.0 16.1 95 2.2 Bas ic C C D Theory C C D s or Charged Coupled Devices are usually constructed out of s i l icon 1 that operate v ia the photoelectric effect. The fundamental element of a C C D is the metal insulator semi-conductor (MIS) capacitor which starts with a neutral sil icon crystal upon which a p-type epitaxial sil icon is grown. Th is layer is usually boron-doped to create positive carriers which dramatical ly increases the conductivity of the semiconductor. For a buried channel device, such as CFH12k , a n-type silicon layer is formed on top where photoelectrons can collect. A n insulator layer such as silicon-dioxide is then added wi th a conductive gate layer such as doped poly-sil icon to form the surface 2. When a positive voltage is applied to the gate a potential well for electrons is created wi th in the n-type sil icon layer[35]. Construct ing an array of MIS capacitors creates a C C D . Through manipulat ion of the voltage on the gates the collected charge can be transferred down columns of the array 1 Germanium is sometimes used as well 2For a surface channel device the n-type silicon layer is not present, causing charges to gather at the Si — SiC-2 interface. Chapter 2. DATA COLLECTION 14 towards a perpendicular array that transfers the charge to an onboard amplifier and then digital ly encoded. When photons strike the detector the incident energy allows some electrons to break their bonds wi th the sil icon crystal lattice structure creating an electron-hole (e~ — h) pair as the electron is moved from the valence band into the conduction band. The Quantum Efficiency (QE) is a measure of the precentage of incident photons that are likely to create an e~ — h pair. The Q E is mostly affected by absorption of photons by the gate electrodes, especially at short wavelengths. To alleviate the problem, the C F H 1 2 k detector is backside i l luminated and thinned. Th is process means that photons do not have to pass through the electrodes and have a smaller distance to travel to create photoelectrons and hence, more detections. 2.2.1 Mosa ic C C D s One of the challenges in the manufacture of C C D s is the creation of large arrays. The two l imi t ing factors are the fabrication process itself and the data transfer rate to read out each element. Gate shorts and opens are the most common failures. These defects can be caused by contamination by dust particles that land on the sil icon wafers during processing, leading to bad columns and pixels or completely inoperative chips. The production of C C D s with greater than 1024x1024 pixels demands an environment wi th less than 100 particles per cubic meter[35]. Readout t ime also becomes a serious factor with the production of large-format C C D s . A single M I T / L L C C I D 2 0 C C D from the C F H 1 2 k camera takes approximately 1.5 minutes to read at a rate of approximately 95 k pixels / sec. For a single 12228x8192 detector the readout t ime would be approximately 18 minutes. W i t h the demand for observing time on large telescopes at a premium, such observing overhead is not acceptable. The alternative is to bui ld mosaic-style detectors which consist of mult iple C C D s Chapter 2. DATA COLLECTION 15 placed next to each other. C F H 1 2 k consists of 12 similar C C D s closely packed together as a 2 x 6 array. Each C C D acts independently of the others allowing for a relatively fast readout t ime and an extremely large field of view. The downside is that gaps are introduced between each C C D ; in the case of CFH12k , the gaps are about 30 pixels wide, or 7", at the C F H T focal plane. Thus observations of a single object wi th a mosaic camera are usually dithered, where the telescope pointing is adjusted for each image to place the missed objects over the detector. This process does have the benefit of filling in data from bad columns and pixels that exist on most of the C F H 1 2 k chips (which can cover as much as 30% of a single C C D ; see F i g 3.1, for example). The gaps between each detector can be treated as bad columns and rows in the data reduction. Table 2.2: Target list F ie ld ID R A D E C M33-1 l h 3 5 m 2 4 s +31°06'30" M33-2 l h 3 2 m 1 8 s +31°06'30" M33-3 l h 3 5 r a 2 3 s +30°39'30" M33-4 l h 3 2 m 1 8 s +30°39'30" 2.3 Observations The four fields in M33 that were observed are listed in table 2.2 wi th J2000 co-ordinates. The four fields cover an area of approximately 80x50 ' or 6 times the size of the ful l moon. Fields 1 and 2 cover the south-west, south and south-east parts of the galaxy and fields 3 and 4 cover the west, east and central parts of the galaxy. Observations were obtained during two separate observing runs. The first run was carried out by Dennis Crabtree on October 30, 1999 to obtain V and I broadband data. Observations for the second run were completed on December 3 and 4, 2000 by myself and James Brewer for the narrowband Chapter 2. DATA COLLECTION 16 T i O and C N filters. A n observing log is given in Table 2.3. Co lumn (1) gives the date of the observation, column(2) gives the target field or type of cal ibration image, column (3) gives the filter used, column (4) gives the number of exposures and exposure t ime in seconds and column (5) gives the average ful l-width-half-maximum ( F W H M ) of stars on each frame in arc seconds. e r 2. DATA COLLECTION Table 2.3: Observation Log Date Target Fi l ter Exp . (s) F W H M (") Oct 30, 1999 M33-3 V 3 x 400 0.68, 0.68, 0.66, M33-3 I 3 x 200 0.62, 0.62, 0.62 M33-4 I 3 x 200 0.62, 0.62, 0.62 M33-4 V 3 x 400 0.68, 0.68, 0.66 M33-1 V 3 x 400 0.62, 0.64, 0.64 M33-1 I 3 x 200 0.8, 0.8, 0.8 M33-2 I 3 x 200 0.8, 0.8, 0.8 M33-2 V 3 x 400 0.87, 0.89, 0.91 Sky F la t V 30, 21, 15, 11, 6, 5, 4 -Oct 31, 1999 Sky F la t I 4, 5, 7, 9, 12, 17, 24 -Bias - 4 x 0 -Dec 3, 2000 M33-3 T i O 3 x 1000 0.62, 0.62, 0.62 M33-3 C N 3 x 1000 0.8, 0.8, 0.8 M33-4 C N 3 x 1000 0.52, 0.48, 0.60 M33-4 T i O 3 x 1000 0.72, 0.72, 0.91 M33-1 T i O 3 x 1200 1, 1.27, 1,30 Sky F la t T i O 3, 7 ,4 -Bias - 0 -Dec 4, 2000 Sky F la t C N 6 x 5,7 -Sky F la t T i O 2 x 12, 2 x 20, 30 -Sky F la t C N 40, 60, 100, 140, 200 -Bias - 0 -M33-1 C N 3 x 1000 0.70, 0.62, 0.70 M33-1 T i O 3 x 1000 0.67, 0.72, 0.70 M33-2 T i O 3 x 1000 0.72, 0.76, 0.76 M33-2 C N 3 x 1000 0.8, 0.8, 0.8 Bias - 6 x 0 -Chapter 3 D A T A ANALYSIS 3.1 Processing Mosaic Images The most common format for the storage and interchange of data is the Flexible Image Transport System (FITS) which has been in use for over two decades as a well defined standard[36],[37]. Its design, however, was for indiv idual images. Using the C F H 1 2 k mosaic camera means that 12 images are produced for each exposure. Rather than save each image individual ly, they are written in multiextension FITS format or M E F . The C C D data are stored in M E F as concatenated F I T S images, each wi th its own header plus global header information, such as exposure t ime, that is inherited by each indiv idual image. Access to indiv idual C C D images within the M E F format is controlled through indexing wi th a Chip-ID, or extension, assigned to each image. The software used to clean the C C D frames was I R A F 1 . Normal ly image processing software such as I R A F can only read and operate on a single C C D image at a t ime, so the M S C R E D package was created by the N O A O and other observatories to help wi th the handling and reduction of M E F data. The M S C R E D package allows tasks such as simple arithmetic to be performed simultaneously on al l C C D images contained in a M E F file, making book-keeping much simpler and providing the abi l i ty to perform global corrections to the data. 1 Image Reduction and Analysis Facility (IRAF), a software package distributed by the National Optical Astronomy Observatories (NOAO) 18 Chapter 3. DATA ANALYSIS 19 Figure 3.1: A close-up of defects in C C D 0 5 . The image on the left is a V-band image showing the brick wall pattern and the image on the right is an I-band image that shows fringing. Bo th also show the many bad columns and non-linear pixels present on this chip. Chapter 3. DATA ANALYSIS 20 3.2 C C D Artifacts A l l images obtained require data processing to remove signals added by the C C D itself. Th is includes correction of bad pixels, overscan and bias subtraction and flat-fielding. These operations were completed using the M S C R E D package in I R A F . The C F H 1 2 k is mostly free of defects, such as bad columns and hot pixels, but some chips show significant cosmetic flaws, such as wi th C C D 0 5 where approximately 30% of the chip is covered in defects (see Figure 3.1). Such regions usually show a non-linear response to the number of detected photons. Normally, the number of analogue-digital-units (ADUs) or counts from the analogue-to-digital converter ( A D C ) reported for each pixel is directly related to the number of photons detected. This is then mult ipl ied by a factor known as the gain. Usual ly the non-linearity of a C C D is a secondary correction and only becomes significant at levels of about 1% when the detector is close to saturation (ie. when the potential well overflows). For CFH12k , the number of counts per pixel at which non-linearity becomes significant is different for each C C D and ranges from 51k to 65k. Individual bad-pixels and columns can be identified by exposing a uniform intensity i l luminat ion at different exposure lengths. These images are part of the standard reduction procedure and are known as flat fields. D iv id ing two images should reveal any bad pixels that deviate from the norm. Bad pixels and columns can be treated in two ways. The first is to ignore them in the reduction, the second is to interpolate over these pixels using surrounding pixels. The general approach taken in this work is to simply ignore bad pixels, especially since the images are dithered so chances are good that every part of the target wi l l be observed at least once. The problem wi th interpolation routines is that one must assume an analytic function to model the missing data where we have no prior knowledge of what to assume. Only in very specific cases do we apply a correction to bad pixels, which wi l l be described in section 3.4. Chapter 3. DATA ANALYSIS 21 For reduction, the data were divided into two groups corresponding to each year of observation. The broadband and narrowband data wre reduced in different ways as described below. 1000 700 h _ | ! ( p. - J I I I I l_ _« L J i i i i i i i i_ _L 0 1000 2000 P i x e l 3000 4000 Figure 3.2: A plot of 5 different rows from the overscan region on C C D 0 5 . Note that two rows overlap at 760 A D U , but there is no consistent value. 3.3 Narrow-band data processing The first step is removal of the electronic bias or zero level known as overscan (or ID -bias) correction. The overscan is measured by reading the C C D beyond its physical l imit , hence measuring the zero level of unexposed pixels. To remove the overscan level, the Chapter 3. DATA ANALYSIS 22 average value for each row is evaluated and then a Legendre polynomial is fit to the data. The fit is then subtracted from each column. Unfortunately, this approach could not be used successfully on some of the CFH12k C C D s , in particular C C D 0 5 . In Figure 3.2 five adjacent rows from the overscan region are plotted and 4 have different means. Proper subtraction of the overscan level is necessary to analyse noise levels and photometric errors and also to normalize each chip in a consistent way to minimize photometric offsets across the mosaic. To deal wi th this, we instead examined the bias frames. Bias frames are similar to overscan regions in that the chip is read out wi th zero exposure t ime, so once again the zero level of unexposed pixels is being measured, except we are also checking that there is no repetitive stationary pattern. For each C C D , an overscan correction based on its associated bias frame was applied. If there is no structure to the bias frame itself then the distr ibution of the pixel values should be a Gaussian wi th the width defined by the read noise [38]. A histogram of pixel values for a 50times50 sample box wi th in a bias image from CCDOO is shown in figure 3.3. No overscan correction has been made so the mean is not zero, but examination of the overscan region shows that the median value is approximately 427.7 A D U - exactly where the peak of the distr ibut ion of pixel values occurs. The read-noise for this C C D is measured to be 2.8 A D U which corresponds to the F W H M of the distr ibution. To recover the overscan value, a flat plane was fitted to averaged bias frames for each C C D , which was then subtracted from the flat field and science frames. After bias corrections, gain differences across the C C D were corrected for by combin-ing sky flats for each filter. The skyflats were obtained by imaging the twil ight sky just after sunset. Exposures of the sky taken at this t ime wi l l only show a few bright stars as short exposure times and the bright sky background wash out d im objects. The large area of sky imaged by C F H 1 2 k means that it is impossible to avoid contamination by Chapter 3. DATA ANALYSIS 23 o o CM O m s= o o 2 o o m o -r-rrl 424 426 428 Pixel Bin 430 432 Figure 3.3: A histogram of bias pixel values for a 50times50 sample box. The Gaussian shape means that there is no 2d-bias to correct for. Chapter 3. DATA ANALYSIS 24 stars. The telescope was in tracking mode when the exposures where taken. Thus nor-mally, on sequential exposures, the stars wi l l appear in the same location on the frame. To a id in removal of stars when mult iple images are combined together, a smal l offset was applied to the telescope's pointing position. When combining frames, rejection criterion are used to eliminate high and low pixel values before averaging. The high value pixels wi l l be dominated by stars. The I R A F task C O M B I N E found in the M S C R E D package was used. Th is task uses a sigma cl ipping routine that eliminates high and low pixels that are more than 3 o away from the mean. Th is works well for the sharp bright centres of stars' P S F s , but the extended wings are too faint to be excluded. Instead, the core of the P S F for a star is used as a tracer to reject al l pixels wi th in a specified radius. For CFH12k , a radius of 15 pixels was found to work well from visual examination of the images. Fringing in C C D s is caused by interference patterns from single colour l ight, which is present in the night t ime sky from emission lines. From examination of Figure 3.1 it is evident that fringing is present in the science images, which occurs for al l I, C N and T i O band frames. The strength of emission lines from the sky is not dependent on the sky brightness and hence longer exposures wi l l be more susceptible to fringing. Sky flats wi l l contain l i tt le or no information about the fringing pattern as exposure times are usually a few seconds compared to a few minutes for the science images. The best way to correct for fringing to take long exposures of blank night time sky. Th is demands large amounts of observing t ime which are usually not available. The science images themselves could be used, but special care must be taken to avoid the gradient caused by the surface brightness profile of M33. Examinat ion of the fringing pattern showed that scale length from peak to peak was approximately 50 pixels which is approximately 10 times larger than the P S F size of a star and wi l l not affect the photometry as the local background level around the star can be calculated and subtracted. Chapter 3. DATA ANALYSIS 25 3.4 Broad-band data processing The flat fields for the broadband data set suffer from a strong, variable, scattered light pattern. F la t fielding wi th these images introduced a 20% response error as a smooth cloud like gradient. The scattered light signal was also found to dramatical ly change wi th each flat field image. Th is effect meant that when the images were averaged together, sigma cl ip routines to remove stars failed as it was impossible to scale each image to a uniform level so that deviant pixel values could be reliably removed. To fix this problem each flat field image was heavily smoothed wi th a 500x500 pixel boxcar filter leaving behind the slowly varying background. Subtracting this signal away from the original image leaves an image containing the pixel-to-pixel sensitivity changes and objects such as stars and cosmic rays. Bad pixels and columns were troublesome, as a column of extremely high or low pixel values would affect al l surrounding pixels where these extreme values are included in the sums. A bad pixel mask was used to identify and correct the defects wi th interpolation from nearby pixels. A l l of the gradient images were then scaled to a common mean pixel value and av-eraged together without any pixel rejection, giving a first-order guess at the true instru-mental gradient. A l l of the residual images were then averaged together wi th a sigma cl ipping algorithm which rejected nearby pixels around P S F peaks, effectively removing the entire P S F profiles. These two averaged images were then summed to produce a flat field that corrects pixel-to-pixel sensitivity differences but st i l l failed to remove the overall gradient. Th is instrumental signature was removed by using the science images themselves. It was assumed that the individual C C D fields on the mosaic, which were farthest from the centre of the galaxy and hence least contaminated by stars, should be completely flat. According to the N A S A Extragalactic Database (NED) M33 reaches 25 m a g / a r c s e c - 2 Chapter 3. DATA ANALYSIS 26 in the B-filter at a major axis radius of 70.8'. The ratio of the major axis to the minor axis is 1.70. Assuming an R 1 / / 4 law (de Vaucouleurs 1948) means that at 28 arcmin the surface brightness is approximately B=24 mag/"2. The average B—V index of M33 reported by N E D is 0.55 and the sky at Mauna K e a is approximately V=21.7 mag/a rcsec 2 [39]. The low surface brightness of M33 at this radius means the assumption that the sky level is flat across the C C D is val id for al l C C D images pointed 28" or more away from the galaxy centre. Individual C C D images located away from the centre of the galaxy meeting the criteria above were flat fielded with the combined flat field images and images for each chip were averaged to create a super flat which was then normalized to unity. Stars were removed from the averaged images by using the same sigma cl ipping algori thm used for the creation of regular flat fields. In total, 3 images per C C D were combined to create the cal ibration image. App ly ing this image to the science images, would increase the background noise level of the science images as the sky background has a high shot noise. Since this cal ibration is being used for the removal of a slowly changing gradient, the image was smoothed using a 3 x 3 boxcar. Subtraction of the smoothed image wi th the original showed a flat image consistent with the expected noise level. The flat fielded science images were then divided by the super flat to remove the instrumental gradient. A caveat to this procedure is that any instrumental signatures that are additive, such as fringing, are incorrectly removed through division by the super flat, which wi l l cause a star's measured magnitude to depend on its posit ion in the image. Fortunately, the C F H 1 2 k detector shows l i t t le evidence of fringing in the V-band. The I-band flat field images also suffer, from scattered light problems, but this is detectable only at the 2% level. A more dominant problem is fringing, wi th a peak-to-peak amplitude as large as 10%. The same procedure used for flat fielding the narrow-band data was used for the I-band images. Simi lar to the narrow-band images, the fringe pattern is smooth and does Chapter 3. DATA ANALYSIS 27 not significantly affect the photometry. 3.5 P h o t o m e t r y The brightness of a star is simply the addit ion of al l of the counts on each pixel that contains light from the star, minus the background. Complicat ions arise as stellar P S F s are rarely isolated and pixels can contain light from several nearby stars (e.g. in crowded stellar fields), or a cosmic ray can contaminate the P S F . Techniques for crowded field photometry, such as P S F fitting, are used. A l l P S F fitting software operates by creating a model P S F for stars across the image. Apart from geometric distortions caused by the instrument, the shape of the P S F across the image should not change and is scaled according to the brightness of the star. A l l stellar photometry was performed using the D A O P h o t / A L L S T A R package [40], [41]. D A O P h o t assumes an analytic function for the general shape of the P S F and uses a lookup table to correct the shape of the P S F as a function of the posit ion on the image compensating for geometric distortions. D A O P h o t is not able to handle M E F images and each mosaic frame was split into its individual frames. Th is gave a total of 612 images which were al l treated independently for the extraction of photometric data. The first stage in extracting photometry from the science images is the identif ication of objects on the frames, through the D A O F i n d task. The only input required from the user is the F W H M of the P S F and the threshold level for the peak above the background noise. The image is then convolved with a symmetric Gaussian, defined by the F W H M , and brightness enhancements are selected and identified as object candidates, wi th extended and spiked objects rejected (e.g. bad columns and cosmic rays). The threshold level was selected by try ing several different values and plott ing them versus the number of detected objects. When the thresholds are too low, the number of objects wi l l asymptotical ly cl imb Chapter 3. DATA ANALYSIS 28 as noise spikes are identified as potential targets. W i t h too high a threshold, the number of stars wi l l decline linearly wi th increasing threshold. The adopted value was chosen in the regime where the number of detected objects begins to dramatical ly cl imb, or at the knee of the plot. A value of 3.5 was chosen for the threshold and used for al l science frames. The number of detected objects ranged from 150 000 per chip near the centre of M33 to a few thousand at large galactocentric radi i . The next step was to perform aperture photometry on al l the detected objects. Th is step defines the instrumental magnitude system for converting the model P S F scale factor to a magnitude. Since the inner fields suffer from extreme crowding, the aperture radius was selected to be 3 pixels, measuring only the inner peak value. W i t h good centroids, the returned aperture magnitudes are internally consistent and adequate to set the magnitude scale. W i t h crowded field photometry the hardest part of profile fitting wi th profile fitting is bui lding a suitable model P S F for the science frame. Seeing conditions also affect the shape of the P S F as a function of t ime. Thus a model P S F must be generated for each science image. W i t h D A O P h o t , this is accomplished by selecting a number of bright isolated stars to constrain the shape of the model P S F and investigating how it changes across an image. In order to account for geometric distortions in the P S F s , 150 P S F Stars were selected for each image. F i rs t , the D A O P h o t P I C K routine was used to find the brightest 200 stars that are relatively isolated from other comparably bright or brighter stars. The centroids for al l of these objects were then passed to the I R A F routine I M E X A M and a simple Gaussian was fitted to each object in the list to return a measured F W H M . A l l objects with a F W H M under 2 pixels were el iminated and then the median and standard deviation were calculated for the remaining stars. A l l stars wi th a F W H M greater than 3 times the mean value or less than 1/3 the mean value were el iminated, and the mean was recalculated. Aga in , high and low values were Chapter 3. DATA ANALYSIS 29 cut. Th is was repeated for 5 iterations. The reasoning for this is that any stars whose P S F significantly overlaps wi th another star 2 would be fitted together by a single wide Gaussian. Galaxies and other non-stellar objects wi l l also return large F W H M values and would be removed by this stategy. Objects wi th small F W H M s are most l ikely to be bad columns, pixels or cosmic rays and are again rejected from the list. Usual ly an in i t ia l list of 150 objects was reduced to 80 - 100. V isua l examination of these objects on a few frames confirmed that this procedure was effective. W i t h a good list of P S F stars, the D A O P h o t routine P S F was run and a model P S F was generated. A first guess at a P S F was made by using a pure analyt ic Gaussian without any lookup tables, so that any faint stars in the wings of the P S F stars are not included in the fit. Th is P S F was then used to subtract al l stars detected by D A O F i n d except the P S F stars. A new P S F was then generated from the subtracted image wi th look-up tables. Th is process was iterated 4 times in total, wi th the order of the polynomial fit to the P S F variations across the image increased by one for each pass. After the th i rd iteration for the generation of a good P S F every object from the D A O F i n d star list was subtracted and D A O F i n d was run again to find any stars missed due to crowding. D A O F i n d was run a third time after a final P S F was generated for a last pass at picking up any missed stars. The photometric measurements were made wi th the D A O P h o t task A L L S T A R , which simultaneously fits groups of stars found close to each other on the frame wi th the generated model P S F . W i t h photometry generated for each C C D chip, registration of the chips relative to one another was done with D A O M a t c h / D A O M a s t e r . Th is worked well wi th each indiv idual chip and a 20 parameter tranformation model was used to model the geometric distortions, so that the measured pixel positions of the stars on each C C D chip could be matched to other observations of the same field on the same chip. For example, for 2 Within the fitting radius Chapter 3. DATA ANALYSIS 30 C C D 0 1 in Fie ld-2, there were 3 sets of observations in each of the four filters. These 12 images were then registered to match common objects for each field. Each observation was slightly offset from each other, which meant that some stars were observed on two adjacent detectors. Using these common observations, the complete photometric catalog was pieced together, placing al l objects on a common co-ordinate system. 3.6 As t rome t r i c Regis t ra t ion In order to identify common objects between adjacent C C D s the pixel co-ordinate sys-tem had to be transferred to J2000 co-ordinates. The reason for this is that the D A O -M a t c h / D A O M a s t e r failed to converge to a proper registration solution, as less that 5% of the area of two chips overlap from the dithered observations. When D A O M a s t e r finds a transformation, it is only val id for the objects in common between the images. Ex t rap-olation of the solution to the next C C D would inherit large distortions that D A O M a s t e r could not account for. Instead, the pixel co-ordinate system for each C C D chip was mapped to the J2000 co-ordinate system. Common stars between this survey and the U S N O - A 2 astrometric catalogue were identified by using the M S C Z E R O and C C F I N D I R A F commands found in the M S C R E D and I M C O O packages. The M S C Z E R O routine wi l l display the C C D image using the header information for a C C D chip and retrieve stars from the U S N O - A 2 catalog and plot their location on the image. The user then matches approximately 3 stars for each chip to find the mean zero point offset for the co-ordinate transformation. The C C D header information was found to be offset by approximately 30" and 40" in Right Ascension and Decl inat ion, respectively. The values are quite large as the positions were not corrected at the telescope. Once these gross corrections were applied, the C C M A P program was used to automatical ly cross-identify 100 common stars in each C C D frame by finding Chapter 3. DATA ANALYSIS 31 the brightest star wi th in a 20 x 20-pixel search box. The success rate was approximately 75%, wi th a majority of failures due to catalogue stars located outside the imaged area. The C C M A P program was then used to compute a rough astrometric solution based on al l cross-identifications, including incorrect ones, since the number of true matches dominates the list. These solutions had an R M S error of approximately 6". W i t h this plate solution, the program G A I A was used to properly identify al l common stars between the two catalogues. G A I A is an interactive program that wi l l plot the posit ion for each cross identification. The user can then independently adjust the posit ion of each star to properly account for optical distortions at the edge of the C C D array, wi th the click of a mouse. The user can then ask the program to properly centroid the posit ion of each object to better than 1 pixel and export the list of objects with their pixel and J2000 co-ordinates. Th is list was input into the C C M A P program to compute an accurate plate solution. The average R M S error was reduced to 0.5"or approximately 2 pixels, which is about the internal accuracy of the U S N O - A 2 catalog. The entire photometric catalogue was then transformed onto the J2000 co-ordinate system. This new catalog was searched for duplicate objects that were imaged on adjacent C C D s . These objects were located by identifying the closest neighbour to each object and the closest objects to that neighbouring star. If two stars were found to be closer than 1.5" and their instrumental magnitudes differed by less than 0.1 magnitudes, then those stars were assumed to be the same and their photometry was combined. The reason for requiring that each star be each other's closest neighbour is to eliminate any star being identified wi th two different objects by the matching routine. Due to crowding and the lack of efficiency of D A O F i n d at faint magnitudes, it is not true that every detected source wi l l appear on every science frame. Whi le the algorithm is good at rejecting false detections, some stars in the gaps were not cross identified so they appear twice in the catalogue. This can be seen in Figure Chapter 3. DATA ANALYSIS 32 4.3 as an artifact of a straight line of apparent stars from the centre of the galaxy, where Fields 1 and 4 overlap. Whi le the astrometric solutions are very good in the center of the frame, pin-cushion effects from optical distortions become most severe at the edges of the mosaic image, causing a systematic shift between object centroids greater than the rejection radius of 1.5". Mak ing the radius larger would not help, as the closest neighbour is not necessarily a counterpart for observations of the other fields. As long as an equal number of stars is detected in the overlap region for both images, then comparing the ratio of C-stars to M-stars is not affected. If one wishes to examine the star maps for structural information, then either al l stars from one of the fields in this gap must be excluded or the distortion must be corrected for and then registered. For science results in this thesis based on stellar ratios and stellar counts over the area imaged, one of the fields in the overlap regions is always ignored, wi th a preference for Fields 3, as this frame has the most observations. 3.7 Pho tomet r i c Ca l ib ra t ion The master astrometric catalogue was corrected for zero-point instrumental magnitude offsets between each observation, chip and field. These values were calculated from the identification of common objects in the master catalogue. Figure 3.4 shows the cal ibrat ion data for stars common to F ie ld 1 and F ie ld 2 for each filter. The lack of scatter, other than the expected photometric errors, confirms that the cross-identification of common objects works very well. The average error for al l fits to the data is approximately 0.01 magnitudes and the standard deviation from the fit for stars wi th an instrumental magnitude greater than 14 is approximately 0.02 magnitudes. Th is is also a measure of the quality of the flat-fielding using stars common to F ie ld 1 and F ie ld 2. If any gradients exist then one would observe a systematic offset in Figure 3.4 from flat fielding errors. Chapter 3. DATA ANALYSIS 33 One potential problem is that the calibration of each chip is dependent only on adjacent chips, thus the offset wi l l inherit errors from every other chip other than the C C D selected as the zero point reference. A C C D chip that is 5 C C D s away from the reference chip could suffer from a large (0.1 magnitude) systematic offset. Th is effect was monitored by plott ing the colour magnitude diagram for the reference chip overlaid wi th that for the C C D chip being corrected. Examinat ion of the C M D s on opposite sides of the C C D arrays shows no difference greater than 0.05 magnitudes, which is the accuracy at which any offsets could be detected through the examination of colour-magnitude diagrams. W i t h al l of the photometry set to a common instrumental photometric system, trans-formation to the standard system for the V and I filters was computed using data on M33 from the D I R E C T project (Macr i et a l . 2001). Their catalog of stars in the central 20' of M33 was cross-identified with the catalog from this study by converting al l J2000 coordinates into a pixel-l ike co-ordinate system using a conversion factor of 0.204"/pixel , wi th is the C F H 1 2 k plate scale. The two catalogues were then used by D A O M a s t e r to identify common stars. One of the output files produced by DAOMas te r is a transfer list that matches up the IDs of common stars. The photometry of these stars was then directly compared as shown in Figure 3.5. The scatter in this fit for stars brighter than V , 1=12 is 0.03 and 0.08 magnitudes respectively. Th is is consistent wi th the internal magnitude cal ibration of the D I R E C T project, as seen in Figure 9 of Marc i et al . (2001). W i t h errors this large, a reliable colour term could not be determined. Instead, only bright stars wi th a V—I colour less than 0.3 magnitudes were used to determine the zero-point offsets; otherwise the average colour terms for C F H 1 2 k from the online observer's manual was used. The adopted transformation equations are V = V0 + 7.39 + O.OOlfVo - h) I = I0 + 6.42 - O.OlOCVo - h) Figure 3.4: The photometric offsets between the instrumental magnitudes of F ie ld 1 and F ie ld 2 for each filter. Each field is identified with a subscript. Chapter 3. DATA ANALYSIS 35 where V0 and I0 are the observed instrumental magnitudes. Better photometric cal ibra-tions are needed but do not affect the results of this thesis, which depend more on the internal magnitude cal ibration. Cal ibrat ion of the T i O and C N magnitudes was much easier. It is expected that the C N — T i O measurements for stars not on the A G B , such as the M S should have C N — T i O = 0 . These stars lack the strong T i O and C N absorption band found in the cooler A G B stars and the T i O and C N filters measure the flux of a black body spectrum. The T i O magnitudes were adjusted so that C N — T i O has an average of zero for stars wi th V—I less than 0.8. The true magnitude of a star observed in these filters is irrelevant, as only the difference between them provides a measurement for identification of C and M-stars. Table 3.1: Object Catalog for M33 (abridged) F i e l d ID H A D E C V "V I "I C N "CN T i O "TiO X S h a r p 1 1 31 04.68 30 52 07.70 15.8437 0.0423 15.1750 0.0118 9.4495 0.0079 9.5432 0.0088 2.8480 0.0670 2 1 30 45.71 30 45 01.00 16.7190 0.0231 99.9990 9.9990 10.0849 0.0366 10.3589 0.0140 4.7347 0.1315 3 1 30 45.15 30 51 37.80 16.5790 0.0048 16.0423 0.0095 10.3286 0.0040 10.2939 0.0036 1.4807 0.1440 4 1 31 03.82 30 51 36.90 17.4459 0.0576 99.9990 9.9990 10.6256 0.1168 10.3792 0.1184 14.6062 0.9263 5 1 31 07.73 30 49 09.80 17.1538 0.1146 16.0570 0.0768 10.2046 0.1594 10.2802 0.0882 18.9920 2.0965 6 1 30 49.96 30 43 29.50 17.4675 0.0114 15.8900 0.0088 10.2512 0.0408 10.3432 0.0150 6.1065 0.3201 7 1 31 08.18 30 53 58.20 17.0759 0.0027 16.4622 0.0081 10.5756 0.0014 10.6212 0.0023 1.9500 0.1295 8 1 31 06.78 30 46 50.20 17.8246 0.0884 16.1523 0.0920 9.9096 0.1329 10.4712 0.0638 12.3475 1.7407 9 1 31 05.65 30 42 54.00 17.2050 0.0047 16.3471 0.0069 10.6585 0.0048 10.6430 0.0020 1.2079 0.1279 10 1 30 44.15 30 48 05.00 17.4429 0.0169 16.6175 0.0109 10.6377 0.0029 10.6412 0.0030 2.0143 0.1388 11 1 30 55.26 30 50 51.50 17.2177 0.0758 16.7430 0.0427 10.8266 0.1733 10.1712 0.0682 9.5310 1.0812 12 1 31 07.08 30 51 19.10 17.3938 0.0978 16.6291 0.0532 10.5066 0.1703 99.9990 9.9990 10.1503 1.5685 13 1 30 43.27 30 53 20.80 17.4147 0.0169 16.8690 0.0075 10.9416 0.0024 10.9861 0.0076 4.7099 0.2863 14 1 31 12.12 30 40 06.60 23.0335 0.0962 99.9990 9.9990 10.7487 0.0031 10.8056 0.0012 0.6175 0.0393 15 1 30 41.28 30 50 21.10 17.7867 0.0862 16.9119 0.0899 99.9990 9.9990 99.9990 9.9990 8.7010 0.5650 16 1 31 06.57 30 43 05.40 17.8381 0.0019 16.6539 0.0044 10.9620 0.0027 10.9662 0.0017 0.7589 0.0642 17 1 31 03.82 30 51 35.90 17.6926 0.0698 16.8398 0.0374 99.9990 9.9990 10.3787 0.0719 6.4360 -0.0362 18 1 30 52.45 30 42 51.70 18.3690 0.0019 16.4759 0.0058 10.7357 0.0073 10.9156 0.0043 1.2668 0.1228 19 1 30 55.28 30 50 51.00 17.6108 0.0574 17.4944 0.0665 99.9990 9.9990 99.9990 9.9990 7.6340 1.3010 20 1 31 01.29 30 41 47.40 17.9940 0.0020 16.7038 0.0076 10.9967 0.0021 11.0626 0.0035 0.9225 0.0688 21 1 31 12.06 30 47 09.20 18.0950 0.0683 99.9990 9.9990 99.9990 9.9990 10.8962 0.0259 2.6755 0.3100 22 1 31 07.18 30 51 19.50 17.7377 0.0849 99.9990 9.9990 11.4042 0.0710 99.9990 9.9990 12.6357 1.5517 23 1 31 07.94 30 40 15.70 99.9990 9.9990 99.9990 9.9990 8.9516 0.0117 8.9872 0.0045 0.9570 0.1340 Chapter 3. DATA ANALYSIS 36 > i > in Al = 6.42±0.08 AV = 7.39±0.03 0 0 L; : . , 1 , 1 , 1 14 12 10 8 Instrumental Magnitude Figure 3.5: A comparison of photometry with the D I R E C T project for the V and I filters. Uppercase letters refer to standards taken from the D I R E C T project and lower case letter refer to the instrumental photometry from this study. A lso shown is the zero point offset adopted for each filter. Chapter 4 R E S U L T S 4.1 Ste l lar i ty Cu t s W i t h i n the raw photometry list there are many non-stellar sources present, such as bad columns or diffraction spikes from bright stars. To eliminate these objects, stellarity cuts were applied based on the fit of the P S F to the object. A l ls tar provides a sharpness statistic and a x2 statistic. The sharpness statistic is a ratio of the residual inside and outside the f i t t ing radius left from the fit of the model P S F to the object. A cosmic ray or bad pixel wi l l leave a negative residual in the outer radius producing a negative sharpness value. A n extended object, such as a galaxy, wi l l leave a positive residual in the outer radius, producing a positive sharpness value. A stellar object should produce a sharp value of zero. Thus, non-stellar objects can be removed by rejecting al l objects wi th extremely high or low sharp measurements. Th is wi l l not eliminate al l non-stellar objects, as distant galaxies can appear point-like in the image. Crowding wi l l also mean that stellar objects that are blended might be fit wi th a single P S F producing a positive sharp value. The Y 2 statistic provides a measurement of the goodness of the fit based on distr ibut ion of residuals from the P S F fit compared to the expected noise contribution. A x2 value of 1 means that the residual of the fit is consistent wi th noise. Thus, objects that do not match the shape of the P S F , such as diffraction spikes and bad columns are removed. Figure 4.1 shows the measured sharpness values versus I magnitude and Figure 4.2 37 Chapter 4. RESULTS 38 shows the measured x2 values versus I magnitude. The flare of objects observed wi th x2 greater than 2 are from galaxies and stars in crowded fields where P S F fits are difficult. Rejection values were chosen by plott ing the positions of al l objects on the C C D frames, then adjusting the stellarity criteria unt i l detections from bad columns and diffraction spikes were removed without the removal of stellar objects. Based on the distr ibutions presented, al l objects wi th x2 greater than 2.0 were rejected as well as al l objects wi th sharp values less than —2.0 or greater than 1.0. 4 18 20 22 24 26 I mag Figure 4.1: Distr ibut ion of sharpness values wi th I magnitude. Chapters RESULTS 39 Chapter 4. RESULTS 40 4.2 Duplicate Detections In Figure 4.3 the location of al l observed stellar objects that survived stellarity cuts are plotted. The overlap region between fields m33- l and m33-3 and between fields m33-2 and m33-4 show an increase in the density of stars. Th is was due to stars that were not properly cross-referenced during registration. When the co-ordinate transformations for mapping from pixels to J2000 were found, the optical distortions at the edges of the mosaic were the hardest to correct for. It is in the overlap regions between fields where these distortions occur and means that duplicate objects would be found further apart than allowed for when cross-referencing. To eliminate these objects, only stars from fields m33-3 and m33-4 are used in the overlap regions and only objects from m33-3 in the overlap region wi th m33-4. This provides a uniform stellar density across the gaps and avoids double detection of objects, as the detection l imits of each field are the approximately the same, as seen in Figure 3.4. 4.3 Incompleteness Tests Many products of this thesis are relative counts of star types. When observing a large extended object such as a galaxy, it is expected that the number of stars that it is possible to detect wi l l vary as we examine different regions. This l imit wi l l depend on the properties of the galaxy and its environment and constraints due to instrumentation. In order to compare relavitive statistics across the galaxy the detection success rate needs to be understood as a function of position. Est imat ing detection l imits due to the galaxy's structure requires understanding sources of extinction, pr imari ly dust, which is poorly understood. Look ing at Figure 1.1, or any B or V band image of the galaxy, it is easy to identify dust trails in the spiral arms due to extinction. Star counts of this region wi l l be lower because more stars wi l l Chapters RESULTS 41 Figure 4.3: Spat ial map of al l observed stars. The band of stars at 30deg 53' is from duplicate detections between different fields. Once one set of objects in these regions is used for studies. The centre of the galaxy is also lacking in stars due to stellar crowding. Chapter 4. RESULTS 42 fall below the detection l imits. Detection l imits due to instrumental constraints are pr imari ly due to a lack of reso-lut ion. Detecting a star requires isolation of its P S F on an image. When many objects become unresolved due to their projected proximity it becomes impossible to seperate each stellar component. It is possible to test these detection l imits through Monte-Car lo methods. The idea, which has become known as addstar tests, is to artif ically add stars to a frame and attempt to recover them under the same conditions as the original photometry was obtained. Compar ing the input star list to the recovered objects gives a measure-ment of our detection l imits and incompleteness due to instumentatal effects. Addstar tests were preformed using the D A O P h o t and A L L S T A R packages, making use of the A D D S T A R routine. This routine uses the model P S F that was generated from the orig-inal photometry extraction to add artif ical stars to the image. The star must be added to match the same noise characteristics as a star of the same instrumental magnitude. If addstar tests are to be a valid estimation of the true incompleteness, then the test must not significantly alter the image when adding stars to it. For example, i f a frame contains 10 000 detectable stars, adding another 10 000 stars would double the density of stars on the image, making it more likely to find blended stars. The added stellar density must be much less than the population of original objects. Since blending wi l l also alter the colour of the detected P S F , the input stars must have colour indices similar to the original stars in the image. Thus, the orginal photometry list is used to generate the artif icial input stars. It was decided to add 1000 stars per frame. This number d id not appear to make even the most sparse fields over-dense (which only contain just over 1000 stars) appear any more crowded. Quick analysis of these fields, by adding stars wi th 100 sigma detection levels showed that 99.8% of the original stars were recovered, adding confidence that our Chapters RESULTS 43 choice of adding 1000 stars per frame would be sufficient to complete the experiment accuractly and rapidly. To generate the magnitude of the object and its relative colour indices, binned colour-magnitude diagrams and colour-colour diagrams, also called Hess diagrams, (see Sections 4.5 and 4.6) are used to determine the probabil i ty of generating stellar parameters. F i rs t a C N — T i O versus V—I diagram is binned by 0.1 mag. Each bin value is then divided by the sum of al l the bins to make a probability. A random number between 0 and 1 is generated and bins are summed by row (V—I) then incrementing in column (CN—TiO) unt i l the sum of the bin is greater than the random number. Th is bin determines the C N — T i O and V—I indices of the artifical star. Next a C N versus C N — T i O normalized grid is used to determine the C N magnitude based on the corresponding C N — T i O column and likewise a V vs V—I grid was used to determine the corresponding V magnitude. Art i f ica l C M D s appeared identical to the original data set. The artif ical magnitudes were then transformed back to the instrumental magnitude system using the calibrations from Section 3.7. The generated number of C-stars was close to 100, as there is approximately 1 C-star for every 100 other types of star. Since incompleteness tests for C-stars is the most interesting information from this test, the artif ically generated star list was changed by taking the logarithic value of each bin in the weighting grids before normal izat ion. Th is places more weight on generating stars with small populations. Close to a hundred carbon stars were generated wi th the alteration, giving good statistics for incompleteness determinations. There were 51 exposures between al l four filters and there are 12 chips per exposure. The test was run 10 times to obtain good statistics for the incompleteness of the entire stellar populat ion. In total, 6 120 000 stars were added to the frames. Before stars were added to a frame each C C D for the same field of view was registered using M O N T A G E 2 from the D A O P h o t package to match star co-ordinates, using the plate solutions from Chapter 4. RESULTS 44 Section 3.6 to aid in cross identification afterwards. Geometrical ly altering an image can introduce noise and artif ical artifacts, but is minimized if the image is oversampled. A general rule of thumb is that the F W H M of a star should be greater than 2 pixels to avoid registration artifacts. Under the best seeing conditions the F W H M was just under 3 pixels, and since the transformation is dominated by a small linear offset meaning that curvature is not a problem. Otherwise, for each image the photometry steps from Section 3.5 were repeated. The new photometry lists, containing the artif ical stars, are then matched to the artif ical star catalogue, and statistics were gathered on whether the star is recovered and what its recovered magnitude is for each filter and frame. In Figure 4.4 the global incompleteness level is plotted as a function of posit ion. The spatial scale is identical to Figure 1.1. One can see that each of the four pointings has a different incompleteness level, which is due to changing seeing conditions, and that F ie ld 3 had more observations that any other field and hence detected fainter stars. Since no bounds have been placed for selection cr i t r ia, the number of stars increases towards fainter magnitudes, as there is a larger populat ion of low mass stars compared to high mass stars (a product of the I M F ) . Thus, plott ing al l statistics for the global incompleteness simply reflects different detection thresholds for each set of observations and does not reflect the global C-star incompleteness level, as wi l l be discussed in Section 4.7. 4.4 Star Counts In Figure 4.3, the spatial distr ibution of stars is relatively uniform. Th is is different from what is observed in star count distributions for M 3 1 , as presented in Figures 2 and 3 of Ferguson et al . [17]. M31 , like the M i l ky Way, has dwarf spherical companions, and their presence can be detected by streams of stars sharing common orbits. In the Chapter 4. RESULTS 4 5 0 1 h 3 6 m 3 5 m 3 4 m 3 3 m 3 2 m 31 Figure 4.4: Th is figure shows the relative completeness map for the al l areas of observa-tion. Since no magnitude bounds have been selected for completeness calculations this diagram shows which regions reveal fainter stars. F ie ld 3 (bottom left) has more obser-vations that other regions, such as F ie ld 2 (upper right) and has a higher completeness level. Chapters RESULTS 46 M i l ky Way there is the Sagittarius Dwarf Galaxy, which is currently being sheared apart through gravitational interaction with our Galaxy. Mapping the spatial distr ibut ion of evolved stars, such as C-stars [42] or R R Lyrae type variables [43], reveals t ida l tails from the Sagittarius Dwarf. Streams have also been observed for globular clusters such as Pa l 5[44]. Thus, if M33 has unseen companions their presence could be betrayed in a complete star map by selecting specific stellar populations. Figure 4.3 does reveal the extensive disk structure of M33. The V-band image in Figure 1.1 shows very detailed spiral arms for the inner region of M33 which appears completely black in the star-map because of the large stellar density. V isua l examination of the raw star map for M33 does not reveal any obvious pertu-bations. However, if accreted satellites do not have a luminous stellar component [45] [46] their presence could be hidden in stellar density maps. A more detailed exercise is to examine distributions of specific stellar populations that represent different epochs of star formation, tracing the dynamical history of the galaxy through perturbations on the stellar populat ion. To do this, we need to examine the colour-magnitude diagrams of M33 and identify relevant populations. 4.5 Colour-Magnitude Diagrams In Figures 4.5 and 4.6, calibrated colour-magnitude diagrams (CMDs) for V versus V - I and I versus V—I are presented for al l stellar objects from our survey wi th errors in the colour term less that 0.05 mag. The upper value chosen for this stringent error cut is arbitrary and chosen to clean up scatter in the diagrams and aid in the identif ication of important features in the C M D . In Figure 4.6 the magnitude l imit of V=23.5 is an artifact of the choosen error cut. The lack of faint stars blueward of V—1=1.4 is due to the addit ional error cut in the I-band. The M S , super giant branch ( S G B ) , R G B and Chapters RESULTS 47 A G B are al l visible. In Figure 4.6 the main sequence is seen as a strong vertical band between —0.5 ^ V—I ^ 0.35. This represents young, luminous blue stars and provides a tracer of very recent star formation. Using Padova theorical isochromes[47] for a young stellar populat ion (age of 6.310 x 10 7 yr) and adopting a distance modulus of 24.64[48] gives a mass of approximately 5.8 M 0 at V=22 for a stellar populat ion wi th Z=0.008. The large number of M S stars is no surprise, as the spirals arms in M33 are undergoing star formation. The width of the main sequence is due to reddening and stellar evolution. Dust extinsion wi l l shift the observation of a star dimmer and redward. The red S G B is seen as a band of stars extending to V ~ 19 mag,V—I ~ 2 mag out from the R G B which is seen as a large clump centred at V ~ 22.5 mag and V—I ~ 1.5 mag. The A G B populat ion, where C-stars wi l l be found is the band of stars wi th V—I ^ 2 mag and V ^ 21 mag. The red edge of the R G B can also be seen, that separates it from the A G B at V—1=2.5 mag. Foreground contamination from stars in our Galaxy is seen as a vertical sequence at V—I ~ 0.8 mag extending up to V=15 mag, the saturation l imi t of the detector. A C M D is a very useful tool for isolating specific stellar populations as wi l l be seen in Sections 4.5.1 and 4.6.1. The distr ibut ion of stars on the C M D s is a result of star formation, stellar evolution and extinction. The effects of star formation and stellar evolution are observed through the presence of very young O B stars and older R G B and A G B stars. Th is tells us about the star formation history of the galaxy. Ext inct ion has the effect of blurr ing the C M D by shifting observations dimmer and redward. Since the amount of extinction is dependent on the line of sight, two stars with the same intrinsic luminousity and colour can appear at two different locations in the C M D . Ext inct ion wi l l occur from both sources local to M33 and to the M i l ky Way. The mean values for lines of site internal to the M i l k y Way are Av — 1 mag, Aj = 0.43 mag, Ey-i = 0.57 mag [2]. M33 wi l l have similar internal reddening values. Correct ing for reddening within M33 is difficult as there is also a depth Chapter 4. RESULTS 48 effect depending on the location of the star in the galaxy (i.e. is it in front or behind a cloud?). To extract the star formation history, a statistical approach could be used to synthesise stellar populations assuming an I M F , theoretical isochrones and metall icity. The idea is to attempt to create a synthetic C M D that matches the observations[49]. A unique solution is not possible due to non-uniform reddening, reddening-metall icity degeneracy, blending, foreground contamination and various observational constaints. 14 Foreground 16 20 22 18 MS 24 0 2 4 V - I Figure 4.5: Colour magnitude diagram for I versus V—I for al l stars wi th errors less than 0.05 magnitudes in V—I. The major stellar populations are also indicated as described in the text. Chapter 4. RESULTS 49 Figure 4.6: Colour magnitude diagram for V versus V—I for al l stars wi th errors less than 0.05 magnitudes in V—I. See Figure 4.5 for identification of the stellar populations. Chapters RESULTS 50 4.5.1 C M D selected Star Counts The substructure of halos and disks of nearby galaxies contains clues about hierarchical galaxy formation. State-of-the-art simulations [50] [51] show that accreted sub-halos last much longer than previously thought, with the central core lasting several t idal timescales [52], and several hundred cores could reside in galaxies like the M i l k y Way[17] and M33 . W i t h the wide field of view provided by the CFH12k detector, nearby galaxies in the Loca l Group can be directly and uniformally sampled with only a few pointings. Our survey data allows us to select specific stellar populations over most of the galaxy's disk. The observed M S reflects recent star formation since the M S lifetimes for the massive and luminous stars is short (under 1 Gyr ) . M S stars were choosen as stars wi th V—I colours less than 0.35 mag. The resulting distr ibution is shown in Figure 4.7. Th is map is similar to H a images, since young stars are the source of such emission. As should be expected, the spiral arm patterns seen in Figure 1.1 are also well traced by luminous M S stars. Figure 4.8 is a binned map of stars with 15 mag < V < 22 mag and have been incompleteness corrected using the data from Section 4.3. This map shows al l M S stars wi th masses greater than 5 . 9 M 0 and the major spiral arms of the galaxy are well traced. The centre of the galaxy appears as a hole, as stellar crowding is too great to allow reliable detection of any stars in the region. The application of stellarity cuts el l iminated al l detections in this region of the galaxy. This tells us that P S F fits d id not work well as most stars are blended. The same exercise can be applied to the S G population. S G stars were identified by selecting al l stars with a V—I colour greater than 1.2 mag and having a V magnitude less than 21.75. Faint stars are excluded to avoid R G B s at the base of the R G B clump. S G distributions are shown in Figures 4.9 and 4.10. Like the M S stars, the S G populat ion is relatively young and wi l l trace out stellar populations with ages less than about 1 Gyr . Chapters RESULTS 51 The S G map suffers from foreground contamination by M-dwarfs, seen as a scatter of stars over al l observed fields, but the galaxy is st i l l identifiable. The S G populat ion is largest in areas containing the most M S stars. Th is occurs because both groups of stars have similar ages and the M S lifetimes are longer than stars found in the S G phase. Bo th the S G and M S maps (Figures 4.7 and 4.9 trace out a high density structure that almost encloses the centre of the galaxy. This feature starts on the east side of the galaxy extending south of the galaxy's centre and then to the west of the galaxy where it then sharply turns eastward toward the galaxy centre and then blends into two spiral arms that extend northward. The structure is not as clearly visible in the binned, incompleteness corrected maps. They show that the high-density structure of young stars is much more extended wi th a deficiency of stars on the east side of the galaxy. Th is is due to extinction internal to the galaxy. M33 has a slight t i l t (i.e. it is not directly face on) so light coming from the farther part of the galaxy has to travel through more interstellar medium than stars on the near-side. Thus, the west side of the galaxy is closer to us than the east side. The same conclusion can be reached by observing the edges of the disk, which represent extremes in distance travelled. The near-side of the disk shows a disk that extends to further galactocentric distance than the far side where the disk appears truncated. A G B populations have characteristic ages of 1—10 Gy r and represent an older pop-ulat ion. The A G B populat ion consists of helium shell-burning stars and are easily rec-ognized in colour-magnitude diagrams by their large luminosities. In coeval populations the positions of A G B stars appears as a curved line extending from the H B , that runs approximately parallel to the R G B . The spatial distr ibution of A G B stars is shown in Figures 4.11 and 4.12. The pop-ulat ion shows a smooth distr ibut ion of stars compared to the clumpy distr ibut ion of M S stars. Th is is due to the greater age of the stars. Star formation is observationally known to be clumpy in nature. M33 itself shows many localized regions of massive star Chapter 4. RESULTS 52 Figure 4.7: Surface density map of Ma in Sequence stars across the survey area. A l l stars wi th V—I < 0.35 are plotted. The centre of the galaxy appears to have few MS-stars because of incompleteness due to stellar crowding. Chapter 4. RESULTS 5 3 0 1 h 3 7 m 3 6 m 3 5 m 3 4 m 3 3 m 32 31' Figure 4.8: Binned surface density map of Ma in Sequence stars across the survey area. A l l stars wi th V - I < 0.35 are plotted and 15 < V < 22. Th is map has been incompleteness corrected. The density scale is log e(number of stars per square arcsec). Chapter 4. RESULTS 54 Figure 4.9: Surface density map of Super Giant stars across the survey area. A l l stars wi th V - I > 1.2 and V < 21.2 are plotted. The centre of the galaxy appears to have few S G B stars because of incompleteness due to stellar crowding. Chapters RESULTS 55 Figure 4.10: Binned Surface density map of Super Giant stars across the survey area. A l l stars wi th V - I > 1.2 and V < 21.75 are plotted. Th is map has been incompleteness corrected. Density scale is log e(number of stars/ square arcsec). Chapter 4. RESULTS 56 bir th, such as the gas complex N G C 604. Over time, the new stellar association wi l l dis-perse. Thus, the distr ibut ion and structure of M S stars wi l l appear much better defined compared to the A G B stars. The A G B star map does not show any extended stucture apart from gently tracing out the spiral arms. A t semi-major radi i larger than 30', the A G B populat ion of M 3 3 is lost due to foreground confusion from red dwarfs from our Galaxy. Just as wi th M S stars, incompleteness is strongest towards the centre of the galaxy, creating the hole in the galaxy. 4.6 Co lou r -Co lou r Diagrams The broad-band photometry can be combined wi th the narrow-band photometry to iden-tify A G B stars, as discussed in Section 1.4. This allows a discrimination of spectral types, namely C-stars and M-stars. Figure 4.13 shows the colour-colour diagram for the entire M33 field. The carbon stars, which have strong C N absorption bands appear as an isolated group wi th an average C N - T i O index of 0.5. The M-stars, wi th strong T i O absorption bands, tail-off from the R G B population at approximately V—1=2 towards redder colours or later spectral type. There is a difference of about 1 magnitude between the C N - T i O index values of C-stars and M-stars, and many C-stars are visible in M33. The C N and T i O filters appear to do a very good job selecting A G B types. M31 has a distance modulus of 24.47[53] and M33 has a measured distance modulus of 24.64[48]. The 1 o errors in the measurements are approximately ± 0.15, thus, to wi th in 2 o M31 and M33 are at the same distance. To define the selection boxes for choosing M-stars and C-stars, the cr i t r ia of Brewer[12] are adopted directly. App l ing smal l reddening and distance corrections to the C / M - s t a r cr i t r ia w i l l not change the results significantly. The relavitive number of C to M-stars is one of the main quantities Chapters RESULTS 57 03 01 00 LC OS OC 0£ Figure 4.11: Surface density map of A G B stars across the survey area. A l l stars wi th V—I > 2.0 and 19 < I < 21 are plotted. There are instrumental artifacts towards the center of the galaxy due to incompleteness. This can be corrected for when measuring the stellar density as seen in Figure 4.12 Chapter 4. RESULTS 5 8 Figure 4.12: Surface density map of A G B stars across the survey area. A l l stars wi th 4.0 > V—I > 2.0 and 19 < I < 21 are plotted. This map has been incompleteness corrected. The density scale is log e(number of stars per square arcsec). Chapters RESULTS 59 we are interested in , thus as long as the selection cr i t ia are consistant the relative numbers should be unaffected. C-stars are identified wi th C N — T i O > 0.3 and M-stars wi th C N — T i O < 0.2 and both types must have V—I > 1.8. These were originally chosen by spectrally identifying C and M-stars and selecting colour values that encompassed C-stars without contamination (see Brewer, 1995 ch. 7 for details). The V—I colour provides a temperature discriminator, allowing M S , A G B , R G B and S G B stars to be distinguished. However, C and M-stars are both A G B members and have the same temperature range, thus the group is degenerate using solely a V—I colour. However, the C N — T i O filters are able to classify M stars and C-stars in the A G B , but al l other stellar types give a C N — T i O index of 0. Using the two filter indices, C-stars and M-stars are easily classified. Figure 4.14 shows a colour-magnitude diagram for al l C-stars selected using the adopted cr i t ia. The completeness l imit wi l l be discussed later in this section. A s ex-pected, these stars occupy the A G B branch location of the C M D . The C-stars are also well constrained by their I-magnitude, which is useful for el iminating foreground contam-ination in the selection of M-stars. The foreground contamination of C-stars from the M i l ky Way is unimportant, which has a surface density of only 0.019 deg~ 2 [54] down to V=18. However, the M-star population wi l l suffer strong contamination from the M i l k y Way. N G C 6822 (at b=-18°) was observed to have approximately 9000 foreground stars over a 28x42 " field of view[55]. M33 (b=-31 c), while at a higher galactic lat i tude, w i l l st i l l suffer a substantial M-star foreground contamination (see Section 4.6.1). Contami-nation from n o n - A G B members within M33 is not a serious problem, as members of the R G B and S G B populations wi l l not have strong C N or T i O absorption bands. However, choosing an I-band magnitude cut wi l l l imit foreground contamination and contamina-t ion from n o n - A G B stars in M33. Using Figure 4.14, C-stars and M-stars also have I magnitudes between 18.5 and 21. These values were choosen to enclose a majori ty of the detected C-stars, wi th out straying far below the 100% completeness l imi t . To quickly Chapter 4. RESULTS 60 estimate the completeness l imit in the I-band, the raw luminosity function, shown in Figure 4.15, was used. The number of stars rises approximately l inearly towards fainter magnitudes, unt i l approximately 1=22 mag, when the number of objects quickly declines as the detection l imit is reached. The number of stars should continue to increase, as dictated by the I M F and shown observationally by deeper surveys[56]. C—stars V-I Figure 4.13: Colour-colour magnitude diagram for C N - T i O versus V - I for al l stars wi th errors less that 0.05 magnitudes in C N - T i O and V - I . Th is diagram clearly differentiates between C-stars and M-stars. Chapter 4. RESULTS 61 Figure 4.14: Colour-magnitude diagram for all C-stars. The 100% detection completeness l imit is also shown. Chapter 4. RESULTS 62 Figure 4.15: Luminosi ty function for al l detected objects, an estimation of the completeness l imit. The turnover at 22.5 mag gives Chapters RESULTS 63 4.6.1 Co lou r -Co lou r D iag ram Selected Star Counts As a continuation of Section 4.5.1 we can now examine the A G B stellar content of M33. Figures 4.16 and 4.17 show the spatial distr ibution of C-stars in M33. The distr ibut ion of C-stars traces out the extent of M33's disk very well, as there is very l i t t le foreground contaimination. The distr ibution is also very smooth. V isua l comparison of Figure 4.16 wi th the M S map in Figure 4.7 shows that the C-star distr ibution exhibit some spiral structure. Th is is not unexpected, as the C-star population represents older stars that were produced in sprial arms just like the current populat ion of young stars. Their velocity dispersion as well as differential galactic rotation has slowly begun to smooth out the older populat ion. There is no evidence of t idal disruption within the C-star populat ion, neither is there indication of C-stars originating from a different system, such as the Sagitarius Dwarf Galaxy wi th in the M i l k y Way. The lack of external interactions may be a reason why M 3 3 displays beautiful grand design spiral arms that can be traced from the outer most regions of the disk directly towards the center of the galaxy. M33 is also a disk galaxy without a bulge, and hence there is no evidence for a black hole at its centre. Th is is different from M31 or other galaxies containing bulges, that have black holes wi th masses that correlate wi th the velocity dispersion of the bulge[57], suggesting that galaxy mergers and interactions may be related to bulge and black hole formation. Th is makes M33 an ideal target for morphological comparsion of N-body codes under different galaxy formation and evolution scenarios. Figure 4.18 shows the corresponding M-star distr ibution. It is similar to the C-star distr ibut ion, except that foreground contamination from the M i l k y Way is stronger. None of the star maps show any sign of external perturbations. However, this survey is l imited by the field of view. The structure seen in M31 is in the outer disk. Thus a large survey Chapters RESULTS 64 area would be needed to reveal any companions to M33. The radial distr ibution of stars in a galaxy allows a quantitative measurement of the galaxy's morphology. To extract radial profiles from M33, its t i l t must be taken into account. To do this, shape parameters for M33 from the Th i rd Reference Catalogue of Bright Galaxies (RC3) was obtained from the N A S A Extragalact ic Database ( N E D ) , specifically the length of the semi-major axis and the ratio of the semi-major axis to the semi-minor axis. If M33 was seen face on its shape would be a circle. Ell ipses centred on M33 were constructed wi th different radi i , and star counts were made for each radius using incompleteness corrected C and M-star counts. Figures 4.19 and 4.20 show the deprojected radial profile for M33 for C-stars and M-stars, respectively, in units of log e(number of stars per a r c m i n - 2 ) . To roughly convert from arcminutes to kiloparsecs, one must divide by four. Examin ing the C-star profile, we see that i t is flat from the centre of the galaxy out to 15 arcmin and then the number density of stars decreases out to 50 arcmins. Here the slope changes again, and becomes flat out to approximately 70 arcmin beyond which there are not enough C-stars to provide useful statistics. The M-star profile is qualitatively similar to the C-star profile. The number density of M-stars decreases out to about 20 arcmins from the centre of the galaxy, where the slope decreases and the distrubution drops off. Th is feature can be seen in Figure 4.18 as a separation between the inner and outer disk in the distr ibution. A t 45 arcmins, the foreground populat ion of M-stars becomes dominant, reducing the slope of the M-star populat ion out to the edge of the field of view. The t ime needed for a stellar population to produce the majority of its carbon stars is about 1 Gy r , thus for stellar populations older than this the C / M - r a t i o is independent of the star formation history [6]. Since the ratio of C-stars to M-stars is a tracer of metal l ici ty Chapter 4. RESULTS 65 Figure 4.16: Spat ial map of C-stars. As seen in previous star-maps, incompleteness is strongest towards the centre of the galaxy giving the appearance of a hole. Chapter 4. RESULTS 66 Figure 4.17: Binned surface density map of C-stars. Th is map has been incompleteness corrected. The density scale is log e(number of stars per square arcsec). Chapter 4. RESULTS 6 7 Figure 4.18: Binned surface density map of M-stars. Th is map has been incompleteness corrected. The density scale is log e(number of stars per square arcsec). Chapter 4. RESULTS 68 0 h Q . -4 h -6 r-100 Figure 4.19: Stellar density profile for C-stars in M33. The units of density are loge(number of stars per a r c m i n - 2 ) Chapter 4. RESULTS 69 3 c 0 - 2 ~l T" 0 _i_ i i_ 50 r (arcmin) _i i i_ 100 Figure 4.20: Stellar density profile for M-stars in M33. The units of density are loge(number of stars per a r c m i n - 2 ) Chapter 4. RESULTS 70 the C-star and M-star profiles can be converted into an incompleteness corrected C / M -ratio profile. Before this can be done, the foreground population of M-stars needs to be estimated. It is assumed that the population of M-stars is uniform across the field, then the M-star profile is used to estimate the foreground population. Th is was done by assuming that the slope of the M-star profile remains constant beyond 25 arcmins obeying an exponential disk profile. The foreground M-star population was in this way estimated to be 0.50 ± 0.03 a r c m i n - 2 . Th is gives approximately 2300 foreground M-stars over the F O V . As a check the foreground population can also be easily calculated by counting stars at the perify of the image. A l l M-stars with an R A greater than l h 36m were considered to be foreground M-stars as this area contains few C-stars. The incompleteness corrected stellar density of M-stars in this region was found to be 0.55 a r c m i n - 2 consistent wi th our derived value. Th is is smaller than the number found in front of N G C 6822, but M33 is at a higher galactic latittude. Figure 4.21 shows the C / M - r a t i o as a function of galactocentric radius. The ratio increases to a radius of 12 arcmins and then flattens for the outer regions of the disk. Th is result indicates that the metal l ici ty of the galaxy is high in the centre and low in the outer parts of the disk, wi th a change in the gradient along the way. Th is is consistent with other metall icity gradient measurements. In fact M33 was the first galaxy where the abundance gradient was noticed to steepen in the inner disk[60]. These results are consistant wi th viscous disk formation models that predict expo-nential surface luminosity profiles of spiral galaxy disks[22]. The rotation curves of spiral galaxies show solid body rotation in the inner parts of the disk and flat rotation curves in the outer part of the disk, where the rotation curve is dominated by dark matter. For solid body rotation there is no angular velocity difference between material at different radi i , meaning that there is no viscous drag or turbulent diffusion. In the outer parts of the disk, the opposite is true with the production of radial gas flows. In galaxy formation Chapter 4. RESULTS 71 models, negative abundance gradients are produced[61], the evolutionary effect of rota-tion then smooths the metall icity gradient in the outer disk where the rotation curve is flat. Rad ia l outflows wi l l transfer metal-rich material into metal poor material , and vice versa with radial inflows. This produces a metall icity distr ibution wi th a change in slope where the rotation curve flattens. Examinat ion of the 21cm rotation curve for M33[62] reveals that, in fact, the rotation curve flattens around 10—15 arcmins, consistent wi th our findings. \ 0 . 5 o 0 0 20 40 60 r (arcmin) Figure 4.21: The C / M - s t a r ratio as a function of galactocentric radius. It is also possible to produce a C / M - r a t i o map for the M33 dataset. Th is incom-pleteness corrected map is shown in Figure 4.22. The increase in the C / M - r a t i o wi th Chapters RESULTS 72 increasing radius is apparent, as are two regions with a high value of C / M . The number of M-stars and C-stars drops towards the edge of the disk, thus the error in the C / M - s t a r measurement wi l l be higher in these regions. Figures 4.23 and 4.24 show the associated error and the signal-to-noise ratio (S /N) for each region in the C / M - r a t i o map. The peak in the northern region of high C / M has a S / N less than 3 and its associated error in the ratio is approximately 0.35, making the detection of the peak wi th the used bin size uncertain. The same argument applies to the south-west region of the map. To test whether these features are real the S / N can be increased by increasing the bin size to avoid small number statistics. The C / M - r a t i o map was rebinned wi th an area four times greater. The north and southwest regions each have average C /M- ra t i os of 0.5 and 0.6 ± 0.04 respectively. Other regions around the edge of the disk show C /M- ra t i os no higher than 0.4, thus it appears that the higher C /M- ra t i os are real. These regions could simply mark the outer reaches of spiral arms with lower metall icit ies. Bo th regions do have spiral arm structure within them. These regions could also represent old galactic remnants. Figure 4.25 shows a C M D for a region located at the edge of the visible disk of M33. The stellar populations and features of the C M D s in Figures 4.6 and 4.5 are st i l l visible. However, the C M D does not show any significant differences. A deeper survey is necessary to search for a distinct stellar population in the region, that could consist of an old, low-luminousity stellar population. Figure 4.22 also shows that the C /M- ra t i o is a function of galactocentric radius. Th is gives the galaxy the appearance of being surrounded by a r ing of material wi th a lower metall icity. It has recently been suggested that the M i l ky Way is also surrounded by a r ing traced by stars of lower metallicitiy[21]. As suggested by Ibata et a l . (2003), this feature could be extended spiral arm structure. In galaxy formation simulations the edge of the disk is expected to be young and contain metal poor gas[25]. In M33 , the regions of low metall ici ty also correspond to the edge of the disk, as traced by C-star and MS-star Chapters RESULTS 73 populations. In the M i l k y Way, distanct spiral arm structure has been identified from 21-cm emission[63],[21]. Th is similarity suggests that the M i l k y Way "r ing" is consistent with spiral arms and does not require t idal interaction of dwarf galaxies for its formation. 0.5 Figure 4.22: Spatial map of the C / M - s t a r ratio. 4.7 C-star Luminosity Function This study has identified 7936 C-stars and Figures 4.26, 4.27 and 4.28 show the cor-responding incompleteness corrected luminosity functions (LF) for V , I and bolometric magnitudes. The L F is similar to those observed in other systems such as M31 and the S M C as shown in Figures 1.2 and 1.3. To calculate absolute bolometric magnitudes for Chapter 4. RESULTS 74 Figure 4.23: Spat ial map of the associated error in the C / M - s t a r ratio. Chapter 4. RESULTS Figure 4.24: Spat ia l map of the associated S / N in the C / M - s t a r ratio. Chapters RESULTS 76 1 6 h 18 -> 20 -24 i i i i i L 0 2 4 V - I Figure 4.25: Colour-magnitude diagram for V versus V—I for a 10' box centered at approximately lh35.45m -|-31degl0', near the edge of the visible disk. Chapter 4. RESULTS 77 the C-stars we used a distance modulus of 24.64[48] wi th the bolometric correction (BC) given by Bessel & Wood [64] for M-stars [65]. Mbol =I + BC- 24.64; (4.1) BC = 0.3 + 0.38(V - I) - 0.14(V - I)2. The C-star L F has a narrow peak. This indicates that the C-stars could be good distance indicators as wi th their high intrinsic luminosities they can be observed over large distances, similar to Cepheids. Using evolutionary populat ion synthesis models it is found that for stellar populations older than 1 Gy r , the mean C-star bolometric magnitude wi l l be constant for a wide range of metall icity and star formation histories as shown in Figure 10 of Mouhcine and Lancon[6]. In M33 the average bolometric magnitude is found to be -4.2 mag ± 0 . 1 which is similar compared to M31 or the S M C (both have M b o i = —4.3). When examining studies of carbon stars in the local group, there is a large spread in the measured mean bolometric magnitude for systems wi th well populated L F s there is scatter greater than 0.5 mag. Many of the systems with dramatical ly different L F s are due to a lack of recent starformation retarding the formation rate of C-stars or have a stellar population dominated by current star formation and C-stars have yet to form. Thus, systems such as M31 and M33 have similar L F s which suggests C-stars could be used as potential distance indicators. Ciapfcer 4. RESULTS o • o Lf) I i i i i | r — i i i | i 1 1 1 1 r O O O 25 24 23 22 21 V mag Figure 4.26: Magnitude distr ibution of C-stars for V-f i l ter. Chapter 4. RESULTS o o LO I 1 1 1 1 I 1 1 1 1 I ' 1 1 1 I r 22 21 20 19 18 I mag Figure 4.27: Magnitude distr ibution of C-stars for I-filter. Chapter 4. RESULTS o o If) I i i i i | i i i i | i 1 1 1 1 1 1 1 r O O O M b o l Figure 4.28: Bolometric L F for C-stars. Chapter 5 CONCLUSIONS A N D DISCUSSION 5.1 Data reduction Improvements There are a number of improvements that could be made to the data reduction, the first being a uniform photometry list for D A O P h o t and A L L F R A M E for each science frame. The current photometry database assumes that the double pass detection method using D A O F i n d wi l l find the same stars on al l frames. In practice this is not true, as stars wi th extreme colours may be detected in one filter, but not independently detected in another. Th is is true for A G B stars. The effects on A G B detection are not cr i t ia l , as stars wi th large errors in the measured colour term are excluded from C M D and colour-colour diagrams and it is the stars with extreme colour terms that would be missed by D A O P h o t that would be excluded by error cuts. Another improvement, especially for registration and cross identification of stars wi th positions in the gaps between detectors, would be to transform each C C D mosaic onto a single large image. The in i t ia l difficulties in performing this operation lie in determining the size of the gaps between each C C D and correcting for al l geometric distortions. W i t h al l of the data on a common co-ordinate system, the gap sizes could be determined and a single image could be created from the original mosaic. A more serious problem is that the available computing resources were not capable of handling these extremely large images and the D A O P h o t / A L L F R A M E code does not handle co-ordinates larger than 9999 whereas the single combined mosaic would be longer than 12 000 pixels. Wi thout 81 Chapter 5. CONCLUSIONS AND DISCUSSION 8 2 writ ing the code, it would therefore st i l l be necessary to divide the image into smaller components. 5.2 S U M M A R Y A N D F U T U R E S T U D I E S Using a four-band-pass photometric system, the A G B stars in the nearby, sprial galaxy M33 where classified as C or M-star types. The photometry catalogue allowed an ex-amination of the different stellar populations of M33. M33 has a large number of M S O B stars being produced by current star formation. The extent of the disk and spiral arm structure was shown through examinations of the spatial distributions of M S and S G B stars. The A G B populat ion, being older, is dispersed hiding the spiral arms. A G B stars d id not reveal any smaller galactic companions, such as those found in the local environments of M31 or the M i l ky Way. The phenomena of C-star production has allowed for a study of the morphology and environment of a galaxy wi th a stellar population of intermediate age (a few Gyrs) . Using colour-colour diagrams, the C-star and M-star populations were used to map the C / M -star ratio. The C / M - s t a r ratio is known to trace metallicity, and the C / M - r a t i o profile and C / M - s t a r map were produced. The C / M - s t a r profile shows a metal l ici ty gradient dependant on galactocentric radius. The profile was found to flatten at the same radius at which the radial-velocity profile also flattens. These results are consistent wi th visous-disk formation models where the metall icity gradient becomes flattened in the outer part of the disk as material originating at different ini t ia l radi i become mixed. The C / M - s t a r map shows that the outer parts of the galactic disk are metal poor. Th is can give the appearance to an observer located inside the galaxy that they are surrounded by a r ing of metal poor material. Th is suggests that the "r ing" around the M i l k y Way could be extended disk material and does not need to be a t idal ly distrupted Chapter 5. CONCLUSIONS AND DISCUSSION 83 galaxy. The C / M - s t a r map also shows two regions with an enhanced C / M - s t a r ratio. These regions may be a natural occurance at the end of a spiral arm, or may trace a different underlying population. These regions wi l l require deep follow-up photometry surveys to examine the stellar population to explain the impl ied lower metal l ici ty in these regions. The C-star L F was produced for M33. The shape of the L F is similar to those in other systems such as M31 and the S M C . Stellar populations wi th ages greater that 1 G y r are expected to show C-stars with similar luminosity distributions and hence the mean C-star magnitude could be used as a distance indicator. There are many aspects of M33 yet to be discovered with this data set. The C M D s can be used to estimated the star formation history of the galaxy. The spatial distr ibutions of each stellar populat ion represent different epochs of star formation and can be used to measure the dispersion of stars with time which traces the graviational potential of a galaxy. The C-stars themselves are excellent probes of galactic structure and are potential targets for spectroscopy surveys. Spectroscopic not only gives the radial velocity of the star, but also reveals the chemical contents in its atmosphere. 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