BROADBAND PHOTOMETRIC ANALYSIS OF THE STELLAR
POPULATIONS IN BRIGHTEST CLUSTER GALAXIES OF X-RAY
LUMINOUS GALAXY CLUSTERS
^ 5 A thesis presented to the faculty of San Francisco State University 2 . c ! 4 In partial fulfillment of The Requirements for The Degree
Master of Science In Physics (Astronomy)
by
Yuzo Ishikawa
San Francisco, California
May 2019 Copyright by Yuzo Ishikawa 2019 CERTIFICATION OF APPROVAL
I certify that I have read BROADBAND PHOTOMETRIC ANALY
SIS OF THE STELLAR POPULATIONS IN BRIGHTEST CLUSTER
GALAXIES OF X-RAY LUMINOUS GALAXY CLUSTERS by Yuzo
Ishikawa and that in my opinion this work meets the criteria for ap proving a thesis submitted in partial fulfillment of the requirements for the degree: Master of Science in Physics (Astronomy) at San Francisco
State University.
Joseph A. Barranco Chair of Physics & Astronomy
4 ^ --• Adrienne Cool Professor of Physics & Astronomy BROADBAND PHOTOMETRIC ANALYSIS OF THE STELLAR POPULATIONS IN BRIGHTEST CLUSTER GALAXIES OF X-RAY LUMINOUS GALAXY CLUSTERS Yuzo Ishikawa San Francisco State University 2019 We have analyzed broadband Hubble photometry available to study the brightest cluster galaxies (BCGs) in X-ray luminous clusters of galaxies. 18 cool-core (CC) and non-cool-core (NCC) BCGs span a redshift interval of 0.15 < z < 0.55 and were identified by the Canadian Cluster Comparison Project (CCCP). I used this sample to build an analysis pipeline that reduces photometric data from the Hubble Space Telescope to probe the properties of the stellar populations in the BCGs. We apply the observed colors to constrain the parameters in the simple stellar population synthesis models to produce the best fitting SEDs of the BCGs. By applying variable fit-parameters, we can build radial metallicity and mass density profiles and trace the star-formation histories in the BCG. The stellar mass estimates will allow us to build improved mass profiles of the clusters and probe the evolutionary history of the BCGs and the host clusters. I certify that the Abstract is a correct representation of the content of this thesis. ACKNOWLEDGMENTS First and foremost, I would like to thank my mother and sister for their support. Without their support, I would not be here. I would like to thank all the amazing professors and colleagues at SFSU for reinvigorating joy in doing physics and astronomy. I thank my M.S. advisor, Andy Mahdavi, for providing me the research opportunity, the guidance, and the support for my A AS conference debut. I also want to thank the committee members (Dr. Barranco, Dr. Coble, and Dr. Cool) for their support in allowing me to continue this project. I want to especially thank my mentors at UCB Space Sciences Labora tory, LBNL, and Caltech (Jerry Edelstein, Martin Sirk, Steve Gibson, Andrew Howard, and many others) for providing me with stimulating research opportunities and training me into a scientist, in addition to my studies at SFSU. I am extremely grateful for their guidance. Finally, last but not least, I thank all my friends and colleagues for making my life outside of work/school meaningful and enriching. I look forward to advancing my astronomy career at Johns Hopkins University. v TABLE OF CONTENTS 1 Introduction...... 1 1.1 The universe in a n u tsh ell...... 1 1.1.1 Big Bang cosm ology ...... 2 1.1.2 What is our universe made o f ? ...... 4 1.2 How did galaxies form ?...... 5 1.3 Probing the evolution of galaxy clusters...... 6 1.3.1 Brightest Cluster G alaxy...... 8 1.3.2 Cooling flo w ...... 10 1.4 Goals and ou tlin e...... 10 2 Stellar populations in galaxies...... 12 2.1 Classifying stars: Hertzsprung-Russell Diagram ...... 12 2.2 Light to mass: stellar astrophysics...... 14 2.2.1 Quick derivation ...... 14 2.2.2 Chemical evolution of stars ...... 16 2.2.3 S u m m a ry ...... 17 2.3 Stellar population synthesis (S P S )...... 17 2.3.1 Building model SE D s...... 18 2.3.2 Ingredients for S P S ...... 19 2.3.3 Extracting physical param eters...... 21 vi 3 Observational t o o ls ...... 23 3.1 Interpreting the S E D ...... 23 3.1.1 Cosmic distance ladder...... 23 3.1.2 Magnitude system ...... 24 3.1.3 E xtinction...... 25 3.2 Broadband photom etry...... 26 3.2.1 Photometric filt e r s ...... 26 3.2.2 AB m agnitudes...... 27 3.3 Hubble Space Telescope ...... 28 4 M ethods...... 30 4.1 Data: Target S election...... 31 4.1.1 The Canadian Cluster Comparison Project (C C C P )...... 31 4.1.2 Hubble archival data - M A S T ...... 32 4.2 Photometric red u ction ...... 33 4.2.1 Identifying the B C G ...... 34 4.2.2 A strom etry ...... 34 4.2.3 P hotom etry...... 35 4.2.4 Surface brightness profiles of BCG ...... 37 4.3 SPS analysis...... 37 4.3.1 Ezgal SPS model generator ...... 38 4.3.2 Python SPS analyzer...... 39 vii 5 Results 44 5.1 SSP (single starburst) fitting...... 44 5.1.1 SSP: Surface brightness p rofiles...... 45 5.1.2 SSP: Mass and Metallicity profiles...... 46 5.1.3 SSP: Estimating a g e ...... 48 6 Discussion...... 53 6.1 Error analysis...... 53 6.2 Probing galaxy evolution...... 54 6.3 How good is SPS with broadband photometry? ...... 56 6.4 Implications for future w o r k ...... 57 7 Conclusion...... 59 Bibliography ...... 61 viii LIST OF TABLES Table Page 3.1 (Left) HST as seen from STS Discovery and (right) Cutaway diagram with instruments labeled...... 29 3.2 Relevant instrument characteristics for ACS WFC and WFPC2 Wide- Field. Details can be found in their respective instrument handbooks [26, 3 7 ]...... 29 3.3 HST filter curves. The ACS detector is optimized in the visible spec trum...... 29 4.1 List of the cool core clusters with X-ray properties [22, 2 3 ] ...... 33 4.2 List of the non-cool core clusters with X-ray properties [22, 23] . . . . 33 4.3 HST filters used for each target with properties [24, 37]. Target with ^indicate WFPC2 observation. Filter with t indicate EzGal normal ization...... 36 4.4 EzGal model set parameters used for the Python analyzer. *CSP models were considered if SSP failed. By default EzGal uses Z; conversions to Z@ and [Fe/H] are shown. ^MACSJ0717-3745 and MS0451-0305 did not use zj = 0.5...... 41 5.1 Summary of results. M+^o is integrated mass for r < 20 kpc. rage is median age since starburst at the median formation redshift Zf. . . . 48 ix LIST OF FIGURES Figure Page 1.1 Illustration of the hierarchy of the observed structures in the universe. Images taken from Sloan Digital Sky Survey [40] and Hubble [17]. . . 2 1.2 The matter-energy composition of the A-CDM universe...... 5 1.3 A schematic representation of a “merger tree” depicting the growth of galaxy clusters and their halos as a result of series of mergers. . . . 7 1.4 Galaxy morphology tuning fork. Ellipticals on the left represent galaxies with low SFR, and spirals on the right represent high SFR galaxies. Irregular galaxies do not fall under the late vs. early type classifications...... 9 2.1 Hertzsprung-Russel diagram plots L* vs. T*. Main sequence stars age and enter the evolutionary phase, turning redder and cooler [10]. 13 2.2 A schematic overview of SPS, adapted from Conroy (2013) [7]...... 22 4.1 General flowchart of my analysis...... 31 4.2 Color images of target clusters, taken from HST and SDSS. The BCGs are located near the center of each image. CC are rows 1-3, NCC are rows 4-5...... 43 5.1 Surface brightness profiles of the BCGs (CC are rows 1-3, NCC are rows 4-5) fit with SSP m o d e ls ...... 49 x 5.2 Metallicity profiles of the BCGs (CC are rows 1-3, NCC are rows 4-5) fit with SSP m odels...... 50 5.3 Mass density profiles of the BCGs (CC are rows 1-3, NCC are rows 4-5) fith with SSP m o d e ls ...... 51 5.4 Formation redshift as a function of radius with SSP models (CC are rows 1-3, NCC are rows 4 - 5 ) ...... 52 6.1 (Top left) Calculated M* vs redshifts. (Top right) Known Mwl,20o vs redshift [23]. (Bottom left) Ratio of calculated M* to M w l,200 vs. redshift. (Bottom right) Correlation plot of calculated M* vs M v l,200- Data corresponding to cluster type is color coded: CC (blue) and NCC (red) clusters...... 55 xi 1 Chapter 1 Introduction Throughout human history, the night sky has been a source of wonder and inspi ration. Our ancestors learned to use the stars to track time, to design cities, and to navigate across the Earth. Despite their apparent usefulness, the origins and nature of stars and the Milky Way remained a mystery. We now know that we live in a massive spiral galaxy, which is only one of millions of billions of galaxies scattered across the universe. We have better questions now: How did galaxies form and evolve? How did the universe form? Advances in physics and telescope obser vations has greatly expanded our knowledge; however, the quest for understanding the nature of our universe is far from over. 1.1 The universe in a nutshell Prom elegant star-forming spirals to massive ellipticals, galaxies are not only inter esting to study, but they also play a pivotal role in the formation and evolution 2 of structure in our universe. Figure 1.1 illustrates the hierarchy of structure in the universe. At the smallest scales, we have billions of star systems that make up galax ies. Then, galaxies aggregate into gravitationally bound groups and clusters, which are finally part of even a larger structure forming the large-scale-structure. This hierarchical picture suggests that the building blocks of the universe are galaxies. Thus the study of galaxies lies at the interface of stellar astrophysics, high-energy physics, and cosmology [28] and is directly tied to the study of the universe. Large-scale structure Some solar system Figure 1.1: Illustration of the hierarchy of the observed structures in the universe. Images taken from Sloan Digital Sky Survey [40] and Hubble [17]. 1.1.1 Big Bang cosmology Galaxies are bright, long-lived, and abundant, making them unique tracers of evolu tion of the universe [28], effectively driving modern cosmology. In the 1920s, Edwin 3 Hubble discovered that distant galaxies are receding based on the redshift of their spectra. His data also revealed that more distant galaxies moved away faster than nearby galaxies [16]. This relationship between the recessional velocity v and proper distance D to each galaxy is known as the Hubble Law, shown in Eq.1.1. v = H0(t)D (1.1) Hubble’s observations revolutionized our understanding of the universe in the fol lowing ways: he showed (1) that other galaxies exist outside of our Galaxy, and (2) that the universe is expanding. This meant that the Hubble constant H0(t) is directly related to the expansion of the universe now known as the Big Bang Theory. Around the same time, Einstein’s General Theory of Relativity provided a ro bust framework to describe the relationship between spacetime and matter. The Friedmann-Robertson-Walker (FRW) equation is an exact solution to Einstein’s field equations, which describes a homogeneous, isotropic, expanding universe, shown in Eq.1.2 [36]. The FRW equation provided the Big Bang Theory with a mathemati cally rigorous description in terms of the “stuff” that make up our universe. From this we can predict the past, present, and future of our evolving universe. The FRW-equation here is written in terms of the present-day density parameters by: H 2 = ^0,R a 4 + &0,Ma 3 + ^0,/c® 2 + ^0,A (1-2) 4 where Qo,r is the radiation density, flo,M is the matter (dark and baryonic), f2oi/t is the curvature density, and fio,A is the cosmological constant (i.e. Dark Energy) [36]. This means that the choice of H0 specifies the cosmology as it encodes the expansion history and matter-energy content of the Universe. Therefore, efforts to characterize the makeup of our universe is synonymous to understanding the formation and evolution of the universe. 1.1.2 What is our universe made of? If we look at Figure 1.1, the answer is simple: stars! However, the past 100 years of observations including Hubble’s has revealed more mysteries about the universe. Ordinary visible matter like stars, planets, and gas (what we see in Figure 1.1) make up only less than 5% of the universe. On the other hand, the remaining 95% of the universe is made of the Dark Matter and Dark Energy, the nature of which still remain a mystery. Dark Matter makes up 25% of the universe and dominates the mass content of galaxies. In fact, nearly 85% of a typical galaxy consists of a halo of dark matter, which was discovered by Fritz Zwicky [44] and Vera Rubin [35]. Meanwhile, the even more mysterious Dark Energy drives the accelerated expansion of the Universe [31, 34] and accounts for nearly 70% of the universe. The matter content of the universe is summarized in Figure 1.2. Although our ability to measure the Universe is outright impressive, the values obtained are extremely unsettling. Since current observations and models point to 5 a cold dark matter (CDM) and dark energy (A) dominated universe, the currently favored cosmology is known as the Lambda-CDM (A-CDM) model. Recent mea surements by the Planck survey correspond to H0 = 67.74 ± 0.46 km s_1Mpc_1, O0>M = 0.3089 ± 0.0062, and Q0,a = 0.6911 ± 0.0062 [2]. Figure 1.2: The matter-energy composition of the A-CDM universe. 1.2 How did galaxies form? Introduced by the Press-Schecter theory [33], the bottom-up model is the currently favored model for structure formation. To understand this model, we consider this thought experiment to collapse a blob of matter. In order for the object to collapse, that parcel of mass must be Jeans unstable. There is a relationship between the allowed collapse time and the mass of the object. As long as the Jeans criterion 6 is satisfied, objects that are less massive yet more dense will collapse faster than more massive objects. Thus the monolithic collapse (e.g. a massive clouds of mass collapsing) is less likely to occur. Instead, we have a ensemble of smaller galaxies falling together to form larger ones, which is called the bottom-up or “hierarchical” model for structure formation driven by dark matter. This idea is best illustrated by the “merger tree” in Figure 1.3 [19]. If we trace the “merger tree” towards the present epoch, we find that massive clusters of galaxies are the most recently formed gravitationally bound structures in the Universe, effectively making them the most basic building blocks in our universe [6]. Thus, galaxy clusters can be exploited as precision probes of cosmology [23]. This hierarchical model is strongly supported by many observations and computational simulations. 1.3 Probing the evolution of galaxy clusters One of the primary goals of galaxy evolution studies is to understand how galaxies assembled their stars. Star-formation rates (SFR) and stellar masses. However, the assembly histories of the most massive galaxies not well understood. Cosmo logical simulations of the A-CDM model predict that the evolution of dark matter distributions results from formation of dark matter halos and their mergers. Gas distribution follows the dark matter halo. As soon as the gas (i.e. baryons) be comes dense enough, physical baryonic processes take over, eventually leading to star-formation and other visible processes. This means that regions of high galaxy 7 f formation f Present ------t Figure 1.3: A schematic representation of a “merger tree” depicting the growth of galaxy clusters and their halos as a result of series of mergers. density make them ideal laboratories to study the interations between galaxies and effects on populations. 8 1.3.1 Brightest Cluster Galaxy Many galaxy clusters were first identified by George 0 . Abell via the Palomar Sky Survey. He identified clusters and divided them into “richness” classes based on the number of cluster members [1]. Prom Figure 1.1, we can see different types of galaxies. Galaxies are typically classified by their morphology according to the Hubble Tuning Fork in Figure 1.4. Spirals (late-types) like our Galaxy appear bluer and have higher SFR. Ellipticals (early-types) are redder with lower SFR, often referred to as “red and dead.” Many of these clusters contain cD-type elliptical galaxies at the centers. These galaxies are known as brightest cluster galaxies (BCGs). BCGs are among the largest, brightest, and most massive galaxies in the universe today. Located in the cores of galaxy-rich clusters, BCGs outshine and outweigh (i.e. more dark matter, gas, and stellar mass) other cluster members. The dominance of BCGs means that BCGs will serve as a probes to understanding the global properties of the host galaxy cluster. Also, their luminosity makes them easily identifiable observationally at extremely large distances (redshift), which also means that we can study the evolution of BCGs and the host cluster across the evolutionary history of our universe [21]. On the other hand, BCGs that aren’t yet dominant galaxies in the cluster suggest a recent merger activity, and therefor not completely relaxed. This would mean that BCGs would also reflect the environment of the host cluster [20]. Figure 1.4: Galaxy morphology tuning fork. Ellipticals on the left represent galaxies with low SFR, and spirals on the right represent high SFR galaxies. Irregular galaxies do not fall under the late vs. early type classifications. In addition, BCGs exhibit evolutionary histories different from typical ellipticals, especially in that some BCGs have bluer cores indicating ongoing star-formation. Some BCGs are known to host radio-loud Active Galactic Nuclei (AGN) that con tribute to the feedback processes that counteracts radiative cooling and effectively regulates star-formation in the galaxy [22]. BCGs are ideal laboratories to study galaxy evolution and effectively the evolution of structure in the universe. 10 1.3.2 Cooling flow In general, galaxy clusters are conventionally classified as cool-core (CC) or non- cool-core (NCC) clusters. This classification is marked by the properties of their X-ray emission caused by bremsstrahlung radiation when gas from the intercluster medium (ICM) falls onto a cluster an is gravitationally shocked and heated. CC clusters show strongly peaked X-ray surface brightness and higher X-ray luminosity, while NCC clusters have broader and flatter X-ray profiles [23]. CC clusters also tend to exhibit “blue cores,” which point to the presence of young stars [22].This would mean that the BCGs sitting at the centers of these X-ray luminous clusters will experience unique star-formation histories [3, 22], and therefore become a probe the global evolutionary properties of CC and NCC clusters. 1.4 Goals and outline In this paper, I investigate the properties and evolution of BCGs by studying a small sample of X-ray luminous galaxy clusters both cool-core and non-cool-core clusters. The overarching objective of this project is to perform a photometric analysis of the bright central galaxy using Hubble Space Telescope (HST) images to accomplish the following: 1. dissect the observed light in BCGs using broadband stellar population synthe sis (SPS) technique; 11 2. explore the baryonic properties of the BCG - metallicity, mass-halo relations, and the status of the hydrodynamical properties; 3. probe the galaxy and the cluster’s evolutionary history and constrain the star- formation history of the cluster With the backdrop of the current cosmological theory, I will further explore the physics of galaxies and stellar populations in the next few chapters. In Chapter 2, I will briefly outline the properties of stars and populations of stars to introduce stellar population synthesis. In Chapter 3 ,1 will discuss the observational tools and observables that we must use to deduce the physical properties that are introduced. Specifications of Hubble Space Telescope are also introduced. The second half of the paper will delve into the meat of the analysis. Chapter 4 will explain the methods and analysis used, including a brief exposition of the EzGal model generator. Finally, in Chapters 5 and 6 I will present the analysis results and discuss the astrophysical implications. 12 Chapter 2 Stellar populations in galaxies The light of galaxies (spectral energy distribution) mostly originates from stars. The spectral energy distribution (SED) describes radiation intensity as a function of wavelength. Thus, to characterize the stellar content in galaxies, we must treat the observed SED of a galaxy as a superposition of a population of stars with different properties [39]. In this chapter, I will explore the properties of stars to understand their contribution to their galaxy’s SED and introduce the stellar population syn thesis technique. 2.1 Classifying stars: Hertzsprung-Russell Diagram In principle, measuring the stellar mass in galaxies is simple. If a galaxy is observed to be as bright as 100 billion Suns, then we would expect that galaxy to have a mass 1011 M q . Unfortunately, it turns out that there is a diverse population of stars with different ages, masses, and luminosities that affect the observed SED. 13 30,000 10,000 4,000 T RWCepta* Rig^0 ODt^tb 105 SUPERGiANTS Canopus Bete*geuse O 10* Achefnar 10J § o 'MB HHLyrafr Aldebaran GIANTS O SUBGIANTS 101 102 Sirius B to* Bama Procyon B ID"4 FO GO KO Spectral Class Figure 2.1: Hertzsprung-Russel diagram plots L* vs. T*. Main sequence stars age and enter the evolutionary phase, turning redder and cooler [10]. The diversity in stellar properties can be mapped elegantly onto the Hertzsprung- Russell diagram (HRD). Developed by Ejnar Hertzsprung and Henry Norris Russell in the early 1900s, the HRD plots the luminosity of stars against their temperatures, 14 as seen in Figure 2.1. A variant of the HRD is the color-magnitude diagram, which is based on observables (more in Ch.3). The HRD can be further sub-divided into spectral and luminosity classes. Spectral classes are determined from the ratio of spectral line strengths and are identified by the letters: OBAFGKM [4, 6]. The simplicity of this plot is remarkable as it reveals different the properties and evolution cycles of stars. The most prominent feature is the main sequence, which describe stars like the Sun that spend their lives fusing hydrogen into helium in the core. However, as hydrogen supply is exhausted, fusion in the core is dominated by fusion of heavier elements; this marks the evolution into giants and/or supergiant stars. This evolutionary stage is marked by their departure from the main-sequence, resulting in changes in SED - redder and cooler [4, 6, 38]. 2.2 Light to mass: stellar astrophysics 2.2.1 Quick derivation For physical and mathematical interpretations of the HRD, we need to understand the physics of stars. Stars are to good approximation, perfect blackbodies, which means the Planck blackbody curve describes the radiated spectral energy density at all energies for a given temperature. We define the Planck spectrum in terms of 15 wavelength and the temperature of the star T*: B^’T) = 2-WeMhcjU)-l ^ From Eq.2.1, we can extract the the Wien’s law solution, which relates the peak emission wavelength Apeak to temperature T*: . 2.897729 x 10-3m • K Apeak = ------j ------(2.2) The relationship between B*(A,T*) and Apeak show that bluer (early-type) stars are intrinsically more luminous and hotter than redder (late-type) stars. Then, we may apply the Stefan-Boltzmann law to the result in Eq. 2.2 to relate the luminosity L* and temperature T* to obtain information about the size R* of a star, where <7sb is the Stefan-Boltzmann constant: u = 47ri£<7SBI? (2-3) Finally, we solve the luminosity-mass relation. Assuming hydrostatic equilibrium for a typical main-sequence star, dP = Gm(r)p(r) . . dr r2 16 Using Eq.2.3 and Eq.2.4 we can solve for the mass-luminosity relation of stars given by L* oc M*. For much larger masses, the radiation pressure overwhelms the gas pressure, so we get L* oc M*. This shows that more massive stars are more luminous. Luminosity also provides an insight to the star’s Hydrogen consumption rate, thus the lifetime. Early-types have higher luminosity, so they have shorter lifes pans compared to late-types. So populations of old stars like some galaxies would generally appear redder, while blue colors would indicate a recent history of active star-formation. 2.2.2 Chemical evolution of stars Starlight is produced by nuclear fusion. Main-sequence stars fuse hydrogen, while massive stars and evolved stars fuse heavier elements. This means that chemical abundance is an important indicator of stellar evolution and hence galaxy evolution. In astronomy, elements heavier than hydrogen are considered “metals.” Metal- licity quantifies the chemical enrichment of stars, and is denoted by Z [28]. The Sun’s metallicity is Z q ~ 0.02. Relative chemical abundance to Z q is a common way to indicate metallicity. Traditionally, the iron(Fe)-to-hydrogen(H) ratio [Fe/H] is used. If the element distribution is assumed to follow then we can relate Z and [Fe/H] by [Fe/H] = log 10[Z(r)/ZQ], where [.Fe/H]@ = 0. Stars with different metallicity have unique evolutionary tracks in the HRD, resulting in different mass, temperature, and luminosity properties, which can be exploited from observations. 17 During stellar evolution, metals enrich the surrounding interstellar medium by stellar winds, planetary nebulae, and supernova explosions [39]. In a closed-box model of a stellar population, the metal-enriched gas gets recycled into new stars. Thus, an older population typically has higher metallicity. This model is complicated in the presence of gas flows or differences in the distribution of available masses. 2.2.3 Summary To quickly summarize stellar properties: (1) Early-type ( OBAF) stars are hotter, brighter, and bluer. (2) Late-type ( GKM) stars are cooler, dimmer, and redder. (3) Luminosity correlates with mass. (4) The short lifetime of early-types makes their presence reliable tracers for recent star-formation/star-burst activity. (6) Metallicity affects the observed SED. 2.3 Stellar population synthesis (SPS) Since stars in distant galaxies are not resolvable, we are left to work with the inte grated galaxy SED. Fortunately, many of the fundamental properties of unresolved stellar populations are still encoded in the SED, which means we can still extract them. We can say that the process of characterizing stellar content in galaxies is to deconstruct the observed SED and to map the properties onto a model HR- diagram. The properties of stars (e.g. star-formation history, metallicity, abundance 18 patterns), dust, and interstellar medium, all provide insight into the formation and evolution of galaxies [7]. If the distribution of stars in a galaxy is known as a function of mass, chemi cal composition, and evolutionary age, then we can model the observed SED [39]. Stellar population synthesis (SPS) is a powerful technique that applies stellar evolution theory to model the SEDs of stellar populations (e.g. galaxies), which was pioneered by Beatrice Tinsley [42]. The principal goal of SPS is to extract the physical properties of the stars from observed SEDs by constructing a model SED that best fits the observation. Since the goal of this project is not to provide an exhaustive derivation of SPS, I will give a brief overview key items. Detailed discussions of SPS can be found in dedicated sources [7, 28, 38, 39, 42]. 2.3.1 Building model SEDs The basic idea of SPS is to do the following, as outlined in Figure 2.2 [7]: 1. start with some population of stars defined by some distribution of masses; 2. at r = 0, run the clock forwards in time and let the stars evolve their SED, ac cording to their evolutionary tracks prescribed by the HR-diagram (isochrone); 3. stop the clock at rage and integrate the spectra of all the stars in the population; 4. the product is the final SED of the stellar population of the galaxy. 19 The process described above corresponds to the simple stellar population (SSP), which is the most elementary model describing a population of stars born in the same burst of star formation activity. Despite the simplicity, observations of some star clusters, elliptical galaxies, and some dwarf galaxies have shown SSPs to be the best fit [38]. Thus, it makes the choice of SSPs an excellent starting point for BCGs. Any deviations would suggest a more complex formation/evolution history. It is also possible to model additional complexities into SSPs like star- formation histories (SFH), chemical evolution histories, and dust processes to build a composite stellar population (CSP). 2.3.2 Ingredients for SPS The most elementary SPS model, SSP, takes in 3 basic inputs: stellar evolution theory (isochrones), stellar spectral libraries, and an initial mass function (IMF), as shown in Figure 2.2 [7]. Each of these inputs can also be a function of metallicity. These ingredients are combined in the following way: fssp(t,Z) = J fi,[Tir(M),logg(M)\t,Z}^(M)dM (2.5) summing over all stars with different initial masses M, spectra /*, and IMF For a more complex stellar system, CSPs are combined according to Eq.2.6, integrat ing over age and metallicity, in which P(Z , t — t') is the time-dependent metallicity distribution. If we consider a population with uniform Z, single-burst SFH, and no 20 dust, then CSP Eq.2.6 reduces to SSP Eq.2.5 [7]. rt' —t /» Z m a x / fcsp(t) = SFR(t-t')P(Z, t-t')fssp(t', Z )e -T^ + A f dust(t\ Z) ^jdt'dZ Jt'=o Jz=o V (2.6) 1. Initial Mass Function: The IMF is the initial distribution of stellar masses of a population. We consider three models - Salpeter, Chabrier, and Kroupa. 2. Isochrones: Isochrones specifies the location of a star in the HR-diagram with a common age and metallicity, constructed from stellar evolution theories. 3. Stellar spectral libraries: Convert the output of the stellar evolution cal culations for each Z into corresponding SEDs 4. Star formation history: SFH describes how star formation occurred. SSP assumes a single burst of star formation. A common SFH model is the expo nential relation e~Td^ as seen in Eq. 2.6, in which I will use. Differing SFH models will also contribute to variations in the chemistry. 5. Dust: Interstellar dust is a component of nearly all galaxies, especially in those that are actively star-forming. Dust can both contribute to attenuation and addition (emission) of flux, which may cause biases in observed populations. 21 2.3.3 Extracting physical parameters The SPS models are finally used as a measure of the parameters (M/L ratio, stellar masses, metalliticy, SFH, SFR, etc.) describing the stellar populations. This is achieved by fitting the model SEDs to observed data, typically by minimizing x 2 over a grid of various model parameters. It is important to note that since the shape of the SED is the only thing used to constrain model parameters, the accuracy of the fit depends strongly on the quality and accuracy of both data and model. Given the difficulties in creating an accurate SPS model, it is not surprising that results would vary depending on model assumptions. Stellar mass is the product of the model M/L-ratio and observed luminosity. Specific SFR is the product of the model SFR and mass, obtained from M/L [7]. a IMF Isochrones Stellar spectra Stellar Isochrones IMF a log Z/Z© SFR CT dN/d/W iue .: ceai vriwo P, dpe rm ory 21) [7]. (2013) Conroy from adapted SPS, of overview schematic A 2.2: Figure X(Mm) 22 23 Chapter 3 Observational tools The beauty of astrophysics is our ability to extract complicated physics just from telescope observations. Our basic measurements of the universe reveal to us the positions, motions, and distribution of energy across the electromagnetic spectrum. Despite the elegance, this is not an easy task, since everything we wish to understand about the universe must be deduced from analyses of observational data “using the laws of physics established in terrestial laboratories” [6]. 3.1 Interpreting the SED 3.1.1 Cosmic distance ladder The measurement of starlight is inextricably linked with determining distances [6]. As discussed in Ch.2, stars have intrinsic luminosity L*. However, the observed flux F* decreases with increasing distance D since the energy gets dispersed according 24 to the inverse-square relation F*(A) = L*(A)/47rD2, Distance measurements that exploit this relationship is known as the standard candle technique. For extragalactic sources like galaxy clusters, we must also account for the ex pansion of the universe. According to the Hubble’s law (Eq. 1.1) and A-CDM model, the expansion of the universe imparts a redshift 2 to the observed F(A) by Eq.3.1. If we know 2 then we can derive a distance measurement from Eq. 1.1 to get Eq. 3.2. (3.1) cz = HqD (3.2) 3.1.2 Magnitude system Historically, the apparent brightness of stars are expressed in terms of apparent magnitudes, m*. This system originates from Hipparchus’s, an ancient Greek as tronomer, method based on naked eye observations of stars [6, 4]. Since our eyes have a logarithmic response, we can systematically define m* as follows: — 2.51og10(/*//ref) “f“ ^ref (3.3) where mTef and / ref are the magnitude and flux of a reference. The convention is to use Vega as the standard reference to set / ref such that mref = 0 [6]. The choice of 25 reference is by nature arbitrary, which means we can generalize Eq. 3.3 to Eq. 3.4: ra* = -2 .5 log10 F* + ZP (3.4) 3.1.3 Extinction During real observations, the observed incoming flux are sometimes obscured by things in-between. The resultant change in magnitude is called extinction. For ground-based observations, we account for atmospheric transmission, which can be avoided by using space telescopes like the Hubble Space Telescope. In addition to our atmosphere, astrophysical sources and phenomena (e.g. interstellar medium, intergalactic medium, expansion of the universe) can cause extinction. Thus, these changes in flux must be corrected for by the following: m* — —2.5 log 10 F* + ZP + TiKi (3.5) Ki represent different extinction corrections. Redshift corrections is [4] K — K motion + 2.5 log10(l + Z) (3.6) 26 3.2 Broadband photometry A direct way of extracting the detailed SED is by performing spectroscopy. How ever, photometry is used more frequently due to the abundance and ease of such observations. The use of imaging detectors like CCDs in conjunction with narrow band/broadband filters to measure the apparent brightness of objects in various bands is called astronomical photometry [4]. 3.2.1 Photometric filters Just like how extinction obscures starlight, in practice, the telescope system also affects the observed flux. The detector measures source flux Fx reduced by atmo spheric transmission A\ and instrument efficiency R\, summarized in Eq. 3.7 [4]. (3.7) Most importantly, the flux the detector sees has a limited wavelength dependence that primarily depends on the optics throughput, the detector quantum efficiency, and filters used. Filters are used to extract flux in a certain passband. Thus we are more interested in flux averaged over a standard photometeric band X [4]: Jo” dvSx {v)U (3.8) !X J T A 'S x M 27 A photometric system is a set of well-defined passbands (or filters) used. Each filter is defined by its central wavelength Ac and full-width-at-half-max AA. The standard filter set is the UB VRI photometric filters, which evolved from the 1950s designs that simulate naked eye observations. Advances in filter technology over the decades led to the development of filters with better defined bandpass profiles that probe scientifically interesting wavelengths. For example, the Gunn filters were designed to measure the Balmer jump. This has evolved into the SDSS (u ’,g ’,r ’,i’,z ’) system commonly used today [15]. 3.2.2 AB magnitudes Observations of the same star using different filter sets will result in differing m* measurements. To standardize flux measurements according to absolute (physical) units, the AB-magnitude (ABMAG) system was developed, such that a source with F*tV = 3.63 x 10_20erg • cm-2 • s- 1 • Hz- 1 has m*;a b = 0. ABMAG is defined in Eq.3.9. This makes ZP the same for all filtered magnitudes, and that it is not necessary for arbitrary observation-dependent calibrations, making them truly standardized. I will use the ABMAG system. m*)t, = —2.51og10 - 48.60 (3.9) 28 3.3 Hubble Space Telescope The Hubble Space Telescope (HST) or simply the Hubble is one of the largest and one of the most versatile spaceborne observatories. Launched in 1990 by Space Shuttle (STS) Discovery, Hubble is a Ritchey-Chretien reflector telescope with a 2.4 m primary mirror optimized to observe from the ultraviolet (UV) to near-infrared (NIR). Also, its orbit outside the Earth’s atmosphere allows for high-resolution images that are unparalleled to those of ground-based observatories, leading to many breakthroughs in astrophysics. Since the last servicing mission in 2009, HST has a main suite of four active instruments outlined in Figure 3.1. The instruments used for this project are the Advanced Camera for Surveys (ACS) and Wide Field and Planetary Camera 2 (WFPC2 ), which are optimized for observations in the NUV, VIS, and NIR. ACS is a third-generation instrument with 3 channels: WFC, HRC, and SBC. W FPC2 is a 2nd generation HST instrument with 3 Wide-Field channels and a smaller high- resolution channel; W FPC2 was replaced by WFC3 [26]. The instrument specifica tions are outlined in Table 3.2 [37], and the appropriate photometric filter curves are shown in Figure 3.3. 29 Table 3 .1 : (Left) HST as seen from STS Discovery and (right) Cutaway diagram with instruments labeled. Table 3 .2 : Relevant instrument characteristics for ACS WFC and W FPC2 Wide- Field. Details can be found in their respective instrument handbooks [26, 37] ACS WFC WFPC2 (Wide Field) Field of View 202” x 202” 150” x 150” Plate scale 0.05 x 0.05 arcsec/px 0.1 arcsec/pixel Image format 2 x 2048 px x 4096 px 3 x 800 px x 800 px Spectral response 3500 to 11000 A 1200 to 10000 A Table 3.3: HST filter curves. The ACS detector is optimized in the visible spectrum. 30 Chapter 4 Methods The goal for this project are to develop an IDL and Python pipeline to: 1 . Use Hubble images of the BCGs to perform broadband multi-color photometry 2 . Obtain surface brightness profiles /J,Ax(r) of BCGs for available filters 3. Produce a grid of SPS model predictions f°r different model parameters using publicly available SPS models and model generator (EzGal) 4. Find the best fit model to extract physical parameters: M*, Z, and Zf, The general flow of the analysis is outlined in the flowchart in Figure 4.1. I will give an overview of target selection and initial data reduction, then discuss analysis. 31 r a (1) Photometric Reduction (2) Stellar population synthesis Obtain HST images of target galaxy For each color use the EzGal SPS model clusters from the MAST archives generator to produce a grid of magnitude • Identify BCG core and build surface predictions n'(r, Zf, Z) brightness profiles ji(r) for each color SPS model inputs: (3) Find best model parameters • Star-formation history Fit predicted |i'(r, Zform, Z) to observed Initial mass function (IMF) \x(r) to find the best model parameters • Formation redshift Z /orm Extract the physical parameters • Metallicity Z q M * ( r ) stellar mass Assumptions: E(r) surface density • Conroy 2009 stellar evolution Simple stellar population (SSP) Z ( r ) metallicity • Sal peter IMF Zf formation redshift (age) Figure 4.1: General flowchart of my analysis. 4.1 Data: Target Selection 4.1.1 The Canadian Cluster Comparison Project (CCCP) The Canadian Cluster Comparison Project (CCCP) consists of a sample of 50 clus ters studied in [23] (see also [12, 13, 22]). The galaxy clusters in this selection span a redshift range of 0.15 < z < 0.55. The CCCP was established primarily to study the different baryonic tracers of cluster mass and to explore the insights about the thermal properties of the hot diffuse gas and the dynamic states of the clusters. The CCCP project has obtained hydrostatic mass Mgas and weak lensing mass M wl proxies, and stellar population analysis using spectrscopic analysis [1 2 , 2 2 , 23]. The complete list of clusters studied by the CCCP can be found in [23]. 32 4.1.2 Hubble archival data - MAST For my analysis, I used images observed with the Hubble, since it is the best NUV/VIS/NIR telescope free from atmospheric contamination. Since applying for and obtaining new Hubble observations was not feasible, I used archival Hubble data stored in the Mikulski Archive for Space Telescopes (MAST). MAST is a NASA funded project, operated by the Space Telescope Science Institute, to support and provide a variety of astronomical data archives, and is the primary archive and distribution center for Hubble data [IT]. Since I am using MAST archival data, my analysis depended on data availability. My target selection was based on the following requirements: (1) Data is available on MAST; (2) more than 1 HST filter set data is available for robust SPS fitting (3) the filter data is compatible with publicly available SPS models (details later); (4) targets are not double clusters; and (5) that clusters have a clearly dominant BCG. Requirements (4) and (5) are based off Loubser’s methodology [3, 22], From Figure 4.2 we see that the BCG dominates the cluster in size and luminosity. This leaves with 12 cool-core clusters and 6 non-cool-core clusters to analyze, listed in Tables 4.1 and 4.2. Also listed are published X-ray properties (coordinates, luminosity, and hydrostatic gas mass proxies) and weak lensing mass proxies from CCCP [23]. 33 Table 4.1: List of the cool core clusters with X-ray properties [2 2 , 23] Cluster Name z a 8 Lx m wl Mx moo J2000 (keV) (1014M(7)) (10u M(7)) Abell 209 0.206 01:31:53.42 -13:36:46.3 1.77 ± 0.02 6.8 ± 1.4 1.02 ± 0.02 Abell 383 0.187 02:48:03.33 -03:31:45.1 0.96 ± 0.01 4.0 ± 1.8 0.39 ± 0.01 Abell 611 0.288 08:00:56.96 +36:03:22.0 1.61 ± 0.05 5.7 ± 1.3 0.66 ± 0.05 Abell 697 0.282 08:42:57.29 +36:21:56.2 3.15 ± 0.07 9.7 ± 1.3 1.56 ± 0.03 Abell 1689 0.183 13:11:29.52 -01:20:29.8 4.48 ± 0.02 13.7 ± 2.7 1.27 ± 0.01 Abell 1763 0.223 13:35:18.16 +40:59:57.7 1.91 ± 0.03 10.1 ± 2.5 1.34 ± 0.01 Abell 1835 0.253 14:01:01.90 +02:52:42.7 4.51 ± 0.02 8.4 ± 1.3 1.21 ± 0.01 Abell 2218 0.176 16:35:50.89 +66:12:36.9 1.28 ± 0.02 5.1 ± 1.4 0.72 ± 0.01 Abell 2261 0.224 17:22:27.12 +32:07:58.9 2.59 ± 0.03 12.9 ± 1.6 1.46 ± 0.13 Abell 2390 0.228 21:53:36.82 +17:41:44.7 5.99 ± 0.03 8.6 ± 1.5 1.48 ± 0.01 Abell 2537 0.295 23:08:22.23 -02:11:30.3 1.37 ± 0.03 7.2 ± 1.1 0.86 ± 0.06 MS1455+2232 0.258 14:57:15.05 +22:20:33.2 1.84 ± 0.01 4.2 ± 0.8 0.56 ± 0.01 Table 4 .2 : List of the non-cool core clusters with X-ray properties [2 2 , 23] Cluster Name z a 6 Lx MWl Mx J2000 J2000 (keV) (1014M 0 ) (1014M « ) Abell 2163 0.203 16:15:46.05 -06:09:036 6.45 ± 0.1 9.5 ± 2.5 2.33 ± 0.03 CL0024+1652 0.390 00:26:35.94 +17:09:46 0.34 ± 0.02 9.8 ± 2.7 0.45 ± 0.08 MACSJ0717-3745 0.548 07:17:35.60 +37:44:44 5.55 ± 0.12 16.6 ± 3.4 2.35 ± 0.03 MS0451-0305 0.550 04:54:11.24 -03:00:57.3 3.25 ± 0.12 4.5 ± 1.7 1.03 ± 0.02 MS1008-1224 0.301 10:10:32.52 -12:39:53.1 0.77 ± 0.02 4.8 ± 0.9 0.58 ± 0.04 MS1358+6245 0.328 13:59:50.56 +62:31:05.3 1.19 ± 0.03 5.9 ± 1.6 0.67 ± 0.07 4.2 Photometric reduction Calibrated (CTE-corrected, Drizzle corrected, flat-field corrected) HST .FITS im ages were obtained from MAST, such that special pre-processing necessary for space- borne data has been taken care of [15]. Initial data reduction involvesmy custom 34 IDL program galaxClust.analy. pro to perform astrometry (identify the BCG co ordinates) and photometry (produce surface brightness profiles). 4.2.1 Identifying the BCG Since the targets were filtered to guarantee a bright and dominant BCG, visually identifying the BCG was relatively simple. To ensure that the BCG is correctly iden tified, the approximate pixel coordinates on the images were first visually identified with DS9, an astronomical imaging program. The coordinates were then passed to IDL to locate the exact BCG centroid that utilizes the DAOPHOTS fin d .p ro algo rithm. This algorithm looks for positive brightness perturbations in an image and returns the centroid and flux (counts) of the target. These steps proved to be re liable since BCGs in some CC clusters are known to be displaced from the cluster center (X-ray peak), making the X-ray coordinates in Tables 4.1 and 4.2 difficult to utilize for fully automated centroid-finding. 4.2.2 Astrometry Astrometry exercise was conducted on each image to convert from pixels to observed angular scales 0(x,y) to physical distances (i.e. pixels —>■ arcseconds —► kiloparsecs). To obtain #(X)y), detector plate scale corrections from Table 3.2 were extracted from 35 the .FITS image headers to solve Eq.4.1 and 4.2 for RA and DEC [15]. a(x, y) = a0 + ai&x + a20y (4.1) 6(x, y) = d0 + diOx + d20y (4.2) Using our knowledge that r^pc = 9(x cz r [kpc] — $(x,y )D = ^(x,y)77“ (4-3) ^ 0 4.2.3 Photometry Counts per image pixel are converted into ABMAG according to Eq. 3.4 and 3.9 using IDL routines. However, since Eq. 3.4 and 3.9 are based off the energy flux, they are converted to photon counts by Eq.4.4. rriAB = —2.5 log10(countrate) - ZPABmag (4.4) The zero-point ZP abmag flux conversion values were extracted from the . FITS image header. The key header variables are PHOTFLAM and PHOTPLAM. Prom this we get 36 Eq.4.5 in terms of HST variables. ZPabmag = -2 .5 log10(PHOTFLAM) - 5 log10(PHOTPLAM) - 2.41 (4.5) The broadband Hubble filters used are listed in Table 4.3. By default I chose ACS- WFC data. W FPC2 data was used for Abell 2390 since ACS data was not available. Table 4.3: HST filters used for each target with properties [24, 37]. Target with ^indicate WFPC2 observation. Filter with * indicate EzGal normalization. F435W F475W F555W F606W F625W F775W F814W F850LP Ac [A] 4318 4746 5360 5921 6311 7691 8055 9013 A A [A] 845 1359 1124 1992 1308 1320 1733 1239 Abell 209 X X - X x t X XX Abell 383 - X - X x t XX - Abell 611 X -- x t - XX X Abell 697 X -- x t - - X - Abell 1689 - X -- X t XX X Abell 1763 X - - x t - - X - Abell 1835 ------X t X Abell 2218 XX X - X t X XX Abell 2261 X X - X X t X XX Abell 2390* - - X t - -- X - Abell 2537 X -- X t - - X - MS1455+22 - --- - X t - X Abell 2163 X - - X t -- X - CL0024+1652 X XX - x t X - X MACSJ0717-3745 - - - - X t X - X MS0451-0305 - - X -- X XX MS1008-1224 X -- x t - X - X MS1358+6245 X - X - X t X - X 37 4.2.4 Surface brightness profiles of BCG My IDL program uses the radplotf .pro procedure, which determines the ellipticiy of the target and builds a count vs. isophotal pixel radii map along the semi-major axis. Since surface brightness profiles fi(r) have units of [mag/arcsec2] [4], the counts are converted into ABM AG and divided by the subtended area (arcsec2 per pixel). The steps above are repeated for every filter image available, and the set of /i(r, AA)s will serve as our “observed” SED. 4.3 SPS analysis As discussed in Ch.2 , SPS analysis infers physical parameters from observed SEDs by modeling the SED. SPS models predict the evolution of SEDs as a function of age, SFH, IMF, and metallicity. However, in practice, SPS models are most useful when translated into predictions of observables (i.e. magnitudes). To do this, I use the EzGal SPS model generator [24] to produce magnitude predictions. Then I used my Python SPS analyzer, ezgal_analy2. py, to determine the EzGal predictions that best match observations and to deduce corresponding stellar parameters (mass-to- light ratio, metallicity, mass, and age) as indicated in Figure 4.1. Here I will briefly describe EzGal and then discuss my Python SPS analyzer. 38 4.3.1 Ezgal SPS model generator EzGal is a flexible Python program designed to generate observable parameters [24]. EzGal accomplishes this by assuming a formation redshift Zf (redshift at be ginning of star-formation), calculating a cosmology-dependent luminosity distance, and projecting the SED through appropriate filter response curves to calculate mag nitudes, e-corrections, and /^-corrections. EzGal comes with a variety of filter re sponse curves - including HST filters. EzGal takes in various publicly available SPS models [5, 8 , 25, 30]. Rather than examining all available models, I used the Con roy 2009 (C09) model [8], because it was the most recent model and had the most comprehensive IMF and metallicity parameter selections. Also, other studies have shown that there is a good agreement between different models [24]. By default, EzGal employs a WMAP cosmology; however, I used the Planck cosmology [2]. 1. Calculating magnitudes: EzGal calculates apparent magnitudes, absolute magnitudes, e-corrections, and ^-corrections as a function of redshift. EzGal uses Eq.4.6, to calculate the observed-frame absolute magnitude as a function of 2 and Zf for different filters using standard STScI definitions [24], fZo v H1 + z)puW0- + z),t(z, zj)]R{y)dv' MAB[z,t(z,zf )] = — 2.51og10 fZo v~lR{y)dv (4.6) 2 . Composite stellar populations: Both SSP and CSP models can be gener- 39 ated. CSP is calculated with Eq.4.7 below: (4.7) 3. Mass-to-light ratios and Mass: EzGal uses Eq.4.8 to calculate the rest- frame mass-to-light ratios. The galaxy stellar mass M*iS at z with Zf is calcu lated with Eq.4.8 for a given filter passband F and the corresponding apparent magnitude mZjZf. M* M*[t(z,zf )\ (4.8) LF Zf) 10-OAx(MF[t(z,zf)]-MQ F) (4.9) 4.3.2 Python SPS analyzer The IDL photometric reduction code described earlier packages the surface bright- ness profiles for each filter into a . DAT file, which are then fed into my Python E z G a l wrapper program. I have written a Python wrapper program ezgal_analy2 .py that builds a collection of simulated magnitude predictions for various combinations of SPS parameters, and then finds the model predictions that best fit the observed surface brightness profiles. 40 First, my code selects the target and reads in all the available data files that store the surface brightness profiles. Accuracy of SPS modeling depends on the ability to constrain the predicted SED to match the broadband observations, so it is preferable to process as many filter data as possible. Then I take the one filter data, closest to the V-band, and normalize the EzGal model by the observed filter magnitude with the ezgal.set_normalization() function. The normalization filter is indicated in Table 4.3. This step sets the model prior, which constrains the initial set of probable SEDs at the target’s observed redshift 2 . At this step, I also ensure all calculations are done using ABM AGs with ezgal. set _ab .output (). To model the full SED (i.e. the collection of magnitude predictions for each broadband filter), I feed the EzGal generator with the different formation and evo lution parameters (SPS model, IMF, SFH, Z, Zf, and z). The parameter choices considered are listed in Table 4.4. With these parameters, EzGal will create a stellar population of metallicity Z and IMF that evolves over time from Zf to z according to the input SFH. In the initial analysis, I selected a SSP SFH that models just a single burst of star formation (Ch.2 for details). An advantage in using high resolution HST data of large and bright target is that I am able to build a detailed surface brightness profile. This in turn allows me to perform a more detailed SPS analysis of the target BCG. For each filter magnitude data point in /i(r), I produced a grid of template SEDs using EzGal with the selected model parameters out to a rest-frame radius of 20 kpc. 41 Table 4.4: EzGal model set parameters used for the Python analyzer. *CSP models were considered if SSP failed. By default EzGal uses Z\ conversions to Zq and [Fe/H] are shown. ^MACSJ0717-3745 and MS0451-0305 did not use Zf = 0.5. Parameter Parameter values S P S model Conroy 2009 SFH S S P or C S P * IMF Salpeter Metallicity Z 0.002, 0.0049, 0.0096, 0.019, 0.024, 0.03 [Zq \ 0.11, 0.26, 0.51, 1.0, 1.26, 1.58 [Fe/H] -1, -0.6, -0.3, 0, 0.1, 0.2 Formation redshift zf 0.5*, 0.75, 1, 1.5, 2, 2.5, 3, 4, 5, 7, 10 To find the “best” model I compare the predicted magnitudes against measured magnitudes. Model magnitudes are extracted using ezgal.get_apparent_mags() for each filter of interest. Physical parameters like M/L and M* are extracted with ezgal.get_rest_ml_ratios() and ezgal.get_masses(). I repeated the steps above at each radial step of the surface brightness profiles, iterating for different Z and Zf to build a grid of n(r) predictions. The goal is to find the right Z and Zf. Broadband SED fitting works by comparing a grid of template galaxy SEDs to observational data. Although fittings techniques may vary, x 2 minimization tech nique is most common. Since there are many possible degenerate solutions (i.e. combination of Z and Zf models) that can produce matching magnitudes, I broke down my fitting routine into two loops: find best Z then Zf. First, I loop though the various Zf cases and find the best Z model that minimizes X2(Z) over all observed magnitudes at each radial step r. With this, I build a matrix of “best metallicity” 42 models for different Zf. This means I compared all possible magnitude predictions for different metallicity models with observed data and chose the one that minimized the reduced x l over all filter data. The model that best match all filter observations, corresponds to the best SED. The x l is calculated by Eq.4.10, in which //(r, Z, 2/)data,F is the observed mag nitude and /i(r, Z, -2/ ) modei,F is the predicted SPS magnitude for N filters, aj is the error in the measured flux. Since we are working with HST data on a relatively bright source, this value is small. The degree of freedom is defined as, v = n — m. (4.10) F= 1 Since a SSP model assumes the same Zf for the entire population, I then take the average x 2 °f all Z models for different zj and choose the model that minimizes X 2(Z, Zf). With this, I can build model radial surface brightness, metallicity, and stellar mass profiles for a given formation redshift, which will allow me to probe the properties and evolutionary histories of the BCG. Figure 4.2: Color images of target clusters, taken from HST and SDSS. The BCGs are located near the center of each image. CC are rows 1-3, NCC are rows 4-5. 44 Chapter 5 Results The highlight of this project is that I now have a successful IDL-Python pipeline that reduces Hubble data to produce radial surface brightness profiles and performs stellar population synthesis fitting to produce M/L-ratio, mass, and metallicity relations assuming a single-burst SSP model. A multi-burst CSP model (no dust) was attempted, but was not successful. 5.1 SSP (single starburst) fitting As discussed earlier, SSP is the simplest case with a single burst of star formation activity, making it a good starting point for SPS modeling. The SSP fitting is pri marily constrained by metallicity, and formation redshift (i.e. time since starburst) provides a secondary constraint. Thus the choice of the “best” SSP model is very sensitive to metallicity. This means that it is valuable to compare the fi(r) fit to the corresponding Z(r). 45 5.1.1 SSP: Surface brightness profiles In Figure 5.1,1 have the surface brightness profiles for the BCGs studied. Each data point represents an observation by the HST filters. Each filter data is color-coded to from violet/bluer to red following the colors in the visible spectrum (F435W is violet and F850LP is dark red). Overplotted on the data points are the best SPS SSP model fits in solid lines. Elliptical galaxies in general have red colors, which would indicate a stellar pop ulation dominated by old, metal-rich stars [28]. BCGs is a type of elliptical galaxy, so we would expect our results to follow this textbook definition. Looking at /x(r) for both CC and NCC clusters, we see this prediction confirmed, in which flux from redder filters (e.g. F850LP, F814, F775) appear much brighter. From Figure 5.1, we immediately see that the ability to find the best fitting SPS model depends on the alignment of the fi(r) for each different filters and accounting of the background. If the BCG centroids observed at slightly different coordinates, then the ratio of the broadband filter flux (i.e. color) would differ and would point to a completely different SPS model. Although I tried a careful treatment of the filter data, the presence of satellite galaxies like in Abell 209, 697, 1689, and 2218 made alignment tricky for CC clusters. Also, CC BCGs with broad or complex core features like Abell 383 and 2261 has added difficulties. Abell 2261 is known to have a complex core with 4 bright knots, which complicated the centroid locating [32]. On the other hand, NCC clusters like MS1008-1224 and MS1358+6245 exhibited 46 even more variabilities, in which some features jump out in the blue, indicating a more complex evolution history. Overall, alignment is good to within A r < 1 kpc. As for goodness of fit, we see that if we assume the same Zf for the BCG stellar population at all radii, then we get discrepancies between inner and outer regions. This would suggest the possibility of different epochs of starbust activity, otherwise the ratio of the colors would have been the same. To understand the fit, it is valuable to examine the mass and metallicity relations. 5.1.2 SSP: Mass and Metallicity profiles One of the primary goals of SPS models is to use the observed SEDs to understand how galaxies assembled their stars. This means we want to know the age, mass, and metallicity content of the stellar content. In Figure 5.2, I plot the radial [Fe/H] profile. The conversions to standard Z can be found in Table 4.4. In general, we see that for a given population with the same age, the metallicity relation is fairly flat at all radii with some exceptions. BCG with a high metallicity (i.e. Z > Zq ) maintains the high Z property despite some fluctuations. This flatness appear for both CC and NCC clusters. However, we can see that Abell 1689, 1835, 2390, 2537, and MS0451-0305 show a sharp gradient in the Z(r) profile. The shape of the metallicity gradient is important as it allows us to probe the evolutionary history. We know that a flat Z(r) would indicate dissipationless merg ers, while a steep Z(r) point to major events like a core-collapse or major merger 47 involving high gas fractions [1 1 , 14, 18, 29]. The later is of high interest since CC clusters experience cooling-flows. We also expect massive ellipticals to be more enriched in metals, where the inner regions are more enriched than the outer re gions. This means that inner regions are slightly younger than outer parts [28]. Unfortunately it is hard to identify this slight gradient. In Figure 5.3, I plot the radial stellar mass profile M*(r). A quick comparison of the metallicity and mass profiles in Figures 5.2 and 5.3, we see that the shape of M*(r) follows Z(r). This may not be surprising since there is high correlation between the type of stars available in the population (age) and metallicity. There is increasing observational and theoretical evidence for a correlation between the metallicity and stellar mass of galaxies, reflecting merger histories [9]. In Table 5.1, I have a summary of the SPS modeling using SSP star-formation history. To defined the total BCG stellar mass M*)2o as the integrated mass over the 20 kpc radius. M*i2o showed agreement to other studies [21]. Finally, I calculated the stellar mass fraction in the cluster, assuming the BCG contains all of the stellar mass in the cluster. I took the known weak lensing mass proxies from the CCCP project, and divided the measured M* shown in Table 5.1. We see that M* contributes to less than 1 % of the total mass, and the majority of the mass is in the gas and dark matter. This would suggest that stars is not the main driver of the cluster evolution. 48 5.1.3 SSP: Estimating age The Zf profile is shown in Figure 5.4. We see that the fit is not very good, with large scatter, at times jumping erratically from Zf — 1 to nearly Zf = 10 over a few kpc. To get the effective age since the initial starbust, I took the median Zf value and calculated the difference between the observed age t{z) and formation age t(zf) to get age in Gyr. t(z) was calculated using the online cosmology calculator [43]. Since I assumed a single-burst model, the ages calculated correspond to old, passively evolving clusters. Table 5.1: Summary of results. M*)2o is integrated mass for r < 20 kpc. rage is median age since starburst at the median formation redshift Zf. Cluster Name SFH < Zf > A/*,20 Mt^o/MwL < T'age > SSP/CSP (10n M o ) (%) (Gyr) Abell 209 S SP 2 6.71 0.09 7.938 Abell 383 S SP 2 7.04 0.18 8.146 Abell 611 SSP 4 7.88 0.08 8.845 Abell 697 SSP 2 9.22 0.16 7.161 Abell 1689 SSP 1 5.17 0.05 5.612 Abell 1763 SSP 2 7.70 0.06 7.757 Abell 1835 S SP 1.75 8.0 0.10 7.005 Abell 2218 SSP 1 4.19 0.08 5.691 Abell 2261 S SP 2.5 11.0 0.09 8.413 Abell 2390 S SP 0.75 4.05 0.05 3.957 Abell 2537 SSP 4 8.33 0.11 8.778 MS1455+22 SSP 2.5 8.15 0.19 8.063 Abell 2163 SSP 10 3.35 0.04 10.793 CL0024+1652 SSP 1.25 4.50 0.05 4.496 MACSJ0717-3745 SSP 0.75 4.70 0.03 1.231 M S0451-0305 SSP 4 3.68 0.08 8.470 MS1008-1224 SSP 4 5.64 0.12 6.708 MS1358+6245 SSP 5 5.65 0.10 9.089 49 Figure 5.1: Surface brightness profiles of the BCGs (CC are rows 1-3, NCC are rows 4-5) fit with SSP models i ih S models SSP with fit iue .: ealct poie o h BG (C r rw 13 NC r rw 4-5) rows are NCC 1-3, rows are (CC BCGs the of profiles Metallicity 5.2: Figure log»[Z I(r) (solar mass per kpc*] I(r) [solar mass per kpc2) I(r) [solar mass per kpc*] 0451-0305 S M IKtMttkpc) S1008-1224 M L0415 MACSJ0717-3745 CL0024+1652 radius [kpc) I 1 I’ I’ 2 S135S+6245 M M S 1455+2232 S M 51 52 , ♦*! If inyv radius [kpcj Abell 1763 MS 1455+2232 CL0024+1652 MACSJ0717-3745 MS0451-0305 MS 1008-1224 MSI358+624 5 Figure 5.4: Formation redshift as a function of radius with SSP models (CC are rows 1-3, NCC are rows 4-5) 53 Chapter 6 Discussion 6.1 Error analysis The majority of the work was completed using HST images taken with the ACS WFC detector. Although ACS WFC is one the newer cameras installed, the WFC3 is much newer, which would’ve given us a higher resolution. Nonetheless, since I am working with pre-processed HST data, we can expect the errors in the measured magnitudes to be less than 0 .1 mags. Also, we have filtered the targets to guarantee bright BCGs, so we can expect Poisson noise to be minimal. As is common with other analyses, systematic uncertainty is likley the dominant source of error in this analysis. Despite this, there are some data reductions that I did not do. I did not subtract any background light - either from the intracluster light or from neighboring member galaxies. Although the surface brightness profiles at radii less than lOkpc did not get 54 affected, some clusters (ie. Abell 209, 697, 1689, 2218, and MS1008-1224) showed some member galaxies situated very close to the BCG between 10-20 kpc. These contamination appear as bumps in the surface brightness profiles shown in Figure 5 .1 . Since my SSP modeling determines Zf by weighing all radial data points equally, it is very possible that they would skew the fit. As mentioned briefly, I did not use WFC3 data. Unlike ACS, which is optimized in the VIS, WFC3 has 2 channels to the UV and IR. If I built my observed SEDs from the UV to IR, we can expect the SPS SED fit to be much more robust. Also, since I do not have any IR data, it is likely that the SPS fit is biased against redder and older evolved stars with more complex spectra in the IR. Without IR, I cannot model the absorption and emission caused by dust, leading to an underestimate of stellar mass. However, since BCGs and other ellipticals are known to have less complex structure compared to late-type spiral galaxies, dust contribution may be negligible. 6.2 Probing galaxy evolution To explore the evolution of BCGs, it is valuable to plot the measured parameters with respect to redshift. Figure 6.1 shows 4 plots that plot the measured M*, total mass proxy A / w l ,200 [2 3 ], and the mass fraction M * / M w l ,200 against their observed redshifts. The data points are color-coded to differentiate CC and NCC clusters. Since I only examined 18 BCGs, it is difficult to confirm strong redshift depen- 55 lel2 lel5 1 G 1 2 0.200 - ♦ 1.1 - * 0.175 - ♦ 1.0- ♦ A 0.9 - 0.150 • * o GO * * £ 0.125 - A ♦* £ 0.7 - A 2 A 0.100- ♦ ♦ ♦ z 0.6 - ♦ 4 ♦ ♦ A A 0.075 - A 0.5 - A ♦ A A 0.050 - ♦ ♦ 0.4 - A A ♦ A ♦ 0 3 - 0.025 - 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 Mw l [Solar mass] le l5 Redshift z Figure 6.1: (Top left) Calculated M* vs redshifts. (Top right) Known M w l,200 vs redshift [23]. (Bottom left) Ratio of calculated M* to A / w l , 2oo vs. redshift. (Bottom right) Correlation plot of calculated M* vs Mwl,20o- Data corresponding to cluster type is color coded: CC (blue) and NCC (red) clusters. dent trends. However, if we examine the ovs.2 plot, it appears that BCGs in CC clusters consistently have higher o at low redshifts compared to BCGs in 56 NCC clusters. This may indicate that CC clusters have some level of continued star- formation, most likely driven by cooling-flows [22, 41]. This trend is also seen with M*!2o/-Mwl,20c>vs.2:, which removes the cluster mass dependence. Unfortunately, the sample of CC BCGs only go out to about z — 0.3, we cannot do a comparison at higher redshifts. We can also study the relationship between the stellar mass and the halo mass determined from weak lensing [23]. As seen in Figure 6.1 , we do not see any corre lation between the weak lensing mass and the stellar mass. This may indicate that the changes to the stellar mass content is not driven by the dark matter halo mass, rather it is driven by baryonic processes like mergers, gas-flows, and feedback. 6.3 How good is SPS with broadband photometry? Since SPS is a theoretical estimation of reality, not surprisingly, uncertainties can result from biases from the adopted assumptions for star formation, chemical en richment histories, dust attenuation, etc. Mitchell et al. (2013) showed that fixing metallicity in SED fitting or even using sparsely sampled metallicity grids can in troduce mass-dependent systematics into M* estimates [27]. Surprisingly, the M*)2o estimates in Table 5.1 showed agreement with Lidman (2 0 12 ) [2 1 ], which performed a very comprehensive BCG study. The agreement correspond only to overlapping targets: Abell 209, 1763, 1855, 2163, 2218, 2261, 2390, MS1455+22, MS0451-0305, and MS1008-12. Metallicity values obtained were 57 also in agreement with Loubser (2015) [22], However, almost all of the BCGs did not show agreement in rage. Only Abell 1763 was in agreement. Loubser used spec troscopy to study the BCGs, which may highlight the importance and perhaps the limitation of broadband photometry. Also, Loubser had a more extensive SSP/CSP modeling. Unfortunately, this project did not have CSP modeling. Other studies have also shown that there are fundamental limits to SED fitting, which arises from a degeneracy between stellar age and metallicity. A population of young stars with high metallicity has a SED that is very similar to that of an older population with lower metallicity, which obviously can be problematic. To break this age-metallicity degeneracy, spectral line intensities of H/3 and H7 and metals are used [28]. This project did not make use of narrow band filters. Fortunately, BCGs are essentially massive ellipticals so the likelihood of encountering is lower than probing a starburst galaxy. However, given the unique physics observed at the cores of cool-core clusters, it would have been valuable to apply a more comprehensive study. 6.4 Implications for future work To improve the SED modeling, it would be valuable to take spectra of these galaxies to directly compare against the model SED spectra. Also, it would be valuable to expand the wavelength bands studied to include both the UV and NIR. It would be ideal to expand the BCG target selections, especially at redshifts greater than 58 z = 0.3, so that we may be able to do a more comprehensive study of BCG evolution. One aspect that I did not get to explore in this project is the interaction between star-formation activity and other processes visible in the Radio and X-ray. With X-ray we can study the effects of gas inflow and outflow within the intracluster medium. With radio, we can study how AGN feedback and galactic winds may contribute to the stellar content. Progress in extragalactic astronomy is achieved by obtaining better information from observations using improved instruments and by refining theoretical under standing of the astrophysical processes [39]. There are many questions that are left unanswered. The Hubble Space Telescope has been the most successful astronomical obser vatory for nearly thirty years. The successor to Hubble is the James Webb Space Telescope (JWST), which is a much larger space-telescope optimized in the NIR. Despite years of delays, JWST is planned for launch in mid-2020 and will provide data at even high resolution and probing deeper into the IR. 59 Chapter 7 Conclusion I have built an IDL-Python pipeline that reduces broadband HST data of bright est cluster galaxies in X-ray luminous galaxy clusters. Due to data and analysis limitations, I focused on using ACS WFC data in the NUV to NIR. These clusters are both cool-core and non-cool-core clusters. My Python analyzer performs stellar population synthesis to fit the observed radial SED profiles (broadband magnitudes) with model SEDs to infer their physical parameters. I modeled the SEDs using sim ple stellar population that models a single-burst of star-formation from Zj to the observed z. I produced a series of simulated model SEDs to find the best fitting SED profile with corresponding radial metallicity and stellar mass profiles, which provide probes to the evolutionary histories of the target BCGs and their host clusters. Although the algorithm was successful in finding best fitting SED models, accu rately modeling the metallicity relations was a challenge due to the existence degen erate solutions (i.e. permutations of Z and zf) that produce matching magnitudes. 60 Also, the data, which did not include UV or IR photometry, was not comprehensive enough to accurately model the effect of interstellar dust and the complex spectra of older populations and evolved stars in the AGB branch, which would cause the SPS models to bias younger, brighter, and more massive stars. These issues were not resolved in this analysis. The summary of the results are as follows: (1 ) BCGs in CC clusters tend to show a more complex structure in the radial metallicity profiles, showing gradients in which the core has higher metallicity. (2) These BCGs also showed a sharp increase in surface brightness (and mass surface-density) at all wavelengths in the core, which would suggest the presence of younger population of stars. (3) However, BCGs in CC clusters all showed higher M* compared to those in NCC clusters even at low redshifts z < 0.3, which may point to some level of continued star-formation activity caused by cooling-flows. (4) No correlation between the M wl proxy (halo mass) and M* was observed, indicating M* is driven by baryonic processes. (5) Although M*>2o and [Fe/H] showed agreement with other studies, rage showed poor fit, which would highlight the need for detailed SSP and CSP SED model. Overall, this project has demonstrated that despite their simple morphology resembling typical elliptical galaxies, BCGs are complex objects. 61 Bibliography [1 ] G. O. Abell, H. G. Corwin, Jr., and R. P. Olowin, A catalog of rich clusters of galaxies, Astrophysical Journal Supplement Series 70 (1989), 1-138. [2] N. Aghanim et al., Planck 2018 results. VI. Cosmological parameters, (2018). [3] C. Bildfell, H. Hoekstra, A. Babul, and A. 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