The Pennsylvania State University The Graduate School Eberly College of Science

ILLUMINATING THE STAR CLUSTERS AND DWARF GALAXIES

BY MULTI-SCALE BARYONIC SIMULATIONS

A Dissertation in Astronomy & Astrophysics by Moupiya Maji

© 2018 Moupiya Maji

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

August 2018 The dissertation of Moupiya Maji was reviewed and approved∗ by the following:

Yuexing Li Associate Professor of Astronomy & Astrophysics Dissertation Advisor, Chair of Committee

Robin Ciardullo Professor of Astronomy & Astrophysics

Donghui Jeong Assistant Professor of Astronomy & Astrophysics

Jane Charlton Professor of Astronomy & Astrophysics

Sarah Shandera Assistant Professor of Physics

Donald Schneider Professor of Astronomy & Astrophysics Chair of Graduate Program

∗Signatures are on file in the Graduate School.

ii Abstract

Over the past decade, advances in computational architecture have made it possible for the first time to investigate some of the fundamental questions around the birth and the growth of the building blocks of the universe; star clusters and galaxies. In these stellar and star-forming systems, baryonic physics play an important role in determining their formation and evolution. Therefore, in my research I have explored star-forming systems using high resolution baryonic cosmological simulations and explored the origin of star clusters, anisotropic spatial distribution of satellite galaxies and the effect of reionization on the evolution of dwarf galaxies. Observations of globular clusters show that they have universal lognormal mass 5 functions with a characteristic peak at 2 × 10 M , although the origin of this peaked distribution is unclear. Here I have investigated the formation and evolution of star clusters (SCs) in interacting galaxies using high-resolution hydrodynamical simulations performed with two different codes. I have found that massive star clusters in the 5.5 7.5 range of ∼ 10 − 10 M form preferentially in extremely high pressure gas clouds in highly-shocked regions produced by galaxy interactions. These findings provide the first simulation confirmation of the analytical theory of high pressure induced cluster formation. Furthermore, these massive star clusters have quasi-lognormal initial mass 6 functions with a peak around ∼ 10 M . The number of clusters declines with time due to destructive processes, but the shape and the peak of the mass functions do not change significantly during the course of galaxy collisions. These results suggest that gas-rich galaxy mergers provide a favorable environment for the formation of globular clusters, and that the lognormal mass functions and the unique peak may originate from the extreme high-pressure conditions of the birth clouds and may survive the dynamical evolution. Observations of classical Milky Way satellites suggest that they are aligned in a plane inclined to the Galactic stellar disk, a phenomenon which later became known as the “disk of satellites”(DoS). However, N-body simulations of galaxies predict an isotropic distribution of subhalos around the host galaxy and this discrepancy has been strongly criticized as a failure of ΛCDM. In this thesis, I have explored this highly debated topic by reanalyzing the observations and exploring the satellite distributions

iii in high-resolution baryonic simulations. In particular, I have demonstrated that a small sample size can artificially produce a highly anisotropic spatial distribution and a strong clustering of the angular momenta of the satellites and have shown that the current Milky way DoS is transient. Furthermore, I have analyzed two cosmological simulations using the same initial conditions of a Milky-Way-sized galaxy, an N-body run with dark matter only, and a hydrodynamic one with both baryonic and dark matter, and found that the hydrodynamic simulation produces a more anisotropic distribution of satellites than the N-body one. These results suggest that an anisotropic distribution of satellites in galaxies can originate from baryonic processes in the hierarchical structure formation model, but the claimed highly flattened, coherently rotating DoS of the Milky Way may be biased by the small- number selection effect. Finally, I have investigated the distribution and kinematics of satellites around a large sample of few thousand host galaxies in the Illustris simulation and found that the DoS become more isotropic with increasing number of satellites and no clear coherent rotation is found in most (∼ 90%) of the satellite systems. Furthermore, their overall evolution indicates that the DoS may be part of large scale filamentary structure. These findings can help resolve the contradictory claims of DoS in galaxies and show that baryonic processes may be the key to solve the so-called small scale ΛCDM problems. Additionally, I have also explored the effects of reionization on the star formation histories of dwarfs galaxies, using a cosmological hydrodynamic simulation of Milky Way and its satellite galaxies. I have found that most dwarfs are extremely old systems and star formation is quenched earlier in lower mass galaxies. During reionization, most of the lower mass dwarfs are destroyed while the remaining massive dwarfs become severely baryon deficient. The dwarf galaxies play a very important role in shaping the path of cosmic history, especially in terms of reionization. Observing and studying the ultrafaint dwarfs hold the key to understanding the physics of early universe in great depth.

iv Table of Contents

List of Figures viii

List of Tables xvii

List of Symbols xviii

Acknowledgments xxi

Chapter 1 Introduction 1 1.1 The mysteries above ...... 1 1.2 Star clusters ...... 2 1.2.1 Open Clusters ...... 2 1.2.2 Globular clusters ...... 4 1.2.3 Young massive star clusters ...... 7 1.3 Puzzles of star clusters : Origin of the GCLF ...... 9 1.4 Dwarf galaxies ...... 10 1.4.1 Observations ...... 11 1.4.2 Properties ...... 12 1.4.3 Star formation history ...... 13 1.4.4 Theory ...... 14 1.5 Puzzles of dwarf galaxies : Disk of Satellites ...... 15 1.6 Thesis Outline ...... 16

Chapter 2 The formation and evolution of star clusters in interacting galaxies 17 2.1 Introduction ...... 17 2.2 Method ...... 19 2.2.1 Hydrodynamic Codes ...... 20 2.2.2 Galaxy Model ...... 21 2.2.3 Star Cluster Identification ...... 22

v 2.3 Formation of Star Clusters ...... 23 2.3.1 Starbursts in Interacting Galaxies ...... 23 2.3.2 Initial Cluster Mass Functions ...... 28 2.3.3 Physical Conditions of Cluster Formation and Origin of Log- normal Cluster Mass Functions ...... 30 2.4 Evolution of Massive Star Clusters ...... 35 2.5 Discussion ...... 39 2.6 Conclusions ...... 41

Chapter 3 Is there a Disk of Satellites around the Milky Way? 43 3.1 Introduction ...... 43 3.2 Methods ...... 44 3.3 Results ...... 46 3.3.1 DoS properties with different methods and sample sizes . . . . 46 3.3.1.1 Structural properties ...... 46 3.3.1.2 Kinematic properties ...... 48 3.3.2 Dynamical evolution of satellites ...... 50 3.3.3 Evolution of DoS isotropy in simulations ...... 52 3.4 Conclusions ...... 55 3.5 Acknowledgments ...... 55

Chapter 4 The nature of Disk of Satellites around Milky Way-like galaxies 57 4.1 Introduction ...... 57 4.2 Methods ...... 60 4.2.1 Plane Identification Methods ...... 60 4.2.1.1 Principal Component Analysis (PCA) ...... 60 4.2.1.2 Tensor of Inertia method ...... 63 4.3 Abundance and Spatial Distribution of Satellites at z=0 ...... 64 4.3.1 Effects of Baryons ...... 64 4.3.2 Effects of Sample Size and Plane Identification Method . . . . 66 4.4 Kinematic Properties of Satellites at z=0 ...... 69 4.5 Evolution of Satellites ...... 74 4.5.1 Evolution of Spatial Distribution ...... 74 4.5.2 Evolution of the Kinematics ...... 76 4.6 Discussions ...... 77 4.7 Summary ...... 81

vi Chapter 5 Disks of Satellites around Galaxies in Illustris Simulation 83 5.1 Introduction ...... 83 5.2 The simulation ...... 86 5.3 Satellite Systems in Illustris ...... 86 5.3.1 Abundance ...... 86 5.3.2 Spatial distribution of satellite systems ...... 87 5.3.3 Kinematic properties of satellite systems ...... 90 5.3.4 Evolution of the satellite systems ...... 92 5.4 Discussions ...... 94 5.5 Conclusions ...... 96

Chapter 6 Evolution of dwarf galaxies 98 6.1 Introduction ...... 98 6.2 Method ...... 99 6.3 Results I: Present day properties of dwarf galaxies ...... 100 6.3.1 Abundance of Dwarfs ...... 100 6.3.2 Baryon fraction of dwarfs ...... 100 6.4 Results II: Star Formation History in dwarfs ...... 103 6.4.1 Star formation quenching in dwarfs ...... 105 6.4.2 Age of Dwarfs ...... 107 6.5 Results III: Evolution of the Dwarfs ...... 107 6.5.1 Evolution of the mass function ...... 108 6.5.2 Evolution of the baryon fraction ...... 110 6.5.3 Effect of Reionization ...... 111 6.6 Discussions ...... 114 6.7 Summary ...... 116

Bibliography 118

vii List of Figures

1.1 Open Cluster M25. First observed in 1745, this open cluster lies in the Sagittarius constellation, about ∼ 600 parsecs away from Milky Way and is about 6 parsecs in diameter. It has an estimated age of 90 Myr, the young stars of this cluster is shown as blue points here. Image Credit : Image Jean-Charles Cuillandre (CFHT) and Giovanni Anselmi (Coelum Astronomia), Hawaiian Starlight ...... 3 1.2 Globular cluster M13. First observed in 1714, this cluster lies in the Hercules constellation, about 6.8 Kpc from MW, and is about ∼ 45 5 pc in diameter. The estimated mass of this GC is 6 × 10 M and it is ∼ 11.65 Gyrs old. Image credit : ESA/Hubble and NASA . . . . . 4 1.3 Metallicity distribution of 137 MW globular clusters. The bimodal distribution are fitted with two gaussian curves. Figure credit : Zinn 1985 (original), Harris 1996...... 5 1.4 Luminosity function of globular clusters around Virgo giant elliptical galaxies. The data points represent the GCs in four galaxies : NGC 4365, 4472, 4486 and 4649 and the line is the best fit gaussian curve. Figure Credit : Harris (1991)...... 6 1.5 Young star cluster R136 in the center of a star forming region 30 Doradus (also called tarantula nebulae) in our neighboring LMC galaxy. Credit : NASA, ESA, and F. Paresce (INAF-IASF), R. O’Connell (U. Virginia), and the HST WFC3 Science Oversight Committee . . . . . 8

viii 2.1 The star formation histories of galaxy mergers in both Gizmo (black curve) and Gadget (red curve) simulations. Both simulations show two starburst episodes during the close encounters of the two galaxies, at times ∼ 0.2 − 0.45 Gyr and ∼ 0.8 − 1.1 Gyr, respectively. In order to investigate the triggering source of star formation, we calculate gravitational torques on star forming gas during three star formation peaks as labeled: minor peak 1a at 0.23 Gyr and major peak 1b at 0.4 Gyr during the first close passage, and major peak 2 at 1 Gyr during the final coalescence, and show the results in Figure 2.3...... 24 2.2 Snapshots of the galaxy merger at three different times, 0.40 Gyr, 0.41 Gyr and 0.42 Gyr during the first starburst phase when most clusters form, from both Gizmo (top panels) and Gadget (bottom panels) simulations. The images are projected gas density maps color- coded by gas temperature (the colors from blue to red indicates hotter gas, the brightness from dark to white measures increasing density). The red dots are stars, and the filled maroon circles represent newly formed star clusters. The maroon region in the center of each galaxy indicates overlapping star clusters. The box length is 100 kpc in physical coordinates...... 25 2.3 Evolution of the gravitational torques on the gas particles that eventu- ally form stars during the three star formation peaks, 1a (at time 0.23 Gyr, blue), 1b (at 0.4 Gyr, green), and 2 (at 1 Gyr red), as labeled in Figure 2.1. The solid and dashed lines represent internal and external torques, respectively. Note that during the final coalescence at time ∼ 0.8 − 1.1 Gyr, only internal torque is available...... 27 2.4 Mass functions of star clusters formed at 0.40 Gyr, 0.41 Gyr and 0.42 Gyr during the first starburst phase when most clusters form, from both Gizmo (grey) and Gadget (red) simulations. The total number of clusters in the three snapshots from Gizmo (Gadget) simulation is 158 (170), 171 (221), and 197 (151), respectively...... 29

ix 2.5 Correlation between pre-cluster gas pressure distributions and initial cluster mass functions at 0.40 Gyr, 0.41 Gyr and 0.42 Gyr during the first starburst phase, when most clusters form, from both Gizmo (black) and Gadget (red) simulations. The pressure derived from the observed pre-super star cluster cloud in the Antennae by Johnson et al. (2015) is represented by the blue cross where the error bars reflect the 6 observational uncertainties in cloud mass (3.3 − 15 × 10 M ), radius (24 ± 3 pc) and velocity dispersion (49 ± 3 km/s). The pressures derived from observed star clusters in the Antennae using velocity and radius data compiled in Portegies Zwart et al. (2010) and presented by Mengel et al. (2002, 2008) are represented by blue diamonds. The pressure is expressed as P/k where k is the Boltzman constant. . . . 31 2.6 Evolution of the total velocity dispersion of gas and stars in the central region of one galaxy (5×5×5 kpc3) (dashed) and the entire simulation box (solid) from both Gizmo (black) and Gadget (red) simulations, respectively...... 33 2.7 Probability density function of star cluster mass distribution from both Gizmo (left panel) and Gadget (right panel) simulations at different times, as indicated by the different colors. A Gaussian profile is used as the kernel density estimator. The PDFs are normalized such that the area under each curve is unity...... 35 2.8 The most probable star cluster mass as a function of time from both Gizmo (black) and Gadget (red) simulations. The data points correspond to the snapshot times in Figure 2.7...... 36 2.9 Density of the simulated clusters from both Gizmo (black) and Gadget simulations. The symbols follow the same meaning as described in Figure 2.5...... 37

3.1 A comparison of the DoS structure using different sample size and plane fitting method: “isotropy" (top) as indicated by the ratio between semi-minor and semi-major axes, c/a (c/a = 0 means completely anisotropic planar distribution); and “thickness" (bottom) as indicated by the root-mean-square height of the fitted plane. The plane fitting methods include PCA and TOI with different weight function. The complete sample includes 39 confirmed satellites of the MW (Koposov et al. 2015; McConnachie 2012)...... 46 3.2 Effects of sample size on the anisotropy measurement of a system. The red and blue lines represent the c/a and b/a ratio of the sample, respectively, and the shaded regions indicate the 1σ error bar of the measurements...... 47

x 3.3 Distribution of the angle between the satellite angular momentum and the DoS normal, with their respective error bars resulting from the uncertainties in velocity measurements. Satellites can be considered as corotating on the DoS if this angle is within 45 degrees (pink region) and counter-rotating if they are within 135 - 180 degrees (green region). 49 3.4 Half apex angle of the cone vs. the number of points found in them. We draw random data points from a isotropic point distribution in a sphere and search for clustering within different half apex angle cones in each of 104 trials. The numbers on the contours represent bias parameters. For 11 satellites in a uniform distribution, there is a 6% chance that 6 of them are clustered within 45 degree...... 50 3.5 Positions of 11 classical satellites in galactocentric co-ordinates at the present (left), 0.5 Gyr (middle) and 1 Gyr from now (right), respectively. The solid lines in each panel represent the fitted DoS at that time and the dashed lines represent the r.m.s. height of the plane. The blue shaded region in each panel depicts the present-day DoS. . . 51 3.6 A comparison of the spatial distribution of satellites, as indicated by the “isotropy" c/a, at different redshift between the Hydro and DMO cosmological simulations. We consider three satellite samples: the 11 most massive dwarfs within the virial radius (left panel), dwarfs within the virial radius (Rvir) of the central galaxy (middle panel) , and dwarfs within 1 Mpc from the central galaxy (right panel). Note in this Figure, the “Hydro dwarfs" (in red in all three panels) refers to star-forming dwarfs from the Hydro Simulation within a given distance at different redshift (for convenient comparison, let Nzbar be the number of these baryonic dwarfs at a given z), the “DMO dwarf subsample" (in black in the middle and right panels) refers to a selective DMO dwarf sample which has the same number as that of the Hydro dwarfs, the Nzbar most massive ones from the DMO Simulation at the same redshift and within the same distance considered, and “All DMO dwarfs" (in grey in the middle and right panels) refers to all dwarfs formed from the DMO Simulation at the given redshift. All distances are in comoving coordinates...... 53

xi 4.1 A comparison of the projected positions of dwarfs with total mass 7 above 10 M , as represented by filled circles, in the X-Y plane at z=0 within 1 Mpc from the central galaxy between the hydrodynamical (left) and the dark matter-only (right) simulations. The size of the circle is proportional to the halo mass, and the open circle in the center of the two plots indicates the virial radius of the simulated Milky Way at ∼ 240 kpc at z=0...... 62 4.2 Three-dimensional spatial distribution of satellites (black dots) within 1 Mpc from the central galaxy in the hydrodynamical simulation. The fitted plane of the satellites, using PCA method, is shown as the black plane and the disk plane of the simulated Milky Way is depicted as the brown plane...... 65 4.3 Distribution of the residual distances of the simulated satellites from the fitted DoS plane. The width between the two magenta dotted lines shows the root-mean-square height of the plane, ∼ 145 kpc. . . . 66 4.4 The “isotropy " of the simulated satellite distribution, as indicated by c/a, as a function of the sample size. We have used four samples here with 11, 27, 39 and 106 dwarf galaxies respectively. The different colors denote the different plane fitting methods : Principal Component Analysis (black) and Tensor of Inertia with three types of weight functions, 1 (red), 1/r (green) and 1/r2 (blue)...... 67 4.5 The root-mean-square (rms) height of the DoS plane fitted to a sample of simulated dwarfs as a function of the sample size. We have used the same four samples here with 11, 27, 39 and 106 dwarf galaxies respec- tively. The different colors denote same four plane fitting methods : Principal Component Analysis (black) and Tensor of Inertia with three types of weight functions, 1 (red), 1/r (green) and 1/r2 (blue). . 68 4.6 Comparison of galactocentric velocity between the simulated (blue points) and observed (purple crosses) dwarfs as a function of galac- tocentric distance. The observed data is taken from McConnachie (2012), and velocities are calculated with respect to the Galaxy. The red points are the 27 most massive dwarfs within 257.4 kpc of galactic center from the simulation...... 69 4.7 Distribution of the angle between velocity vector of simulate dwarfs and the DoS plane. The dwarfs whose velocity lies within -45 degree to +45 degree (magenta dotted lines) of the DoS are considered to be moving on the DoS...... 70 4.8 Distribution of angle between angular momentum of simulated dwarfs (residing in the DoS plane) and the DoS normal. There are 18 coro- tating (blue) and 19 counter-corotating (orange) dwarfs...... 71

xii 4.9 Vertical distance of the simulated dwarfs from the DoS vs their pro- jected radial distance (i.e. the distance component lying on the DoS) from the center of the DoS (center-of-mass of the satellite galaxies). The red points show corotating dwarfs and blue points show counter- corotating dwarfs...... 72 4.10 Positions and angular momenta of the observed (red symbols) satel- lites and simulated dwarfs (blue symbols) in Galactic coordinates are projected onto an Aitoff Hammer sphere. The filled circles and triangles represent the positions and angular momenta of the satel- lites, respectively. Satellites can be considered as corotating when their angular momenta are clustered in the same direction. For the observed momenta of 11 satellites, only 6 dwarfs near the center can be considered co-rotating; they are also within 45 degree of the DoS normal (depicted by red circle). Among the simulated momenta, no strong clustering of the majority of dwarfs are observed...... 73 4.11 Spatial distribution of all dwarfs (blue points) within 3 Mpc of Milky Way (comoving scale) at different redshifts, namely z = 10, 6, 4, 1 and 0. The red points are the 27 most massive satellites within 257.4 kpc of the galactic center at z = 0 which were tracked at higher redshifts. The overall distribution of the dwarfs is nearly isotropic at high redshifts but it gradually evolves to be anisotropic with time. . . 75 4.12 Evolution of the isotropy ratio (c/a) of the simulated satellite distri- bution within 1 Mpc. Different colors the figure denote different plane fitting methods : Principal Component Analysis (black) and Tensor of Inertia with three types of weight functions, 1 (red), 1/r (green) and 1/r2 (blue)...... 76 4.13 Three dimensional plot of simulated dwarf positions (blue points), within 3 Mpc of the galactic center, along with the DoS plane (blue plane) fitted by PCA method. The 3D velocities of these dwarf galaxies are represented by the magenta arrows and the length of these arrows is proportional to the velocity magnitude...... 77 4.14 Evolution of the fraction of dwarfs (within 1 Mpc of galactic center) with different kinematical properties : the fraction of dwarfs moving on the DoS plane (black), the fraction of dwarfs co-rotating in DoS (red), the fraction of dwarfs counter co-rotating in DoS (blue), and the total fraction of dwarfs rotating (corotating and counter-corotating) in DoS (magenta)...... 78

xiii 4.15 The c/a ratio (red) and the b/a ratio (green) of the dwarf distribution as a function of the maximum distance of the dwarfs from galactic center. For each distance, we take all dwarfs within that radius and calculate these two ratios using PCA method...... 79 4.16 Distribution of output galaxy c/a for different input values (c/a = 0.4 top left panel, 0.6 in top right panel, 0.8 in bottom left panel and 1.0 in bottom right panel) in a Monte Carlo simulation with 100,000 galaxies. The c/a ratio is calculated by two methods: weighted by 1 (red), and weighted by 1/r2 (blue). The violet region shows the overlap between the distributions with two methods. The dashed vertical lines in red and blue shows the observed c/a value calculated with 11 MW satellites with these two methods respectively. The median c/a values for the systems are shown with vertical red (weight 1) and blue (weight 1/r2) solid lines...... 80

5.1 No. of satellites within the virial radius of the host galaxies vs. their total mass. The host galaxies are divided into ellipticals (red) and spirals (blue)...... 87 5.2 c/a ratio of the galaxy systems (within 1 virial radius) vs the total mass of the host galaxy. The different colors represent hosts with three satellite populations; systems with 10-12 satellites (red), 30 - 40 satellites (blue) and more than 50 satellites (black). The round points indicate elliptical hosts and the cross points represent spiral hosts. The dashed (elliptical) and dotted (spiral) lines represent median c/a values for the three populations (the colors represent the same scheme as points)...... 89 5.3 The median c/a ratio of the satellite systems as a function of the scaled maximum distance of the dwarfs from their host. The symbols and the colors are same as in Figure 5.2...... 90 5.4 Histogram of fraction of satellites corotating on the DoS around the elliptical and spiral host galaxies...... 91 5.5 Fraction of co-rotating satellites on the DoS as a function of number of satellites in the system for elliptical (red) and spiral (blue) host galaxies...... 92 5.6 Median c/a ratio of satellite systems calculated with satellites within virial radii. The error bars are standard deviation of the c/a dis- tribution at each redshift. The different colors represent hosts with three satellite populations; systems with 10-12 satellites (red), 30 - 40 satellites (blue) and more than 50 satellites (black)...... 94

xiv 5.7 Left : Evolution of the c/a of four MW type hosts with satellite systems within their virial radius...... 95

6.1 Histogram of the radial distribution of simulated (blue) and observed (orange) dwarfs (McConnachie 2012). The number of dwarfs decreases with increasing distance from the Milky way center, as seen in both simulated dwarfs and the observed ones...... 101 6.2 Stellar mass of dwarfs vs their total mass. The blue points are simu- lated dwarfs and the orange ones are observed dwarfs (Walker 2009, McGaugh 2009). The black line indicates the the universal baryonic fraction, Mb/M? = 0.17. The dwarfs lie much below this value. The simulated points match closely to the observed ones. The apparent 4 cut of blue ones at 10 M is because of the resolution limit of the simulation...... 102 6.3 Baryon fraction of simulated dwarfs vs their total mass. Observed dwarfs are overplotted in orange. The points have the same meaning and source as in the previous figure. Notice that the baryonic fraction of dwarfs are very low in general, 10−1to10−4...... 103 6.4 The overall star formation rate of the simulation at different redshifts. 104 6.5 We plot the quenched fraction of the simulated dwarfs as a function of 4 5 5 look back time for four different mass groups, M? −10 −10 M , 10 − 6 6 7 7 8 10 M , 10 −10 M , 10 −10 M . The blue lines show the SFH of the simulated dwarfs and the red solid lines are SFH of observed dwarfs (data from Weisz et al. (2015)). The red dashed lines show the 68% confidence interval for the observed dwarf sample...... 106 6.6 Histogram of the lookback ages of the dwarfs simulated here. Most of the dwarfs are old with age > 12 Gyr although there are few which are intermediate aged, around 8 Gyr and still fewer around 1 Gyr. . 108 6.7 Total mass of dwarfs vs their median age plot. The different colors and sizes of points indicate different stellar mass ranges of the dwarfs. 4 5 The maroon points represent dwarfs with M? ∼ 10 − 10 M , orange 5 6 6 7 is M? ∼ 10 − 10 M , purple M? ∼ 10 − 10 M and blue M? ∼ 7 8 10 − 10 M . The larger points has higher stellar mass...... 109 6.8 The total mass function of the dwarfs at 8 different redshifts. At all the redshifts the mass function takes the form of a peaked function but the position of the peak changes from lower value to higher value as redshift decreases...... 110 6.9 Left : The probability density of total mass of the dwarfs at different redshifts. The different colors denote the redshifts here. Right : The most probable mass of the dwarfs as a function of redshift...... 111

xv 6.10 The baryonic fraction of the dwarfs at the same redshifts. The black dashed line in the histograms represent the universal baryon fraction, fb = 0.17 (Planck Collaboration et al. 2014)...... 112 8 6.11 We plot the fraction of small (Mtot < 10 M ) dwarf galaxies (left y axis) and the absolute number of small dwarfs (right y axis) as a function of redshift. Both the numbers (red points) and the relative fraction (blue points) of these galaxies take a sharp downward jump at z=6, around the time reionization ends...... 114 6.12 The total mass of different components (blue lines) trapped in dwarfs (left y axis) against the redshift. The solid blue line denotes the total mass of dwarfs, the dot dashed line shows the dark matter mass, the dotted line is the total gas mass and the dashed line is the total stellar mass in all the dwarfs. All the mass components rises till z 6 and then they decreases, albeit at different rates. We overplot the total number of dwarfs (magenta line) against redshift (right y axis) and find that numbers of dwarfs decrease with redshift after z = 6...... 115

xvi List of Tables

1.1 Comparison of properties of Open clusters, Globular clusters and Young massive clusters. Here, OC - Open Cluster, YMC - Young Massive Cluster, GC - Globular Cluster, M - cluster mass, rvir - cluster virial radius, ρ - cluster density, Z - cluster metallicity and tdyn - dynamical time scale. Table adapted from Portegies Zwart et al. (2010). 3

xvii List of Symbols

Telescopes and Surveys HST Hubble Space Telescope Spitzer Spitzer Space Telescope HETDEX Hobby Eberly Telescope Dark Energy Experiment JWST James Webb Space Telescope DES Dark Energy Survey PISCeS Panoramic Imaging Survey of Centaurus and Sculptor SDSS Sloan Digital Sky Survey PAndAS Pan-Andromeda Archaeological Survey LSST Large Synoptic Survey Telescope Astronomical Observing RA Right ascension Dec Declination IR Infrared NIR Near-infrared UV Ultraviolet λ Wavelength of observation FoV Field of view LOS Line of Sight Star Clusters SC Star Cluster YMC Young Massive Cluster GC Globular Cluster ICMF Initial Cluster Mass Function GCMF Globular Cluster Mass Function M∗ Stellar mass P Pressure

xviii CO Carbon Monoxide GMC Giant Molecular Cloud ISM Interstellar Medium SFR Star Formation Rate SED Spectral energy distribution PDF Probability Density Function

Galaxies

NGC New General Catalogue (of Nebulae and Clusters of Stars) HI Neutral (not ionized) hydrogen atom HII Singly ionized hydrogen atom (H+) MW Milky Way M31 Messier 31 or Andromeda Galaxy LMC Large Magellanic Cloud SMC Small Magellanic Cloud UMi Ursa Minor MN3 Miyamoto-Nagai potential, a potential model for Milky Way DoS Disk of Satellites c/a ratio of minor and major axis of an ellipsoid ΛCDM Lambda cold dark matter cosmology model PCA Principal Component Analysis TOI Tensor of Inertia AGN Active Galactic Nuclei NFW Navarro-Frenk-White profile, a model for the spatial distribution of dark matter. DM Dark Matter BH Black Hole

Codes

SPH Smooth Particle Hydrodynamics AHF Amiga Halo Finder FOF Friends of Friends AMR Adaptive Mesh Refinement DMO Dark Matter Only, also known as N-body simulation

Units of Measure

AU Astronomical Unit pc Parsec Kpc Kilo-parsec, 103 pc

xix Mpc Mega-parsec, 106 pc Gyr Gigayear, 1 × 109 years Myr Megayear, 1 × 106 years M Mass of the Sun kB Boltzmann constant nm Nanometers, 1 × 10−9 meters, typically used for ultraviolet and optical measurements µm Micrometers, 1 × 10−6 meters, typically used for infrared measurements

xx Acknowledgments

First of all, I would like to thank my advisor, Yuexing Li, for her excellent guidance, constant encouragement, ample academic freedom and for teaching me how to be a scientist. I am deeply indebted to you for being so patient and understanding which has helped me through the years to keep a good work-life balance.

To Jane Charlton, thank you for your constant support and all the life advice, you have been an excellent mentor to me. To Robin Ciardullo, Donghui Jeong, Sarah Shandera, Mike Eraculous and Caryl Gronwall, thank you for being such great research mentors, for always being there to answer my questions and for your guidance on navigating life in academia.

To my senior, Qirong Zhu, thank you for teaching me the basics of cluster computing and always patiently answering my questions. To my department friends, Kim, Henry, Mallory, A.I., Michael, Alex and Lea, cheers for making the workplace so much fun and supportive. Through the years of doing homework together, going for outreach in a bunch of far-off schools and the daily sassy grad school banter, it has kept me sane.

To my state college friends, Ahana, Saranya, Sumitha, Manjari, Punya, Rajarshi, thank you for always being there! The endless chats about grad school, love, life, family, philosophy, feminism and politics have been so entertaining and enriching. You have all been so instrumental for my well-being during all these years, and I will always cherish these friendships!

To my parents, Lochan Chandra and Alpana, and my brother Soham, without your unwavering support and constant encouragement I would not have reached here now. Thank you so much for always believing in me! Thank you so much to my aunts and uncles, in-laws, and my mom-in-law for being so supportive through the years.

Last but not least, to my husband, Saswata, for giving me endless support and

xxi love throughout all these years! I cannot thank you enough for believing in me and for giving me endless hope. No matter if we were continents apart, as we were for the first three years, or living only hours apart, you have always been there to cheer me up during my most trying times. I feel so lucky to have you in my life as my life partner.

xxii Dedication

This dissertation is dedicated to my parents Alpana Maji and Lochan Chandra Maji, whose constant encouragement and unwavering support has been the driving force behind this long and arduous academic journey in a land far, far away from home.

xxiii Chapter 1 | Introduction

1.1 The mysteries above

The night sky has fascinated the humankind from time immemorial. We have always been remarkably curious about the twinkling stars and pondered about our place among these celestial bodies. Consequently, astronomy rose as one of the oldest natural sciences. Ancient records of celestial objects and their motions have been found in all major early civilizations, e.g. Indian, Mesopotamian, Greek, Egyptian, Chinese, and Mayan, with some references dating back to as long as 4000 years ago. As time progressed, the study of astronomy evolved from a collection of observations to understanding the underlying physics and chemistry that govern these behaviors. With the invention of Galilean telescope (1609), the modern era of astronomy began. In the early years of 20th century, another breakthrough period of astronomy, the debate about if all observed ‘spiral nebulae’ are part of our own galaxy or if they could be separate galaxies themselves, raged on. Finally, in the aftermath of the great debate in 1920 between Shapley (argued in favor of one galaxy) and Curtis (argued for many galaxies), observations by Edwin Hubble made it clear that the Universe consists of many independent galaxies. In a matter of decades, the horizon of astronomy has broadened exponentially. It was now apparent that groups of stars can be two distinct classes of objects, star clusters and other galaxies, most of whom are dwarfs Mateo (1998). In this thesis, I aim to improve our understanding of a few key issues about the origin and evolution of the building blocks of the universe, star clusters and the star-forming dwarf galaxies. Most of these studies have been performed with computational simulation at different scales - star clusters forming in interacting galaxies (100 Kpc), dwarf galaxies forming

1 in a Milky Way formation simulation (scale ∼ 10 Mpc ) and thousands of galaxies forming in a large cosmological simulation of the observable universe (scale ∼ 100 Mpc). In this chapter, I will give brief introductions on star clusters and dwarf galaxies.

1.2 Star clusters

Stars form mostly in clusters (Lada & Lada 2003; de Wit et al. 2005) and as such, star clusters are considered to be the building blocks of galaxies. These clusters can contain few hundreds to millions of stars in them. They are generally thought to be formed from a single giant molecular cloud, so the cluster members have the same age and similar metallicity. This is a very useful criterion to reliably determine cluster properties, e.g. age, distance, metallicity etc. Studying the star clusters is one of the most important avenues to investigate the stellar birth, stellar evolution and the giant molecular clouds (GMCs) they are often embedded in. They are also excellent tracers of galactic archeology and the oldest star clusters provide important constraints for the formation of the universe itself. Star clusters were traditionally classified into two broad groups: open clusters and globular clusters. Open clusters are loosely bound, have low mass and are very young systems, whereas globular clusters are massive and very old. In the past few decades, observations have found several star clusters in the Milky Way galaxy which have properties at the intersection of these two populations; these clusters are tightly bound, massive and relatively young. These are now referred to as young massive clusters (YMCs). Below, I discuss these three types of star clusters in more detail. The comparative properties of these clusters are shown in Table 1.1.

1.2.1 Open Clusters

Open clusters (OCs) are a collection of a hundred to a few thousands of loosely bound 4 stars (Figure 1.1). These clusters have masses in the range of 50 - 5 × 10 M , with a mean mass ∼ 500M . There are 2,167 open clusters in the Milky Way galaxy according to the latest version (2016) of DAML02 catalog (Dias et al. 2002). The birth rate of these clusters is ∼ 0.2 − 0.5/Myr/kpc2 (Battinelli & Capuzzo-Dolcetta 1991; Piskunov et al. 2006). These clusters are young (age < 300 Myr) with a mean

2 Age M rvir ρ Z tdyn Cluster 3 Location [Gyr] [M ] [pc] [M /pc ] [Z ] [Myr] 3 3 OC . 0.3 . 10 1 . 10 ∼1 Disk ∼1 5 3 GC & 10 & 10 10 & 10 <1 Halo &1 4 3 YMC . 0.1 & 10 1 & 10 &1 Galaxy .1 Table 1.1: Comparison of properties of Open clusters, Globular clusters and Young massive clusters. Here, OC - Open Cluster, YMC - Young Massive Cluster, GC - Globular Cluster, M - cluster mass, rvir - cluster virial radius, ρ - cluster density, Z - cluster metallicity and tdyn - dynamical time scale. Table adapted from Portegies Zwart et al. (2010).

Figure 1.1: Open Cluster M25. First observed in 1745, this open cluster lies in the Sagittarius constellation, about ∼ 600 parsecs away from Milky Way and is about 6 parsecs in diameter. It has an estimated age of 90 Myr, the young stars of this cluster is shown as blue points here. Image Credit : Image Jean-Charles Cuillandre (CFHT) and Giovanni Anselmi (Coelum Astronomia), Hawaiian Starlight age of ∼ 250 Myr. They are usually ∼ parsec across in size and have a typical density 3 of ∼ 10 M . Open clusters are loosely bound by the gravitational pull of its member stars. As they move through the galaxy orbiting around the galaxy center, they often have close encounters with GMCs or other clusters which can disrupt the cluster system resulting in a loss of member stars. Thus, open clusters steadily dissipate and

3 eventually dissolve into moving stellar groups (unbound association of stars) before finally becoming dispersed as galactic field stars. Their average lifetime is ∼ few hundred Myrs, although the most massive ones can survive for few Gyrs (Zhao & Chen 1994; Mathieu 1985) These clusters are generally found in the Galactic plane. Since they are young, they are found in places where star formation is ongoing, so in spiral galaxies, e.g. our Milky Way, they are readily found in the dense regions of the spiral arms. Open clusters have been found in spirals and irregular galaxies but they are not seen in ellipticals, presumably because star formation activity in ellipticals is very low. These clusters are generally metal rich and do not have a strong age-metallicity relationship.

1.2.2 Globular clusters

Figure 1.2: Globular cluster M13. First observed in 1714, this cluster lies in the Hercules constellation, about 6.8 Kpc from MW, and is about ∼ 45 pc in diameter. 5 The estimated mass of this GC is 6 × 10 M and it is ∼ 11.65 Gyrs old. Image credit : ESA/Hubble and NASA

Globular clusters (GCs) are one of the oldest structures in the universe. They 4 6 are compact spherical massive star clusters with a mass range of 10 − 10 M and typical half-light radius of only a few parsecs (< 10 pc). They contain no gas, has no young stars and no dark matter. GCs are mainly found in the halo of galaxies. There

4 Figure 1.3: Metallicity distribution of 137 MW globular clusters. The bimodal distribution are fitted with two gaussian curves. Figure credit : Zinn 1985 (original), Harris 1996. are 157 globular clusters in our Milky Way (Harris 1996, 2010 edition), although large elliptical galaxies can contain tens of thousands of GCs (e.g. M87) (Binney & Tremaine 2008). The GCs are also highly centrally concentrated, the typical GC 4 3 5 central density is ∼ 10 M /pc , which is about 10 times higher than the density in our solar neighborhood. GCs are extremely old, with a typical age of > 10 Gyr. However, these clusters have a typical crossing time of ∼ Myr only, so the typical stars in GCs have completed about ∼ 104 orbital rotation, which implies that the GCs are dynamically old and are very relaxed systems. Observations of GCs have been extensively used to constrain the star formation history of galaxies, galaxy assembly history, the structure formation and the age of the universe itself (Harris 1996; Dinescu et al. 1999; Forbes & Bridges 2010).

Globular clusters have a wide range of metallicity, from Z ∼ 0.005−1 Z . Accurate photometry of GCs has shown that there is a clear bimodality in their metallicity distribution (Zinn 1985). About 80% of GCs in MW have a metallicity of Z < 0.1Z while the other 20% have Z > 0.1Z (Figure 1.3). It was also discovered that the metal poor GCs generally reside in the galactic halo and the metal rich ones are primarily found in the MW disk and bulge. These observations suggest that there

5 Figure 1.4: Luminosity function of globular clusters around Virgo giant elliptical galaxies. The data points represent the GCs in four galaxies : NGC 4365, 4472, 4486 and 4649 and the line is the best fit gaussian curve. Figure Credit : Harris (1991).

are two different populations of GCs. There have been three major theories proposed to explain these two distinct populations: galaxy mergers, multiphase GC formation and accretion. Ashman & Zepf (1992) and Zepf & Ashman (1993) proposed that metal poor GCs are formed in early spiral galaxies and during the major mergers of these progenitor spirals in the galaxy assembly era, the metal rich GCs were formed. In an alternative explanation, Forbes et al. (1997) proposed that metal poor GCs were formed in the very early phases of galaxy formation, where there was less metal to begin with. Then the GC formation went dormant for several Gyrs (because of feedback, gas depletion or effects of reionization) before the second phase of star formation and metal-rich GC formation began. In the accretion scenario, Côté et al. (1998) proposed that metal-rich GCs formed in-situ as their host galaxies were forming, whereas metal poor GCs were accreted from neighboring low mass older galaxies. The most remarkable feature of globular clusters is their luminosity function. The globular cluster luminosity function (GCLF) is defined as the number of globular

6 clusters per unit magnitude interval (denoted by φ(m) for apparent magnitude and φ(M) for absolute magnitude). Observations of GCs have consistently found the GCLF can be very well fitted by a Gaussian distribution with a characteristic peak at

MV = −7.4.This shape and the peak is so consistent (Figure 1.4) that GCs have been used as ’standard candles’ for measuring cosmic distances (Whitmore 1997). The luminosity function of these clusters is the visible byproduct of its more fundamental property, the globular cluster mass function (GCMF). GCMF is defined as the number of GCs per unit mass interval, often expressed as dN/d log M (M is mass here). The 5 GCMF is also Gaussian shaped, with the characteristic peak mass at 2 × 10 M . The shape and the peak of GCMF remain almost unchanged with variations in the host galaxy morphology, size and environment. However, the origin of the universal GCMF remains poorly understood (Fall & Zhang 2001). The GCMF of today is the byproduct of two factors; the initial mass function (IMF) and the dynamical evolution of GCs over their lifetime of ∼ 10 Gyrs. We present more details about the theories of GCMF origin and evolution in Chapter 2 of this thesis.

1.2.3 Young massive star clusters

In the last few decades, observers have found another class of star clusters that are young like open clusters but have mass similar to GCs. These clusters are known as the young massive clusters (YMCs). The YMCs are generally younger than 100 Myr and are in the early phases of star formation. They are massive clusters with 4 typical mass > 10 M , similar to the GC mass. YMCs are also extremely dense, with 3 3 an average density of > 10 M /pc . These clusters are also gravitationally bound and this criterion helps to distinguish them from stellar associations, collections of similarly young and massive but unbound stars. The initial cluster mass function (ICMF) of these young clusters is not well determined. Some studies suggested that it can be described as a falling power law with dN/dM ∝ M −2 (Bik et al. 2003; Fall & Chandar 2012; McCrady & Graham 2007; Zhang & Fall 1999), some argued that it might be better fit by a Schechter 6 function with power index -2 and a characteristic mass of few 10 M (Bastian 2008; Portegies Zwart et al. 2010), and some proposed that it is not a power law at all mass scales but has a turnover at the low mass end (Anders et al. 2007; Cresci et al. 2005). Many YMCs have been observed in our MW and the neighboring LMC, SMC

7 Figure 1.5: Young star cluster R136 in the center of a star forming region 30 Doradus (also called tarantula nebulae) in our neighboring LMC galaxy. Credit : NASA, ESA, and F. Paresce (INAF-IASF), R. O’Connell (U. Virginia), and the HST WFC3 Science Oversight Committee galaxies (Hodge 1961; Hunter et al. 2003; de Grijs & Anders 2006) but they are found most abundantly in starburst (e.g. M82, NGC 1569) and interacting galaxies (e.g. merger of NGC 7252 and NGC 3597) (Bastian et al. 2006; Holtzman et al. 1992; Schweizer et al. 1996; Whitmore et al. 1999). A famous example is the cluster R 136, 5 (Figure 1.5), a 10 M YMC in the center of the star forming region of 30 Doradus in the LMC galaxy (Massey & Hunter 1998; Andersen et al. 2009; Campbell et al. 2010).

8 1.3 Puzzles of star clusters : Origin of the GCLF

In the early days of globular cluster discoveries, GCs were thought of as unique products of the special conditions of the early universe, e.g. high jeans mass of metal poor gas clouds (Peebles & Dicke 1968; Fall & Rees 1985). However, as discoveries of YMCs in many galaxies kept piling up, the similarities between YMCs and GCs in mass and density strongly suggested that clusters like GCs can form in the present universe too and that YMCs could be analogs of the progenitors of GCs in high redshift universe (Tacconi et al. 2010; Genzel et al. 2010; Swinbank et al. 2011). However, the globular cluster mass function (GCMF) has a lognormal shape, (Harris 2001; Jordán et al. 2007), which is remarkably different from the power law mass function of YMCs (de Grijs 2007; Longmore et al. 2014).. In order to explain the discrepancy between mass functions of YMCs and GCs, we need to understand their formation mechanisms. Over the years, a number of studies have focused on the formation and dynamical evolution of GCs. Some theorized that the GCs were formed by the collapse of proto-galactic clouds and these clusters had bell shaped ICMFs to begin with (Fall & Rees 1985; Parmentier & Gilmore 2007; Vesperini 2000, 2001). The more prevalent theory suggested that young GCs start with a power-law ICMF, and during evolution they are affected by a number of destructive processes that can disrupt the lower mass clusters more easily and more frequently than their higher mass counterparts, resulting in a lognormal profile (Baumgardt 1998; Fall & Zhang 2001; Gnedin & Ostriker 1997). Such destruction can rise from two-body relaxation, shock heating, supernova explosions, tidal shocking and stellar dynamical evaporation (e.g., Fall & Zhang 2001; Gnedin et al. 1999a; McLaughlin & Fall 2008). In particular, tidal forces induced by galaxy interactions or GCs passing through a galactic disk can generate efficient heating from strong tidal shocks, which significantly affect the evolution of GCs (Combes et al. 1999; Gnedin et al. 1999a,b). However, little is known about the formation conditions that determine the mass functions of YMCs.It has long been suggested that globular clusters preferentially form in regions with extremely high pressure (Ashman & Zepf 2001; Elmegreen & Efremov 1997). High pressure in molecular clouds can result in high velocity dispersions (several tens of km/s) which lead to larger binding energy. This helps the cloud not to get dispersed by typical HI clouds. With rising pressure, the specific

9 star formation efficiency of the region can increase significantly by up to one order of magnitude (Jog & Das 1996; Jog & Solomon 1992). High binding energy and high specific star formation efficiency are critical to the formation of massive, bound SCs. From the present-day properties of GCs, it is suggested that the cluster-forming 8 −3 clouds should have experienced high pressure on the order of P/kB & 10 Kcm , 4 which is & 10 times larger than the ambient interstellar medium pressure in our galaxy (Boulares & Cox 1990; Elmegreen & Efremov 1997; Jenkins et al. 1983; Welty et al. 2016). However, these extreme pressures can be easily produced in interacting galaxies by violent shocks, so they are theoretically expected to be ideal formation sites for GCs. In order to investigate the formation and evolution of SCs and their mass functions, we need realistic simulations of galaxies with SC systems to understand the complex interplay of all the creation and destruction processes. Simulation studies till date have mostly focused on semi-analytical prescriptions for ICMFs or explored particular aspects of this problem, e.g. effects of tidal fields on cluster evolution. It is also extremely important to include baryonic physics in the simulation as star clusters are fully baryonic systems. To this end, I perform two fully hydrodynamical simulations of interacting galaxies using Gadget and Gizmo codes and follow the star clusters formed in these galaxies directly. I study the formation condition of these young clusters and then follow their evolution to determine if they may indeed be GC progenitors. This is one of the first studies to realistically identify SCs and follow their formation and evolution in galaxy mergers. I present this study in Chapter 2 of this thesis.

1.4 Dwarf galaxies

The exact definition of a dwarf galaxy has been widely debated in the literature, with variations stressing on their small sizes, low brightness or their low mass. Following some recent reviews of dwarfs (Drlica-Wagner et al. 2015; McConnachie 2012), here galaxies with absolute visual magnitude MV fainter than -18 are considered as dwarf galaxies. Studies of the galaxy luminosity function have found that majority of galaxies in the universe are dwarf galaxies (Mateo 1998; Marzke et al. 1998).

10 1.4.1 Observations

Dwarf galaxies have always been challenging to observe due to their inherent faintness. However, in the recent decades, with the advent of powerful telescopes (e.g. surveys by HST and SDSS) and sophisticated software, there have been an explosion of data in the field of dwarf observations. For example, the number of Local Group dwarfs have increased more than threefold, from a mere 38 (Mateo 1998) in late 1990’s to more than 100 (Drlica-Wagner et al. 2015; McConnachie 2012) now. Some excellent review articles on dwarf galaxies can be found in Gallagher & Wyse (1994); Mateo (1998) (on early discoveries of dwarfs), Koposov et al. (2011); McConnachie (2012); Walker et al. (2009) (on Milky Way dwarfs) and (Chapman et al. 2013; Collins et al. 2013; Ho et al. 2012; Tollerud et al. 2012) (on dwarfs around M31). In rcent years, more dwarf galaxies are being discovered around our Galaxy. The Dark Energy Survey (DES) has discovered very faint 9 new satellite galaxies within 22 - 338 Kpc of the Galactic Center (Koposov et al. 2015; The DES Collaboration 2015). Subaru/Hyper Suprime-Cam survey have discovered two additional satellites, Virgo I and Cetus II (Homma et al. 2018). The Magellanic Satellites Survey (MagLiteS) have discovered two ultra-faint satellites, Carina II and III, near the Large Magellanic Cloud (LMC) (Torrealba et al. 2018). Furthermore, recent observations br GAIA mission have revolutionized the field of MW satellites by determining unprecedentedly precise position and proper motion detections of 39 satellites for the first time (Fritz et al. 2018; Gaia Collaboration et al. 2018). Historically, most dwarf galaxy discoveries have happened within our Local Group (LG). However, in the last few years there have been significant efforts in observing dwarfs around distant galaxies, which is extremely important to understand the effects of different environments on these galaxies. Merritt et al. (2014) have found 7 ultra-faint dwarf galaxies around M101 that is about 6 Mpc away from our Galaxy. PISCeS survey (Sand et al. 2014) has found a new dwarf around NGC 253 which is at a distance of 3.9 Mpc from us. A very isolated faint dwarf galaxy has been discovered at about 12 Mpc distance away, with no apparent host galaxy within its 4 Mpc radius (Monachesi et al. 2014). The SUBARU telescope found a dwarf galaxy at a distance of 5.27 Mpc, hosted by NGC 6503 (Koda et al. 2015). The HST has recently discovered the most distant ultrafaint dwarf galaxy in our Local Universe, at a distance of 19 Mpc from us. This galaxy is known as Fornax UFDI and

11 is probably a part of the Fornax cluster (Lee et al. 2017). Aside from these individual discoveries, statistical analysis of 274 massive (MW type) galaxies from SDSS survey, all of which resides within 42 Mpc of Galaxy, shows that every galaxy should host at least 5 satellites (excluding the most and the least compact dwarfs) within 40-500 kpc of their center (Speller & Taylor 2014). It is very difficult to observe dwarfs at high redshift, but recently some very distant dwarfs have been observed by means of gravitational lensing. In these cases, typically the massive host galaxy is lensing some high redshift galaxy directly behind it and the satellite dwarf galaxy causes some perturbation in the lensed image, from which the existence of this dwarf can be inferred. Using this method, in 2012, Vegetti et al. (2012) discovered a dwarf with 8 9 mass of 1.9 × 10 M at z = 0.881. Another dwarf of mass 3.5 × 10 M was found at z = 0.222 (Vegetti et al. 2010). It is very likely that we will discover many more dwarfs in the future.

1.4.2 Properties

7 11 Dwarf galaxies are low mass galaxies (∼ 10 − 10 M ) with a significant amount of dark matter. The Tully-Fisher relation (Tully & Fisher 1977) states that there is a strong correlation between the luminosity and the rotation speed of a galaxy. Later it was revealed that replacing luminosity by a more fundamental quantity, the total baryonic mass, makes the correlation even tighter (McGaugh et al. 2000). The baryonic mass is linearly correlated to the rotation velocity or the halo mass in log space over five decades of mass range (Gurovich et al. 2010; McGaugh 2012; McGaugh et al. 2010); this is known as the Baryonic Tully Fisher Relation (BTFR). However, it is unclear if this relation is extended to the dwarf galaxies too. McGaugh et al. (2010) showed that the dwarfs roughly stay close to the linear correlation but they have a slightly different slope with much larger scatter. Also the dwarfs are extremely baryon deficient, i.e. they retain less than 1% of the baryons available to them from the universal baryon fraction. It has been discussed that the various feedback mechanisms may be responsible for the under-abundance of baryonic matter in dwarfs, but the details remain poorly understood (Kereš et al. 2009).

12 1.4.3 Star formation history

Dwarfs are very difficult to observe at high redshifts and consequently, directly observing their formation and evolution is currently not feasible. However, signatures of their evolution are preserved in the Star Formation Histories (SFH) of the dwarfs. A number of local dwarfs have resolved stellar populations with precise color, distance and brightness measurements. Comparing those with stellar evolution models can yield their star formation histories (Aparicio & Hidalgo 2009; Dolphin 2012; Skillman et al. 2003; Tolstoy et al. 2009; Tosi et al. 1989). A complete list of articles analyzing SFHs of different dwarfs is given in Table I of Weisz et al. (2014a). Most of these studies are detailed but the total sample is inhomogeneous owing to different models and algorithms used. Recently, Weisz et al. (2014b, 2015) have analyzed 38 local dwarfs using a consistent method. Well constrained SFHs exist for a few dwarfs outside Milky Ways virial radius also (Monelli et al. 2010a,b; Weisz et al. 2014c). These studies suggest that the average SFHs are spanned over a few Gyrs. Generally 5 the low mass galaxies (< 10 M ) formed most of their stars (80%) before z=2, whereas higher mass dwarfs have formed stars later. It is also hypothesized that reionization may have had a significant effect on the evolution of dwarf galaxies in the early universe (Babul & Rees 1992; Bullock et al. 2000; Busha et al. 2010; Simpson et al. 2013; Weisz et al. 2014b). The sweeping effect of reionization would destroy many dwarfs outright by stripping them off baryons. In some cases they can overheat the gas content and quench the star formation severely. However, observationally it is challenging to identify the effects of reionization because there are several processes which can affect the SFH in a similar way, such as ram pressure, tidal effects etc (Gatto et al. 2013; Łokas et al. 2012). Star formation histories can also be used to reconstruct the orbital motion of dwarfs by theoretical modeling, as has been illustrated in Sohn et al. (2013) for LeoI with HST ACS/WFC images. SFHs are, summarily, an extremely important tool in understanding the formation and evolution of dwarfs and their role in the early universe. In Chapter 6 of this thesis, I study the star formation history of a population of dwarfs using a cosmological baryonic simulation and explore the effects of reionization on their evolution.

13 1.4.4 Theory

For last two decades, significant effort have been spent in building a coherent and detailed theory of dwarf galaxies. Initially the simulations were mostly dark matter (DM) only where the dark matter subhalos were thought to be proxies of dwarf galaxies. Slater & Bell (2013) analyzes the transformation between star forming dwarfs and non star forming dwarfs using the DM only Via Lactea simulation. The DM only ELVIS simulation explores 48 Galaxy sized halos and Garrison-Kimmel et al. (2014) studied the stellar mass function of the dwarfs in those halos. However, these simulations faced many problems; e.g. they over predicted the number of dwarfs around host galaxies (Missing Satellite Problem) and do not produce observed dwarf properties accurately (density profile, baryon fraction etc.) Recently, with the advancement of computing, it has become possible to perform simulations of dwarf galaxies including both baryons and dark matter. Baryons solve a number of problems with dwarfs since in their mass and size range the baryonic physical processes are extremely important. The differences between DM only and DM-baryon simulations are discussed in detail in (Brooks & Zolotov 2014; Zolotov et al. 2012) using dwarf simulations by GASOLINE code. Brooks et al. (2013) implemented baryonic correction in the dark matter only Via Lactea simulation and found that baryons largely solve the problem of dwarf overabundance. Ricotti et al. (2002a,b, 2008) have performed a baryonic cosmological simulation of dwarf galaxies in a 1 Mpc box and explored their properties. It includes detailed feedback mechanisms, but due to limited volume, the simulation was stopped at redshift 8 - 10. González-Samaniego et al. (2014) explored the mass assembly history of six isolated dwarf galaxy halos using an adaptive mesh refinement (AMR) code. Wheeler et al. (2015) performed a FIRE/GIZMO simulation of 6 dwarf galaxy halos and studied their star formation histories and the possibility of the dwarfs having their own small satellites. In APOSTLE suite of hydrodynamic simulations Sawala et al. (2016) analyzed 12 Local Group like volumes and deduced that baryonic physics can indeed help reproduce the observed dwarf abundance and showed that satellite distributions around hosts may be anisotropic. Recently, AURIGA simulations have produced a suite of 30 Milky Way sized halos and their satellite galaxies and Simpson et al. (2018) showed that after the satellites infall, most of the star formation quenching happens within 1 Gyr with ram pressure stripping being the primary quenching mechanism.

14 1.5 Puzzles of dwarf galaxies : Disk of Satellites

Observations of the Milky Way (MW) satellites have discovered (Lynden-Bell 1976; Kroupa et al. 2005; Kunkel & Demers 1976), rather unexpectedly, that the 11 brightest satellite galaxies of the Milky Way (MW) have a highly anisotropic distribution. These satellites reside in a plane inclined to the Galactic stellar disk. Such planar structure is now commonly referred to as “disk of satellites” (DoS, Kroupa et al. 2005). To date, more than two dozens new dwarf galaxies have been detected around the MW (e.g., Helmi 2008; Willman 2010; Koposov et al. 2015; McConnachie 2012). It has been reported that these new dwarfs also have an anisotropic distribution and can be interpreted as lying in a disk (Pawlowski et al. 2015). Looking at the nearby M31 galaxy, it was found that 15 out of the 27 dwarfs around Andromeda, detected by Pan-Andromeda Archaeological Survey (PAndAS; McConnachie et al. 2009), also follow an anisotropic planar distribution (e.g., Conn et al. 2013; Koch & Grebel 2006; McConnachie et al. 2009; Metz et al. 2007; Pawlowski et al. 2013; Ibata et al. 2013). On the kinematics side of these satellites, among the original 11 “classical” MW satellites, 6 to 8 galaxies preferentially co-orbit in a similar direction (Maji et al. 2017; Pawlowski et al. 2013). Ibata et al. (2013) used line-of-sight (LOS) velocities to suggest that 13 out of 15 coplanar satellites of Andromeda are co-rotating. Outside of the Local Group, Ibata et al. (2014) used the SDSS catalog and identified 22 galaxies with diametrically opposed satellite pairs and found that 20 of them have anti-correlated velocities, suggesting that co-planar and co-rotating satellite galaxies may be common in the Universe. Initially, N-body simulations were largely unsuccessful to reproduce the observed anisotropic distribution. The dark matter sub-halos around the main galaxy were found to be isotropically distributed in the standard Lambda Cold Dark Matter (ΛCDM) simulations (Kang et al. 2005). This has been strongly criticized as a failure of ΛCDM by some authors (Kroupa et al. 2010; Metz et al. 2007; Pawlowski & Kroupa 2014; Pawlowski et al. 2012; Kroupa et al. 2005). In order to realistically study the DoS in simulations, we need to explore satellite distributions in baryonic simulations. In recent years, some efforts have gone into studying DoS structures with baryons, however, for a systematic investigation of this problem, we need to - i. reanalyze the observed dwarfs to find out the effects of small sample statistics on the analysis, explore if the present observed MW DoS is stable

15 in the long term or just a transient structure; ii. compare the satellite distribution in a baryonic simulation and its N-body counterpart to understand if baryonic physics can help solve this problem; iii. study the satellite systems around a large number of host galaxy systems to determine the statistical variations of DoS properties and if these depend on host galaxy properties. I will discuss these three aspects of the problem in Chapters 3, 4 and 5 respectively.

1.6 Thesis Outline

This thesis is organized as follows. In Chapter 2 I have investigated the formation of star clusters in interacting galaxies using two baryonic simulations and explored the origin of the universal globular cluster mass function. In Chapter 3, 4, and 5 I have studied the problem of the Disk of Satellites in detail. Specifically, in chapter 3, I reanalyzed the observed data of all Milky Way dwarfs, demonstrated the effects of small sample statistics on this problem and predicted the future evolution of the classical Milky Way DoS to show that the DoS structure is transient. In chapter 4, I analyzed a baryonic MW galaxy simulation and its N-body counterpart to explore the effects of baryons on the DoS and showed that an anisotropic distribution of satellites in galaxies can naturally originate from baryonic processes in the hierarchical structure formation model, unlike the isotropic subhalo distribution found in N-body simulations. In chapter 5, I expanded this study further to explore the general nature of satellite anisotropy in different galaxy systems. I have analyzed all 2,591 satellite galaxy systems in the baryonic cosmological simulation Illustris-1 and found that the DoS properties are far more sensitive to the sample size of the satellites in the system, compared to variations of host galaxy properties. In chapter 6, I study the general properties of dwarf galaxies, especially their star formation history and the effects of reionization on dwarf galaxy population by analyzing a baryonic simulation of a Milky Way type galaxy and its surrounding dwarf galaxies.

16 Chapter 2 | The formation and evolution of star clusters in interacting galaxies

2.1 Introduction

Star clusters (SCs) are building blocks of galaxies, so their origin and evolution are important aspects of the study of galaxy formation. Over the past two decades, numerous young massive clusters (YMCs) have been observed by the Hubble Space Telescope in interacting and merging galaxies, such as NGC 1275 (Holtzman et al. 1992), NGC 7252 (Whitmore et al. 1993), NGC 3921 (Schweizer et al. 1996), NGC 4038/39 or the Antennae Galaxies (Whitmore et al. 2010; Whitmore & Schweizer 1995; Whitmore et al. 1999), NGC 4449 (Annibali et al. 2011), and NGC 7176/7174 (Miah et al. 2015). The YMCs formed in these environments are compact (∼ few 4 parsecs), gravitationally-bound objects with masses > 10 M , ages ∼ 10 − 100 Myr (Portegies Zwart et al. 2010) and initial mass function that resembles a falling power law with dN/dM ∝ M −2 (Bik et al. 2003; Fall & Chandar 2012; McCrady & Graham 2007; Zhang & Fall 1999) On the other end of the SC spectrum are old globular clusters (GCs) that have been observed extensively in nearby galaxies (e.g., Brodie & Strader 2006; Gratton 4 6 et al. 2012; Harris 1991; Kruijssen 2014, 2015). These are massive (∼ 10 − 10 M ), gravitationally-bound, compact (few pc) and old (age ' 10 − 13 Gyr) systems that formed in the early universe and have survived to the present-day (Forbes & Bridges 2010; VandenBerg et al. 2013). The observed globular cluster mass functions (GCMFs) are bell-shaped or lognormal-shaped with a characteristic peak mass around 5 1.5 − 3 × 10 M (Harris 2001; Jordán et al. 2007).

17 Many studies have suggested that the YMCs could be analogs of the GC progen- itors, (de Grijs 2007; Longmore et al. 2014), however, in that case, the significant difference between the ICMF of GCs and YMCs becomes extremely intriguing. In addition, the formation conditions of YMCs, which presumably determine their ICMF, is not well known (more details in § 1.3). On the observational front, it has been difficult to directly observe the physical conditions of a proto super-star cluster cloud (SSC - star clusters with the possibility of evolving into GCs). Wei et al. (2012) observed molecular cloud regions in the 6 Antennae Galaxies and found very massive (& 10 M ) clouds in the centers of high star formation regions with large velocity dispersion. Recently, Johnson et al. (2015) have studied the properties of a pre-SSC cloud in the merging galaxies of the Antennae in detail via CO observations. This cloud is not yet forming stars, but is expected to begin doing so in less than 1 Myr, which makes it an ideal candidate to investigate SSC formation conditions. Direct measurements of the cloud suggest that it has mass 6 of > 5 × 10 M and a radius of ∼ 25 pc which falls in the range of GC properties. 8 −3 The cloud is experiencing a tremendously high external pressure P/kB > 10 K cm . Adamo et al. (2015) studied the SCs in M83 at different radii from the galaxy center and concluded that high gas pressure increases cluster formation efficiency. However, due to the large dynamical range (from sub pc for star formation to kpcs 4 12 for galaxies), mass scale (from star clusters of ∼ 10 M to galaxies of 10 M ), and the various physical processes involved (cluster formation in GMCs, stellar evolution, binary interaction, shocks, tidal disruptions etc), it has been a challenge to study formation and evolution of SCs in galaxies numerically. Most of the early simulation efforts assumed a shape for the ICMF, generally power laws or Schechter functions, and then simulated their evolution using N-body codes (Baumgardt & Makino 2003; Lamers et al. 2010; Vesperini & Heggie 1997). Some simulations have focused on particular aspects of the problem, such as the evolution of GCs in the tidal fields of mergers (Renaud & Gieles 2013), star escape rate from GCs (Gieles & Baumgardt 2008) and the effects of intermediate mass black holes on GCs (Lützgendorf et al. 2013). A few simulations explore SCs in specific environments such as high redshift galaxies (Prieto & Gnedin 2008) and dwarf galaxies (Kruijssen & Cooper 2012). Some variants of N-body simulations have also been applied, for example, Renaud et al. (2011) used a tensor field to describe tidal fields. It is very important to include hydrodynamics of the gas in the galaxy to fully

18 understand SC formation and evolution, but it can be highly computationally ex- pensive to explore the entire range of processes. For example, Li et al. (2004) used sink particles to represent SCs in high-resolution, smoothed particle hydrodynamics (SPH) simulations but could not follow the structure of clusters; Kruijssen et al. (2012, 2011) used N-body/hydro simulations for the galaxies but followed the cluster evolution semi-analytically. A more complete treatment of galaxy simulation and SC identification emerged recently. Renaud et al. (2015) modeled an Antennae-like merger using an adaptive mesh refinement (AMR) grid-based code and identified SCs with a friends-of-friends (FOF) group finding algorithm. They found that the cluster formation rate roughly follows the star formation rate, and that clusters formed in interacting galaxies are up to 30 times more massive than those formed in isolated galaxies. However, a detailed study of the formation conditions of SCs and the evolution of cluster mass functions is needed. So, in this study, we perform fully hydrodynamic simulations of galaxy mergers using two different codes: Gadget (Springel 2005; Springel et al. 2001) and Gizmo (Hopkins 2015). We identify the SCs in them as overdense groups of bound particles, using the Amiga Halo Finder (AHF1, Gill et al. 2004; Knollmann & Knebe 2009). We investigate the physical conditions of SC formation by tracking the properties of the nascent birth clouds. We follow the early evolution of their mass function to understand the connection between YMCs and GCs and the origin of the mass function peak of GCs. This is one of the first studies to realistically identify SCs and follow their formation and evolution in galaxy mergers. This chapter is organized as follows: in § 2.2 we describe the methods, which include the numerical codes, galaxy model and cluster identification; in § 2.3 we present the results of cluster formation and physical conditions, and the initial cluster mass functions; in § 2.4 we explore the evolution of cluster mass functions; in § 2.5 we discuss the limitations of our study; and we summarize our findings in § 2.6.

2.2 Method

In this study, we perform hydrodynamical simulations of a galaxy merger of two Milky Way-size progenitors using two different hydrodynamics codes: the improved

1The AHF code is available at http://popia.ft.uam.es/AHF/Download.html

19 SPH code Gadget developed by Springel et al. (2001) and Springel (2005), and the new meshless code Gizmo developed by Hopkins (2015). In order to reduce numerical artifacts on the physical results, we have implemented the same physical processes in both codes, and use the same initial conditions in the simulations. The SCs are identified in the simulations using a density-based group finding algorithm Amiga Halo Finder (AHF, Gill et al. 2004; Knollmann & Knebe 2009). In what follows we briefly describe the codes, galaxy model and SC identification used in the simulations; we refer the reader to read the references therein for detailed descriptions.

2.2.1 Hydrodynamic Codes

Gadget (Springel 2005; Springel et al. 2001) is a massively parallel N-body/SPH code. It handles the components of a galaxy in two distinct ways: it treats the motions and evolution of dark matter and stars as collisionless particles in an N-body problem, while the gas is dealt with using the SPH method (Gingold & Monaghan 1977; Hernquist & Katz 1989). The N-body particles are described by the collisionless Boltzman and Poisson equations, and the hydrodynamics of the fluid is followed using properties of neighboring gas particles smoothed by a kernel function. The gravitational force of each particle is calculated with a tree algorithm in which particles are grouped together and their effect is taken as a single multipole force, which reduces the computation cost greatly to O(NlogN) compared to the direct summation of each particle pair with complexity O(N 2). In this code, an artificial viscosity term is introduced into the equation of motion of SPH to represent the viscosity which often arises in ideal gases due to shocks caused by microphysics. The Gadget-2 we use explicitly conserves energy and entropy in the SPH formulation (Springel & Hernquist 2002). This version and its variants have been widely used in a large number of applications, from large-scale cosmological simulations (e.g., Feng et al. 2013; Schaye et al. 2015; Springel & Hernquist 2003b; Springel et al. 2005b) to galaxy mergers (e.g., Cox & Loeb 2008; Hayward et al. 2014; Hopkins et al. 2005, 2008, 2006; Li et al. 2007, 2004; Springel 2000; Springel & Hernquist 2005). Gizmo (Hopkins 2015) is a new Lagrangian code developed to circumvent the many problems encountered by SPH methods (Agertz et al. 2007; Bauer & Springel 2012; Kereš et al. 2012; Nelson et al. 2013; Sijacki et al. 2012; Vogelsberger et al. 2012; Zhu et al. 2015, 2016). It derives the hydrodynamic equations using a kernel

20 function to partition the volume, and a Riemann solver to evolve the equations at the Lagrangian face co-moving with the mass. Gizmo implements strict conservation of mass, energy and linear and angular momentum and it does not require any artificial diffusion terms to deal with shocks, embodying the advantages of both SPH and grid-based methods. It captures the instabilities of fluid mixing well, greatly reduces numerical noise and artificial viscosity and as a result calculates fluid physics at smaller Mach number more accurately. Gizmo treats the contact discontinuities and shocks more precisely and more efficiently, generally within one kernel length instead of 2-3 as in Gadget, and it does not have the zeroth order and first order errors that are present in SPH (Zhu et al. 2015), so it can attain higher accuracy with a much smaller number of neighbors which results in a faster convergence. We have used the meshless finite-mass mode of Gizmo for our project. The mass of an individual gas element is conserved in this mode, which allows us to trivially trace the history of star particles to their progenitor gas particles (otherwise, one needs tracer particles to do so). A detailed comparison between Gadget and Gizmo in galaxy simulations has been conducted by Zhu et al. (2016), who showed a general agreement between the two simulations but there were notable differences in a number of galaxy properties such as star formation history, gas fraction and disk structures. In this study, our motivation for using these two codes to perform the same merger simulation is to reduce the possibility of numerical artifacts affecting our results. As we will show in § 2.3, although the detailed star formation history of the mergers is different between the two simulations, the overall distribution functions of the cluster mass and the pre-cluster gas pressure agree well, which suggests that our results are physical and robust, because we can argue against the effects of numerical artifacts such as the number of neighbors and artificial viscosity on these results.

2.2.2 Galaxy Model

Our simulations consider major mergers of two equal-mass Milky Way - sized galaxies. The galaxy is constructed using the model of Mo et al. (1998), which has a dark matter halo with a Hernquist density profile (Hernquist 1990), a thin disk with gas and stars, and a black hole in the center. The galaxy properties are similar to those 12 of the Milky Way: the total mass is 10 M , the gas fraction fgas = 0.2, the radial

21 scale length of the galaxy is 3 kpc, and the disk height is one-fifth of it. The disk 5 contains 4% of its total mass, and the seed mass of the black hole is 10 M . The interstellar medium (ISM) in these galaxies is modeled using a sub-grid multi- phase recipe, and the star formation rate follows the empirical Schmidt- Kennicutt law (Kennicutt 1998; Schmidt 1959) where the surface density of star formation is related 1.4 to the surface density of gas (ΣSFR ∝ Σgas). The radiative cooling and heating in the ISM is modeled with the assumption that the medium is in collisional equilibrium and there is an external UV background (Haardt & Madau 1996). We have also followed feedback processes from both supernovae (Springel & Hernquist 2003a) and active galactic nuclei (Springel et al. 2005a). Supernova feedback includes thermal energy and galactic winds. The wind energy efficiency is 5% of the supernovae energy, and the wind direction is anisotropic: winds carry energy and matter perpendicular to the disk plane. The feedback from the black holes is in the form of thermal energy deposited isotropically into the surrounding gas. We note that Renaud et al. (2015) have performed a simulation of Antennae-like merger. In order to explore a more extreme merger environment, we simulate a head- on collision of two Milky Way-sized galaxies, in which the progenitors are initially placed on a parabolic orbit with the inclination of both with respective to the orbital plane as θ = 0 and φ = 0. In the simulations, each galaxy is initially started with 82,000 gas particles, 328,000 star particles and 1,476,860 dark matter particles, which 4 5 yield a mass resolution of 5 × 10 M for the gas and star particles, and 6 × 10 M for each dark matter particle.

2.2.3 Star Cluster Identification

Finding groups or structures in a given set of data is a classic problem in data mining. There are many algorithms for group finding, which essentially differ in their notion of groups and in their methods. The two main classes are particle-based and density-based algorithms. The most widely used method of group finding in astronomy is the FOF algorithm (Davis et al. 1985). It is a particle-based algorithm where all particles within a given linking length are considered as a group. However, there are two significant downsides of this approach even with an adaptive linking length (Suginohara & Suto 1992): i) if two groups have a linking bridge, they will be identified as one group; ii) it cannot identify substructures within a structure.

22 The other class of group-finding algorithms is density-based, which identify over- densities in the field as groups (Bertschinger & Gelb 1991; Gill et al. 2004; Klypin & Holtzman 1997; Warren et al. 1992). These methods do not suffer from the problems of the FOF methods described above. For this reason, we adopt the density-based hierarchical group finding algorithm AHF (Knollmann & Knebe 2009) to identify SCs in the simulations using the following procedures. First, AHF divides the simulation box into grid regions. It determines the particle density inside each grid cell and compares the density to a threshold or background density value. If the computed density exceeds the threshold, it divides the grid into half of its initial size. It computes the particle densities in each of the refined grid cells (where it exists) and compares with another given threshold (the refinement criterion on refined grids). This process goes on recursively until no cell need anymore refinement. Next, it starts from the finest grid and marks isolated overdense regions as possible clusters. It goes on to the next coarser level and again identifies possible regions as clusters. Importantly, it links the possible clusters in finer grids to their respective coarser parts (linking daughters to parents). This continues until it has reached the coarsest grid and finally it builds a tree of clusters with subclusters. Considering the observed physical properties of young massive clusters, we impose a few criterions on the groups identified by AHF to qualify them as SCs. Each group should be gravitationally bound and have no substructures in order to only include individual star clusters. It should contain stars and have at least 4 baryonic particles, 5 which means the minimum cluster mass is 2 × 10 M . The upper limit of group mass 8 is set at 10 M , and the baryonic fraction (mass ratio of baryons to dark matter) of each group should be larger than unity in order to distinguish the star clusters from dwarf galaxies that may form in our simulations. Such an approach provides a holistic identification of star clusters in our study.

2.3 Formation of Star Clusters

2.3.1 Starbursts in Interacting Galaxies

In the simulations, the progenitor galaxies start moving towards each other at t = 0 on a parabolic orbit. They have their first close encounter at t ∼ 0.23 Gyr, and the second one at t ∼ 0.9 Gyr until the final coalesce at t ∼ 1 Gyr. During the close

23 yr)

/ ☉ (M

SFR

log 1a 1b 2

Gizmo simulation Gadget simulation 0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 Time (Gyr)

Figure 2.1: The star formation histories of galaxy mergers in both Gizmo (black curve) and Gadget (red curve) simulations. Both simulations show two starburst episodes during the close encounters of the two galaxies, at times ∼ 0.2 − 0.45 Gyr and ∼ 0.8 − 1.1 Gyr, respectively. In order to investigate the triggering source of star formation, we calculate gravitational torques on star forming gas during three star formation peaks as labeled: minor peak 1a at 0.23 Gyr and major peak 1b at 0.4 Gyr during the first close passage, and major peak 2 at 1 Gyr during the final coalescence, and show the results in Figure 2.3. passages, vigorous star formation is triggered by the compression of gas by tidal forces and rising gas densities in the inner region of the galaxies due to gravitational torques (Barnes & Hernquist 1996, 1991). As shown in Figure 2.1, the first starburst occurs at t ∼ 0.2 − 0.5 Gyr, when the star formation rate (SFR) increases by nearly 3 two orders of magnitude and reaches a peak of ∼ 10 M /yr at t ∼ 0.4 Gyr. The 2 second starburst takes place at t ∼ 0.9 − 1.1 Gyr, and the SFR peaks at ∼ 10 M /yr at t ∼ 1 Gyr. The star formation history of galaxy mergers depends strongly on the progenitor

24 Figure 2.2: Snapshots of the galaxy merger at three different times, 0.40 Gyr, 0.41 Gyr and 0.42 Gyr during the first starburst phase when most clusters form, from both Gizmo (top panels) and Gadget (bottom panels) simulations. The images are projected gas density maps color-coded by gas temperature (the colors from blue to red indicates hotter gas, the brightness from dark to white measures increasing density). The red dots are stars, and the filled maroon circles represent newly formed star clusters. The maroon region in the center of each galaxy indicates overlapping star clusters. The box length is 100 kpc in25 physical coordinates. properties and orbital parameters. The SFR in our simulation is higher than typical mergers at the local universe. Renaud et al. (2015) estimated from their simulation 2 that the SFR of Antennae merger at its starburst phase is ∼ 10 M . However, star formation in ultra-luminous infrared galaxies (ULIRGs) in nearby universe can have comparable intensity. For example, radio recombination line studies of merer driven starburst galaxy Arp 220 (77 Mpc away) suggest a mean SFR of ∼ 240 M /yr 3 or more plausibly short periods of intense starbursts with SFR of ∼ 10 M /yr (Anantharamaiah et al. 2000; Thrall 2008; Varenius et al. 2016). We note that the 10 mass of Arp220 is estimated as ∼ 10 M (Scoville et al. 1997), much lower than our modeled galaxies. The high SFR in our simulated galaxies may be a product of both their high mass progenitors and their extreme orbital parameters with the head-on collision. As demonstrated in Figure 2.1, there is a remarkable difference in the star formation histories between the two simulations in that Gizmo produces higher SFR peaks than Gadget by a factor of 3 − 5. This is due to the more accurate treatments of fluids and shocks in Gizmo. Similar differences have also been seen in the code comparison study of galaxy mergers using Gadget and the moving-mesh code Arepo by Hayward et al. (2014), who reported that Arepo produces higher SFRs than Gadget by up to a factor of 10 for mergers of Milky Way - size galaxies. The strong compression and shocks produced by the galaxy interaction fuel rapid formation of SCs during the starbursts. As demonstrated in Figure 2.2, most of the SCs form in the nuclear regions of the two merging galaxies, with a few spread in the tidal tails and the galactic bridges. Similar distributions of YMCs have also been observed in galaxy mergers, including nuclear region clusters by Miller et al. (1997); Whitmore & Schweizer (1995), and tidal tail clusters by Barnes & Hernquist (1992); Bastian et al. (2005); Knierman et al. (2003); Mullan et al. (2011). In order to investigate the triggering source of star formation during the merging process, we track the gas particles that form stars at the three star formation peaks, minor peak 1a at 0.23 Gyr and major peak 1b at 0.4 Gyr during the first close passage, and major peak 2 at 1 Gyr during the final coalescence, as labeled in Figure 2.1. It was shown by Hernquist (1989) that the major star formation episodes in galaxy mergers are marked by a rapid loss of the angular momentum of the star forming gas driven by the gravitational torque. We follow the procedure of Barnes & Hernquist (1996) and calculate the gravitational torque, τ = r ×F , exerted on these star-forming

26 int. tor. 1a int. tor. 1b 30

) int. tor. 2 2 ext. tor. 1a ext. tor. 1b ext. tor. 2 (kpc/Gyr) ☉ log (Torque) (M 15 20 25 0.2 0.4 0.6 0.8 1.0 Time(Gyr)

Figure 2.3: Evolution of the gravitational torques on the gas particles that eventually form stars during the three star formation peaks, 1a (at time 0.23 Gyr, blue), 1b (at 0.4 Gyr, green), and 2 (at 1 Gyr red), as labeled in Figure 2.1. The solid and dashed lines represent internal and external torques, respectively. Note that during the final coalescence at time ∼ 0.8 − 1.1 Gyr, only internal torque is available. gas particles by the gas and stars in the same galaxy (internal torque), and by gas, stars and halo particles of the other galaxy (external torque). As shown in Figure 2.3, the internal torque is higher than the external counterpart by orders of magnitude for all tracked star-forming gas particles during the galaxy interaction. Similar results have been reported by a number of theoretical studies of major mergers ( e.g. Barnes & Hernquist 1996; Hernquist 1989; Hopkins et al. 2009; Mihos & Hernquist 1994), which show that the internal torque is the dominant source of torque that drives the loss of angular momentum in these interacting galaxies. The close encounter of the galaxies produces strong tidal forces that results in a non-axisymmetric response in the galaxy disks. These forces deform the galaxy disks and form gaseous and stellar

27 bars in the galaxies. These gas bars lead the stellar bars by a few degrees (Barnes & Hernquist 1991) which eventually produces a strong torque on the gas near the center that drives rapid gas inflow towards the nuclear region, resulting in vigorous starburst. From Figure 2.2, the majority of clusters formed at the starburst phase are highly clustered in the center region of each galaxy, indicating their origin from the nuclear gas inflow, while the few clusters formed in the bridge and tidal tails may be triggered by tidal force, as suggested by Renaud et al. (2009) and Renaud et al. (2014). We note that the first major star formation peak 1b (at 0.4 Gyr) takes place about 160 Myr after the first close pericentric passage at ∼ 0.24 Gyr. Similar time delay has been found in other simulations of galaxy mergers (e.g., Cox & Loeb 2008; Hayward et al. 2014; Mihos & Hernquist 1994, 1996), as the timescale to build up the gas density driven by internal torque for star formation. In addition, we note that there is a minor star formation peak of ∼ 15 M /yr at 1a (0.24 Gyr) preceding the the major one of ∼ 800 M /yr at 1b (0.4 Gyr). We find that the ratio of external to internal torque peaks during the 1a phase, suggesting that external torque from tidal force may contribute to the star formation as well. Studies by Renaud et al. (2009, 2014) have shown that tidal force during galaxy interaction may compress the gas and enhance the star formation.

2.3.2 Initial Cluster Mass Functions

The resulting mass functions of the SCs formed during the first close encounter are shown in Figure 2.4. Although the total number of clusters in the same snapshot differs between the Gizmo and Gadget simulations by a factor of ∼ 1.3, the range of ∼ 150 − 200 is in good agreement with observations of galaxy mergers such as the Antennae (Larsen 2010; Whitmore et al. 1999). More interestingly, both simulations produce similar mass distributions which resemble a peaked or a quasi-lognormal 5.8−6 6−6.2 function, with a Gizmo peak around 10 M and the Gadget peak at 10 M . Our mass functions do not show a purely declining power law, as suggested by many observations of YMCS (e.g., Bik et al. 2003; Fall & Chandar 2012; McCrady & Graham 2007; Zhang & Fall 1999). This could be due to the limited resolution in our 5 simulation so we cannot resolve clusters at mass lower than 10 M . However, Renaud et al. (2015) also reported lognormal-shape ICMFs from their Antennae simulation

28 t = 0.40 Gyr t = 0.41 Gyr

60 70 Gizmo simulation Gizmo simulation Gadget simulation Gadget simulation 60 80 No. of star clusters No. of star clusters No. 0 10 20 30 40 50 0 20 40 5.0 5.5 6.0 6.5 7.0 7.5 8.0 5.0 5.5 6.0 6.5 7.0 7.5 8.0 log10 (MCluster / M☉) log10 (MCluster / M☉)

t = 0.42 Gyr Gizmo simulation Gadget simulation 60 80 No. of star clusters No. 0 20 40 5.0 5.5 6.0 6.5 7.0 7.5 8.0 log10 (MCluster / M☉)

Figure 2.4: Mass functions of star clusters formed at 0.40 Gyr, 0.41 Gyr and 0.42 Gyr during the first starburst phase when most clusters form, from both Gizmo (grey) and Gadget (red) simulations. The total number of clusters in the three snapshots from Gizmo (Gadget) simulation is 158 (170), 171 (221), and 197 (151), respectively.

even though they have a much higher mass resolution (∼ 70 M ). It is also possible that the power-law phase is extremely short lived (< 10 Myr) in violent mergers and our snapshot interval (every 10 Myr) misses that phase. We note, however, some observations have suggested that the power law ICMF for YMCs is not universal, rather they have a turnover at low mass (Anders et al. 2007; Cresci et al. 2005). The peak masses of these ICMFs are higher than those of the observed GCMFs, 5 ∼ 1.5 − 3 × 10 M , but it can be predicted that after an evolution of Gyrs, stellar evolution, tidal stripping and other disruptive processes will cause them to lose some

29 of their mass (Kruijssen 2015; Webb & Leigh 2015). We discuss their evolution in more detail in §5.3.4. It is encouraging that both of our simulations, together with that by Renaud et al. (2015), produce similar quasi-lognormal ICMFs with similar peak positions, despite having vastly different hydrodynamic solvers, feedback processes and numerical resolutions. This agreement suggests that the lognormal mass function is unlikely due to numerical artifacts but has a physical origin, which will be investigated in the next section.

2.3.3 Physical Conditions of Cluster Formation and Origin of Log- normal Cluster Mass Functions

In order to explore the physical origin of the quasi-lognormal ICMFs in Figure 2.4, we examine the physical conditions of cluster formation. As mentioned in § 2.1, massive SCs form in molecular clouds with very high gas pressures (Ashman & Zepf 2001; Elmegreen & Efremov 1997). When a star-forming cloud is under high pressure, the efficiency of star formation increases and the gas velocity dispersion becomes higher, which in turn help to keep the cloud bound (Jog & Solomon 1992). These physical conditions create an ideal nursery to form massive, gravitationally-bound clusters. Recently, Zubovas et al. (2014) performed an N-body simulation of a molecular cloud and concluded that high external pressures drive efficient star formation and can cause cloud fragmentation, leading to the formation of star clusters. Quantitatively, the external pressure P on a nascent molecular cloud is given by Elmegreen (1989):

3ΠM σ2 P = cloud v (2.1) 4πr3

where Mcloud is the mass of the cloud, σv is the velocity dispersion and r is the size of the cloud. The factor Π is given by the ratio of density at the cloud edge and the average density, Π = ne/hnei. This Π ratio is dependent on the density profile of the parent molecular cloud. Locally the probability distribution function of ISM density due to turbulence can be approximated as lognormal but at high density regions (> 103 cm−3), such as at the center of molecular cloud, density profile can develop a power law tail. At these dense places the Π value can be >> 1 and consequently it can increase the amount of gas above a density threshold which facilitates further star formation (Elmegreen 2011; Renaud et al. 2014). Elmegreen & Efremov (1997) estimated that the pressure in the birth clouds of

30 N N 0 30 60 0 20 ) ) -3 -3 cm cm

(K (K

P/k P/k

log Gizmo - 0.40 Gyr log Gadget - 0.40 Gyr Antennae clusters Antennae clusters

6 8Proto 10 SSC 12 14 cloud Proto SSC cloud 6 8 10 12 14

5.0 6.0 7.0 8.0 0 20 50 5.0 6.0 7.0 8.0 0 20 40 log10 (MCluster / M☉) N log10 (MCluster / M☉) N N N 0 30 60 0 30 60 ) ) -3 -3 cm cm

(K (K

P/k P/k

log Gizmo - 0.41 Gyr log Gadget - 0.41 Gyr Antennae clusters Antennae clusters

6 8Proto 10 SSC 12 14 cloud 6 8Proto 10 SSC 12 14 cloud

5.0 6.0 7.0 8.0 0 20 40 5.0 6.0 7.0 8.0 0 40 80 log10 (MCluster / M☉) N log10 (MCluster / M☉) N N N 0 40 80 0 20 40 ) ) -3 -3 cm cm

(K (K

P/k P/k

log Gizmo - 0.42 Gyr log Gadget - 0.42 Gyr Antennae clusters Antennae clusters

6 8Proto 10 SSC 12 14 cloud 6 8Proto 10 SSC 12 14 cloud

5.0 6.0 7.0 8.0 0 30 5.0 6.0 7.0 8.0 0 30 70 log10 (MCluster / M☉) N log10 (MCluster / M☉) N

Figure 2.5: Correlation between pre-cluster gas pressure distributions and initial clus- ter mass functions at 0.40 Gyr, 0.41 Gyr and 0.42 Gyr during the first starburst phase, when most clusters form, from both Gizmo (black) and Gadget (red) simulations. The pressure derived from the observed pre-super star cluster cloud in the Antennae by Johnson et al. (2015) is represented by the blue cross where the error bars reflect 6 the observational uncertainties in cloud mass (3.3 − 15 × 10 M ), radius (24 ± 3 pc) and velocity dispersion (49 ± 3 km/s). The pressures derived from observed star clusters in the Antennae using velocity and radius data compiled in Portegies Zwart et al. (2010) and presented by Mengel et31 al. (2002, 2008) are represented by blue diamonds. The pressure is expressed as P/k where k is the Boltzman constant. 8 −3 4 typical GC progenitors or SSCs is & 10 K cm , which is & 10 times higher than the ISM pressure in the Milky Way (Boulares & Cox 1990; Jenkins et al. 1983; Welty et al. 2016). In the simulations, in order to determine the pressure of the clouds from which the SCs form, we track the cluster members back in time. We take the constituent star particles of a cluster and identify the gas particles from which they formed. We then measure the velocity dispersion of these gas particles and approximate the gas cloud radius as the average distance from gas particles to the center of mass of the cloud. Due to the limited spatial and mass resolutions, we cannot directly probe the cloud density profile for estimating Π, so we approximate Π = 0.5 following Johnson et al. (2015). We note that realistically Π can be higher, but it would increase all our pressure measurements similarly. With these parameters, we can then calculate the cloud pressure using Equation 2.1. In Figure 2.5, we show the resulting pressure distributions against the cluster mass distributions, in comparison with the pressure of a pre-SSC cloud observed in the Antennae by Johnson et al. (2015). We also calculate the pressures of observed SCs in the Antennae Galaxies using the velocity and radius data compiled in Portegies Zwart et al. (2010) and Mengel et al. (2002, 2008) for comparison. As shown in Figure 2.5, the pre-cluster cloud pressures from both the Gizmo and Gadget simulations fall in the range of P/k ∼ 108 − 1012 Kcm−3, in good agreement with observations of a proto-SSC cloud in Antennae (Johnson et al. 2015), but they are 104 − 108 times higher than the typical pressure in the ISM (Boulares & Cox 1990; Jenkins et al. 1983; Welty et al. 2016). Our results support the theoretical expectations that massive SCs form in high-pressure clouds. Moreover, the pressure distributions have near lognormal-shape profiles in all panels. Such a quasi lognormal-shape pressure distribution may be the cause of the quasi lognormal-shape ICMF. If we assume a certain cluster formation efficiency η (η that varies with galactic environment, from 0.01 in quiescent galaxies to > 0.4 in interacting galaxies, as suggested by Goddard et al. 2010; Kruijssen 2015), then the mass of a SC Mcluster may be related to that of the birth clouds Mcloud as

Mcluster ∝ ηMcloud; then by inverting Equation 2.1 we get Mcluster ∝ ηMcloud ∝ ηP. This qualitative relation, as can be inferred from Figure 2.5, suggests that the distribution of cluster mass depends on that of the cloud pressure, so a lognormal pressure distribution may lead to a lognormal mass distribution of the resulting

32 ●

1200 Gizmo whole box Gadget whole box ●

Gizmo galaxy central region ● ● ● ● 1000 Gadget● galaxy central region 800 ●

600 ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● 400 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Velocity dispersion (km/s) Velocity ● ● ● ● ● ● ● 200 ● ● ● ● ● ● ● ● ● ● 0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 Time (Gyr)

Figure 2.6: Evolution of the total velocity dispersion of gas and stars in the central region of one galaxy (5 × 5 × 5 kpc3) (dashed) and the entire simulation box (solid) from both Gizmo (black) and Gadget (red) simulations, respectively. clusters. Furthermore, Figure 2.5 also shows that the pressure profiles have a peak at 5.8−6 6−6.2 cluster mass around 10 M in the Gizmo simulation and around 10 M in the Gadget simulation, which are exactly the same peaks of their corresponding mass functions. This striking correlation may explain the preferred mass range around 6 the characteristic peak 10 M , as determined by the cloud pressure, for the newly formed SCs in galaxy mergers. In order to understand the possible physical processes behind the high pressure of the pre-cluster clouds in our simulations, we compare the evolution of the total velocity dispersion of gas and stars in the central region of one galaxy (since the two merging galaxies are identical), i. e., within 5 kpc from the galactic center, and that of the entire simulation box, as shown in Figure 2.6. We find that the peaks of the total

33 velocity dispersion correspond to those of the star formation as in Figure 2.1, and that velocity dispersion of the galactic central region is higher than that of the whole box during the major starburst phases at 0.4 Gyr and 1 Gyr. These results suggest that high velocity dispersion around galaxy center, which leads to high pressure, and strong circumnuclear starburst, may result from the same mechanism, compressive shocks driven by gravitational torques during galaxy merger. Our theoretical findings may provide explanation to a number of observations. In addition to the recent observations of high pressure in a proto-SSC cloud in Antennae (Johnson et al. 2015), measurements of molecular clouds in the Antennae galaxies have revealed very high velocity dispersion in high star-forming regions (Zhang et al. 2010), which can be explained by compressive shocks (Wei et al. 2012). Herrera et al. (2011) carried out near infrared imaging spectroscopy of the same region and found extended line widths in H2 emission, which indicates powerful shocks in the region. Similarly, measurements of the CO emission from the starbursting merger of M81 /M82 by Keto et al. (2005) suggest that the molecular clouds undergoing star formation are driven by shock compression. Theoretical studies (Ashman & Zepf 2001; Jog & Solomon 1992) have also shown that during the galaxy encounters, the giant molecular clouds undergo significant shock compression which leads to an increase in the cloud pressure. We also note that during 1a phase at 0.23 Gyr, the velocity dispersion of the central region is similar that of the whole box, which suggests a spatially extended star formation probably influenced by tidal forces, as discussed in §3.1. Simulation of Antennae galaxies by Renaud et al. (2015, 2014) have shown that compressive tides during the galactic encounter can cause high star formation over extended volumes. We can see from Figure 2.5 that the pressures of our simulated clouds are somewhat higher than that of the observed systems. This can arise from the fact that in our simulation the two equal-mass, Milky Way - size galaxies collide mainly head on and merge violently, whereas the Antennae Galaxies have a smaller mass and they are on a milder pericentric passage (Renaud et al. 2015). The extreme conditions in the simulated galaxies produce more powerful shocks which in turn help increase the gas pressure. Such an extreme high-pressure environment may preferentially form massive SCs in a narrow mass range as shown in Figure 2.4, which may help to explain why we do not see a power-law ICMF in the simulations. Our simulations bridge the observations and theories of cluster formation and

34 Gizmo simulation Gadget simulation 0.40 Gyr 0.40 Gyr

0.45 Gyr 6 8 0.45 Gyr 0.50 Gyr 0.50 Gyr 10 15 1.01 Gyr 1.01 Gyr 1.04 Gyr 1.04 Gyr 1.10 Gyr 1.20 Gyr Probability density Probability density Probability 0 5 0 2 4

5.0 5.5 6.0 6.5 7.0 7.5 8.0 5.0 5.5 6.0 6.5 7.0 7.5 8.0

log10 (MCluster / M☉) log10 (MCluster / M☉)

Figure 2.7: Probability density function of star cluster mass distribution from both Gizmo (left panel) and Gadget (right panel) simulations at different times, as indicated by the different colors. A Gaussian profile is used as the kernel density estimator. The PDFs are normalized such that the area under each curve is unity. we confirm that massive SCs can form in gas-rich galaxy mergers due to the high gas pressure produced by strong gravitational interactions. Moreover, the special pressure range in such merger environments preferentially forms SCs in a narrow 6 mass interval around the peak mass at ∼ 10 M . Furthermore, the quasi-lognormal pressure distribution may lead to the quasi-lognormal ICMF of SCs formed in colliding galaxies. Our results, therefore, provide clues to the formation of globular clusters and their universal lognormal mass functions, which will be explored in the next section.

2.4 Evolution of Massive Star Clusters

In order to track the change of the cluster mass functions over time, we follow the evolution of the massive SCs in our simulations up to 1.3 Gyr when the progenitors completely coalesce. After the initial bursts of star and SC formation during the first close passage at t ∼ 0.2 − 0.5 Gyr, the activity decreases, and many of the clusters are destroyed over time. However, the starburst activity is renewed again at t ∼ 0.9 − 1.1 Gyr during the final coalescence, although at a lower amplitude than the first burst.

35 ) ☉ M

/

Clus Gizmo simulation (M

Gadget simulation 10 (log

5.6 5.7 5.8 5.9 6.0 6.1 6.2

Most probable cluster mass Most probable 0.4 0.6 0.8 1.0 1.2 Time (Gyr)

Figure 2.8: The most probable star cluster mass as a function of time from both Gizmo (black) and Gadget (red) simulations. The data points correspond to the snapshot times in Figure 2.7.

Figure 2.7 shows the probability density function (PDF) of the cluster mass distribution at different times from both Gizmo and Gadget simulations. Interestingly, the PDFs from the Gizmo simulation have similar narrow profiles, and the position of the peak remains nearly the same over 1 Gyr, while those from the Gadget simulation show a slow evolution from a broad profile to a narrow one and a shift of the peak mass by 0.3 dex over 1 Gyr. The narrowing of the PDF is due to destruction of SCs at both low- and high-mass end by a variety of processes. After ∼ 1 Gyr of evolution, about one fourth of the SCs are left, most of them just around the peak mass. The difference in the narrowness of the PDFs from the two simulations is also present in their initial mass functions in Figure 2.4. This probably stems from the different pressure distributions (Figure 2.5) owing to different treatments of shocks between Gizmo and Gadget, as discussed in § 2.2.1.

36 N N 0 30 60 0 30 60 ) ) -3 -3 pc

pc

☉ ☉ (M (M

density

density

Gizmo - 0.41 Gyr Gadget - 0.41 Gyr 0 2 4 6 0 2 4 6

Antennae clusters log Antennae clusters log Proto SSC cloud Proto SSC cloud

5.0 6.0 7.0 8.0 0 10 20 5.0 6.0 7.0 8.0 0 60 log10 (MCluster / M☉) N log10 (Mtot / M☉) N

Figure 2.9: Density of the simulated clusters from both Gizmo (black) and Gadget simulations. The symbols follow the same meaning as described in Figure 2.5.

The peak for each density curve is the value of the most probable mass of the clusters for that time, as shown in Figure 2.8. The most probable cluster mass in the 5.8 Gizmo simulation is remarkably consistent at ∼ 10 M over 1 Gyr, while that of 6.09 the Gadget simulation changes slightly from ∼ 10 M at the initial starburst to 5.8 ∼ 10 M after 1 Gyr. Since these are isolated merger simulations, it is meaningless to continue the simulations for a longer time, but in a cosmological context, it can be predicted that the SCs will lose some of their mass due to stellar evolution and other destructive processes. Semi-analytical and N-body simulations by Kruijssen (2015) and Webb & Leigh (2015) found that clusters can lose mass by a factor of 2 − 4 after a Hubble time of evolution. The eventual mass of our simulated clusters 5 can be similar to the observed peak mass of globular clusters at 1.5 − 3 × 10 M (Harris 2001; Jordán et al. 2007). These results show that the shape of the mass function and the position of the mass peak of massive clusters have little evolution over the course of the galaxy collision of more than 1 Gyr. We note that the evolution of star clusters is subjected to several destructive processes (e.g., Fall & Zhang 2001; Gnedin et al. 1999a). For 5 low-mass clusters (< 10 M ), the destruction is mainly dominated by two-body relaxation processes, in which the mass of a cluster linearly decreases with time until it is destroyed. For more massive clusters, the evolution is primarily influenced by stellar evolution at early times (. 100 Myr) and by gravitational shocks at later

37 times. These effects are included in our hydrodynamic simulations but the mass resolution is not high enough to resolve the processes realistically, since the two-body relaxation and stellar evolution depend on individual stars. However, the cluster disruption time-scale due to two-body relaxation is proportional to the cluster mass, 4 0.62 4 −2 −0.5 trlx ∼ 1.7 Gyr × (Mclus/10 M ) × (T/10 Gyr ) , where Mclus is the cluster mass and T is the tidal strength around the clusters (Kruijssen et al. 2012). Using the 5 minimum cluster mass of 2 × 10 M in our simulation, and a typical range of tidal strength in the nuclear region (since most of these clusters are concentrated around galaxy nuclei) T ∼ 0.1 − 50 × 10−30 s−2 (Renaud 2010), we find that the range of the disruption time-scale is trlx ∼ 4.88−108.8 Gyrs. For more massive SCs, the time-scale is even longer, beyond our run time of 1 Gyr. Therefore, the two-body relaxation may not have a major disruptive effect on these SCs. Furthermore, the mass loss time-scale due to gravitational shocks (tsh) depends strongly on the cluster density, 4 3 tsh ∼ 3.1 Gyr × ρ/10 M /pc (Kruijssen et al. 2012). The majority of our clusters 5 6 3 have a density range of ρ ∼ 10 − 10 M /pc , as shown in Figure 2.9, which suggests tsh ∼ 30 − 300 Gyrs, much longer than the Hubble time. So gravitational shocks may not have a significant impact on the clusters in our simulation. In addition, as demonstrated by Renaud & Gieles (2013), star clusters formed in galaxy mergers are also affected by the intense tidal field of the galaxies, more so for clusters in the merger remnant compared to the ejected ones. We note, however, the clusters in 4 their simulations have masses . 3 × 10 M , and mass loss decreases as the cluster mass increases. For example, for a cluster to increase its mass by a factor of 2, from 4 4 1.6×10 M to 3.2×10 M , its survival rate (fraction of initial mass survived) after 1 Gyr increases from 0.6 to 0.7. Extrapolating this trend to our clusters which are ∼ 10 times more massive than those in Renaud & Gieles (2013), we argue that destruction from tidal fields likely has negligible effects on the clusters we consider here. Our results suggest that the observed globular clusters may form in high pressure environments induced by galaxy interaction at high redshift when the merger rate was high (e.g., Mistani et al. 2016; Rodriguez-Gomez et al. 2015). The extremely high gas pressures in the merging environments produce lognormal ICMFs with a 6 peak mass around ∼ 10 M , and they evolve slowly over a Hubble time into the 5 universal lognormal profiles with a peak at ∼ 1.5 − 3 × 10 M as observed today.

38 2.5 Discussion

We have used the two codes Gadget and Gizmo with significantly different hydrody- namical solvers to simulate the formation and evolution of SCs in galaxy mergers and found similar results. This helps us to reduce the possibility of significant numerical artifacts in our results and suggests that our findings are physical and robust. In Gadget, the hydrodynamic solver uses a smoothing scheme (Springel 2005), where the physical properties are averaged over a given number of neighboring particles, which is 32 in our simulation. The mass of 32 star particles for our resolution is close to the peak cluster mass seen in the Gadget simulation. However, the Gizmo simulation has no smoothing procedure and the properties do not depend on the number of neighbors but we still see the cluster mass peak at similar masses. This suggests that the peak cluster mass found in our simulation is likely not a numerical artifact, but rather may be a physical feature of SCs formed in such extreme environments. One very potent source of the high pressure in our simulations is the shocks produced during the close passages of galaxies and starburst periods. Gizmo handles shocks much better than Gadget, and it calculates the effects of contact discontinuities more precisely, captures fluid mixing instabilities well and has less numerical noise. These differences are pronounced in Figure 2.5, where the pressure distribution is more cleanly peaked in Gizmo whereas it is quite spread out in Gadget. In our simulations, feedback mechanisms from supernovae and active galactic nuclei in the form of thermal energy and galactic winds are included. However, other feedback processes such as photoionization and radiative pressure may affect star formation (Krumholz et al. 2014). On the one hand, high-energy UV photons from OB stars can ionize the HII clouds in ISM, the expanding HII clouds can compress the neutral gas in the outskirts of molecular clouds and the fragmentation of these dense gas can increase the star formation (positive feedback). On the other hand, the momentum imparted on HII gas by ionizing photons can drive gas out of the central regions of GMCs which may suppress star formation or unbind star clusters (negative feedback). Simulations by Dale et al. (2005) show that for very dense clouds (core density ∼ 108 cm−3), a highly collimated gas outflow can carry the extra momentum out of the cloud without unbinding the cluster. The photoionization also drives the Jeans mass down, resulting in higher star formation. In the context of star formation in galaxy mergers, comparative studies of merger simulations with and without these

39 feedback processes by Hopkins et al. (2013) showed that detailed feedback promote more extensive star formation in tails and bridges, but the global star formation properties remain similar. We plan to explore the effects of radiative feedback on the formation and properties of star clusters in a future project. We have seen from Figure 2.4 that the ICMF in our simulations does not have the shape of a falling power law, which is commonly observed for many YMC systems. Rather, the ICMF has a quasi-lognormal shape which is preserved in later 4 stages. We doubt that this is due to the limited mass resolution (5 × 10 M ) in our simulations, as similar ICMFs were also reported by Renaud et al. (2015), who performed a simulation of the Antennae using a grid-based AMR code with very high mass resolution (∼ 70 M ). The agreement among the merger simulations using different codes, various feedback prescriptions and across resolution suggest that the lognormal-shape ICMFs and the unique mass peak are mostly likely special features of clusters formed in the extremely high pressure environments produced by galaxy collisions. In fact, some studies of active galaxies, such as the starburst galaxy NGC 5253 (Cresci et al. 2005) and the interacting Antennae pair (Anders et al. 2007) have shown that the ICMF for YMCs is not a power law for all mass scales, but may rather have a turnover at low mass. As indicated by Figure 2.7 and Figure 2.8, over the evolution of more than 1 Gyr, the mass functions of our star clusters in both the Gadget and Gizmo simulations survives destructive processes and retain the same quasi-lognormal shape with a 5.8 consistent peak at around ∼ 10 M . This mass is quite close to the observed 5 GCMF peak at ∼ 1.5 − 3 × 10 M . Ideally we would like to have a fully cosmological hydrodynamic simulation of galaxy formation and evolution with a very high mass 3 resolution (∼ 10 M ) to identify SCs and evolve them for ∼ 13 Gyr to explore the fate of the globular cluster mass function, but that remains computationally very expensive. However, the strong trend of survival of the lognormal shape of the ICMFs in our simulations lends support to our speculation that the origin of the lognormal mass functions of the globular clusters may come from the extremely high pressure formation conditions in interacting galaxies.

40 2.6 Conclusions

We have performed high-resolution hydrodynamic simulations of galaxy mergers using two different codes and studied the formation and evolution of SCs in them. We obtained consistent results from both codes, suggesting that our results are physical and robust. Here is a summary of our findings:

• A strong galaxy interaction produces intense shocks and compression of gas, which triggers global starbursts and the formation of massive SCs in the nuclear regions of the mergers and in the tidal bridges and tails. The massive star 5.5−7.5 clusters show quasi-lognormal ICMFs in the range of ∼ 10 M with a peak 6 around 10 M .

• The nascent cluster-forming gas clouds have very high pressures in the range of P/k ∼ 108−12 K cm−3, in good agreement with observations and theoretical expectations that massive SCs form in high-pressure environments, which naturally arise in violent galaxy collisions. Moreover, the gas pressures show quasi-lognormal profiles, which suggest that the quasi-lognormal ICMFs of the clusters may be caused by the pressure distributions in the birth clouds. Furthermore, the peak of the pressure distribution correlates with the peak of 5.8−6.2 the cluster mass function at 10 M , indicating that clusters formed in such 6 extremely high pressure clouds have a characteristic mass around ∼ 10 M .

• The cluster mass functions evolve slowly over time with a declining cluster number due to destructive processes, but the quasi-lognormal shape and the peak of the mass functions do not change significantly during the course of galaxy collisions over 1 Gyr.

Our results suggest that the observed universal lognormal globular cluster mass 5 functions and the unique peak at ∼ 2 × 10 M may originate from the high-pressure formation conditions in the birth clouds. Globular clusters may have formed in extremely high pressure environments produced by violent galaxy interactions at high redshift when mergers were more common. The lognormal cluster mass functions with 6 a preferred most probable cluster mass around ∼ 10 M may be unique products of such extreme birth conditions, and they evolve slowly over 13 Gyrs but retain the lognormal shape and peak against destructive processes.

41 Acknowledgement

We thank Dr. Bruce Elmegreen and Dr. Phil Hopkins for valuable discussions, and Dr. Florent Renaud for his constructive comments which have helped improve the paper significantly. YL acknowledges support from NSF grants AST-0965694, AST-1009867, AST-1412719, and MRI-1626251. AK is supported by the Ministerio de Economía y Competitividad and the Fondo Europeo de Desarrollo Regional (MINECO/FEDER, UE) in Spain through grant AYA2015-63810-P as well as the Consolider-Ingenio 2010 Programme of the Spanish Ministerio de Ciencia e Innovación (MICINN) under grant MultiDark CSD2009-00064. He also acknowledges support from the Australian Research Council (ARC) grant DP140100198. We acknowledge the NSF award MRI- 1626251 for providing computational resources and services through Institute for CyberScience at The Pennsylvania State University that have contributed to the research results reported in this paper. The Institute for Gravitation and the Cosmos is supported by the Eberly College of Science and the Office of the Senior Vice President for Research at the Pennsylvania State University.

This chapter has been published as a paper titled ‘The Formation and Evolution of Star Clusters in Interacting Galaxies’ in The Astrophysical Journal, Volume 844, Issue 2, article id. 108, 13 pp. (2017).

42 Chapter 3 | Is there a Disk of Satellites around the Milky Way?

3.1 Introduction

Four decades ago, it was first reported that five bright satellite galaxies of the Milky Way (MW) align in a plane inclined to the Galactic stellar disk (Lynden-Bell 1976), a phenomenon later dubbed as “disk of satellites" (DoS) (Kroupa et al. 2005) that included 11 bright MW dwarfs. Recently, it was claimed that 8 of these satellites co-rotate in the DoS (Metz et al. 2008; Pawlowski et al. 2013). Numerical simulations with the standard Lambda Cold Dark Matter (ΛCDM) model have been largely unsuccessful to reproduce such a spatially-thin, kinematically-coherent structure, which has been strongly criticized as a failure of the standard ΛCDM cosmology (Pawlowski et al. 2015a; Kroupa et al. 2005). To date, more than three dozens of dwarf galaxies have been detected around the MW (Koposov et al. 2015; McConnachie 2012), and it was suggested that all satellites lie in the original DoS formed by the 11 classical satellites (Pawlowski et al. 2015). More intriguingly, it was recently reported that about half of the satellites in Andromeda (15 out of 27) form a DoS around the host (Conn et al. 2013; McConnachie et al. 2009; Pawlowski et al. 2013), and that 13 out of the 15 co-planar satellites co-rotate based on line-of-sight velocities (Ibata et al. 2013). Outside of the Local Group, one study (Ibata et al. 2014) found 22 galaxies in the Sloan Digital Sky Survey (SDSS) catalog which have diametrically opposed satellite pairs with anti-correlated velocities, and the authors suggested that co-planar and co-rotating DoS is common in the Universe.

43 The origin of the DoS, however, has remained an unsolved mystery. On the one hand, many advanced ΛCDM simulations have failed to produce such thin, co-rotating DoS in galaxies. While some sophisticated simulations have managed to produce an anisotropic distribution of satellites (Papastergis & Shankar 2016; Pawlowski et al. 2015a; Buck et al. 2016; Sawala et al. 2016; Zhu et al. 2016), no consensus of coherent motion was found in the DoS (Bahl & Baumgardt 2014; Buck et al. 2016; Cautun et al. 2015b; Sawala et al. 2016). On the other hand, the interpretation of DoS from observations has been called into question. Buck et al. (2016) demonstrated that line-of-sight velocities are not representative of the full 3-D velocity of a galaxy and they cannot be used to derive coherent motion in Andromeda satellites. Furthermore, recent investigations of the SDSS galaxies by Cautun et al. (2015a) and Phillips et al. (2015) found that the excess of pairs of anti-correlated galaxies is very sensitive to sample selection and it is consistent with the random noise corresponding to an under-sampling of the data. In order to resolve the controversies surrounding the DoS, we reanalyze the observed satellites of the MW and compare them with advanced simulations. We focus on the following important issues: (1) effects of the plane identification method and sample size on the DoS properties, (2) the stability of the planar structure; and (3) effects of baryons on the distribution and evolution of satellites. The chapter is organized as follows. In §3.2 we introduce the methods used in this study, including the techniques to identify the planar structure, the model to project future evolution of the current satellites, and the cosmological simulations with and without baryons. We present our results in §3.3, namely the structural and kinematic properties of the observed satellites,the dynamical evolution of the observed 11 classical satellites, and the DoS structure and its evolution from two cosmological simulations. We summarize our findings and their implications in §3.4.

3.2 Methods

We use two types of techniques to analyze the present distribution of the positions of the observed satellites around the MW: the Principal Component Analysis (PCA) and the Tensor of Inertia (TOI). For our specific case of 3D positional data, PCA can be thought of as fitting an ellipsoid to the data, where the ratio of minor and major axis (c/a) indicates the

44 anisotropy of the dwarf distribution. If the distribution of the dwarfs is perfectly planar, then c/a → 0. In the TOI method, which is often used in literature (Allgood et al. 2006), we calculate the moment of inertia matrix of the satellites and diagonalize it. The eigenvalues of this matrix gives the three axes (a, b, c) of the fitted ellipsoid to the dwarf distribution. It has been argued that distant dwarfs in this distribution have a greater chance of being outliers, hence they should carry less weight in the TOI calculations. Here we consider three different weights for satellite distances, namely 1, 1/r and 1/r2, respectively, as used by different groups in literature (Pawlowski et al. 2015a; Cautun et al. 2015a; Sawala et al. 2016). We discuss these methods in more detail in chapter 4. Moreover, in order to investigate the stability of the DoS, we employ the galaxy dynamics software Galpy 1 (Bovy 2015) to predict the future position and velocity of the observed 11 classical satellites. We use a realistic MW potential with three components: a power-law density profile (cut-off at 1.9 kpc) for the central bulge, a stellar disk represented by a combination of 3 Miyamoto-Nagai potentials (MN3 model) with varying disk mass and radial scalelength (Smith et al. 2015), and Navarro- Frenk-White (Navarro et al. 1996) density profile for the dark matter halo. We take the initial position and velocities in galactic coordinates from Pawlowski et al. (2013) and convert them into galactocentric cartesian coordinates (Johnson & Soderblom 1987). Finally, in order to understand the origin of the DoS, we compare two cosmological simulations of a MW-size galaxy, one with both baryons and dark matter (hereafter referred to as “Hydro Simulation", Marinacci et al. 2014) and the other with dark matter only (hereafter referred to as “DMO Simulation", Zhu et al. 2016). The Hydro simulation includes a list of important baryonic physics, such as a two-phase ISM, star formation, metal cooling, and feedback from stars and active galactic nuclei (AGN). We refer the reader to Marinacci et al. (2014) for more details on the this simulation. The dwarf galaxies (subhalos) in the simulations are identified using the Amiga Halo Finder (Knollmann & Knebe 2009), a density-based group finder algorithm.

1http://galpy.readthedocs.io/en/latest/

45 40 1.0 PCA ToI, weighted by 1 11 dwarfs 27 dwarfs 39 dwarfs ToI, weighted by 1/r 35 0.8 2 ● ToI, weighted by 1/r ●

● ● 30 0.6 ● ● ● ● c / a ● ● ● 25 0.4 ●

● ● ● ● ● PCA

rms height of DoS (kpc) ●

● ●

20 ToI, weighted by 1 0.2 ToI, weighted by 1/r 11 dwarfs 27 dwarfs 39 dwarfs ToI, weighted by 1/r2 15 0.0 10 20 30 40 50 10 20 30 40 50 number of observed dwarfs number of observed dwarfs

Figure 3.1: A comparison of the DoS structure using different sample size and plane fitting method: “isotropy" (top) as indicated by the ratio between semi-minor and semi-major axes, c/a (c/a = 0 means completely anisotropic planar distribution); and “thickness" (bottom) as indicated by the root-mean-square height of the fitted plane. The plane fitting methods include PCA and TOI with different weight function. The complete sample includes 39 confirmed satellites of the MW (Koposov et al. 2015; McConnachie 2012).

3.3 Results

3.3.1 DoS properties with different methods and sample sizes

3.3.1.1 Structural properties

A comparison of the DoS structure using different plane identification methods (PCA and TOI) and different sample sizes is illustrated in Figure 3.1. The sample of 39 currently confirmed dwarfs of the MW (Koposov et al. 2015; McConnachie 2012) includes the 11 classical satellites (Kroupa et al. 2005) and the 27 most massive nearby ones in the previous analysis (Pawlowski et al. 2013). Clearly, when the satellite number increases from the original 11 to the full sample of 39, the “isotropy" of the DoS (represented by the ratio between semi-minor and semi-major axes of the principal components, c/a) increases from c/a ∼ 0.2 to ∼ 0.26 using the PCA and unweighted TOI methods, and the “thickness" of the DoS (represented by the root-mean-square height of the fitted plane) increases rapidly from ∼ 20 kpc to ∼ 30

46 ● ● ● ● ●

1.0 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.9 ● ● ● ● ● ● 0.8

● 0.7 ● result

● 0.6 0.5 ● b/a ● c/a 0.4

101 102 103 104 sample size N

Figure 3.2: Effects of sample size on the anisotropy measurement of a system. The red and blue lines represent the c/a and b/a ratio of the sample, respectively, and the shaded regions indicate the 1σ error bar of the measurements. kpc. For a weighted TOI with 1/r2 typically used in the analysis of cosmological simulations (Sawala et al. 2016), the DoS becomes more isotropic and thicker. This figure demonstrates that the DoS structure is subjected to selection effects, which explains the different claims reported in the literature using different methods and sample sizes (Pawlowski et al. 2015; Sawala et al. 2016). In order to test the effect of sample size on the anisotropy measurements in more detail, we sample an isotropic distribution (input c/a and b/a = 1) with 104 objects. We repeatedly draw random samples with given size from the sphere and calculate c/a and b/a ratios of the sample using the unweighted TOI method. The variation of these anisotropy ratios with the sample size is shown in Fig 3.2. For large sample size N, the output ratios do point to the true results of both ratios being 1. On the other hand, for small (e.g. N∼10), it does not adequately sample the sphere,

47 resulting in very biased estimates (for N = 10, median c/a = 0.58, b/a = 0.8). We discuss this effect in more detail in chapter 4 where we place 11 satellites at their observed distances, vary the input c/a from 0.4 to 1.0 and perform a Monte Carlo simulation with 105 realizations. We find that for all input c/a values, the output c/a is consistently biased towards lower value. With an input c/a ∼ 0.4, there is a 20% 2 chance that the system has c/a . 0.18. We also find that weighted TOI method (1/r ) consistently gives better result (closer to true value) compared to the unweighted method. This analysis indicates that the system appears to be more anisotropic when the sample size is very small because a small sample size systematically yields a lower c/a ratio than the true underlying anisotropy of the system.

3.3.1.2 Kinematic properties

In a recent study by Pawlowski et al. (2013), it was suggested that 7 to 9 out of the 11 classical MW satellites are co-rotating because the angles between their angular momenta and the DoS normal of the 11 satellites fall within 45 degrees. We use the same criterion for corotation in this study and show the angular momentum distribution of the satellites in Figure 3.3. As shown in the left panel of the figure 8 satellites appear in the corotation region (similar to the result of Pawlowski et al. 2013), but given the large error bars of Sextans and Carina, only 6 (LMC, SMC, Draco, UMi, Fornax and LeoII) can be robustly considered as corotating. However, this sample size is very small and apparent clustering can often be found in random distributions. This effect, known as the clustering illusion (Clarke 1946), can lead to misinterpretation of the data as we demonstrate below. In order to understand the significance of the co-rotation and the effect of sample size, we perform a “clustering" test. Our null hypothesis is that there is no coherent motion on the DoS plane, i.e. there is no clustering of the angular momentum on the sphere. We use Monte Carlo simulations to numerically test the apparent clustering seen in the observed satellite angular momenta. We draw N random data points from a uniform distribution on a sphere and search for clustering for each draw within a given apex angle. This experiment is repeated for 104 trials. First, we carry out this experiment with a fixed number N = 11, i.e. the number of classical MW satellites. It is found that the median number of clustered points within 45 degrees is 4, and the chance of finding 5 or 6 clustered points within 45 degrees, similar to the clustering for observed satellites, is ∼ 19% for 5 and ∼ 6% for 6 points, respectively. Next,

48 180 Sculptor Counter−rotating ● 135

● Sagittarius Sextans Carina LeoI ● 90

Draco UMi SMC ● ●

45 ● Fornax LMC ● ●

● ●

Angle between ang. mom. and DoS normalAngle between Co−rotating LeoII ● 0 1 2 3 4 5 6 7 8 9 10 11 Satellite index

Figure 3.3: Distribution of the angle between the satellite angular momentum and the DoS normal, with their respective error bars resulting from the uncertainties in velocity measurements. Satellites can be considered as corotating on the DoS if this angle is within 45 degrees (pink region) and counter-rotating if they are within 135 - 180 degrees (green region). we repeat the simulation with a varying number of points. To quantify the effect of sample size, we define a bias parameter as the ratio between the observed number of clustered points and an expected number proportional to the solid angle (S) of the cone (S/4π × N). The resulting distribution of clustering from these experiments are shown in Figure 3. This figure demonstrates that for smaller sample size, the clustering bias is significantly higher at given small angles. A strong clustering factor (2.5 - 3.5) at N < 20 and angle < 45 can be found due to the intrinsic fluctuations of random points alone. This test shows that, even though the intrinsic distribution is uniform, the points can appear highly clustered for a small sample size. Therefore, we caution that the evidence of coherent rotation in the 11 observed satellites may not be conclusively different from that of a random data sample.

49 clustering bias distribution

80 1.5

60 1.5

2.5 40 half apex angle

3.5 4.5 2.5 20 5.5 6.5 3.5 5.54.5 20 40 60 80 number of points

Figure 3.4: Half apex angle of the cone vs. the number of points found in them. We draw random data points from a isotropic point distribution in a sphere and search for clustering within different half apex angle cones in each of 104 trials. The numbers on the contours represent bias parameters. For 11 satellites in a uniform distribution, there is a 6% chance that 6 of them are clustered within 45 degree.

3.3.2 Dynamical evolution of satellites

Recently, Lipnicky & Chakrabarti (2016) studied the dynamics history of the 11 “classical" satellites and suggested that the DoS would lose its significance in less than one Gyr in the past. In order to investigate the future evolution of DoS, we use the galactic dynamics software Galpy (Bovy 2015) to predict the future trajectories of the 11 classical satellites. Figure 3.5 shows the future positions of the 11 satellites using a realistic MW potential with three components: a dark matter halo with the NFW density profile (Navarro et al. 1996), a central bulge with a power-law density profile cut off at 1.9 kpc, and a stellar disk with the MN3 potential (Smith et al. 2015). Note that the points only represent the final positions at these times, not the detailed orbits of the

50 t = 0 t = 0.5 Gyr 300 300 ● ● ● LeoII LeoI ● 200 200

● ●

100 UMi 100 ● Sextans ●●● Draco ●

0 Sagittarius ● 0 ● ● Carina ● ● LMC Z (kpc) Z (kpc) ● ● ● SMC Sculptor ●●

−100 Fornax ● −100 −300 −300

−300 −100 0 100 200 300 −300 −100 0 100 200 300 X (kpc) X (kpc)

● t = 1.0 Gyr 300 ●

● 200

● ● 100 ● ● 0 ● Z (kpc) ● ● −100 ● −300

−300 −100 0 100 200 300 X (kpc)

Figure 3.5: Positions of 11 classical satellites in galactocentric co-ordinates at the present (left), 0.5 Gyr (middle) and 1 Gyr from now (right), respectively. The solid lines in each panel represent the fitted DoS at that time and the dashed lines represent the r.m.s. height of the plane. The blue shaded region in each panel depicts the present-day DoS. satellites, and that nearby satellites such as Sagittarius may complete more than one orbit in 1 Gyr while distant ones such as LeoII may move only a fraction of their orbits. To estimate the error bars in the positions, we model the present velocities as a normal distribution taking as a standard deviation their present-day uncertainties. We take 1000 random samples from this velocity distribution, calculate their future trajectories and take the 16th and 84th percentile value (which approximate the 1σ confidence interval) of these future position distribution as our lower and upper error

51 bars. Some of these satellites have large proper motion errors which propagates a significant uncertainty in far future positions, so predictions beyond 1 Gyr are not trustable (Lipnicky & Chakrabarti 2016). From this figure, we find that the 11 satellites are moving away from the present DoS at future times. The new fitted DoS is thicker with c/a ∼ 0.36 (height 45 kpc) at t = 0.5 Gyr and c/a ∼ 0.42 (height 64 kpc) at t=1 Gyr, compared to the thin DoS (c/a 0.18, height 19.6 kpc) at the present time. We have also explored two different MW potentials, by replacing the stellar disk with a one component Miyamoto-Nagai potential (Bovy 2015, MW2014 model), and a NFW dark matter halo only potential, but the resulting positions (not shown to avoid overcrowding) are very similar to those from Figure 3.5. These calculations show that, for these idealized potentials, the MW satellites tend to move away from the present DoS, increasing its thickness and suggesting that the current thin DoS may be a transient structure.

3.3.3 Evolution of DoS isotropy in simulations

In order to understand the nature and the origin of the DoS, we analyze the satellites from two cosmological simulations of a MW-sized galaxy, the Hydro Simulation with comprehensive baryonic physics including star formation and feedback processes (Marinacci et al. 2014), and the DMO Simulation which is a pure N-body run (Zhu et al. 2016). We find that baryons can significantly affect the abundance and spatial distribution of satellites (see also Zhu et al. 2016). For example, within 1 Mpc, only 106 luminous subhalos with star formation are found in the Hydro Simulation and they are distributed anisotropically, in sharp contrast to the ∼ 21220 subhalos which show isotropic distribution in the DMO Simulation. Figure 3.6 shows the isotropy ratio c/a of both simulations as a function of redshift for three samples: the 11 most massive dwarfs within the virial radius (which have a similar mass range as the observed 11 “classical” satellites of the MW), dwarfs within the virial radius of the central galaxy, and dwarfs within 1 Mpc from the galaxy. These groups show three distinct trends in the evolution of c/a. When we select only the 11 most massive halos within the virial radius, the two simulations show similar highly anisotropic distribution throughout time, and at z = 0 the c/a ratio is close to the observed value (∼ 0.2). For dwarfs within Rvir, the c/a ratio generally increases as redshift approaches z = 0 for all three samples i.e., the Hydro dwarfs, all DMO

52 1.0 1.0

●

● ● ●

● ●

● ●

0.8 0.8 ●

● ● ● ● ● ● ● ● ●

● ● ● ● ● ● ● 0.6 0.6 ●

● ● ● ● ● ● ● ● ● ● ● ● ● c / a c / a ● ● ● ● ● ● ● ● ● ● ● ● ● 0.4 ● 0.4 ● ● ● ● ● ● ● ●

0.2 0.2 All hydro dwarfs within Rvir

Most massive 11 Hydro dwarfs < Rvir ● All DMO dwarfs within Rvir Most massive 11 DMO dwarfs < Rvir DMO dwarf subsample within Rvir 0.0 0.0 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1.2 1.0 0.8 0.6 0.4 0.2 0.0 log (1+z) log (1+z) 1.0

●

● ●

● 0.8

● ● ● ● ● ● ●

● ● ● ● ● ● ● ● ● ● ● ● ● ●

0.6 ● ● ● ●

●

●

c / a ● ● ● ● ● 0.4 ●

0.2 All hydro dwarfs within 1 Mpc All DMO dwarfs within 1 Mpc DMO dwarf subsample within 1 Mpc 0.0 1.2 1.0 0.8 0.6 0.4 0.2 0.0 log (1+z)

Figure 3.6: A comparison of the spatial distribution of satellites, as indicated by the “isotropy" c/a, at different redshift between the Hydro and DMO cosmological simulations. We consider three satellite samples: the 11 most massive dwarfs within the virial radius (left panel), dwarfs within the virial radius (Rvir) of the central galaxy (middle panel) , and dwarfs within 1 Mpc from the central galaxy (right panel). Note in this Figure, the “Hydro dwarfs" (in red in all three panels) refers to star-forming dwarfs from the Hydro Simulation within a given distance at different redshift (for convenient comparison, let Nzbar be the number of these baryonic dwarfs at a given z), the “DMO dwarf subsample" (in black in the middle and right panels) refers to a selective DMO dwarf sample which has the same number as that of the Hydro dwarfs, the Nzbar most massive ones from the DMO Simulation at the same redshift and within the same distance considered, and “All DMO dwarfs" (in grey in the middle and right panels) refers to all dwarfs formed from the DMO Simulation at the given redshift. All distances are in comoving coordinates.

53 dwarfs, and DMO dwarf subsample (massive DMO dwarfs with same sample size as the Hydro counterpart). This is mainly due to the rising abundance of dwarfs within the virial radius and phase mixing (Henriksen & Widrow 1997). The satellite infall near the center can be chaotic and even if some satellites are accreted as a group from similar directions, as they move through the galactic potential, the neighboring satellites in phase-space can become out of phase with time, resulting in a smooth phase-space distribution of satellites. This phase mixing is more effective for satellites closer to the center (Helmi et al. 2003), which may explain the increased c/a inside

Rvir. On a galactic scale of 1 Mpc from the central galaxy, we find a remarkable difference between the Hydro and DMO simulations. At high redshift (z ∼ 10) the satellite distributions are almost isotropic but over time the c/a ratio of both simulations declines, although the decrease is much more significant in the Hydro simulation (c/a ∼ 0.4 at z = 0) compared to the DMO one (c/a ∼ 0.64 at z = 0), even with the same sample size. On a cosmic scale (> 1 Mpc), we find that both ratios (b/a and c/a) continue to decrease, which suggest that the anisotropic dwarf distribution may be part of the large scale filamentary structure. We discuss this in more detail in chapter 4.. Our results suggest that on Mpc scales, the distribution of dwarfs around a central galaxy is anisotropic as part of the large-scale filamentary structure. It has been suggested by many detailed DMO simulations that anisotropic satellite distribution can result from filamentary accretion of the satellites around the host galaxy and the infall history can impact the final orientation of the satellites in the position-velocity space (Aubert et al. 2004; Libeskind et al. 2005, 2014; Lovell et al. 2011; Tempel et al. 2014; Buck et al. 2016). There are two factors responsible for the different satellite distributions between Hydro and DMO simulation: the difference in the satellite abundance and the effects of baryonic processes. Overall, the satellite abundance in DMO simulation is much higher than that in the Hydro run, which in turn results in a more isotropic distribution, which is evident in Fig 3.6 (middle panel). Furthermore, in the Hydro Simulation the dwarfs are subjected to additional baryonic processes, e.g. adiabatic contraction, tidal disruption and reionization (Zhu et al. 2016) that can significantly change the abundance, star formation activity, infall time, and trajectory of the satellites. For very massive subhalos the effects are mild and the most massive halos

54 in both simulations are essentially the same, resulting in very similar c/a evolution for the 11 massive satellites. However, for intermediate mass halos the tidal effects impacts the dynamics of the halos and even in similar mass range, halos in DMO and Hydro simulation have different properties. Hence, in spite of having the same sample size, the halos within 1 Mpc shows a significantly different distribution for simulations with and without baryons. Similar results have also been suggested by recent studies (e.g., Ahmed et al. 2016; Sawala et al. 2016; Zhu et al. 2016; Zolotov et al. 2012). Therefore, the inclusion of baryonic impacts may solve the discrepancy in the DoS anisotropy from previous simulations (Pawlowski et al. 2015a; Sawala et al. 2016).

3.4 Conclusions

In summary, we have performed a comprehensive reanalysis of the observed satellites of the MW using different plane identification methods and sample size. We have carried out Monte Carlo simulations to investigate the effects of sample size on the DoS properties, have calculated the future evolution of the 11 classical satellites in order to test the stability of the current DoS, and have compared two cosmological simulations in order to understand the evolution of satellites and effects of baryons on the DoS properties. We find that the measured DoS properties strongly depends on the plane identification method and the sample size, and that a small sample size may artificially show high anisotropy and strong clustering. Furthermore, we find that the DoS structure may be transient, and that baryonic processes play an important role in determining the distribution of satellites. We conclude that the evidence for an ultra-thin, coherently-rotating DoS of the MW is not conclusive. Our findings suggest that the spatial distribution and kinematic properties of satellites may be determined by the assembly history and dynamical evolution of each individual galaxy system, rather than being a universal DoS phenomenon.

3.5 Acknowledgments

YL acknowledges support from NSF grants AST-0965694, AST-1009867, AST-1412719 and MRI-1626251. We thank the anonymous referee, and Dr. Marcel Pawlowski and Dr. Yohan Dubois for thoughtful comments which have helped improve our manuscript.

55 We acknowledge the Institute For CyberScience at The Pennsylvania State University for providing computational resources and services that have contributed to the research results reported in this paper. The Institute for Gravitation and the Cosmos is supported by the Eberly College of Science and the Office of the Senior Vice President for Research at the Pennsylvania State University.

This chapter has been published as a paper titled ‘Is There a Disk of Satellites around the Milky Way?’ in The Astrophysical Journal, Volume 843, Issue 1, article id. 62, 6 pp. (2017).

56 Chapter 4 | The nature of Disk of Satellites around Milky Way-like galaxies

4.1 Introduction

In the ’70s Lynden-Bell (1976) and Kunkel & Demers (1976) found that the 11 brightest satellite galaxies of the Milky Way (MW) have a highly anisotropic distribution and that they align in a plane inclined to the Galactic stellar disk. Such planar structure is now commonly referred to as “disk of satellites” (DoS, Kroupa et al. 2005). To date, more than two dozens new dwarf galaxies have been detected around the MW (e.g., Helmi 2008; Willman 2010; Koposov et al. 2015; McConnachie 2012). Pawlowski et al. (2015) suggested that these new dwarfs also have an anisotropic distribution and can be interpreted as lying in a disk , although the new DoS is thicker and has a higher minor-to-major axis ratio (more details in chapter 3). It was reported that 15 out of the 27 dwarfs around Andromeda, detected by Pan-Andromeda Archaeological Survey (PAndAS; McConnachie et al. 2009), also follow an anisotropic planar distribution (e.g., Conn et al. 2013; Koch & Grebel 2006; McConnachie et al. 2009; Metz et al. 2007; Pawlowski et al. 2013; Ibata et al. 2013). Among the original 11 “classical” satellites around Milky Way (MW), 7 to 9 galaxies preferentially co-orbit in a similar direction (Pawlowski et al. 2013), which have been interpreted as coherent motion of the DoS. Ibata et al. (2013) used line-of- sight (LOS) velocities to suggest that 13 out of 15 coplanar satellites of Andromeda are co-rotating. Outside of the Local Group, Ibata et al. (2014) used the SDSS catalog and identified 22 galaxies with diametrically opposed satellite pairs and found that 20 of them have anti-correlated velocities, suggesting that co-planar and co-rotating

57 satellite galaxies are common in the Universe. However, these claims have been rebuffed recently. In chapter 3, we performed a comprehensive reanalysis of the observed Milky Way satellites. We found that the DoS structure depends strongly on sample size and the plane identification method, and that only 6 out of the 11 “classical" dwarfs may be considered as corotating, in contrast to previous claims (Pawlowski et al. 2015a, 2013). Moreover, Buck et al. (2016) performed 21 cosmological simulations to investigate the kinematics of M31 satellites, and they concluded that LOS velocities are not representative of the 3D velocities of the galaxies themselves. When only LOS velocities are used, the results can apparently agree with the observations, but when the full 3D angular momenta of the galaxies are considered no coherent motion can be found on the DoS plane. Furthermore, investigations on SDSS galaxies by Cautun et al. (2015a) and Phillips et al. (2015) found that the excess of pairs of anti-correlated galaxies is very sensitive to sample selection parameters and sample size, and it is consistent with random noise corresponding to an under-sampling of the data. The origin of the anisotropic distribution of satellites has been a hotly debated issue. Some early studies suggested that satellite galaxies preferentially avoid regions near host galaxies equator plane and tend to cluster near the poles (Holmberg 1969; Zaritsky et al. 1997), but later observations showed that this may only be true for certain type of galaxies (e.g., Agustsson & Brainerd 2010; Azzaro et al. 2007; Bailin et al. 2008; Brainerd 2005; Sales & Lambas 2004). In recent years, a number of simulations have been aimed at explaining the DoS. Initially, N-body simulations were largely unsuccessful to directly predict the DoS because they produced an isotropic distribution of dark matter sub-halos around the main galaxy in the standard Lambda Cold Dark Matter (ΛCDM) cosmology (Kang et al. 2005). This has been strongly criticized as a failure of ΛCDM by some authors (Kroupa et al. 2010; Metz et al. 2007; Pawlowski & Kroupa 2014; Pawlowski et al. 2012; Kroupa et al. 2005). Recent developments in numerical techniques and computational power have made it possible to study the DoS phenomenon in a more realistic manner. Bahl & Baumgardt (2014) investigated the probability of finding satellite planes similar to the DoS around M31 in the Millennium II Simulation, and found that such planes occur frequently. Sawala et al. (2016) analyzed the APOSTLE simulations, a suite of smoothed particle hydrodynamics (SPH) simulations of the Local Group, and found that satellite systems form with a wide range of spatial anisotropies and it is

58 possible to reproduce the observed DoS of 11 brightest MW satellites. Cautun et al. (2015b) analyzed two high resolution N-body cosmological simulations (Millennium-II; Boylan-Kolchin et al. 2009 and Copernicus Complexio; Hellwing et al. 2016) and found that planar distribution of satellites are very common and the degree of anisotropy vary from system to system. The controversies surrounding the DoS stem from three separate issues: (i) the plane detection method or the definition of plane is not well specified or uniform across different studies, which results in obtaining different results using the same sample; (ii) different sample sizes have been used in various studies and most of them are using very small number of galaxies (11 for MW and 15 for M31), and (iii) the majority of theoretical studies did not include the effect of baryons in the cosmological simulations which can strongly affect the distribution and abundance of galaxies. In order to address these controversies, we investigate all the three issues men- tioned above in this study by analyzing a high-resolution cosmological hydrodynamic simulation of a MW-sized galaxy by Marinacci et al. (2014), and compare it to its DM-only counterpart. The dwarf galaxies in the simulations are identified with a density-based hierarchical algorithm, the Amiga Halo Finder (Gill et al. 2004; Knollmann & Knebe 2009). A more detailed description of the simulations is given in Marinacci et al. (2014) and Zhu et al. (2015). To perform our analysis we divide the dwarfs into four different sample sizes as found in observations and analyze their spatial and kinematic properties. We also adopt two different types of plane identification methods used in literature. In addition, we track these satellites to high redshift in order to understand the nature and origin of the distribution of the satellite system. This chapter is organized as follows. In § 4.2we describe the numerical techniques used in this investigation, which include the plane identification methods, the cos- mological simulations and dwarf galaxy identification code used. In § 4.3,we present the abundance and spatial distribution of satellites at the present day, by comparing hydrodynamical and N-body simulations. In § 4.4, we show the kinematic properties of the satellites at redshift z = 0. The evolution of the satellite system is explored in § 4.5.We discuss the various selection effects on the DoS, which include the sample size, the distance of satellites from central galaxy, and plane detection methods in § 4.6, and we summarize our findings in § 4.7.

59 4.2 Methods

In this chapter we use the hydrodynamical cosmological simulation of a Milky Way- sized galaxy (Aq-C-4 halo) by Marinacci et al. (2014) (hereafter referred to as Hydro simulation), and a dark matter-only run of the same halo from Zhu et al. (2016) (hereafter referred to as DMO simulation) for comparison. The Hydro simulation was performed with the moving mesh code AREPO (Springel 2010), and it models, other than gas dynamics, a set of baryonic processes playing a key role in galaxy formation. The model includes an effective ISM model describing a two-phase interstellar medium, star formation, metal-dependent cooling, metal enrichment and mass return from stellar evolution, and both stellar and AGN feedback. 1 12 The modeled galaxy has a virial mass of 1.59 × 10 M , similar to that of the 4 Milky Way. The mass resolution for baryonic particles is 5 × 10 M and for DM 5 particles it is 2.7 × 10 M in the hydrodynamic simulation. In the DMO run, the DM particles has the summed mass of the two types of particles in hydro run, namely 5 3.2 × 10 M . We use the density based group finder Amiga Halo Finder (AHF) (Knollmann & Knebe 2009) to identify the star forming subhalos in this simulation, which constitute the dwarf galaxy population in this simulation (details of this code is presented in Chapter 2.2.3).

4.2.1 Plane Identification Methods

We have used two types of methods for plane identification in this chapter: Principal Component Analysis (PCA) and Tensor of Inertia (TOI) method. The TOI method is used in conjunction with with 3 different weighting functions. We give a more detailed description of both plane identification techniques in the subsections below.

4.2.1.1 Principal Component Analysis (PCA)

PCA is a common method used for multivariate data analysis in statistics. The goal of PCA in general is to explore linear relationships between different variables in the dataset and, thus simplifying the data by reducing its dimensionality. In our specific

1total mass inside virial radius (234 kpc). Here the virial radius is defined as the radius of the sphere which encloses an overdensity of 200 with respect to the critical density.

60 case we aim to find out to what extent the 3D distribution of the satellite galaxies can be expressed as 2D, i.e. galaxies lying on a plane (DoS). In this application, the method of PCA can be viewed as fitting an ellipsoid to the data. The anisotropy of the distribution can thus be expressed as the ratio of minor axis to the major axis (c/a). If the distribution is perfectly 2D (i.e. tha data lie on an infinitely thin plane), c/a = 0, while if it is perfectly isotropic, c/a = 1. PCA is an orthogonal linear transformation of the data which finds and projects the data on a new co-ordinate system where the highest data variance lies on the new x-axis, the second highest variance lies on the new y-axis and so on. The steps of this procedure are shown below.

Let the positions of the dwarfs be denoted by (xi, yi, zi) where i runs from 1 to n, the number of dwarfs in the system. First the data is centered by subtracting the mean of the x, y and z positions of the dwarfs from their original co-ordinates. The new position matrix is :

 0 0 0  x1 y1 z1    0 0 0  0  x2 y2 z2  I =   (4.1)    ......   0 0 0  xn yn zn

where ,

n n n 0 1 X 0 1 X 0 1 X xi = xi − xj; yi = yi − yj; zi = zi − zj (4.2) n 1 n 1 n 1

Now we find the covariance matrix of the new positions given by :

0 0T 0 Icovariance = I I (4.3) This is a 3 × 3 dimensional matrix given by:

 02 0 0 0 0  xi xiyi xizi n   0 X  0 0 02 0 0  Icovariance =  xiyi yi yizi  (4.4) i=1  0 0 0 0 02  xizi yizi zi

61 1.0 1.0 ● Hydro, N = 106 ● DMO, N = 21220 ● gal ● su● b ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.5 0.5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 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● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●●● ●● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● 0.0 0.0 ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ●● ●● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ●● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● y (Mpc) y (Mpc) ● ● ● ●● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● −0.5 ● −0.5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

● ● ● ● ● ●

● ● ● ● ● ● ● ●

● −1.0 −1.0 −1.0 −0.5 0.0 0.5 1.0 −1.0 −0.5 0.0 0.5 1.0 x (Mpc) x (Mpc)

Figure 4.1: A comparison of the projected positions of dwarfs with total mass above 7 10 M , as represented by filled circles, in the X-Y plane at z=0 within 1 Mpc from the central galaxy between the hydrodynamical (left) and the dark matter-only (right) simulations. The size of the circle is proportional to the halo mass, and the open circle in the center of the two plots indicates the virial radius of the simulated Milky Way at ∼ 240 kpc at z=0.

We find the eigenvalues, λ = (λ1, λ2, λ3) and eigenvectors V = (V 1, V 2, V 3), of this matrix and these eigenvectors form the orthogonal basis of the new co-ordinate system (the eigenvector with the highest eigenvalue is new x axis and the one with smallest value is new z axis). We now find our centered data in this new co-ordinate system 0 Inew = I × V (4.5)

We obtain the 3 axes of the fitted ellipsoid a, b and c by taking the standard deviation (σ) of the new data:

s 1 σ = IT × I (4.6) n new new The off diagonal entries in this multiplied matrix are all zero as the cross correlation between positions are zero now and we are left with only the diagonal terms : q 2 2 2 1 2 xnew, ynew, znew. So, we have c = n znew and similarly for a and b.

62 4.2.1.2 Tensor of Inertia method

This is a common method that has been used in literature (Pawlowski et al. 2015a) to determine the a, b, and c axes of satellite distribution. In this method we find the moment of inertia of the dwarfs and diagonalize it to find the axes length (a, b, c) of the distribution. Let the position vector of a dwarf be given ri = (xi, yi, zi). We calculate the tensor of inertia (TOI) matrix, weighted or unweighted and find the eigenvalues of that matrix. The TOI is a 3 × 3 matrix which is given by

 2  xi xiyi xizi n   X  2  Icovariance =  xiyi yi yizi  × wi (4.7) i=1  2  xizi yizi zi

This matrix has the same form as the covariance matrix discussed in PCA method.

The term wi in the above equation refers to the weight assigned to the dwarfs in the system according to their distances. If wi = 1, then this reduces to the standard method where all dwarfs have the same weight irrespective of their distances. It has been argued that the far off dwarfs should carry less weight in determining the DoS plane as they have higher chances of being outliers (Bailin & Steinmetz 2005). For 2 completeness, we use two cases of reduced weights, wi = 1/ri and wi = 1/ri where q 2 2 2 ri = xi + yi + zi . The three eigenvalues of this matrix ITOI, gives the three axes of the dwarf distribution a, b, c (largest eigenvalue is a and the smallest one is c). The anisotropy of the distribution is characterized by the ratio of the minor-to-major axis, c/a (for isotropic distribution c/a = 1). We will use the two methods, PCA and reduced TOI with weights 1, 1/r and 1/r2 for determining the c/a ratios of our various samples in this chapter. This will enable us to get a description of the dwarf distribution and examine the effects of the different methods discussed above.

63 4.3 Abundance and Spatial Distribution of Satellites at z=0

4.3.1 Effects of Baryons

Early N-body simulations of galaxies generally showed a rather isotropic distribution of dark matter subhalos surrounding the central galaxy (Kang et al. 2005), which has often been interpreted as a failure of ΛCDM cosmology (Kroupa et al. 2010; Metz et al. 2007; Pawlowski & Kroupa 2014; Pawlowski et al. 2012; Kroupa et al. 2005). However, these simulations did not include the effect of baryons. Recent studies have shown that baryons play an important role in determining the properties of both subhalos and the main host (e.g. Sawala et al. 2016; Zhu et al. 2016), but little is known about how baryons affect DoS structure. In this study, we investigate the effect of baryons on the abundance and distribution of satellites of a MW-like galaxy, by comparing the baryonic simulation and its N-body counterpart (details in §4.2.1). Figure 4.1 shows the projected spatial distribution of all subhalos found within 1 Mpc of the MW center in both simulations. We find that there are many more subhalos (∼ 21220) within the DMO simulation compared to the 106 luminous subhalos (dwarf galaxies) in the baryonic run, because most subhalos in the DMO simulation do not form stars and hence they are not identified as galaxies. In Zhu et al. (2016), we identified three major baryonic processes, namely adiabatic contraction, tidal disruption, and reionization, that significantly affect the density distribution of dark matter halos and their ability to retain gas, thus reducing the star formation activity in many low-mass halos. Moreover, the DMO dwarfs are distributed noticeably more isotropically compared to baryonic dwarfs, which have a clear anisotropic distribution as a result of reduced abundance of star-forming dwarfs and interactions with the central galaxy. Similar results of anisotropic distribution in baryonic simulations were also reported by Sawala et al. (2016). Even early studies (Zentner et al. 2005) showed that the N-body subhalos are not fully isotropic and the likely luminous subhalos (satellites) are even more anisotropically distributed. This figure demonstrates that baryonic processes have a profound impact on the abundances and spatial distribution of satellite galaxies around a central MW-type galaxy, and it illustrates the difference between N-body simulations and hydrodynamical simulations on the study of the DoS phenomenon (e.g. Pawlowski et al. 2015a; Sawala et al. 2016). Hereafter, we are

64 Figure 4.2: Three-dimensional spatial distribution of satellites (black dots) within 1 Mpc from the central galaxy in the hydrodynamical simulation. The fitted plane of the satellites, using PCA method, is shown as the black plane and the disk plane of the simulated Milky Way is depicted as the brown plane. going to focus on the detailed analysis of the dwarfs in the baryonic simulation. In Figure 4.2 we fit the distribution of 106 dwarfs within 1 Mpc of the central galaxy with the PCA method (see § 4.2.1). Among the 106 dwarfs, about 77% can be considered as residing in the same plane (dwarfs within the rms height), as indicated by the blue plane in the figure. The angle between our fitted DoS plane and the simulated MW disk (as indicated by the orange plane) is ∼ 75 degrees, which is very close to the observed angle of ∼ 77.3 degrees (Pawlowski et al. 2013). However, as shown in Figure 4.3, the r.m.s. height of the DoS, fitted to 106 dwarfs within 1 Mpc, is ∼ 145 kpc, which is much larger than those reported from observations (∼ 30 kpc for 39 dwarfs within 365 kpc) which typically use a much smaller sample (Maji et al. 2017; Pawlowski et al. 2015). We will address the effect of sample size on the DoS properties in the next section.

65 10 8 6 4 No. of dwarfs No. 2 0 −200 0 200 400 600 Residual distances (kpc)

Figure 4.3: Distribution of the residual distances of the simulated satellites from the fitted DoS plane. The width between the two magenta dotted lines shows the root-mean-square height of the plane, ∼ 145 kpc.

4.3.2 Effects of Sample Size and Plane Identification Method

In chapter 3, we reanalyzed all dwarfs currently detected around the MW and grouped them in three subsets, as used by different groups in the literature: the 11 ’classical’ dwarfs (Kroupa et al. 2005), the 27 most massive nearby dwarfs and the complete sample of 39 dwarfs (Pawlowski et al. 2015). We fit the three samples using both PCA and TOI methods (4.2.1) and found that both the isotropy (as indicated by c/a ratio) and the thickness (characterized by the root-mean-square or r.m.s. height) of the DoS increase with sample size: the c/a goes from ∼ 0.2 for the 11 dwarfs to ∼ 0.26 for the 39 dwarfs, and the r.m.s. height goes from ∼ 20 kpc to ∼ 30 kpc. To directly compare our simulated DoS with observations, we first calculate the farthest distance of the dwarfs from MW center for these three subsets and find them

66 1.0 0.8

● ● ● ●

●

0.6 ● ● ●

●

c / a ● 39 dwarfs 106 dwarfs 0.4 ● ● PCA 27 dwarfs ToI, weighted by 1 0.2 ToI, weighted by 1/r 11 dwarfs ToI, weighted by 1/r2 0.0 20 40 60 80 100 120 number of simulated dwarfs

Figure 4.4: The “isotropy " of the simulated satellite distribution, as indicated by c/a, as a function of the sample size. We have used four samples here with 11, 27, 39 and 106 dwarf galaxies respectively. The different colors denote the different plane fitting methods : Principal Component Analysis (black) and Tensor of Inertia with three types of weight functions, 1 (red), 1/r (green) and 1/r2 (blue). to be 257.4 kpc (Leo I), 257.4 kpc (Leo I) and 365 kpc (Eri II) for the sample of 11, 27 and 39 dwarfs respectively. Then we divide our simulated dwarfs into 4 subsets: 11 most massive (total mass) dwarfs within 257.4 kpc, 27 most massive dwarfs within 257.4 kpc, 39 most massive dwarfs within 365 kpc and for completeness, all 106 dwarfs within 1 Mpc. We apply the 4 methods discussed in § 5.2 and determine the c/a ratio for these four samples, as shown in Figure 4.4. For the 11 dwarfs, the c/a ratio is ∼ 0.3 in our simulation, close to the value of ∼ 0.2 for the observations (Metz et al. 2007; Pawlowski et al. 2015). However, with the full sample of 106 simulated dwarfs (< 1 Mpc), the ratio increases to ∼ 0.44 for PCA method, and it goes upto 0.68 for ToI method weighted by 1/r2. Similar range of c/a was also reported by Sawala et al.

67 200

●

● ●

● 150

● ● ● 106 dwarfs

100 39 dwarfs

● PCA rms height of DoS (kpc) 50

● ToI, weighted by 1 ● 27 dwarfs ● ToI, weighted by 1/r 11 dwarfs ToI, weighted by 1/r2 0

0 20 40 60 80 100 120 number of simulated dwarfs

Figure 4.5: The root-mean-square (rms) height of the DoS plane fitted to a sample of simulated dwarfs as a function of the sample size. We have used the same four samples here with 11, 27, 39 and 106 dwarf galaxies respectively. The different colors denote same four plane fitting methods : Principal Component Analysis (black) and Tensor of Inertia with three types of weight functions, 1 (red), 1/r (green) and 1/r2 (blue).

(2016). This plot demonstrates that the DoS isotropy is subject to selection effect. Furthermore, in Figure 4.5 we show the r.m.s. heights of the simulated DoS plane for the four samples using four different methods and find that the DoS plane height increases with sample size. Using PCA method, the r.m.s. height for 11 dwarfs is ∼ 30 kpc, and it rises to 120 kpc for 39 dwarfs and to 145 kpc when we include all dwarfs out to 1 Mpc. The thickness of the fitted DoS is even larger when ToI methods are used, as shown in the figure. For comparison, when Kroupa et al. (2005) took into account all known observed dwarfs upto 1 Mpc, the calculated r.m.s. DoS height was 159 kpc, close to our simulated height. These results demonstrate that the DoS properties change significantly with the

68 ● ● Simulated dwarfs ●

400 Nearby tracked simulated dwarfs ● ● Observed dwarfs

●

300 ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● 200 ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 100 Galactocentric velocity (km/s) Galactocentric velocity ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 0 200 400 600 800 1000 Distance from MW (kpc)

Figure 4.6: Comparison of galactocentric velocity between the simulated (blue points) and observed (purple crosses) dwarfs as a function of galactocentric distance. The observed data is taken from McConnachie (2012), and velocities are calculated with respect to the Galaxy. The red points are the 27 most massive dwarfs within 257.4 kpc of galactic center from the simulation. sample size of the satellites and the plane identification method. We have seen similar trends of changing DoS properties in observed satellites too as discussed in chapter 3. These considerations suggest that the properties of the highly flattened DoS of the MW derived from a small set of observed dwarfs (Pawlowski et al. 2015a; Ibata et al. 2013) may not be robust .

4.4 Kinematic Properties of Satellites at z=0

Another claim of the DoS is that the satellites have coherent rotation in the same plane. It was suggested by Pawlowski et al. (2013) that, of the 11 “classical" dwarfs

69 10 8 6 4 Number of galaxies dwarf Number 2 0 -90 -70 -50 -30 -10 10 30 50 70 90 Angle between velocity vector and DOS

Figure 4.7: Distribution of the angle between velocity vector of simulate dwarfs and the DoS plane. The dwarfs whose velocity lies within -45 degree to +45 degree (magenta dotted lines) of the DoS are considered to be moving on the DoS. that have proper motion measurements, 7 to 9 are corotating on the DoS. However, in the analysis of Maji et al. (2017) we found that only 6 meet the criterion of corotation, and no firm coherent motion can be inferred. Moreover, these studies suffer from a very large uncertainties in the velocity measurements and a relatively small sample size. A larger sample size and precise measurements of 3-D velocity components of dwarfs from our simulation provide an advantageous study of the kinematic properties of the satellites. Figure 4.6 shows the galactocentric velocity of the simulated dwarfs within 1 Mpc from the central galaxy, compared to Milky Way observations McConnachie (2012). Most of the observed dwarfs are located within 300 kpc from the MW, and they have a velocity range from ∼ 10 to ∼ 400 km/s. While the simulated ones have a similar velocity range, they have a higher median velocity (∼ 150 km/s compared to ∼ 100 km/s from the observations). To investigate the kinematic coherence of the DoS, we first calculate the fraction

70 6 N = 18 N = 40 N = 19 5 4 3 2 Number of dwarf galaxies Number of dwarf 1 0 0 20 40 60 80 100 120 140 160 180 Angle between angular momentum and DoS normal

Figure 4.8: Distribution of angle between angular momentum of simulated dwarfs (residing in the DoS plane) and the DoS normal. There are 18 corotating (blue) and 19 counter-corotating (orange) dwarfs. of dwarfs moving in the DoS plane. We use a criterion to define a satellite as moving on the DoS when it total velocity vector falls from -45 to +45 degree of the DoS plane. As shown in Figure 4.7, 77 out of 106, or 73% of dwarfs within 1 Mpc, meet this criterion and are considered to be moving on the DoS. These dwarfs can be moving either mostly circularly (clockwise or counter clockwise) or mostly radially on the DoS. Next, we calculate the fraction of dwarfs in the same circular motions (either corotation or counter-corotation) to determine whether or not the DoS is rotationally supported. We use a criterion to define a satellite as rotating on the DoS when its angular momentum vector falls from 0 to 45 degree of the DoS normal, or counter- corotating when the angle between the two is from 135 degree to 180 degree. As shown in Figure 4.8, out of the 77 satellites moving on the DoS, 18 are corotating

71 1.0

● Co−orbiting dwarfs ● Counter co−orbiting dwarfs ● 0.5

● ● ● ● ● ● ● ● ● ● 0.0 ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● −0.5 Vertical distance from DoS (Mpc) Vertical

−1.0 0.0 0.2 0.4 0.6 0.8 1.0 Projected radial distance (Mpc)

Figure 4.9: Vertical distance of the simulated dwarfs from the DoS vs their projected radial distance (i.e. the distance component lying on the DoS) from the center of the DoS (center-of-mass of the satellite galaxies). The red points show corotating dwarfs and blue points show counter-corotating dwarfs. and 19 are counter-corotating. If we consider all 106 satellites within 1 Mpc from the simulation, only 17% are corotating and 18% are counter-corotating. These numbers strongly argue against any trend of corotation or counter-corotation, instead they show that the DoS is not rotationally supported. To further explore the coherent motion of the DoS, we examine the locations of the 18 corotating and 19 counter-corotating dwarfs, as shown in Figure 4.9. Not surprisingly, there is no correlation between spatial distribution and kinematic orientation of the satellites, the co-rotating or the counter-coorbiting dwarfs are not grouped in either radial or vertical direction, rather have a random distribution. This can be further demonstrated in the position – angular momentum distribution of the satellites. In Figure 4.10, we compare the Aitoff-Hammer projection of position and

72 Figure 4.10: Positions and angular momenta of the observed (red symbols) satellites and simulated dwarfs (blue symbols) in Galactic coordinates are projected onto an Aitoff Hammer sphere. The filled circles and triangles represent the positions and angular momenta of the satellites, respectively. Satellites can be considered as corotating when their angular momenta are clustered in the same direction. For the observed momenta of 11 satellites, only 6 dwarfs near the center can be considered co-rotating; they are also within 45 degree of the DoS normal (depicted by red circle). Among the simulated momenta, no strong clustering of the majority of dwarfs are observed. angular momentum of the 27 most massive satellites within the virial radius from the simulation with 27 observed dwarfs of the MW (though only 11 have angular momentum data). Although 6 observed dwarfs (Draco, Umi, SMC, Fornax, Leo II and LMC) may appear to be clustering in the angular momentum distribution (within 45 degree of 180 degree longitude and 0 degree latitude), spatially they are located far apart in different longitude–latitude planes. Similarly, no strong angular momentum clustering, or position – angular momentum correlation, is seen in the simulation. These results suggest that the DoS does not have coherent rotation. Similar conclusions have been reported by other studies on DoS. Cautun et al. (2015b) and Phillips et al. (2015) found that the apparent excess of corotating dwarfs around SDSS galaxies, as claimed by Ibata et al. (2014a), is highly sensitive to sample selection criterion and sample size, and it is consistent with the noise expected from an under-sampled data. These findings suggest that the DoS in general is not a

73 kinematically coherent structure.

4.5 Evolution of Satellites

4.5.1 Evolution of Spatial Distribution

In order to directly probe the origin of the DoS or the anisotropic distribution of the satellite system, it is essential to observe them at high redshift. However, due to the low luminosity of the satellite galaxies, it is extremely difficult to observe them in the distant universe. Other than the satellites in our Local Group, we have observations of possible DoS around SDSS galaxies only up to z = 0.05 (Ibata et al. 2014a). However these claims have been largely refuted (Cautun et al. 2015a; Phillips et al. 2015). In the simulations we can track the satellite systems to very high redshift. In Fig 4.11, we follow the 3D distribution of the satellites from redshift z = 10 to the present day, with the 27 most massive ones highlighted in order to understand those observed in the MW. At redshift z = 10, the overall distribution of the galaxies is almost isotropic. After z = 6, the number of dwarfs decreases significantly, mostly due the disruption of low-mass halos after reionization (Zhu et al. 2016). After z = 4, the galaxies become more strongly clustered along the filaments, as expected from the standard hierarchical structure formation model (Springel et al. 2005; Vogelsberger et al. 2014a), and the distribution becomes more anisotropic with time. As it approaches to z = 0, the distribution of the satellite system becomes strongly anisotropic. To quantify the change over time, we fit the satellite system at different redshifts with 4 different plane identification methods (discussed in section 4.2.1). The resulting evolution of the c/a ratio is shown in Figure 4.12. We find that all methods give a consistent high c/a ratio at high redshift, which generally decreases with time. This change is most prominent with both PCA and the unweighted ToI method, where the “isotropy” index starts at c/a ∼ 0.7 at z = 10 but drops to c/a ∼ 0.44 at z = 0. These results suggest that the DoS structure is a result of the galaxy formation and evolution process and part of the large-scale filamentary structure. To investigate the large scale dynamics of the dwarfs, we show their 3D velocity vectors in Figure 4.13. Around the galactic center, the velocity vectors appear to be

74 z=10 z=6 4-4 -2 0 2 4 4-4 -2 0 2 4 2 4 2 4 0 0

-2 2 -2 2 -4 -4 0 0

-2 -2

-4 -4

z(Mpc) z(Mpc) y(Mpc) y(Mpc)

x(Mpc) x(Mpc) z=4 z=2 4-4 -2 0 2 4 4-4 -2 0 2 4 2 4 2 4 0 0

-2 2 -2 2 -4 -4 0 0

-2 -2

-4 -4

z(Mpc) z(Mpc) y(Mpc) y(Mpc)

x(Mpc) x(Mpc) z=1 z=0 4-4 -2 0 2 4 4-4 -2 0 2 4 2 4 2 4 0 0 -2 2 -2 2 -4 -4 0 0

-2 -2

-4 -4

z(Mpc) z(Mpc) y(Mpc) y(Mpc)

Figure 4.11: Spatial distributionx(Mpc) of all dwarfs (blue points)x(Mpc) within 3 Mpc of Milky Way (comoving scale) at different redshifts, namely z = 10, 6, 4, 1 and 0. The red points are the 27 most massive satellites within 257.4 kpc of the galactic center at z = 0 which were tracked at higher redshifts. The overall distribution of the dwarfs is nearly isotropic at high redshifts but it gradually evolves to be anisotropic with time. 75 1.0 0.8 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.6 ● ● ● ● ● ● ● ● ● ● ● ● ● c / a ● ● ● ● ● ● ● 0.4 Dwarfs within 1 MPc ● PCA ToI : Weight 1 0.2 ToI : Weight 1/r ToI : Weight 1/r2 0.0 1.2 1.0 0.8 0.6 0.4 0.2 0.0 log (1+z)

Figure 4.12: Evolution of the isotropy ratio (c/a) of the simulated satellite distribution within 1 Mpc. Different colors the figure denote different plane fitting methods : Principal Component Analysis (black) and Tensor of Inertia with three types of weight functions, 1 (red), 1/r (green) and 1/r2 (blue). random and do not show any preferential rotation, as we have also seen in previous sections. This is the result of different accretion history and trajectory of individual dwarfs into the main galaxy as shown in Zhu et al. (2016). However, at large distances the dwarfs are moving toward a narrow elongated direction, which suggests that they are part of the large scale filamentary structure.

4.5.2 Evolution of the Kinematics

The evolution of the kinematic properties of the dwarfs is shown in Figure 4.14, in which we track dwarf subsets with different kinematical properties: dwarfs moving on the DoS and rotating ones which include corotating and counter-corotating. We find that over the redshift range from z = 2 to z = 0, the different fractions remain nearly

76 Figure 4.13: Three dimensional plot of simulated dwarf positions (blue points), within 3 Mpc of the galactic center, along with the DoS plane (blue plane) fitted by PCA method. The 3D velocities of these dwarf galaxies are represented by the magenta arrows and the length of these arrows is proportional to the velocity magnitude. the same. Around 80% of these galaxies are primarily moving on DoS (as opposed to normal to DoS) and around 45% of them are rotating on the DoS, the rest is moving radially. Interestingly, the fractions of corotating and counter-corotating dwarfs are com- parable at around 20% throughout the time. This reaffirms our conclusion that the DoS has no coherent rotation and it is not rotationally supported.

4.6 Discussions

In order to investigate how the DoS structure changes with the distance from the central galaxy, we plot the two different axis ratios (c/a and b/a) of the dwarf distribution at different radii from the galactic center in Figure 4.15. We find that both ratios decreases with increasing distance, by 3 Mpc, c/a ∼ 0.25 and b/a ∼ 0.5,

77 100 Moving Co−rotating Rotating Counter co−rotating ● ● 80 ● ● ●

●

60 ● ●

● ● ● ● 40 ● ● ●

fraction of dwarfs, % of dwarfs, fraction ● ● ● ● ● ● ● ● 20

● 0

2.0 1.5 1.0 0.5 0.0 redshift

Figure 4.14: Evolution of the fraction of dwarfs (within 1 Mpc of galactic center) with different kinematical properties : the fraction of dwarfs moving on the DoS plane (black), the fraction of dwarfs co-rotating in DoS (red), the fraction of dwarfs counter co-rotating in DoS (blue), and the total fraction of dwarfs rotating (corotating and counter-corotating) in DoS (magenta). which may resemble the large-scale filamentary structure. However, we note that when we include all the dwarfs (not just the most massive ones as in the previous sections), the distribution becomes more isotropic close to the galactic center compared to the distribution of only massive dwarfs. Furthermore, we note that the c/a ratio may not adequately represent the underly- ing distribution of the system. To demonstrate this, we take the observed positions of the 11 classical dwarfs and perform four tests on them. In the first test, we distribute the 11 dwarfs in their observed distances but placing them in a way such that their input c/a = 0.4. Now we perform a Monte Carlo simulation for 100,000 realizations of this system and calculate the c/a ratio of each realization using two weighted

78 1.0 ● c/a ● ● b/a ● 0.8 ● ● ●

● ● ●

● 0.6

● ● ●

●

● Axis ratio 0.4

● ● ●

● 0.2 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance from GC (Mpc)

Figure 4.15: The c/a ratio (red) and the b/a ratio (green) of the dwarf distribution as a function of the maximum distance of the dwarfs from galactic center. For each distance, we take all dwarfs within that radius and calculate these two ratios using PCA method. methods (weights 1, and 1/r2 respectively, details in §2.3.2). We plot the distribution of the output c/a ratio of these galaxies in Figure 4.16 (top left panel) and find that although the input c/a = 0.4, about ∼ 20% of the systems have an output c/a . 0.18, the observed anisotropy ratio for the observed 11 galaxies (with weight 1 method). We repeat this test with three other input c/a, 0.6, 0.8 and 1.0 respectively and find that for each of them there is non-negligible probability that the system has a lower output c/a than the input value. We also notice that the method used to determine the c/a ratio also influences the output, for all samples, the weighted by 1/r2 method produces higher c/a than the unweighted method. This shows that very small samples, i.e. 11 dwarfs, may artificially indicate a higher anisotropy and they may not contain the full information of the underlying distribution.

79 30000 Input c/a 0.4 30000 Input c/a 0.6 ToI : Weight 1 ToI : Weight 1 ToI : Weight 1/r2 ToI : Weight 1/r2 20000 20000 Number of galaxies Number of galaxies Number 10000 10000 5000 5000 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Output c/a Output c/a

30000 Input c/a 0.8 30000 Input c/a 1.0 ToI : Weight 1 ToI : Weight 1 ToI : Weight 1/r2 ToI : Weight 1/r2 20000 20000 Number of galaxies Number of galaxies Number 10000 10000 5000 5000 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Output c/a Output c/a

Figure 4.16: Distribution of output galaxy c/a for different input values (c/a = 0.4 top left panel, 0.6 in top right panel, 0.8 in bottom left panel and 1.0 in bottom right panel) in a Monte Carlo simulation with 100,000 galaxies. The c/a ratio is calculated by two methods: weighted by 1 (red), and weighted by 1/r2 (blue). The violet region shows the overlap between the distributions with two methods. The dashed vertical lines in red and blue shows the observed c/a value calculated with 11 MW satellites with these two methods respectively. The median c/a values for the systems are shown with vertical red (weight 1) and blue (weight 1/r2) solid lines.

80 Finally we stress that our results are subject to the limitations of our study, as we have only analyzed one particular realization of a MW-sized galaxy. In future projects we plan to pursue a more systematic study by extending our simulated galaxy sample.

4.7 Summary

We have investigated the spatial distribution and kinematic properties of satellites of a MW-sized galaxy by comparing a high resolution hydrodynamical cosmological simulation with its DM only counterpart. Our main results are summarized as follows:

• Baryons play a significant role in determining the abundance and distribution of the satellite system of a galaxy. Within 1 Mpc from the central galaxy, only 106 dwarf galaxies containing stars are found at the present day in the hydrodynamic simulation and they show an anisotropic distribution, in sharp contrast to 21,220 subhalos in the N-body simulation, which are distributed isotropically;

• The DoS in our simulation is not rotationally supported and there is no coherent motion of the satellites, as the fraction of corotating and counter-corotating satellites are comparable and around 19% across cosmic time.

• The distribution of the (baryonic) satellite galaxy system evolves significantly with time. It is highly isotropic at high redshifts but it becomes more anisotropic as redshift approaches to z = 0, and this anisotropic distribution is part of the filamentary structure in the hierarchical structure formation scenario.

• The properties of the DoS strongly depend on the sample size and the plane identification methods. When only the 11 most massive dwarfs similar to those “classical” Milky Way satellites are selected, the DoS becomes more flattened as observed. However, when the sample size increases the DoS becomes thicker. This is consistent with the observational pattern that height and the flatness ratio of the DoS increase with sample size, as shown in Maji et al. (2017).

Our results suggest that the highly-flattened, coherently-rotating DoS claimed in the MW and other galaxies may be a selection effect due to a small sample size, and that different subhalo distributions that we see in our hydrodynamical and N-body

81 simulations are shaped by baryons. Baryonic processes such as adiabatic contraction, reionization, and tidal destruction of galaxies can have significant effects on the abundance, star formation, infall time and trajectories of the satellites which can in turn affect their final distribution. Therefore, effects of baryons should be taken into account in the study of the distribution and evolution of the satellite system of a galaxy.

82 Chapter 5 | Disks of Satellites around Galaxies in Illustris Simulation

5.1 Introduction

Studying satellite galaxies around their hosts is important to understand the formation, growth and the evolution of galaxy systems in general. As discussed in chapter 3 and 4, observations of 11 classical Milky Way satellites have found them to be anisotropically distributed (c/a ∼ 0.2). Analysis of all 39 MW satellites discovered till now find that this larger sample is also anisotropic (c/a ∼ 0.26), although less so compared to the 11 classical ones (Maji et al. 2017). Very recently, the GAIA mission announced its Second Gaia Data Release (here- after DR2, (Gaia Collaboration et al. 2018, 2016)) and this data has opened up a new era in the science of Milky Way and its satellites by providing unprecedentedly precise position and proper motion detections of millions of MW stars and its satellite galaxies. Using this data Gaia collaboration Gaia Collaboration et al. (2018) have shown that the orbital planes of the classical MW satellites, when averaged over 10 Gyrs of integration, stand mostly perpendicular to the MW disk plane, but with a large range of angles 90 ± 20 (angle between the orbit and MW disk). Although spatially they may be distributed in a planar structure, kinematically they don’t share a single plane of motion. When averaged over 10 Gyrs, their orbits have a wide range of orientation, with some satellites rotating in opposite senses and few having orbital planes perpendicular to each other. This study also showed that although these satellites may be positioned in a planar structure, their sense of rotations can be very

83 different from each other. Some of them are rotating in opposite directions, and in few cases, e.g. Sculptor and Sagittarius are rotating almost normal to each other, and both of their orbital planes are also normal to the MW disk. Proper motions of satellite galaxies are extremely difficult to detect. Until the Gaia DR2 release, we only had the proper motion measurements for the 11 classical satellites of the Milky Way. Among these, 6 to 8 could be considered as co-rotating (Maji et al. 2017; Pawlowski et al. 2013) and one is counter-rotating. However, this sample is too small to assert a statistically sound claim about a rotationally supported DoS. Now for the first time, Fritz et al. (2018) have derived the proper motions of 39 satellite galaxies within 420 Kpc of our galaxy using Gaia DR2. Their results are consistent with the known proper motion data of the classical satellites from the literature. Among these 39 dwarfs, 12 satellites have orbits that are not aligned with the DoS, i.e. they are not rotating on the DoS. 16 satellites are rotating on the DoS, with 11 of them co-rotating and 5 galaxies counter-rotating. The rest 11 satellites in the sample do not have sufficient proper motion accuracy to determine if they are rotating on the DoS. So in essence, among the sample of 39 galaxies, 28 satellites have valid data and among these 28, only 11 are co-rotating, i.e. ∼ 39%, which is much less than the co-rotating fraction often quoted in the classical sample, 8/11 ∼ 72%. These measurements with the larger sample support our conclusion from Chapter 3 and 4, that the perceived co-rotating DoS may result from a small sample size and the clustering bias. Looking at the nearby M31 galaxy, it was found that 15 out of the 27 dwarfs around Andromeda, detected by Pan-Andromeda Archaeological Survey (PAndAS; McConnachie et al. 2009), follow an anisotropic planar distribution (e.g., Koch & Grebel 2006; Ibata et al. 2013). Ibata et al. (2013) used line-of-sight (LOS) velocities to suggest that 13 out of 15 coplanar satellites of Andromeda are co-rotating. Outside of the Local Group, recent observations of satellites around Centaurus-A found that its 59 satellites (34 confirmed and 25 candidates) are anisotropically distributed. Ibata et al. (2014) used the SDSS catalog and identified 22 galaxies with diametrically opposed satellite pairs and found that 20 of them have anti-correlated velocities, which were interpreted to suggest co-rotating satellite planes. The case of MW satellites was investigated by Maji et al. (2017), who reanalyzed the dwarf galaxies around the Milky Way and found that the DoS structure depends strongly on sample size and the plane identification method. A small sample size

84 can artificially show very high anisotropy in the system, even if the underlying distribution is isotropic. Similarly, the angular momenta of a small number of satellites are susceptible to clustering bias, i.e. even if the inherent distribution of the momenta is random, they can appear to be highly clustered for a small sample size. To understand the statistical significance and the origin of satellite anisotropy, we need to analyze high resolution baryonic simulations of these systems. Bahl & Baumgardt (2014) investigated the probability of finding satellite planes similar to the M31 DoS in the Millennium II (N-body) simulation, and found that such planes occur frequently. Cautun et al. (2015b) analyzed two high resolution N-body cosmological simulations (Millennium-II; Boylan-Kolchin et al. 2009 and Copernicus Complexio; Hellwing et al. 2016) and found that planar distribution of satellites are very common in these simulations and the degree of anisotropy vary from system to system. Buck et al. (2016) analyzed a suite of 21 cosmological simulations and found that satellite planes are common in high concentration halos and the degree of anisotropy and co-rotation fraction depend on viewing angle and sample size and demonstrated that line-of-sight velocities are not enough to establish kinematical coherence of these planes. However, recent studies (Zhu et al. 2016) have shown that baryonic physics play a vital role in shaping the halo-subhalo distribution through three main processes, adiabatic contraction, tidal disruption, and reionization. So it is imperative to study the satellite systems in a high resolution baryonic simulation. Sawala et al. (2016) analyzed the APOSTLE simulations, a suite of smoothed particle hydrodynamics (SPH) simulations of the Local Group, and found that satellite systems form with a wide range of spatial anisotropies and it is possible to reproduce the observed DoS of 11 brightest MW satellites. Ahmed et al. (2017) investigated four zoom-in baryonic simulations of MW type galaxies and their N-body counterparts and found that the satellite distribution is always more anisotropic in baryonic simulations because when baryons are present, less number of satellites survive, they infall later and they are less radially concentrated which makes these satellite planes statistically significant. To understand the general nature of the satellite anisotropy, we need to study it around a large variety of hosts galaxies in different environments. To this end, in this chapter, we study the satellite systems around 2,591 hosts galaxies in the state-of-the-art cosmological simulation Illustris. This chapter is organized as follows. In § 5.2 we describe the simulation and galaxy selection criterion, in § 5.3, we present the abundance of satellites, their spatial

85 distribution, kinematic properties and evolutionary history. Finally we discuss the limitations of this study and present our conclusions in § 5.5.

5.2 The simulation

Illustris-1 Vogelsberger et al. (2014a,b) is a high-resolution cosmological simulation 5 −1 with a simulation box size of 105 Mpc and baryonic mass resolution of 8.87×10 h M . The model includes gas dynamics, two-phase interstellar medium, star formation, gas cooling with self-shielding corrections, metal enrichment and mass return from stellar evolution, and supernova, stellar and AGN feedback. Galaxies in this simulation are identified using the density based group finding algorithm SUBFIND Springel et al. (2001). For this study, we define the host galaxies to be in the (total) mass 11 13 range between 5 × 10 M and 2 × 10 M . This range covers MW like galaxies and massive galaxies but excludes possible galaxy clusters. At z = 0, there are 2,591 such galaxies in the simulation. We require satellite galaxies to be in the mass range 7 11 of 10 M and 10 M that reflect a broad range satellite galaxy masses, but also exclude possible massive star clusters. Furthermore, we categorize the host galaxies into ellipticals and spirals following the procedure given by Scannapieco et al. (2009); Tenneti et al. (2016); Vogelsberger et al. (2014b). For each star within 10 times the stellar half-mass radius of a host galaxy, we define a circularity parameter given by

 = jz/j(E) where jz is its specific angular momenta and j(E) is the specific angular momenta of a star if it was at a circular orbit at the star’s radius. Stars with  > 0.7 are classified as disc stars. Therefore the bulge-to-total ratio (BTR), i.e. the ratio of the fraction of non-disc stars (bulge stars) to the total, is given by BTR = 1 − f>0.7, where f>0.7 is the fraction of disc stars. Galaxies with BTR < 0.7 are classified as spirals and the rest are elliptical galaxies.

5.3 Satellite Systems in Illustris

5.3.1 Abundance

In Figure 5.1 we plot the number of satellites within virial radius as a function of the total mass of the host galaxy for both ellipticals and spirals. We find that as host mass increase, there are more satellites around them. This is expected because more

86 Ellipticals Spirals 1.5 2.0 (N)

log 0.0 0.5 1.0 12.0 12.5 13.0

log10 (MHost / M☉)

Figure 5.1: No. of satellites within the virial radius of the host galaxies vs. their total mass. The host galaxies are divided into ellipticals (red) and spirals (blue). massive hosts have stronger gravitational pull which can, in turn, bind more satellites around them. We also find that both ellipticals and spirals have a similar number of satellites in the same mass range, although in higher host mass range there are mostly ellipticals and almost no spirals (ellipticals are generally formed by mergers of spirals, so they can be more massive than spiral galaxies).

5.3.2 Spatial distribution of satellite systems

In Figure 5.2 we plot the c/a ratio of fitted DoS around the host galaxies as a function of the host galaxy mass. We intend to easily identify the effects of satellite sample size on their spatial and kinematic properties, so instead of using systems with all possible sample sizes, we divide them into three groups. We divide the host galaxy population into ellipticals and spirals and then subdivide each of these morphological

87 classes into three groups based on the number of satellites around them within virial radius: systems with 10-12 satellites, 30 - 40 satellites and more than 50 satellites. The first group focuses on systems with a small number of satellites, similar to the 11 classical ones, the last group represent systems with a large number of satellites, e.g. 50 and the middle group represent systems with an intermediate number of satellites. We find that although there is a large scatter in the c/a values for each of these populations, e.g. systems with 10 - 12 satellites have c/a ratio ranging from 0.2 (similar to the ’classical’ DoS around Milky Way) to 0.8, generally as host galaxy mass increases, their satellite systems become more isotropic. Additionally, there is a well defined trend between the median value of the c/a ratio and the number of satellites in the system: the median c/a increases with number of satellites in the system. in the galaxy systems. This indicates that although it is possible to have highly anisotropic DoS when calculated with a small number of satellites, as the sample size increases, the satellite system becomes more isotropic. Furthermore, to statistically investigate the randomness of the distribution of c/a values of our entire sample of satellite systems, we perform a Kolmogorov-Smirnov test (KS test) on them. KS test is a nonparametric test that is often used in statistics to verify if a given sample comes from a population with a reference probability distribution. In our case, we compare the distribution of the c/a values of all 2591 galaxies with a uniform random distribution (e.g. in the reference sample data is randomly taken from a uniform distribution between 0 and 1) Feigelson & Babu (2012). We find that the p-value of this test is very close to zero (< 2 × 10−16), which shows that our null hypothesis (which states that the simulated c/a distribution of satellite systems comes from a uniform distribution) is incorrect. This proves that the c/a values in satellite systems is not uniformly distributed and as shown in Figure 5.2, its value increases as the number of satellites in a system increases and the host galaxy becomes more massive. In order to investigate how the DoS structure changes with the distance from the central galaxy, we plot the median c/a ratio of the dwarf distributions within different radii (1 - 5 virial radii of their hosts) as a function of their maximum distance from the host in Figure 5.3. For each host galaxy, we count the number of satellite galaxies within 1, 2, 3, 4 and 5 times its virial radius and for each radii (1 - 5 virial radii), we take the host galaxies (ellipticals and spirals separately) with 10 - 12, 30 - 40 and > 50 satellites respectively and calculate the median c/a for each group. We find

88 Ellipticals Spirals 0.6 0.8 1.0 c/a

Satellites within Rvir No. of satellites 10 - 12 No. of satellites 30 - 40 No. of satellites > 50 0.0 0.2 0.4 12.0 12.5 13.0

log MHost (M☉ )

Figure 5.2: c/a ratio of the galaxy systems (within 1 virial radius) vs the total mass of the host galaxy. The different colors represent hosts with three satellite populations; systems with 10-12 satellites (red), 30 - 40 satellites (blue) and more than 50 satellites (black). The round points indicate elliptical hosts and the cross points represent spiral hosts. The dashed (elliptical) and dotted (spiral) lines represent median c/a values for the three populations (the colors represent the same scheme as points). that for both spirals and ellipticals, in systems with a similar number of satellites, the c/a ratio decreases with increasing distance from the host galaxy. From 1 to 5 virial radii, the median c/a ratio has dropped from ∼ 0.8 to ∼ 0.6 for the systems with > 50 satellites. This indicates that the DoS systems may be part of the large-scale filamentary structure. These results demonstrate that the DoS properties change significantly with the sample size of the satellites. We have seen similar trends of changing DoS properties in observed satellites too as discussed in Chapter 3. These considerations suggest that the properties of the observed MW DoS may not be representative of satellite systems in general.

89 1.0 ● Ellipticals Spirals

0.8 ● ● ● ● 0.6 ● ● ● ● ● ● ●

median c/a ● 0.4

Satellites within Rvir ● 0.2 No. of satellites 10 − 12 ● No. of satellites 30 − 40 ● No. of satellites > 50 0.0 1 2 3 4 5

Rvir /R

Figure 5.3: The median c/a ratio of the satellite systems as a function of the scaled maximum distance of the dwarfs from their host. The symbols and the colors are same as in Figure 5.2.

5.3.3 Kinematic properties of satellite systems

Another important question regarding the DoS is if the satellites lying on the DoS are co-rotating on the plane. Among the 11 “classical" satellites around MW that have proper motion measurements, 6 can be considered strictly co-rotating (Maji et al. 2017). Ibata et al. (2013) suggested that 13 of the 15 coplanar satellites around M31 co-rotate based on their line-of-sight velocities. However, due to the large uncertainties associated with these velocity measurements and the very small sample sizes, the corotation of satellites on the DoS remains an open question. A larger sample size and precise measurements of 3-D velocity components of dwarfs from the Illustris simulation can provide a valuable insight into the kinematic properties of the satellites.

90 Satellite systems with elliptical hosts Satellite systems with spiral hosts 600 s m e t 400 s y s N 200 0

0.0 0.2 0.4 0.6 0.8 1.0

fcorot

Figure 5.4: Histogram of fraction of satellites corotating on the DoS around the elliptical and spiral host galaxies.

To investigate the kinematic coherence of the DoS, we first calculate the fraction of dwarfs co-rotating in the DoS plane. We define a satellite as co-rotating on the DoS when its angular momenta lies within 45 degree of the DoS normal vector and define it as counter co-rotating when this angle lies between 135 degree to 180 degree.

Figure 5.4 shows the histogram of the fraction of co-rotating (fcorot) satellites around elliptical (blue) and spiral (magenta) host galaxies. This figure demonstrates that for both ellipticals and spirals, in most systems the fraction of satellites corotating on the DoS is . 0.1. Among 1665 elliptical hosts, only 150 and among 926 spiral hosts, only 85 hosts have satellite systems have fcorot . 0.5. So, for both types of hosts, about 9% of the hosts have satellite systems where more than (or equal to) half the satellites are co-rotating on the DoS which suggests that in 91% of satellite systems majority of satellites are not co-rotating.

However, we notice that in Figure 5.4 a few of the hosts have fcorot close to 1,

91 ●●●●●●●●●● ● 1.0 ●●● ●● ● ● ●● Ellipticals ●● ● ● ● ● ●● ● ●● ●● Spirals ●● ● ● ● ●

0.8 ● ● ●● ●● ● ● ● ●● ● ●● ● ●●●●●●● ● ●●● ● ●● ● ●● ● ● ● ●● ●● ● ● ● ● 0.6 ● ●● ● ● ●● ● ●●● ● ●● ●● ●● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ●●●● ● ● ●● ●● ● ●● ● ● ● ● 0.4 ●● ● ● ●● ● ● ● ●●●●●●●●● ●● ● ● ● ●●● ●● ●● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ●● ●● ●●●● ● ●● ●● ●● ● ● ●●●● ● ● ● ● ● ● ● ● ● ●● ●●● ● ● ● ●●● ● ● ●●● ● ●● ●●● ●● ● ● ● ●● ● ● ●● ●● ●● ● ●●● ● ● 0.2 ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ●● ●●● ● ● ●● ●● ● ●● ● ● ● ●● ●● ●●● ● ●● ● ● ●●●● ●● ●● ● ●●● ●●●● ●●● ● ●●●● ● ●●● ● ●●● ● ● ●●●●● ●●● ● Fraction of co−rotating satellites within Rvir Fraction ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●● ●●●● ●●● ● ● 0.0 0 50 100 150 200 Number of satellites

Figure 5.5: Fraction of co-rotating satellites on the DoS as a function of number of satellites in the system for elliptical (red) and spiral (blue) host galaxies. i.e. almost all satellites in these systems are corotating on the DoS. To take a closer look at these systems, we plot fcorot as a function of the number of satellites in the systems in Figure 5.5. We find that the systems with fcorot close to 1 all have very few satellites. Additionally, in systems with few satellites, fcorot has very large scatter (with values varying from 0 to 1). As the number of satellites in the system increases, the fcorot of the system decreases. This suggests that the systems with nearly all co-rotating satellites probably result from small sample statistics.

5.3.4 Evolution of the satellite systems

So far we have seen that in almost all satellite systems there is a varying degree of anisotropy in their spatial distribution. However, the origin of this anisotropic distribution of satellites has been unclear. Some early studies suggested that satellite

92 galaxies preferentially avoid regions near host galaxies equator plane and tend to cluster near the poles (Holmberg 1969; Zaritsky et al. 1997), but later observations showed that this may only be true for certain type of galaxies (e.g., Agustsson & Brainerd 2010; Azzaro et al. 2007; Bailin et al. 2008; Brainerd 2005; Sales & Lambas 2004). In order to directly probe the origin of the anisotropic distribution of the satellite system, it is essential to observe them at high redshift. However, due to the low luminosity of satellite galaxies, it is extremely difficult to observe them in the distant universe. Other than the satellites in our Local Group, we have observations of possible DoS around SDSS galaxies only up to z = 0.05 (Ibata et al. 2014a), but these claims have been largely refuted (Cautun et al. 2015a; Phillips et al. 2015). In this study we investigate the DoS evolution in two ways: following the median behavior of all viable satellite systems and following individual Milky Way like galaxies through different redshifts. In the first part, we select the host galaxies with mass 11 13 range 5 × 10 M and 2 × 10 M at different redshifts (same criterion as used in § 5.2) and calculate the c/a ratio of these systems using satellites within virial radius. We again divide our host galaxies into three groups: hosts with 10 - 12 satellites, 30 - 40 satellites and > 50 satellites within virial radius and plot the median c/a of these samples as a function of redshift in Figure 5.6. We find that when we fix the number of satellites in a satellite system, their median anisotropy remain very similar over a redshift range of z = 0 − 6. At each redshift, there are a few thousand host galaxies, with a few hundred hosts in each of these groups. So it is difficult to comment on their individualistic evolutionary behaviors based on the median data of the groups. For this purpose, we track few individual Milky Way like galaxies to understand the details of their 12 evolution. We find galaxies with mass between 1.5 − 2.5 × 10 M (MW mass 12 ∼ 2 × 10 M ) and among them select the ones with at least 30 satellites within virial radius at z = 0 (MW has at least 39 satellites within virial radius). We have identified 4 galaxies which met both conditions and we follow their main progenitor branch through z = 0 − 6. Similar to before, we identify all of their satellites within their virial radius and plot their c/a evolution in Figure 5.7. We find that there is no general trend in these galaxies and they have a very chaotic history. The anisotropy of these galaxies depends on the number of their satellites at that particular redshift and their recent history, e.g. mergers and interactions which tend to disrupt the

93 1.0 0.8 ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.6

● ● ● ● ● ● ● median c/a 0.4

Satellites within Rvir ● 0.2 No. of satellites 10 − 12 ● No. of satellites 30 − 40 ● No. of satellites > 50 0.0 0 1 2 3 4 5 6 z

Figure 5.6: Median c/a ratio of satellite systems calculated with satellites within virial radii. The error bars are standard deviation of the c/a distribution at each redshift. The different colors represent hosts with three satellite populations; systems with 10-12 satellites (red), 30 - 40 satellites (blue) and more than 50 satellites (black). satellite system and increase the c/a.

5.4 Discussions

The Illustris-1 simulation used for our analysis here have a limited mass resolution of 5 8.85 × 10 M . It is also known that low mass dwarf galaxies have very low baryonic fraction (see Chapter 6 for more details). These two factors suggest that at the low 7 8 mass end of our dwarf galaxies (∼ 10 − 10 M ), they may only have a few stars and gas particles in them. The limited resolution also implies that we can’t resolve any 7 satellite galaxies beyond 10 M , and miss a population of ultra faint very low mass dwarfs altogether.

94 1.0

● ● ● 0.8 ● ● ● ● ● ● ● ● ● ● ● ● ● 0.6

● ● ● c/a

● ● 0.4 0.2

4 MW type hosts with satellites within 1 Rvir ● 0.0 0 1 2 3 4 5 6 z

Figure 5.7: Left : Evolution of the c/a of four MW type hosts with satellite systems within their virial radius.

The cosmic star formation density in Illustris-1 simulation is too high in host galaxies at low redshifts (z < 1), probably because of their inefficient quenching mechanisms and this may affect their satellite abundance (Vogelsberger et al. 2014b). Additionally, in high redshifts, about 10% of spiral host galaxies exhibit strong stellar and gaseous ring-like features, which may fragment and give rise to a small population of stellar clumps close to the galaxy, which may be identified (by group finding algorithms) as dwarf galaxies but are not physically well motivated objects. In order to study the satellite population in greater detail, we need to analyze a cosmological simulation with much higher resolution and more realistic implemen- tation of physical processes. The upcoming Illustris next generation (IllustrisTNG) simulation with a box size of 50 Kpc (TNG50) will have a baryonic mass resolution 4 of 8.5 × 10 M . It will also employ additional physics, e.g. inclusion of magnetohy- drodynamics, improved AGN feedback model (may solve star formation quenching)

95 (Pillepich et al. 2018) and would be a very useful simulation to gain more insight into the physics of dwarfs.

5.5 Conclusions

We have investigated 2591 satellite systems in the high resolution hydrodynamical cosmological simulation Illustris and explored their spatial distribution, kinematic properties and evolution. Our main results are summarized below:

• The anisotropy of DoS systems is highly dependent on the number of satellites in the system. Satellite systems with a small number of galaxies are systematically more anisotropic than systems with more galaxies, which suggests that the highly anisotropic DoS might be a small number selection effect. This is consistent with the observational pattern that height and the flatness ratio of the DoS increase with sample size, as shown in Maji et al. (2017).

• The kinematically selected elliptical and spiral galaxies exhibit similar trends for the spatial and kinematic properties of the DoS around them, which suggests that host galaxy type is not important in determining DoS properties.

• The DoS around the Illustris galaxies are generally not rotationally supported. Majority of them (∼ 91%) have less than half of their satellites corotating in the DoS. However, there are a few systems which are even more flattened and more kinematically coherent than the observed DoS around MW. This shows that baryonic ΛCDM simulation can indeed produce highly anisotropic coherent DoS, although they are rather extreme cases. For example, in our sample we found that among systems which have at least 10 satellites (777 such systems),

2 systems have c/a . 0.2 and 20 systems have a fcorot & 0.72 (i.e. 8 / 11, as observed in MW).

• The number of satellites in a system is the main factor that determines its c/a values at all redshifts, and not the redshift itself. When we keep the number of satellites same, the median c/a of those systems remain remarkably similar throughout z = 0 − 6. However, the evolution of individual satellite systems is extremely chaotic, complicated and system dependent.

96 Our results suggest that statistically, satellite systems in the universe becomes more isotropic as their sample size increases and the majority of them are not kinematically coherent. Our findings indicate that most of the satellite systems in the universe have some degree of anisotropy, but in general, their distributions are neither highly flattened nor rotationally supported. The origin of this anisotropy in individual satellite systems is affected by their chaotic dynamical evolution.

97 Chapter 6 | Evolution of dwarf galaxies

6.1 Introduction

Dwarf galaxies are the most populous member among galaxies in universe Mateo (1998); Marzke et al. (1998). Dwarfs are interesting in their own right, and additionally most of them are relics from times before reionization, so they are great targets to study the early universe. The subject of dwarfs is really vast and their different aspects have been discussed separately in a number of studies. I have presented a general review of dwarf galaxy literature in § 1.3. In this chapter, I analyze a high-resolution cosmological simulation of a Milky Way type galaxy, complete with hydrodynamics and realistic feedback mechanisms, and investigate the properties of the dwarf galaxies formed around the MW disk. We analyze their present properties, their star formation history and follow their evolution to investigate the effects of reionization on these dwarfs. The structure of this chapter is as follows. In (§6.2) I discuss the adopted galaxy model and the simulation. The results are presented in three sections. Results I (§6.3) describes their present properties, e.g. abundance and baryon fraction. In §6.4,I present Part II of results which discuss the star formation rate of the simulation, star formation history in dwarfs, and their age. Part III of results are given in §6.5 that discuss the evolution of dwarfs, in particular, the evolution of their mass function and baryon fraction and the effect of reionization on dwarfs. Finally, I discuss the limitations of the study in §6.6 and summarize the results in §6.7.

98 6.2 Method

We have used the simulation by Marinacci et al. (2014) for our galaxy model. In this paper authors have performed eight cosmological hydrodynamical simulations focusing on the evolution of Milky Way type galaxies. The same objects were studied in the Aquarius project (Springel et al. 2008) before but that was a dark matter only simulation. In our current work we have studied the galaxies in the simulation Aq-C-4 which have the highest mass resolution and have produced a central disk-like galaxy as its end product that is very alike our Galaxy. The total mass of the central 12 galaxy in Aq-C-4 is 1.59 × 10 M and the entire box size is 100 Mpc. The simulation has a higher resolution around the central region, which is about 10 Mpc long. Our dwarf study is concentrated with 5 Mpc of the Galactic Centre. Here the baryonic 4 5 (gas/star) mass resolution is 5 × 10 M and the dark matter resolution is 2.7 × 10 M . The maximum gravitational softening length is 340 pc. The physical model used in this simulation closely follows the processes described in detail in Vogelsberger et al. (2013) and Marinacci et al. (2014). The galaxy has both primordial cooling and metal line cooling with self-shielding. The ISM is described by a sub-resolution model which consists of a cold lumpy phase and a hot phase (heated by Supernovae). The model incorporates stellar evolution and consequently the recycling of gas. It follows the overall metal enrichment and tracks nine elements individually. The model includes both stellar and AGN feedback. The stellar feedback is done via a kinetic wind model where the wind velocity is proportional to the local dark matter velocity dispersion. The metallicities of the wind is fixed by a wind metal loading factor. Heavy dark matter halos contain Black Hole (BH) seed which grow into black hole in time. The AGN feedback can be thermal, mechanical or radiative. The most common channel of feedback, i.e. thermal/mechanical is categorized into two types, Quasar mode (high activity BH) and Radio mode (low activity BH). The simulation has a uniform UV radiation field which captures the physics of cosmic ionization (Faucher-Giguère et al. 2009). At z > 3, the star-forming galaxies are the major source of the ionization whereas in lower redshifts quasars also have a significant contribution. The hydrogen reionization ends around z = 6. In this chapter we have used the Amiga Halo Finder (AHF) for the cluster finding algorithm. This hierarchical halo finding algorithm was developed by Gill et al. (2004); Knollmann & Knebe (2009). A short summary of AHF algorithm has been discussed

99 in §2.2.3. We impose three criterion on the subhalos found by AHF to consider them 10 as dwarfs, i.their total mass has to be less than 10 M , ii.they need to have non-zero stellar mass and iii.they have to be bound systems.

6.3 Results I: Present day properties of dwarf galaxies

6.3.1 Abundance of Dwarfs

In our simulation there are 238 dwarf galaxies within 3 Mpc of the Galactic Center. For comparison, there are 100 observed dwarfs listed in McConnachie (2012) that lies within 3 Mpc of our Milky Way center. These observed dwarfs include MW satellites, M31 satellites and isolated field dwarfs. Both sets of dwarfs have a lower limit of an absolute visual magnitude of MV > −20. The discrepancy in the abundance by a small factor of ∼ 2, can be understood by inspecting the limitations of observations. There are almost no observations of dwarfs within galactic latitude |b| < 30 because of severe Milky Way dust extinction. The survey for M31 (PANDAS) is incomplete after a radius of 150 Kpc from Andromeda’s center which, from the trend of data collected, should host a number of dwarfs. The region very close to M31’s center is also difficult to observe because of a high foreground contamination from M31 stars. Discovery of isolated dwarf galaxies in the local group is also very much incomplete due to their faintness and sparse distribution. However, the ongoing or upcoming surveys such as LSST and DES are going to revolutionize the field. DES has already found 8/9 new dwarfs within 22 - 338 Kpc of the Galactic Center (Koposov et al. 2015; The DES Collaboration 2015). Probably about 100 - 200 dwarfs are awaiting discovery in near future (Hargis et al. 2014), which can resolve this abundance discrepancy. It is also interesting to investigate the the radial distribution of the number of dwarfs. In Fig 6.1 we plot both the numbers of simulated dwarfs (blue) and observed (orange) dwarfs (McConnachie 2012) as a function of their distance from the galactic center. As expected, the number of dwarfs decreases with increasing distance, because the overall matter available for forming galaxies is less in far-off regions.

6.3.2 Baryon fraction of dwarfs

The baryon fraction fb of a galaxy is defined as fb = (Mb/Mdark) where Mb =

Mgas + M?. Here Mb is the mass of baryons in the dwarfs which include both gas

100 Simulated dwarfs 80 Observed dwarfs 60 40 Number of Galaxies Dwarf Number 20 0 0 1 2 3 4 5 Distance from center (Mpc)

Figure 6.1: Histogram of the radial distribution of simulated (blue) and observed (orange) dwarfs (McConnachie 2012). The number of dwarfs decreases with increasing distance from the Milky way center, as seen in both simulated dwarfs and the observed ones.

mass (Mgas) and stellar mass (M?). The dark matter mass of the galaxy is denoted by Mdark. The universal baryon fraction is fb = 0.17 (Planck Collaboration et al.

2014) but the different structures in the universe have lower fb. Studies (McGaugh et al. 2010) have shown that although the mean baryonic fraction of galaxy clusters is close to the universal value, the elliptical, spiral and most prominently the dwarf galaxies have significant baryon deficiency. To investigate this using our simulated dwarfs, we plot the stellar mass of the simulated dwarfs (blue points) against their total mass in Fig 6.2. The overplotted orange points are the observed dwarfs in Local Group (McGaugh et al. 2010; Walker et al. 2009). Dwarf galaxies are very gas poor systems, so their baryonic mass can be approximated as equal to their stellar mass. To determine the total mass of observed

101 Simulated dwarfs Observed, Walker'09 10 Universal fb ) n 8 u S M

/

r a t s 6 (M

10 log 4 2

6 7 8 9 10

log10 (Mtot / MSun)

Figure 6.2: Stellar mass of dwarfs vs their total mass. The blue points are simulated dwarfs and the orange ones are observed dwarfs (Walker 2009, McGaugh 2009). The black line indicates the the universal baryonic fraction, Mb/M? = 0.17. The dwarfs lie much below this value. The simulated points match closely to the observed ones. 4 The apparent cut of blue ones at 10 M is because of the resolution limit of the simulation. dwarfs, we assume the velocities of the observed dwarfs are isotropic which gives the √ circular velocity as Vc = 3σ where σ is the velocity dispersion. The total mass is 5 3 then given by Mtot = 1.5 × 10 × Vc (McGaugh et al. 2010). For estimating their stellar mass, we assume a standard mass to light ratio of 1.3 (Mateo et al. 1998) to convert the observed luminosity (LV ) into stellar mass; Mb ' M? = 1.3LV , following McGaugh et al. (2010). Therefore, effectively Fig 6.2 shows the relations of baryonic mass and the total mass. We find that all data points, simulated and observed, lie below the line of the universal baryonic fraction, which shows that dwarf galaxies have a baryon deficiency. The simulated dwarfs fb are in good agreement with the 4 observations. The apparent lack of any simulated dwarfs below M? = 10 M is a

102 0 Simulated dwarfs Observed, Walker'09 -1 -2 ) b (f

-3 10 log -4 -5 -6 6 7 8 9 10

log10 (Mtot / MSun)

Figure 6.3: Baryon fraction of simulated dwarfs vs their total mass. Observed dwarfs are overplotted in orange. The points have the same meaning and source as in the previous figure. Notice that the baryonic fraction of dwarfs are very low in general, 10−1to10−4. reflection of the limited resolution of the star and gas particles in the simulation. Another way of looking at it is to plot the baryonic fraction against the total mass of galaxies (Fig 6.3). Here we can clearly see that the typical fb in the dwarfs ranges from 10−2 to 10−4 for both samples, way below the universal value. To understand how the dwarfs lost most of their baryons, we need to trace their evolution. We discuss this aspect in detail in §6.5.

6.4 Results II: Star Formation History in dwarfs

To investigate the formation and evolution of the dwarfs it is important to observe them at high redshifts, however, it is also extremely difficult, owing to their low

103 40 30 yr)

/

n u S 20 (M

SFR 10 0

12 10 8 6 4 2 0 z

Figure 6.4: The overall star formation rate of the simulation at different redshifts.

brightness (few high z observations exist, see Vegetti et al. (2010, 2012)). However, the present ages of dwarfs and their Star Formation Histories (SFHs) (Weisz et al. 2015) can substantially help resolve their evolutionary history. First, we look at the star formation of the simulation as a whole. We plot the star formation rate (SFR) against redshift of the simulation in Fig 6.4. We notice that the highest star formation peak happened in early universe, around z = 5.5, about 40 M /year. After that, the overall SFR decreases but there are smaller peaks in between. The episodic high star formation rates are caused by mergers and tidal interaction between the main galaxy and its satellites. At z=0, the SFR is about 6

M /year, close to the observed SFR of Milky Way (3 M /year).

104 6.4.1 Star formation quenching in dwarfs

The star formation history of the dwarfs can be deduced from the analysis of color magnitude diagrams (Aparicio & Hidalgo 2009; Dolphin 2012; Tosi et al. 1989). Recently, Weisz et al. (2015) have analyzed data for 38 Local Group dwarfs using HST and deducted their detailed star formation histories. These star formation histories can be used to reconstruct their orbital motion by theoretical modeling, as has been illustrated in (Sohn et al. 2013) for LeoI with HST ACS/WFC images. We can deduce their evolution history from their orbital motion. Well-constrained SFHs exist for a few dwarfs outside Milky Ways virial radius also (Monelli et al. 2010a,b; Weisz et al. 2014c). There have been a few studies which compare the SFHs of observed dwarfs with those obtained from N-body simulation at z = 0 (Phillips et al. 2015; Rocha et al. 2012). But it has been established recently that N-body simulations are not sufficient for analyzing dwarf galaxies; for their mass and size range, the inclusion of baryonic physics is extremely important (Gillet et al. 2015; Sawala et al. 2014). So the necessary next step is to analyze the SFHs of dwarfs from a baryonic simulation of dwarf galaxies. Recently, Auriga simulations of 30 Milky Way size halos and their satellites have analyzed satellites within 150 Kpc of their host and have found that about half of the satellites are quenched within a Gyr of their infall and ram pressure is the dominant mechanism driving it Simpson et al. (2018). In this work, we have analyzed the SFH of all simulated dwarfs (dwarfs are distributed out to 3 Mpc) from our baryonic simulation in Fig 6.5. We define the quenching era of a galaxy to be when 90% of its stars have been born, following the definition in Weisz et al. (2015). We plot the cumulative fraction of quenched galaxies against look back time for 3 different mass ranges, identical to the observational analysis performed in (Weisz et al. 2015). We find that the lower mass dwarfs are quenched earlier and at any given epoch, the quench fraction is higher for the less massive ones, similar to the trend in observed dwarfs. Specifically, we see that the 5 6 less massive dwarfs (10 − 10 M ) were quenched very early on, around 12 Gyrs 7 8 ago. However, the massive dwarfs (10 − 10 M ) have star formation episodes till about 4 Gyrs ago. Star formation in these massive ones is also quite episodic, which indicates that the massive ones have undergone mergers and interactions which has triggered star formation later. The massive ones match quite well with the observed

105 1.0 1.0 6 7 Stellar mass 10 − 10 MSun 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 Fraction of Quenched Galaxies of Fraction Quenched Galaxies of Fraction Quenched 5 6 Stellar mass 10 − 10 MSun 0.0 0.0 14 12 10 8 6 4 2 0 14 12 10 8 6 4 2 0 Lookback age (Gyr) Lookback age (Gyr) 1.0 7 8 Stellar mass 10 − 10 MSun 0.8 0.6 0.4 0.2 Fraction of Quenched Galaxies of Fraction Quenched 0.0 14 12 10 8 6 4 2 0 Lookback age (Gyr)

Figure 6.5: We plot the quenched fraction of the simulated dwarfs as a function of 4 5 5 6 6 look back time for four different mass groups, M? − 10 − 10 M , 10 − 10 M , 10 − 7 7 8 10 M , 10 − 10 M . The blue lines show the SFH of the simulated dwarfs and the red solid lines are SFH of observed dwarfs (data from Weisz et al. (2015)). The red dashed lines show the 68% confidence interval for the observed dwarf sample.

SFH, derived from the data of 38 dwarf galaxies presented in Weisz et al. (2015). In lower mass range, the larger difference of the simulated and the observed dwarfs can be attributed to the limited mass resolution of our simulation and the small sample size of the observed sample.

106 6.4.2 Age of Dwarfs

Determine the age of a galaxy is tricky since galaxies have extended star formation phases. For our purpose here we define the age of a dwarf as its median age, i.e. when 50% of its stars have been formed. The resulting ages of dwarfs have been plotted in Fig 6.6 as a histogram. Most of the dwarfs are very old with age & 12 Gyr and almost all dwarfs are more than 7 Gyrs old. There are very few dwarfs aged less than 1 Gyr which are probably products of recent star formation episodes. Ricotti & Gnedin (2005) discussed ages of dwarfs using high-resolution simulation of dwarf galaxies in high redshift and concluded that age-wise dwarfs can be divided into three groups; true fossils (formed before reionization, most belonged to this group), survivors (formed after reionization) and polluted fossils (mixed population). Similar groupings can be found in our simulation too, most dwarfs are formed before reionization (z ∼ 6; t ∼ 12.6 Gyrs), with few polluted and fewer survivors. To explore the interesting relationship between the mass of dwarfs and their age, we plot the median age vs the total mass of dwarfs in Fig 6.7. The different colored points indicate different stellar mass ranges and the bigger the size of the symbol, higher is its stellar mass. We find the higher mass dwarfs are generally younger than lower mass dwarfs, presumably because more massive dwarfs formed later via mergers or mass accretion. For a fixed total mass, dwarfs with lower stellar mass are older than their high stellar mass counterpart. High stellar mass indicates extended star formation which makes the median dwarf age younger. This supports our conclusion from the previous section that lower mass dwarfs had early star formation quenching and hence they are older. Thus the true fossils from reionizations would probably be ultrafaint dwarfs.

6.5 Results III: Evolution of the Dwarfs

It is extremely difficult to observe dwarfs at high redshift and deduce their evolution history directly. Hence it is important to explore the dwarf evolution in cosmological simulations by following them through the cosmic time and discuss the evolution of mass function, baryonic fraction and the role of reionization in shaping their early growth.

107 Simulated dwarfs 150 100 50 Number of galaxies dwarf Number 0 14 12 10 8 6 4 2 0 Median age of dwarfs (Gyr)

Figure 6.6: Histogram of the lookback ages of the dwarfs simulated here. Most of the dwarfs are old with age > 12 Gyr although there are few which are intermediate aged, around 8 Gyr and still fewer around 1 Gyr.

6.5.1 Evolution of the mass function

The mass function of dwarfs is one of its most important characteristics. The mass function of a sample can be represented by the mass histogram. We plot the total mass histograms of our dwarf population at 8 different redshifts (Fig 6.8), namely z = 8.5, 6.8, 6.1, 5.5, 4.4, 3.5, 2.0, and0.0. At all redshifts, the mass function resembles a lognormal shape with a clear peak. From z = 8.5 to 6.1, the peak is at 7.5 8 mass range 10 −10 M . However its position gradually slides towards more massive dwarfs as redshift approaches z = 0. From redshift 5.5 to 3.5 the peak mass is at mass 8 8.5 8.5 9 range 10 − 10 M and from z = 2 to 0, the peak shifts further to 10 − 10 M . The number of dwarfs also differs widely at different redshifts. At the early times, the typical number is more than 2000, but it drops to ∼ 1000 at z = 5.5 . After that the

108 12 10 8 6 4 Mstar 4 5 10 − 10 MSun

Median age of (Gyr) dwarfs age Median 5 6 10 − 10 MSun 2 6 7 10 − 10 MSun 7 8 10 − 10 MSun 0

6 7 8 9 10

log10 (Mtot / MSun)

Figure 6.7: Total mass of dwarfs vs their median age plot. The different colors and sizes of points indicate different stellar mass ranges of the dwarfs. The maroon points 4 5 5 6 represent dwarfs with M? ∼ 10 − 10 M , orange is M? ∼ 10 − 10 M , purple 6 7 7 8 M? ∼ 10 − 10 M and blue M? ∼ 10 − 10 M . The larger points has higher stellar mass. number decreases slowly until it reaches a moderate population of 280 at the present time. The change of the peak mass is further demonstrated in Fig 6.9 where we show the probability density of the dwarfs mass distribution at different redshifts (left) and the most probable dwarf mass as a function of redshift (right). We find that, on top of a general rising trend, the most probable mass increases sharply around redshift 6. These suggest that there are some physical processes that took place around z = 6 which destroyed many low mass dwarfs. The later gradual decrease in numbers and increase in peak mass possibly points to merger events in recent times. We discuss these underlying reasons in more detail in §6.5.3.

109 1400

z = 8.5 z = 6.8 1200 z = 6.1 1200 1000 1000 800 800 800 600 600 600 400 400 400 No. of dwarf galaxies of dwarf No. galaxies of dwarf No. galaxies of dwarf No. 200 200 200 0 0 0 6 7 8 9 10 6 7 8 9 10 6 7 8 9 10 log10 (Mtot / MSun) log10 (Mtot / MSun) log10 (Mtot / MSun) 700 500 300

600 z = 5.5 z = 4.4 z = 3.5 250 400 500 200 300 400 150 300 200 No. of dwarf galaxies of dwarf No. 100 200 100 50 No. of dwarf galaxies of dwarf No. galaxies of dwarf No. 100 0 0 0 6 7 8 9 10 5 6 7 8 9 10 5 6 7 8 9 10 log10 (Mtot / MSun) log10 (Mtot / MSun) log10 (Mtot / MSun) 100 z = 2.0 z = 0.0 150 80 60 100 40 50 20 No. of dwarf galaxies of dwarf No. galaxies of dwarf No. 0 0 6 7 8 9 10 6 7 8 9 10 log10 (Mtot / MSun) log10 (Mtot / MSun)

Figure 6.8: The total mass function of the dwarfs at 8 different redshifts. At all the redshifts the mass function takes the form of a peaked function but the position of the peak changes from lower value to higher value as redshift decreases.

6.5.2 Evolution of the baryon fraction

To investigate the evolution of the baryonic fraction in dwarfs, we plot the histogram of fb for the same 8 redshifts discussed in § 6.5.1 in Figure 6.10. We notice that in the first three panels, until z = 6.1, almost all dwarfs have baryonic fractions very close to the universal value. After z = 5.5 the histogram widens considerably with some dwarfs having very low baryonic fractions. Finally at z = 0, the entire peak of −3 fb histogram has shifted to fb ∼ 10 . The fall of the baryonic fraction by almost 3 orders of magnitude shows a significant baryon depletion. We analyze the probable

110 1.5 z

8.5 8.6

6.8 ) n u

6.1 S 8.4 M

5.5 / 1.0

e 4.4 l b a

3.5 b o 8.2 r p

2.0 t s o

0.0 m 8.0 (M

0.5 Probability density Probability 10 log 7.8 7.6 0.0 6 7 8 9 10 10 8 6 4 2 0

log10 (Mtot / MSun) z

Figure 6.9: Left : The probability density of total mass of the dwarfs at different redshifts. The different colors denote the redshifts here. Right : The most probable mass of the dwarfs as a function of redshift. reasons in the next section.

6.5.3 Effect of Reionization

It has long been discussed that the reionization in early universe have had a major effect on the formation and evolution of the dwarf galaxies in early universe (Babul & Rees 1992; Benson et al. 2003, 2002; Busha et al. 2010; Efstathiou 1992; Kravtsov et al. 2004; Wyithe & Loeb 2006). There are various sources of heating and cooling in galaxies that can regulate their evolution and star formation. The major heating sources are reionization and supernovae explosion whereas H2 and metal line cooling are the dominant cooling mechanisms. Additionally, there are several environmental factors, such as ram pressure, tidal stripping etc, that also affects the growth of galaxies. The relative contribution of these physical effects on the evolution of dwarfs has been discussed in detail in Simpson et al. (2013) where the authors perform a 9 high-resolution simulation of one dwarf galaxy of mass 10 M with several alternate physical models. They conclude that reionization is the main process that regulates the global star formation or baryon stripping of dwarfs. Supernovae effects are important in expelling metals and cooling is essential in starting the star formation from dense gas. In this light, we discuss the effects of reionization on the evolution of our simulated dwarfs.

111 1500 z = 8.5 z = 6.8 1500 z = 6.1 1500 1000 1000 1000 500 500 500 No. of dwarf galaxies of dwarf No. galaxies of dwarf No. galaxies of dwarf No. 0 0 0 −5 −4 −3 −2 −1 0 −5 −4 −3 −2 −1 0 −5 −4 −3 −2 −1 0 log10 fb log10 fb log10 fb 700 400

z = 5.5 600 z = 4.4 z = 3.5 1200 300 500 400 800 200 300 600 200 400 100 No. of dwarf galaxies of dwarf No. galaxies of dwarf No. galaxies of dwarf No. 100 200 0 0 0 −5 −4 −3 −2 −1 0 −5 −4 −3 −2 −1 0 −5 −4 −3 −2 −1 0 log10 fb log10 fb log10 fb 60 120 z = 2.0 z = 0.0 50 100 40 80 30 60 20 40 10 20 No. of dwarf galaxies of dwarf No. galaxies of dwarf No. 0 0 −5 −4 −3 −2 −1 0 −5 −4 −3 −2 −1 0 log10 fb log10 fb

Figure 6.10: The baryonic fraction of the dwarfs at the same redshifts. The black dashed line in the histograms represent the universal baryon fraction, fb = 0.17 (Planck Collaboration et al. 2014).

We have noticed from our discussion in the previous two sections that a major change occurs in the dwarf population around z = 6. This is also the redshift when the reionization ends in our simulation, suggesting a cause and effect relationship. Before z = 6 there are thousands of dwarfs in the simulation, a majority of which are low 7.5 8 mass dwarfs, 10 − 10 M . Baryons are just falling into the dark matter potential wells, so their baryonic fraction is same as the cosmic fraction. The high gas density in these halos starts star formation, making them luminous dwarf galaxies. After z = 6, the picture changes considerably. The number of dwarfs drops precipitously, the peak

112 of mass function shifts to higher masses and baryon fraction falls. At this period the photons produced by stars in dwarfs ionizes the hydrogen gas in the galaxies. This is known as H2 reionization. The released electrons produce powerful wind which can sweep of baryons (gas) from the galaxies. Evidently, the least massive dwarfs suffer the most as their potential well is comparatively shallow, making their baryons most vulnerable to be swept off. This is illustrated in Fig 6.11 where we plot the 8 number and the fraction of small dwarfs (Mtot < 10 M ) as a function of redshift. We find that both the absolute number (red points) of these less massive dwarfs and their relative fraction (blue points) in the entire population drops sharply around z = 6. After that, their number levels off. As a whole, the baryon fraction drops for the entire population and many less massive dwarfs lose all of their baryons which destroys the galaxy itself. Thus the peak of mass function shifts to a higher mass (Fig 6.9). We also notice that though many of the less massive dwarfs were destroyed, some of them survive (Fig 6.8). The survival of small dwarfs through reionization has been 8 debated. It was argued that halos with mass less than 10 M (Efstathiou 1992) could be easily destroyed even by a single supernovae and it would be highly unlikely for them to survive past reionization. But it has been recently shown that a clumpy center could be an effective resistant to the sweeping effect of a supernovae (SNe), especially if it is off center, as well as reionization effects (Bland-Hawthorn et al. 2011; Webster et al. 2014). After reionization, dwarfs go through mergers, interactions and destruction from SNe, collision etc. We try to understand the overall impact of these processes on their evolution in Fig 6.12. Here we plot the total mass of different components enclosed in dwarfs as a function of redshift. We notice that the number of dwarfs drop rapidly at z = 6 and continue decreasing after that although at a slower rate. However, the total mass in dwarfs decreases only slightly. This suggests that many of the dwarfs are merged with each other and fewer/ mostly low mass dwarfs are destroyed. The main reasons for destruction are probably supernovae explosions and tidal disruptions. Ram pressure on the gas of infalling dwarfs also expels their gas reservoirs which decreases their total mass (Arraki et al. 2014).

113 0.7 1500 0.6 0.5 1000 0.4 Number of small galaxies of small Number 500 Fraction of small galaxies of Fraction small 0.3 0.2 0 10 8 6 4 2 0 z

8 Figure 6.11: We plot the fraction of small (Mtot < 10 M ) dwarf galaxies (left y axis) and the absolute number of small dwarfs (right y axis) as a function of redshift. Both the numbers (red points) and the relative fraction (blue points) of these galaxies take a sharp downward jump at z=6, around the time reionization ends.

6.6 Discussions

Our simulation uses a subgrid model to simulate the ISM with an effective equation of state which assumes a equilibrium state in ism (Vogelsberger et al. 2013). While this is a common practice, it would be more realistic to model ism from first principles that include molecular cloud formation, thermal instability, turbulence effects etc. These small scale details become more important for smaller dwarf galaxies, although resolving these effects in simulations would require a much higher spatial and mass resolution. Though our simulation includes the major physical processes, it leaves out some secondary processes e.g. cosmic rays (Booth et al. 2013), magnetic field (Chyży et al. 2011; Jurusik et al. 2014) etc which might have effects on dwarf galaxy

114 2500 12.0 )

n u S 11.5 M

2000 10

11.0 (log

1500 10.5 Number of dwarfs Number 10.0 1000

9.5 Total mass - Cumulative Total mass in dwarfs Total mass in Total dark matter mass Total gas mass 500 Total stellar mass 9.0 10 8 6 4 2 0 z

Figure 6.12: The total mass of different components (blue lines) trapped in dwarfs (left y axis) against the redshift. The solid blue line denotes the total mass of dwarfs, the dot dashed line shows the dark matter mass, the dotted line is the total gas mass and the dashed line is the total stellar mass in all the dwarfs. All the mass components rises till z 6 and then they decreases, albeit at different rates. We overplot the total number of dwarfs (magenta line) against redshift (right y axis) and find that numbers of dwarfs decrease with redshift after z = 6. formation. 4 5 The mass resolution in our simulation is 5 × 10 M for gas/stars and 2.7 × 10 M for dark matter. The spatial resolution is ∼ 340 pc. While these are fairly high resolution, better resolution is needed to investigate the small scale processes in detail. 3 Since the stellar mass of dwarfs can be very low (< 10 M ), we need higher resolution to resolve the lower end of the stellar mass function. Resolution studies in Simpson et al. (2013) show that higher spatial resolution (10 pc) in dwarfs increase the effect of Supernovae feedback compared to low resolution (43 pc) simulation. Inefficient SNe feedback causes the dense gas in dwarfs to survive for longer time which in turn leads to extended star formation (upto z = 2). Our simulation has much lower spatial resolution than these cases, which suggests that the supernovae feedback is probably

115 too ineffective and the late stage star formation (upto z = 0.5, Fig 6.4) might be in part due to this resolution issue. Lastly, here we have only one realization of a dwarf galaxy system around a MW type galaxy. It will take several realizations of dwarf systems in different environments (different mass of host galaxies, more than one hosts, in different parts of a galaxy cluster or void) to gain an in-depth understanding.

6.7 Summary

We find dwarf galaxies in a high resolution, cosmological, hydrodynamical simulation (AREPO code) of Milky Way type galaxy using the Amiga Halo Finder (AHF). We study the properties of these dwarfs and compare them to present observations of the Local Group dwarfs. We track these dwarfs to investigate their formation and evolution through a wide range of redshifts. The key results from our study are described below:

1. The dwarfs are generally very old, with a median age around 12 Gyr. Analysis of the star formation history of dwarfs shows that star formation was quenched in smaller galaxies earlier, as was found by recent observations too. The higher mass dwarfs have a more extended star formation period, hence they are younger.

2. We follow the dwarf population at different redshifts, from z = 8.5 to z = 0 and study the evolution of their mass function and baryonic fraction. At high redshifts, there are thousands of dwarfs, most of which are low mass 7.5 8 (10 − 10 M ) ones. The dwarfs have baryonic fraction similar to the universal

value, fb ∼ 0.17. After z ∼ 6, the number of dwarfs decreases sharply and the mass function becomes a peaked one. The most probable mass continues to increase with time and the baryonic fraction decreases rapidly.

3. The radical change of dwarfs collective characteristics at z = 6 is most probably brought on by reionization. The free electrons create huge wind which can sweep off baryons from the galaxies. Smaller galaxies, having shallower potential, are more at risk to lose all of their baryons. Thus the most probable mass shifts to higher mass and many of smaller dwarfs get destroyed. The later gradual changes are probably due to galaxy interactions and mergers.

116 The dwarf galaxies play a very important role in shaping the path of cosmic history, especially in terms of reionization. Their cumulative history is complicated and tumultuous at the same time. The dwarfs are major sources of reionization and also the ones to be most affected by it. Observing and studying the ultrafaint dwarfs hold the key of understanding the physics of early universe in great depth. With the advent of newer and bigger telescopes, e.g. JWST, we would be able to observe in much more detail and can directly compare these simulated evolution results with observations.

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138 Vita Moupiya Maji 525 Davey Lab, University Park, PA 16802 email: [email protected] https://sites.psu.edu/moupiyamaji Education The Pennsylvania State University, University Park, PA Doctor of Philosophy in Astronomy & Astrophysics 2018 Master of Science in Astronomy & Astrophysics 2014

Indian Institute of Science, Bangalore, India Master of Science in Physics 2012

Presidency College, Calcutta University, Kolkata, India Bachelor of Science in Physics 2009

Selected Grants and Awards FAMOUS travel grant AAS 231st Winter meeting 2018 Co-I of HST grant to "Star Clusters in Tidal Debris: A UV Survey of Stellar Popula- tions, Galaxy Interactions, and Evolution" Hubble Space Telescope 2017 Zaccheus Daniel Fellowship, Penn State 2016, 2014 Homer F. Braddock and Nellie H. and Oscar L. Roberts Fellowships, Penn State 2012

Publications Maji, M., Zhu, Q., Marinacci, F. & Li, Y. “The Disk of Satellites of Galaxies in the Illustris Simulation”, to be submitted to MNRAS, 2018

Maji, M., Zhu, Li, Y., Charlton, J., Hernquist, L. & Knebe, A. “The Formation and Evolution of Star Clusters in Interacting Galaxies”, 2017, ApJ, 844, 108

Maji, M., Zhu, Q., Marinacci, F. & Li, Y. “Is There a Disk of Satellites around the Milky Way?”, 2017, ApJ, 843, 62

Maji, M., Zhu, Q., Marinacci, F. & Li, Y. “The nature of disk of satellites around Milky Way-like galaxies”, submitted, arXiv:1702.00497

Zhu, Q., Marinacci, F., Maji, M., Li, Y., Springel, V. & Hernquist, L. “Baryonic impact on the dark matter distribution in Milky Way-sized galaxies and their satel- lites”, 2016, MNRAS, 458, 1559