Theoretical and Numerical Galaxy Formation

In the standard model of cosmology, called the ΛCDM model, ordinary luminous matter makes up only a small fraction (about 4 per cent) of the energy content of the Universe. The remaining contents are dark and consist of two dominant components: Dark Matter and Dark Energy. Together, dark energy (described by a cosmological constant Λ) and cold dark matter (CDM) form the foundation of the ΛCDM theory that describes structure formation. In this paradigm, small initial perturbations of the dark matter density field grow in time through gravity and form bound haloes. Small haloes grow first while larger haloes are formed by the coalescence of smaller progenitors. Within this framework, galaxy formation and evolution is a complex combination of hierarchical clustering, gas dissipation and cooling, star formation, feedback processes, merging events, and secular evolution.

The aim of my research is to study how galaxies and dark matter haloes form and evolve through cosmic time, and to better understand the various physical processes that shape their properties. For this use two main methods: 'ab initio' models, where an initial distribution of gas and dark matter is evolved according to a specified set of relevant physical processes, and 'empirical models', which relate the observed galaxy populations to the underlying dark matter distribution in a statistical manner that is as independent as possible of any model assumptions.

Empirical models of galaxy formation have a large potential to yield insights to many aspects of cosmology and galaxy formation. They link observed galaxy properties to the underlying dark matter distribution in an empirical and statistical fashion, that is as independent as possible of any model assumptions. Empirical models have three virtues: the possibility to test the adopted galaxy formation paradigm on the ground of new observations, the ability to make predictions of galaxy properties unbiased by assumptions on baryonic physics, and the option to combine empirical with ab initio models to directly constrain the physical processes that drive galaxy formation.

In our research group, we are developing the next generation of empirical galaxy formation models. In previous models, quantities like stellar mass and SFR have always been predicted only as an average for dark matter haloes of a given virial mass. This owes to the fact that galaxies have always been linked to haloes in a pure statistical way that does not reflect the individual growth histories of the haloes. Thus, inferred galaxy properties such as clustering will also only depend on halo mass. However, it is well established that the spatial distribution of dark matter haloes depends on their formation time. As a consequence, galaxy properties should also depend on the formation history of the halo. As a new development, we model the evolution of individual galaxies by following the growth histories of their dark matter haloes as extracted from numerical simulations.

Unlike in ab initio models, all treatments are as flexible as possible and constrained directly by the relevant available observations in an empirical manner. The model is put on a firm statistical footing using Bayesian inference. We start with very simple models and only increase the complexity if the data require it.

My PhD Thesis

Within the CDM paradigm dark matter first collapses in small haloes, which merge to form progressively larger haloes over time. Major (near-equal mass) and minor (unequal mass) mergers are a generic feature of structure assembly in the hierarchical picture, and are now widely believed to be responsible for shaping many galaxy properties. Major mergers play an important role in transforming disc-dominated spiral galaxies into spheroids and triggering episodes of enhanced star formation and active galactic nuclei. Minor mergers may explain the origin of thick discs and the diffuse stellar halo around galaxies may be produced via tidal destruction of merging satellites.

The large population of merging satellites has raised the question of whether mergers are too common in the CDM scenario. Some studies have questioned whether thin, dynamically fragile discs such as the one observed in the Milky Way can survive this bombardment by incoming satellites and found that the answer depends quite sensitively on the mass ratio of the merging galaxies. There seems to be a consensus that the main danger to thin discs is from events with a mass ratio of (~1:10). However, studies performed so far have only considered the dissipationless components in the galaxy (dark matter and stars), neglecting the presence of a dissipative gas component in the disc. However, the inclusion of gas physics is known to play an important role in stabilizing galactic discs.

In my PhD Thesis I study the effect of dissipational gas physics on the vertical heating and thickening of disc galaxies during minor mergers. I produced a suite of minor merger simulations (using the GADGET code) for Milky Way-like galaxies achieving an unprecedented resolution. I found that in dissipationless simulations minor mergers cause the scale height of the disc to increase by up to a factor of approximately two. When the presence of gas in the disc is taken into account this thickening is reduced by 25% (50%) for an initial disc gas fraction of 20% (40%). I argue that the presence of gas reduces disc heating via two mechanisms: absorption of kinetic impact energy by the gas and/or formation of a new thin stellar disc that can cause heated stars to recontract towards the disc plane. Final disc scale heights found in my simulations are in good agreement with studies of the vertical structure of spiral galaxies. I also found no tension between recent measurements of the scale height of the Milky Way thin disc and results coming from my hydrodynamical simulations and conclude that the existence of a thin disc in the Milky Way and in external galaxies is not in obvious conflict with the predictions of the CDM model.

Hydrodynamical simulation are powerful tools to unveil the physics of galaxy formation. They are necessary to follow the evolution of the internal structure of galaxies as well as the complex interplay between baryon cooling and feedback. There are two main approaches to perform these simulation. The first is to run a dissipationless simulation of a large volume, select a system at z=0 one is interested in and re-simulate this system at a higher resolution including the baryonic component. The limitation of this approach is that these simulations are computationally expensive and typically have a low spatial and mass resolution in the luminous component (e.g. the thin disc). For this reason, these simulations are usually stopped at z>0. The other approach is to divide galaxy evolution into galaxy merger events that can be studied at much higher resolution. This is useful to study the structure of galaxies in detail. However, state-of-the-art merger simulations use initial conditions which have been derived from grid parameters (e.g. orbital parameters, mass and morphology). Also, only binary mergers have been simulated. Merger trees constructed from N-body simulations, however, suggest that multiple mergers (i.e. a second merger event starts before the first is completed) are much more common.

In my PhD Thesis I have developed a new numerical technique that combines Semi Analytical Models (SAMs) with hydrodynamical simulations. In this approach SAMs are used to define the initial conditions of a series of multiple mergers, that are intended to mimic the galaxy evolution from a given redshift to the present day. The method works as follows: I follow the main branch in the semi-analytic merger tree up to a given redshift (e.g. z=1) and create initial conditions for the 'primary' galaxy as specified by the SAM. This system is then evolved in isolation (using GADGET) until the first satellite galaxy in the merger tree enters the virial radius of the primary galaxy. Using the satellite properties given by the SAM, I put the satellite galaxy into the simulation and merge the galaxies until the time the next satellite falls in. This procedure is repeated until z=0. I also take into account both the dark matter and gas accretion in a cosmological fashion. For this I extended the initial conditions code to include a rotating hot halo component with a spherical density profile (either constant density, beta-profile or 'cored-profile').

With this approach is possible to attain spatial and mass resolution much higher than in cosmological hydrodynamical simulations. Additionally, since these merger simulations are computationally less expensive (i.e. they run faster) it is possible to produce larger suites of simulations which results in better statistics in the analysis. This enables me to study several aspects of galaxy formation in great details: disc stability and heating, satellite accretion and destruction, gas stripping, stellar halo formation, stellar dynamics in the solar neighborhood and many others. The high resolution achievable with this approach is of crucial importance in the light of the forthcoming results of the Pan-STARRS survey, that will provide new and extremely tight constraints on the different components (stellar halo, satellites, streams and disc) of the stellar body of the Milky-Way, which carry unique information on the dynamical status and formation history of our Galaxy.

Download the PhD thesis here

My Diploma Thesis

In my Diploma Thesis I obtained a parameterized stellar-to-halo mass (SHM) relation by populating halos and subhalos in an N-body simulation with galaxies and requiring that the observed stellar mass function be reproduced. The derived ratio between stellar mass and halo mass has a characteristic peak at M ~ 10E12 Msun and declines steeply towards smaller mass and less steeply towards larger mass halos. The physical interpretation of this behavior is the interplay between various feedback processes that impact the star formation efficiency. The redshift dependence of the SHM relation has been addressed as well and I have shown that, for low mass halos, the SHM ratio is lower at higher redshift. I used my model to derive the conditional mass function, which yields the average number of galaxies with stellar masses in the range m +- dm/2 that reside in a halo of mass M.

Using the derived mapping between stellar and halo mass and the positions of the halos and subhalos obtained from the simulation, I demonstrated that the model predictions for the galaxy correlation function as a function of stellar mass are in excellent agreement with the observed clustering properties in the SDSS at z=0. I showed that the clustering data do not provide additional strong constraints on the SHM function and concluded that my model can therefore predict clustering as a function of stellar mass. The redshift dependent SHM relation was then used to predict the stellar mass dependent galaxy correlation function and bias at high redshift. My model predicts that massive galaxies are not only more biased than low mass ones at all redshifts, but this bias increases more rapidly with increasing redshift for massive galaxies than for low mass ones.

Deep pencil beam surveys are of fundamental importance for studying the high redshift universe. However, inferences about galaxy population properties (e.g. the abundance of objects) are in practice limited by 'cosmic variance'. This is the uncertainty in observational estimates of the volume density of galaxies arising from the underlying large-scale density fluctuations and can be significant, especially for surveys which cover only small areas and for massive high redshift galaxies. In mt Diploma Thesis I provide tools for experiment design and interpretation: For a given survey geometry I present the cosmic variance of dark matter as a function of mean redshift z and redshift bin size dz. Using the bias predictions of my halo occupation model, I computed the cosmic variance of galaxies which is the product of the squared bias and the dark matter cosmic variance. I presented a simple recipe using a fitting function to compute cosmic variance as a function of the angular dimensions of the field, z, dz and stellar mass m*. I found that for the UDF at z=2 and dz=0.5 the relative cosmic variance of massive galaxies (m*>10E11 Msun) is ~55%, while it is ~38% for GOODS, ~25% for GEMS and ~11% for COSMOS. This implies that cosmic variance is a significant source of uncertainty at z=2 for small fields and massive galaxies, while for larger fields cosmic variance is less serious.

Download the Diploma thesis here