Despite a wealth of observational information on the properties of galaxies, a self-consistent, detailed theoretical model of galaxy formation does not yet exist. The evolution of galaxies has been examined in great detail, and in many wavelength bands, from approximately six hundred million years after the Big Bang to the present day. These observations show that the galaxies that we can see have undergone radical changes in size, appearance, and content over the last thirteen billion years. Complementary observations have provided a rich data set on the kinematics and elemental abundances of stars in our own Milky Way, including large numbers of metal-poor stars in the halo of our own galaxy and in local dwarf galaxies.

In addition, a large amount of debris from tidally disrupted satellite galaxies, in the form of stellar streams, have been observed preferentially in the outer regions of the Galaxy. In principle, this “galactic fossil record” can probe the entire merger and star formation history of the Milky Way and its satellites, and complement direct observations at high redshift. It is important to note that the Milky Way is the only system (for now) for which we have direct access to this information. This is because only in our Galaxy and its nearby satellites can we measure the properties of millions of individual stars. Thus, a comprehensive understanding of how our own Galaxy formed and evolved represents a critical step forward towards understanding the process of galaxy formation in the general cosmological context.

Inspired by the previous arguments, in the past decades several authors have compared observed properties of the Milky Way with those obtained from high resolution N-body simulations of the formation of Milky Way-like galaxies. However, recent studies seem to indicate that our Galaxy may not be a typical galaxy after all. For example, observations of a large sample of the Sloan Digital Sky Survey (SDSS) galaxies have shown that Milky Way has significantly more satellites than a typical galaxy of its luminosity (Busha et al., 2011; Liu et al., 2011). Results such as these cause us to pose the following important questions: To what extent can the Milky Way be regarded a template of galaxies of its type? How dependent are properties such as the chemical composition or the amount of substructure observed in the stellar halo on the particular formation history of our own Galaxy? To fully interpret currently available observations, as well as the large amount of data that soon will become available from surveys such as SkyMapper, LAMOST and LSST it is essential to understand whether or not the Milky Way is a typical galaxy of its kind.

Scientific Motivation

Under the current paradigm of structure formation (White & Rees, 1978), the accretion and merger of satellite galaxies is expected to play an important role in shaping and structuring the present day configuration of a host galaxy. Stellar halos of large galaxies such as our own are believed to be primarily formed as a result of the accumulation of tidal debris associated with ancient as well as recent and ongoing accretion events (Helmi, 2008). In principle, these galactic fossil records can probe the entire merger and star formation history of the Milky Way and its satellites (Freeman & Bland-Hawthorn, 2002). Information is not only encoded in the dynamical distribution of the different Galactic components, but also in the chemical abundances patterns of the individual stars.

After decades where only a relatively small number of stars have been observed in detail, several surveys such as SEGUE (Yanny et al., 2009) and RAVE (Steinmetz et al., 2006), have collected photometric, astrometric, and spectroscopic information of vast samples of stars, primarily in the Galactic disk and stellar halo. The quantity and quality of observational data, which is already staggering, is going to increase exponentially over the next decade. Surveys such as Gaia (Perryman et al., 2001), LAMOST (Cui et al., 2012), The Dark Energy Survey (The Dark Energy Survey Collaboration, 2005), Gaia- ESO spectroscopic survey (Gilmore et al., 2012) and the Large Synoptic Survey Telescope (LSST, Ivezic et al. 2008) will provide measurements of positions, velocities and chemical composition of billions of stars that will strongly inform our understanding of galaxy formation. To unravel the formation history of the Milky Way requires the development of theoretical and statistical tools that can be used to contrast detailed numerical models with this wealth of observations.

Recently, two groups have performed N-body simulations of the growth of Milky Way-type halos to examine structure formation and the hierarchical assembly of large galaxies in unprecedented detail – the Aquarius project of Springel et al. (2008) and the Via Lactea models of Diemand et al. (2007). These works have made it possible to quantify the substructure abundance as a function of subhalo mass and support the view that there is indeed a missing satellite problem. However, both the Aquarius and Via Lactea projects are limited in a number of respects. The Aquarius runs adopted cosmological parameters that are now observationally disfavored at a high level of significance by studies of the cosmic microwave background (Jarosik et al., 2011). It is problematic to extrapolate these results to the non-linear scales of individual galaxies to determine quantitatively the severity of the missing satellite problem. More seriously, the Aquarius project consists of a sample of only 6 well-resolved Milky Way-mass halos, while the Via Lactea study focused on only one such halo. It is apparent from these simulations alone that there is significant halo-to-halo scatter not only in the substructure abundance, but also in the observational properties of the host galaxies and its luminous satellites (e.g. Cooper et al., 2010; Lunnan et al., 2011).

The method typically used to connect simulations with observational data is via semi-analytic modelling. This approach is exemplified in the work of Bullock & Johnston and collaborators (Bullock et al., 2000; Bullock & Johnston, 2005; Robertson et al., 2005; Johnston et al., 2008; Kazantzidis et al., 2008), who use the Extended Press-Schechter formalism to create a “merger tree” that follows the merger history of the Milky Way and its progenitor galaxies. This merger tree is used as the basis for a model for galaxy formation and evolution that includes prescriptions for star formation, gas evolution, radiation transport, and related physics. A more sophisticated and accurate implementation of this technique has been developed by Tumlinson (Tumlinson, 2006, 2010; Okrochkov & Tumlinson, 2010), based on highly-resolved N-body cosmological simulations rather than an analytic formalism for mergers. As a result, this method provides spatial and kinematic information for “live” halos, as well as a merger histories. The Tumlinson ChemTreeN model includes similar physics prescriptions to those used by Bullock & Johnston, but also follows the detailed chemical evolution of the stellar populations and gas residing in the dark matter halos, and allows the prediction of distributions of stellar populations and dwarf galaxies around the Milky Way.

The major limitations of using these dark matter simulations coupled to semi-analytic models are three fold. Firstly, the large number of free parameters (at least 10) that describe gas physics and chemical evolution makes it difficult for such models to be truly predictive. The flip side to this drawback is that these models can explore the effects of uncertain physics much more effectively than multiphysics hydrodynamical simulations: the semi-analytic models are particularly good at identifying how observational quantities respond to changes in input physics (e.g. Gómez et al. 2012). This is their major advantage over fully self-consistent, extremely computationally expensive, hydrodynamical cosmological simulations. More importantly, most dark matter-only cosmological simula- tions used in these models have suffered from the limitation of finite computational power: calculations that were tractable typically had insufficient mass and spatial resolution to probe the entire mass function of all progenitor galaxies, as well as to resolve substructure in the resulting stellar halos, leftover of the multiple accretion events the simulated galaxy undergone. Critically, as previously stated, the biggest limitation is that all studies have only considered a handful of simulations which neglect dependencies in the properties of the resulting galaxies on their formation histories. To make meaningful advances in our understanding of the Milky Way’s formation history we must perform a large number of numerical simulations of Milky Way-like halos, densely sampling the full range of possible formation histories. This must also be coupled with our state-of-the-art semi-analytic model to make robust predictions about the luminous components of the Galaxy itself and its dwarf satellites.

In order to statistically explore the the high-dimensional semi-analytic parameter space and its associated uncertainties, we have developed a set of statistical tools to identify how different parameters are tied to specific observables. As shown in Gómez et al. (2012), statistical emulators can rapidly give predictions of model outputs, and an attendant measure of its uncertainty, at any point in the parameter space. The numerical implementation of these emulators is very computationally efficient, making it feasible to predict vast numbers of model outputs in a short period of time. By defining a statistical measure of plausibility, and contrasting model emulators to mock observational data, we have demonstrated that it is possible to recover the input parameter vector used to create the mock observables (see below). Furthermore, we have performed a sensitivity analysis on ChemTreeN (via the emulators) to statistically characterize its input-output relationship (Gómez et al., 2014). This analysis allowed us not only to densely explore the input parameter space for a set that could best reproduce a given observable, but also to identify what parameters have the largest impact on the prediction of any given observable. It also allowed us to simplify our model by identifying input parameters that have no effect on the available set of observables.

Area A: Statistically probing the merger history of the Milky Way

The details of the formation of our own Galaxy remain a puzzle. Thanks to the latest generation of stellar surveys it is now possible to study in detail how the Milky Way has evolved to become the galaxy we currently observe. These surveys have provided, and will continue to provide, a rich dataset on the kinematics and chemical abundances of stars that can be directly compared with detailed numerical models. A robust and statistical comparison between models and these observations is essential. In Gómez et al. (2012, 2014) we developed the statistical tools that are required to meaningfully compare chemo-dynamical models of galaxy formation to the very large set of available observables. The results presented on these works indicated that, for a given fiducial observational dataset, the best-fitting input parameters selection strongly depends on the underlying merger history of the mock Milky Way-like galaxy. Interestingly, while best-fitting models were able to tightly reproduce the fiducial observables, only one of them successfully reproduced a second and independent set of observables.

On the basis of this analysis it is possible to disregard certain models, and their corresponding merger histories, as good representations of the underlying merger history of the Milky Way. Nonetheless, a robust and statistically significant analysis requires the addition of a large set of possible merger histories. The suite of high-resolution dark matter-only simulations that we are proposing here will allow us to probe different galaxy merger histories, ranging from halos that acquire most of their mass very early on to halos that have had their last major merger episode close to z = 0. To create models of the Milky Way stellar halo and its satellite population, we will couple these simulations to an updated version of the semi-analytical model, ChemTreeN. A statistically best-fitting model for each merger history will be obtained by comparing the mock stellar halos to a fiducial observable dataset. The resulting best-fitting models will be confronted by independent observational datasets, including quantities such as mean halo metallicity and chemical abundances as a function of radius, radial distribution of satellite galaxies, and even the degree of phase-space substructure.

Area B: The origin and evolution of Milky Way-like satellite galaxies

The overarching questions we aim to address concern the nature of the “building blocks” of large galaxies, and to what extent dwarf galaxies play a role in the assembly of old stellar halos. This comes at a time when in particular the population of Milky Way ultra-faint dwarf galaxies (with \({\rm L_{tot} < 105 L_\odot}\); discovered in the Sloan Digital Sky Survey; SDSS, Dark Energy Survey; DES) have been shown to be extremely metal-deficient systems that host ∼ 25% of the known most metal-poor stars. Moreover, they extend the metallicity-luminosity relationship of the classical dwarfs down to \({\rm L_{tot} ∼ 103 L_\odot}\) (see Kirby et al., 2008, for more details). Future observations will reveal how far this relationship can be extended. Due to their simple nature, the ultra-faint systems are expected to retain signatures of the earliest stages of chemical enrichment in their stellar populations. The chemical abundances of individual stars in the faintest galaxies suggest a close connection to equivalent, extremely metal-poor halo stars in the Galaxy. Thus, there is a relation between the universe’s first galaxies, the building blocks of the Milky Way, and the surviving dwarf satellites (Frebel & Bromm, 2012).

However, the assembly of the old Galactic stellar halo from the first galaxy to today can only globally be studied and understood with detailed simulations and in a cosmological context to conclusively learn about the role of dwarf galaxies in the hierarchical assembly processes of larger systems. To learn about the effects that influence the number of small subhalos over the course of the universe, we have already began to quantify the impact of reionization on the faintest halos using the six Aquarius DM halos (Griffen et al., 2010; Lunnan et al., 2011; Go ́mez et al., 2012; Griffen et al., 2013). Specifically, we tested the influence of different physically motivated reionization histories (Zahn et al., 2007; McQuinn et al., 2007) on the population of the smallest, resolved satellites (106 M⊙ halos) (see Figure 2). The effect is largest at the faint end (numbers of satellites vary by a factor of a few), while the brighter end (equivalent to the dSphs galaxies) are unaffected by different reionization histories. Properly accounting for these physical effects can, at least, partly resolve the so-called missing satellite problem (Moore et al., 1999). That is, the observed number of (luminous) Milky Way satellites appears to be significantly lower than the amount of dark matter substructure expected from the CDM theory. However, the overall halo-to- halo scatter in the total amount the dark matter substructure for a Milky Way-like galaxy is yet to be robustly characterized. To study the impact of, e.g., feedback from baryonic processes or heating by cosmic radiation in low-mass dark matter halos, using observations from the Local Universe, it is key to quantify the influence of cosmic variance.

By quantifying the level and extent of variations of the substructure around Milky Way galaxies (see Figure 3), we are in a position to focus on a number of specific details about the origin and evolution of subhalos with different masses equivalent to those of a variety of observed dwarf galaxies, such as massive Magellanic Cloud-sized objects, classical dwarf Spheroidal galaxies, and even fainter systems. The distribution of the Milky Way classical dwarfs and the Magellanic Clouds as they orbit the Galaxy is presented in Figure 4. These topics can be addressed solely with dark matter simulations, but can also be used in combination with semi-analytic prescriptions, such as ChemTreeN, for populating dark halos with luminous matter. The latter requires detailed knowledge of many physical processes that govern the evolution of a luminous halo. We will first use these simplified empirical prescriptions to approximate these processes, but aim to later use results of new large-scale hydrodynamical ΛCDM simulations for the most physically motivated approach to light up our halos. This is an unparalleled opportunity to study the assembly of galaxy halos and to compare the results with the latest observations of dwarf galaxies, halo stars and stellar streams, both for the Milky Way and Andromeda.

Area C: Is the Milky Way Unusual

How good is the Milky Way in representing a typical, large spiral galaxy? It is often used as a reference point, especially when comparing its general properties with those derived from cosmological simulations of the formation of large galaxies. But recent works, observationally and theoretically, have shown that our Galaxy may at least have a few unusual features. Examples are the existence of the long discovered Magellanic Cloud satellites and its theoretically inferred accretion history.

The Magellanic clous have recently garnered significant attention (Boylan-Kolchin et al., 2011a; Liu et al., 2010) in this respect. Observational analyses using Sloan Digital Sky Survey data of many other large spiral galaxies confirmed that galaxies like the Milky Way are very unlikely to have two companions as bright as the Magellanic Clouds. Indeed, less than 5 − 10% of galaxies host two such bright companions, and more than 80 percent host no such satellites at all. Previously, Boylan-Kolchin et al. (2011a) have examined this issue using the Millenium simulation of Springel et al. (2005a) and found that the Milky Way was unusual in hosting the Magellanic Clouds.

The accretion history of the Milky Way has been recently inferred from the shape of its stellar halo’s density profile. While our Galaxy shows a clear break in this profile at ∼ 25 kpc, our closest similar galactic neighbour, M31, shows a smooth profile out to 100 kpc with no obvious break (Deason et al., 2013). Simulations of the formation of Milky Way-like stellar halos (Bullock & Johnston, 2005) suggest that differences in the shape of the density profile can be directly linked to the the assembly history of galaxies. However, the simulation suite currently used to explore this issue were not run in fully cosmological and self-consistent context and, more importantly, only consist of 11 realizations. With our large suite of DM simulations based one the latest observationally favored cosmology we can more precisely characterize how unusual our Galaxy is.

We will examine the probability of Milky Way type halos having unusually massive satellites like the Large and Small Magellanic Clouds. Furthermore, we will be able to quantify the evolutionary differences between the Milky Way and Andromeda to establish whether either of these galaxies represents a “normal” galaxy. Statistically assessing these vastly different evolutionary paths will guide our understanding of how these histories influence the extent of surviving substructure and differences in properties such as the stellar mass, disk radius, and metal-deficient halo between the two sister galaxies.

Area D: The Origin of the Old Stellar Halo of the Milky Way

The Milky Way stellar halo contains a significant number of old, extremely metal-poor stars with [Fe/H] < −3.0 (corresponding to 1/1000 of the solar Fe abundance) that have been discovered and analyzed over the past two decades (see McWilliam et al., 1995; Beers & Christlieb, 2005; Frebel, 2010) for reviews). In their atmospheres, these low-mass stars retain the chemical composition of the gas cloud they formed from some 12-13 Gyr ago. Having a larger sample of these objects at hand thus allows one to study the early universe and to carry out near-field cosmology without the need for high-redshift observations. The stellar chemical abundance patterns furthermore reveal information about the enrichment sources and the local star forming environment. Over the past ∼ 3 years, surprisingly many extremely metal-poor stars have been uncovered in the least-luminous dwarf galaxies as well as some of the classical dSphs that orbit the Milky Way (Kirby et al., 2008; Frebel et al., 2010; Simon et al., 2010; Norris et al., 2010). Their nearly identical chemical abundances compared to equivalent metal-poor halo stars suggests that the Milky Way halo assembled from early analogs of these surviving systems. This sparked a lot of interest in the cosmological origin of the most metal-poor halo stars.

Recently, Carollo et al. (2007, 2010) studied the origin of the old Galactic halo populations, finding a dual nature of the stellar halo, which is illustrated below. A large fraction of the most metal-poor halo stars appear to be kinematically associated with the “outer,” retrograde halo dominating beyond 10-15kpc. This component may be the result of a later time accretion event that resulted in the deposit of many of the halo’s metal- poor stars. But where did these star originate? The chemical abundances alone cannot provide conclusive answers. Kinematic information can only provide limited information on the progenitor systems that hosted these old stars prior to their destruction in the tidal field of the Milky Way.

Hence, large-scale simulations are required to gain a more global understanding of the key features of halo assembly. Is the dual nature of the MW halo a generic feature? What is its exact origin? What role do small, faint satellites play in this process? Moreover, can metallicity gradients in a halo be explained this way? Or are such gradients, for example, dependent on a galaxy’s individual merger history and environment? And what is the metallicity distribution function of large galaxies?

To obtain answers to these questions we will use ChemTreeN to follow the cosmic paths of the oldest, most metal-poor stars (star particles) while using them as tracers of the hierarchical assembly of the Milky Way and large galaxies in general. We will go beyond the Cooper et al. (2010) study (which used the six Aquarius DM halos) by applying physically motivated reionization histories, including gas physics effects, and using refined star formation prescriptions, coupled with observational constraints of the latest Galactic halo and dwarf galaxy stellar abundances. One such constraint will come from dwarf galaxy masses enclosed in the half-light radius (as a function of their half-light radius). Such masses are very robust observational measurements (Walker et al., 2010) as opposed to luminosities or the M300 mass (Strigari et al., 2008) at the faint end of the luminosity function.

We will gradually include more and more feedback effects to study what else besides reionization influences the satellite survival rate. Feedback studies within the first-galaxy-environment, e.g., carried out by Wise & Abel (2008); Greif et al. (2011), will therefore provide valuable guidance. By tracing the cosmic merger history of individual subhalos with old stars, we can specifically study the analogs of today’s faintest galaxies.

We will attempt to quantify the extent to which small satellites can be regarded as building blocks of large galaxies by comparing predictions for the number of accreted, old stars from ultra-faint-like systems with estimates for the actual numbers of low-metallicity stars in the Galactic halo. Radial distributions and kinematics of accreted stars will also be derived, which can be observationally tested over the next few years. Specifically, by quantifying the level and extent of cosmic variations between halo assembly histories, we are in a unique position to model the Milky Way and its halo much better than previously possible. Next to quantifying whether the Milky Way is an unusual galaxy, we can address how the metal-poor populations vary from galaxy to galaxy, and what role they played in their host’s respective assembly history.

Take home message

Our primary objective is to characterize the formation and evolution of Milky Way sized halos.