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Within the current cosmological paradigm for structure formation, galaxies are thought to form, at least in part, hierarchically, with small galaxies forming first within small dark matter halos and gradually agglomerating to form larger galaxies within larger dark matter halos. Gas from this agglomeration process can dissipate and fall towards the center of the main halo to form a new generation of stars in the combined object. Unlike the gas, stellar orbits are dissipationless, so, once stripped, the stellar populations of infalling galaxies can be left behind orbiting in the halo of the galaxy. Of course, the orbits of infalling galaxies are affected by dynamical frictiondynamical friction. For those that are more massive than a few percent of the parent this can lead to significant evolution within a few orbital periods so stars from these objects can potentially make a minor addition to the central stellar galactic components that are forming from the in situ gas (i.e. spheroid or disk, as seen in the hydrodynamic simulations of Abadi et al. 2006). In contrast to the spheroid and disk, stellar halos are a great place to look for stars that have been accreted from other objects. Current models and data favor a picture where a significant fraction — and possibly all — of the stars in the halo originally formed in other objects.

The accreted nature of at least a significant fraction of stars in galactic halos suggests their observed properties can be used to address a number of questions. Cosmological parameters dictate the nature of hierarchical clustering: the frequency and epoch of infall of dark matter halos of different mass-scales and their orbital properties. In other words, the cosmology sets the parameters discussed in Sect 4 that fully specify the type and number of tidal disruption events that have occurred. Hence, adopting a given cosmology (with the addition of some assumptions for how stars occupy different dark matter halos) leads to specific expectations for the level of substructure due to accretion within stellar halos (Sect. 5.1) as well as chemical trends between substructure and field stars (Sect. 5.2.2). These understandings can be exploited now and in the future to understand to what extent the distribution on the Milky Way's stellar halo matches our expectations (Sect. 5.3.1), and what we can learn about our accretion history from the extent and properties of substructure (Sect. 5.3.2). In turn — identifying stars that were originally formed in other objects at much higher redshift offers a unique perspective on the stellar populations in these galactic progenitors (Sect. 5.3.3).

5.1. Cosmological simulations of stellar halo formation

Stellar halos are hard to observe because they contain a tiny fraction of stars (and an even tinier fraction of the total mass) in a galaxy, spread out over a large volume. Moreover, surveys need to be sensitive to even smaller fractions of stars to learn about substructure within these halos, and the presence of this substructure makes it challenging to characterize the global characteristics of the halo itself. Early discussions were largely restricted to global properties and formations scenarios (e.g. see classic works by Eggen et al. 1962 and Searle & Zinn 1978) extrapolated from either local studies of high-velocity stars, larger volume surveys with tracer populations where distances could be estimated, or pencil beam surveys. The field has been revolutionized in the last two decades with the emergence of large-scale stellar surveys covering a significant fraction of the sky, such as the Sloan Digital Sky SurveySloan Digital Sky Survey (SDSS) (Abazajian et al. 2003) and the Two Micron All Sky SurveyTwo Micron All Sky Survey (2MASS) (e.g. Majewski et al. 2003).

Models of stellar halos face the same challenges as the observations in resolving such a tiny component of the galaxy, as well as substructure within it. One approach is to restrict attention to only stars that have been accreted from other systems and hence avoid the need to follow gas physics and ongoing star formation explicitly. Bullock et al. (2001) presented a first attempt by combining a semi-analytic, generative model of tidal disruption events (developed in Johnston 1998, and outlined in Section 3.3.2 above) with merger histories for Milky-Way like galaxies predicted in a cosmological context using the Press-Schechter formalism (Lacey & Cole 1993). These models showed abundant substructure in the model halos, which was coincidently being mapped by SDSS in the real stellar halo. Bullock & Johnston (2005) made the next step to a more sophisticated approach by replacing the simple generative model of each disruption event with an N-body simulation to represent the dark matter evolution of the infalling object. Stars were “painted” onto the purely dark matter satellites by assigning a variable weight or mass-to-light ratio to each N-body particle. The weights were chosen in such a way that the properties of the latest infalling objects matched the internal spatial and velocity distributions observed for stars in nearby dwarf galaxies. The Bullock & Johnston (2005) models were limited in that the parent galaxy was represented by (slowly evolving) analytic functions and the results of the separate simulations were superposed only at the present time to make a stellar halo model. Hence they did not include either the influence of the accreting objects on the parent or on each other. Nor did they represent the cosmological context (such as preferential infall along filaments or global tidal influences due to nearby neighboring structures). Computational power is now such that full self-consistent N-body simulations of the formation of a Milky Way sized dark-matter halo are sufficiently resolved to address this limitation and there are now several example of stellar halo models made by painting stars onto these more realistic backdrops (De Lucia & Helmi 2008, Cooper et al. 2010, Lowing et al. 2015).

Of course, the ultimate goal is to simultaneously build a model of all components of a galaxy (dark matter along with stellar and gaseous components) using cosmological hydrodynamical simulations of structure formation capable of following the baryonic as well as dark matter physics. There are several examples already in the literature where the stellar halo components have been resolved in these models and their characteristics and history discussed (Abadi et al. 2006, Zolotov et al. 2009, Font et al. 2011, Tissera et al. 2013). In particular, these models drop the assumption that all stars in the halo come from accretion events and allow an exploration of how much of the stellar halo might have instead formed in situ. However, the properties of the stellar halos vary systematically between the simulations, as prescriptions for star formation and feedback also vary, so the results at this point seem indicative rather than conclusive.

For the remainder of this section we concentrate solely on the accreted component of the stellar halo and illustrate some general results common to all the models using the Bullock & Johnston (2005) simulations.

5.2. General results of cosmological accretion models

5.2.1. Accreted phase-space structure in halos

Figure 7 shows one of the Bullock & Johnston (2005) purely-accreted stellar halo models from external viewpoints, in space and velocity. The simplicity of the model permits sensitivity to both small as well as low surface brightness substructures within the halo. Generic features of this (and other) models are: a smooth, fully phase-mixed inner region; abundant substructure in the outer parts, detectable both in space and velocity; and an increasing prevalence of the substructure with Galactocentric radius. Beyond the phase-mixed inner regions, such model halos typically appear dominated by a handful of striking shells and streams, with shells tending to be more prevalent at the largest distances and streams in the intermediate parts (Johnston et al. 2008).

Figure 7

Figure 7. Surface brightness (left), line-of-sight velocity (middle) and velocity dispersion (right) from external views of two stellar halo models built entirely from accretion events drawn from a merger history consistent with our current expectations (from Bullock & Johnston 2005, Johnston et al. 2008). Each box is 300 kpc on a side. Only the stellar halo component is shown. Image credit: Sanjib Sharma.

These generic features can broadly be explained in the context of the current cosmological expectations which suggest a history for the Milky Way where: (i) the majority of accretion events occurred more than 7-8 Gyrs ago; (ii) the events had a range of luminosities associated with them; and (iii) the accretions occurred on a mixture of orbits. Figure 8 illustrate this with external views of model halos, constructed by Johnston et al. (2008), that are instead built entirely from: (i) ancient or recent accretion events (left panels); (ii) high or low luminosity events (middle panels); and (iii) events evolving on high or low eccentricity orbits (right panels). The consequences of these differences are obvious with a simple visual comparison of the panels and can be easily explained with the physical intuition developed in Sect. 3 and Sect. 4: younger/older halos are more/less substructured because of the time available for phase-mixing; larger/smaller substructures correspond to higher/lower luminosity events because the total mass sets the tidal scales at distruption; and the orbit distribution dictates the debris morphology because more/less eccentric orbits tend to produce shells/streams.

Figure 8

Figure 8. Surface brightness projections for stellar halos with the same total luminosity, but merger histories that were artificially constrained to be dominated by different types of accretion events (following Johnston et al. 2008). In the left panels, the events had the same luminosity and orbit distributions, but were either all accreted a long time ago (upper panel) or recently (lower panel). In the middle panels, the events had the same accretion time and orbit distributions, but were either all of high (upper panel) or low (lower panel) luminosity. In the right panels, the events had the same accretion time and luminosity distributions, but were either all on near-radial (upper panel) or near-circular (lower panel) orbits. Image credit: Sanjib Sharma.

5.2.2. Accreted stellar populations in halos

Figure 9 shows an alternative visualization of the model stellar halos shown in Figure 7, but with the grid points color coded by the average metallicity and [α/Fe] abundance ratio along the line-of-sight. These were derived by assigning a simple star formation history to each infalling dwarf and running a leaky-accreting box model to estimate the associated chemical evolution (Robertson et al. 2005, Font et al. 2006). The parameters of the chemical evolution models were tuned to reproduce known properties of dwarf galaxies in the Local Group today — the observations that more luminous dwarfs tend to be more metal rich (e.g. Grebel et al. 2003), and that all nearby objects contain α-poor populations (e.g. Venn et al. 2004). Star formation was truncated in each dwarf at the time when it was accreted onto the Milky Way, as might be expected given that dwarfs near larger galaxies are observed to be quenched relative to their field counterparts (Grebel et al. 2003, Geha et al. 2012). The last attribute of the model effectively means that the cosmological framework also influences the nature of the stellar populations in accreted components of galactic stellar halos, setting the characteristic time over which star formation can occur.

Figure 9

Figure 9. Average [Fe/H] and [α/Fe] projected along the line-of-sight for the two stellar halo models shown in Figure 7 (using chemical model developed in Robertson et al. 2005, Font et al. 2006). Image credit: Sanjib Sharma.

In the left-hand panels of Figure 9 the mass-metallicity relation is apparent, as the largest and most dominant debris structures tend to be the most metal rich. The influence of the cosmological background is apparent in the right-hand panels; the smooth stellar halo component is α-enhanced relative to both surviving satellites and the brighter debris features. Physically this trend can be attributed to the relative delay expected following star formation of Type Ia Supernovae (SNe) compared to Type II SNe. The progenitors of Type II SNe are massive stars, whose deaths produce both iron and α-elements, within a few million years of a star formation event. In contrast, Type Ia SNe, producing mainly iron, arise from the explosion of an accreting white dwarf star — objects which will not form for hundreds of millions of years after a star formation event. Hence, the oldest stellar populations in infalling dwarf galaxies are not expected to have been polluted by SNe Type Ia and should be rich in α elements, while younger populations will be relatively α-poor. In our accreted halo model, the smooth, fully phase-mixed portion of the halo comes from early infalling objects that do not have a chance to ever make the younger populations. In contrast, these younger populations are apparent in more recently destroyed objects or surviving satellites that generally fell in even more recently. Zolotov et al. (2010) points to analogous trends in α element patterns when contrasting hydrodynamic simulations of the formation of galaxies with differing merger histories.

Distinctions between the chemical properties of field stars in the halo and satellite galaxies that have been known about for some time (Unavane et al. 1996, Venn et al. 2004) can naturally be explained within this cosmological context (Robertson et al. 2005, Font et al. 2006). Moreover, studies of stellar populations in the satellites, stellar halo and debris around M31 suggest this scenario can also be applied to understand variations there (see, e.g., Font et al. 2008, Gilbert et al. 2009, and Chapter 8).

5.3. Implications and applications

5.3.1. Statistical comparisons with observations

As discussed in the previous section, combining our cosmological picture of how structures form in the Universe with tidal disruption and chemical evolution models leads to some specific expectations for phase-space and stellar population characteristics of debris structures as well as some general trends. Both the characteristics and trends are broadly consistent with current observational surveys. However, the stochastic nature of hierarchical structure formation means that there is large variation about the average properties among the stellar halo models produced and more quantitative comparisons employing a statistical approach are just starting.

The average spatial structure of the stellar halo, as well as the level of substructure within it, can be assessed using large scale photometric catalogues of stars. For example: Bell et al. (2008) fitted triaxial, power-law models to star counts of main-sequence turnoff stars selected from SDSS and also quantified the level of deviations around these smooth models; and Sharma et al. (2010) exploited the distinct colors of metal-rich, evolved stars in the 2MASS filters (following Majewski et al. 2003) to select distant M-giant stars and ran a group-finding algorithm on the selection in the space defined by their angular position and apparent magnitude (from Sharma & Johnston 2009). In both studies, the analyses were repeated on equivalent synthetic stellar samples generated from the simulated stellar halos of Bullock & Johnston (2005). The results (both numbers and scales of groups and level of deviations from a smooth model) varied significantly between the eleven different simulated stellar halos, with the results from the analysis of real data sitting within this spread. While this agreement is encouraging, when Helmi et al. (2011) repeated the Bell et al. (2008) analysis on the Cooper et al. (2010) model stellar halos (which were derived by “painting” stars in the “Aquarius” self-consistent dark matter simulations), they found systematically larger deviations from a smooth background than the prior work at a level that was inconsistent with the observations. Recent work by Bailin et al. (2014) contrasting simulations with and without Galactic disk components suggest that this inconsistency with both observations and the Bullock & Johnston (2005) work might be attributed to the Aquarius simulations lacking the extra potential structure due to the disk.

Following photometric surveys with spectroscopic surveys allows assessments of the level of spatially correlated velocity substructure (e.g., using K-giants in the Spaghetti Survey, metal-poor MSTO stars from SEGUE, or BHBs from SDSS, see Starkenburg et al. 2009, Schlaufman et al. 2009, Xue et al. 2011). Currently, comparisons to models seem consistent, but again not conclusive (Xue et al. 2011).

Stellar populations in accreted halos are expected to exhibit spatial variation. These spatial variations have been found photometrically (by looking at the ratio of MSTO to BHB stars across the sky in the SDSS catalogue, see Bell et al. 2010) and spectroscopically (Schlaufman et al. 2012. In particular, Schlaufman et al. (2011, 2012) looked at the Fe- and α− element abundances of the velocity substructures they had found, and concluded that they tended to be chemically distinct from the smooth stellar halo, having systematically higher metallicity and lower [α/Fe], as might be expected for more recently accreted objects (Font et al. 2008). Analogous studies have also found these variations in M31 (Richardson et al. 2008, Gilbert et al. 2009, Bernard et al. 2015).

5.3.2. Recovering accretion histories

If stars, which may now spread throughout our dark matter halo, can be connected in such a way as to reassemble their original associations with infalling satellites, then the understanding of debris evolution outlined in Sect. 3 might be applied to learn about the original masses, orbits and infall times of those satellites. Collectively, these reconstructed groups might tell us the accretion history of our Galaxy from the stellar halo.

Several approaches have been proposed to attempt this reconstruction. Conceptually, the simplest is to take a sample of a single type of star (i.e. with restricted absolute magnitude range) from a large-scale photometric catalogue (e.g. M-giant stars from 2MASS or MSTO and BHB stars from SDSS) and search for groups in the 3-D space of angular position and apparent magnitude (e.g. Sharma et al. 2010). This approach is only effective for more recent accretion events (last several billion years) since earlier events have time to phase-mix and are not apparent as separate spatial groups. Exactly how far back in time, and the lowest luminosity of objects that might be recovered depends on the scale and depth of the survey as well as the stellar population that it is sensitive to (Sharma et al. 2011a).

Helmi & White (2001) proposed a much more powerful approach to recovering stars from early events, but also one that requires rather more data dimensions. If the full six dimensions of phase-space can be measured for stars, then (within a given potential) their orbital properties can be calculated. In a static potential, while they spread out over time in phase-space, they will conserve their orbits and hence remain as a group in the space of orbital characteristics (e.g. energy and actions) indefinitely. Several studies have analyzed prospects for Gaia in this context (Gómez et al. 2010, Sharma et al. 2011b, Gómez et al. 2013).

One limitation to identifying satellite members by using observed orbital properties is defining what those properties are: it is as yet unclear whether the Milky Way can be represented by an integrable mass distribution in which actions can be derived. Moreover, the potential of the Milky Way is time-evolving and this can scatter debris stars away from their original orbits. However, stars can also “remember where they came from” in other ways: their chemical abundances reflect the gas cloud in which they are born. Freeman & Bland-Hawthorn (2002) proposed that, given a large enough sample of high-resolution spectra of disk stars, this chemical memory could be exploited to measure the history of star formation in the disk: while stars might be spread throughout the 6-dimensional phase-space volume occupied by the disk, those born in the same cluster would all lie at a single location in the N-dimensional space of chemical abundances. These distinct chemical abundance patterns could be used to regroup them in their original birth clusters — an approach that Freeman & Bland-Hawthorn (2002) dubbed chemical tagging.

While stellar populations in satellite galaxies are spread out over a range of abundances (i.e. a small volume in N-dimensional chemical abundance space), the trends with satellite mass and assumed accretion time already seen in observations and simulations suggest that an analogous chemical tagging might work in the halo — perhaps not to reconstruct the exact objects from which stars came, but at least to look at the numbers of satellites of a given luminosity that might have accreted onto the Milky Way at different times. And, since the composition of a star cannot be erased by any dynamical evolution, this approach might work to recover the luminosity function of the very earliest infalling objects. Preliminary studies of how feasible this idea is to implement in practice are only just coming to fruition (Lee et al. 2015).

5.3.3. Accreted populations as a window on galaxy formation over cosmic time

Reconstructing the accretion history of our Galaxy is an exciting goal in itself, but it also opens up other possibilities. If we can find the stars — or at least identify the stellar populations — from similar-mass, long-dead objects infalling into the Milky Way at earlier epochs, this can give us a unique window on what baryons were doing in galaxies over cosmic time. In particular we can study baryons in the high-redshift progenitors of Milky-Way-type galaxies that may be impossible to see in situ even with the next generation of space telescopes (Okrochkov & Tumlinson 2010). In fact, the stellar populations in the Milky Way's halo today were originally formed in potential wells of many different depths (from the expected mass-spectrum of infalling dark matter halos) and that formed stars for different lengths of times (dictated by the spread in accretion times for those smaller halos onto the main Milky Way halo). Moreover, these infalling halos may have formed in a variety of environments as later infalling objects are expected to be spread out over a larger volume at early times compared to earlier infalling objects (see Corlies et al. 2013). Indeed, the difference between the abundance patterns in low-metallicity stars in the halo and those observed in several ultra-faint dwarf satellites of the Milky Way can be attributed to differences in the degree to which they evolved in chemical isolation in the early Universe (see Lee et al. 2013, for a discussion). Hence, the study of detailed chemical abundances of stars in the halo can tell us not just about our own Galaxy, but about the properties of stellar populations in many smaller galaxies over cosmic time.

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