SATELLITE DWARF GALAXIES IN A HIERARCHICAL UNIVERSE: INFALL HISTORIES, GROUP PREPROCESSING, AND REIONIZATION

To study the orbital histories of satellite dwarf galaxies, we use ELVIS (Exploring the Local Volume in Simulations), a suite of cosmological zoom-in N-body simulations that are targeted to modeling the LG (Garrison-Kimmel et al. 2014). ELVIS was run using GADGET-3 and GADGET-2 (Springel 2005), with initial conditions generated using MUSIC (Hahn & Abel 2011), all with ΛCDM cosmology based on WMAP7 (Larson et al. 2011): ${\sigma }_{8}=0.801$, ${\omega }_{\mathrm{matter}}=0.266$, ${\omega }_{\lambda }=0.734$, n_s = 0.963, and h = 0.71.

ELVIS contains 48 dark matter halos of masses similar to the MW or M31 (${M}_{\mathrm{vir}}=1.0-2.8\times {10}^{12}\;\;{M}_{\odot }$) within a zoom-in volume of radius $\gtrsim 4\;{R}_{\mathrm{vir}}$ of each halo at z = 0. Half of these halos are located in zoom-in regions that were selected to contain a pair of halos that resemble the masses, distance, and relative velocity of the MW-M31 pair, while the other half are single isolated halos matched in masses to the paired ones. These zoom-in regions are selected from a suite of simulations, each a cube with side length $70.4\;\mathrm{Mpc}$. Within the zoom-in regions, the particle mass is $1.9\times {10}^{5}\;{M}_{\odot }$ and the Plummer-equivalent force softening is 140 pc (comoving at $z\gt 9$, physical at $z\lt 9$). Additionally, three of the isolated halos were re-run at higher resolution, with particle mass of $2.4\times {10}^{4}\;{M}_{\odot }$ and force softening of 70 pc. Using these simulations, we checked that resolution does not significantly affect any results in this work. See Garrison-Kimmel et al. (2014) for more details on ELVIS.

Throughout this work, unless otherwise stated, we use the paired halos, which more accurately capture the environment, assembly history, and massive satellite population (LMC/M33-like satellites) of the LG. More precisely, we use 10 halo pairs (20 halos total), ignoring the pairs Siegfried & Roy and Serena & Venus because they contain a massive halo within $1.2\;\mathrm{Mpc}$ that is not representative of the LG (Garrison-Kimmel et al. 2014). Henceforth, we refer to these paired halos as "MW/M31 halos," and we do not further differentiate between the MW and M31 given their similar masses (van der Marel et al. 2012; Boylan-Kolchin et al. 2013). In the Appendix, we compare our results for paired versus isolated halos.

ELVIS identifies dark matter (sub)halos using the six-dimensional halo finder rockstar (Behroozi et al. 2013b) and constructs merger trees using the consistent-trees algorithm (Behroozi et al. 2013c). For each halo that is not a subhalo (see below), we assign a virial mass, M_vir, and radius, R_vir, using the evolution of the virial relation from Bryan & Norman (1998) for our ΛCDM cosmology. At z = 0, this corresponds to an overdensity of ${{\rm{\Delta }}}_{\mathrm{critical}}=97\;({{\rm{\Delta }}}_{\mathrm{matter}}=363)$ times the critical (matter) density, while at $z\gtrsim 3$ it asymptotes to ${{\rm{\Delta }}}_{\mathrm{critical}}\approx {{\rm{\Delta }}}_{\mathrm{matter}}\approx 178$.

We define a "host halo" as an isolated halo that can host (lower-mass) subhalos within it, and a "subhalo" as a halo whose center is inside R_vir of a (more massive) host halo. When a (sub)halo passes within R_vir, of a host halo, the (sub)halo becomes its "satellite" and experiences "virial infall."

For each (sub)halo, we assign its primary progenitor (main branch) as the progenitor that contains the most total mass summed from the (sub)halo masses over all preceding snapshots in that branch. We then compute the peak mass, M_peak, as the maximum instantaneous mass that a (sub)halo ever reaches along the history of its primary progenitor. For subhalos, M_peak almost always occurs before virial infall. As explored in Garrison-Kimmel et al. (2014), the numerical resolution of ELVIS does not significantly affect its (sub)halo catalogs at (and even below) ${M}_{\mathrm{peak}}\gt {10}^{8}\;\;{M}_{\odot }$, the limit in this work.

Our goal is to map luminous galaxies to the dark matter subhalos in ELVIS. The relation between stellar mass and subhalo mass (or maximum circular velocity) for dwarf galaxies is highly uncertain, likely with significant scatter, especially for our lowest-mass subhalos, some of which might not host any luminous galaxies, a manifestation of the long-standing "missing satellites problem" (Klypin et al. 1999). Nonetheless, we use the relation from abundance matching to ELVIS subhalos in Garrison-Kimmel et al. (2014), which is based on that of Behroozi et al. (2013a) but is modified at the low-mass end according to the observed stellar mass function of Baldry et al. (2012). At the mass scales of dwarf galaxies, this leads to ${M}_{\mathrm{star}}\propto {M}_{\mathrm{peak}}^{1.92}$. This modification reproduces the observed mass function at ${M}_{\mathrm{star}}\lt {10}^{9}\;\;{M}_{\odot }$ in the LG, especially if one accounts for observational incompleteness (Tollerud et al. 2008; Hargis et al. 2014). However, we present most results as a function of both M_star and M_peak, given the uncertainties of abundance matching at these low masses. For reference, each of the MW/M31 halos hosts an average of 230, 28, and 3 satellites with ${M}_{\mathrm{star}}={10}^{3-5}$, 10^5–7, and ${10}^{7-9}\;\;{M}_{\odot }$, respectively, at z = 0 (this is similar for the paired and isolated halos).

In selecting the stellar mass ratio for defining "major" groups or mergers in the histories of satellites in Sections 4.1 and 5, we assume that the slope (but not necessarily normalization) of this relation does not evolve, motivated by the lack of strong evolution observed for slightly more massive galaxies (e.g., Leauthaud et al. 2012; Hudson et al. 2013) and the lack of observational evidence to suggest otherwise. We define major mergers as those for which the ratio in ${M}_{\mathrm{star}}$ is greater than $0.1$. This broadly corresponds to mass ratios at which the lower-mass companion likely has significant dynamical effect on the more massive galaxy (e.g., Hopkins et al. 2010; Helmi et al. 2012; Yozin & Bekki 2012) and for which recent mergers are likely to be observable. Given our relation between M_star and M_peak, this corresponds to a ratio in ${M}_{\mathrm{peak}}\gtrsim 0.3$.

While environmental processes clearly affect satellite galaxies within R_vir of the MW/M31 halos, whether such environmental processing occurs in lower-mass host halos (${M}_{\mathrm{vir}}\ll {10}^{12}\;\;{M}_{\odot }$) remains unclear. Thus, we investigate two metrics of virial infall. First, we examine "first infall": when a satellite first became a satellite within any host halo, that is, first crossed within the virial radius of any halo more massive than itself. We refer to this redshift as z_{first infall} or time as t_{first infall}, with ${t}_{\mathrm{first}\;\mathrm{infall}}^{\mathrm{since}}={t}_{\mathrm{now}}-{t}_{\mathrm{first}\;\mathrm{infall}}$. We also examine "MW/M31 infall": when a satellite first became a satellite in its host MW/M31 halo. We refer to this as z_{MW/M31 infall} or t_{MW/M31 infall}, with ${t}_{\mathrm{MW}/{\rm{M}}31\;\mathrm{infall}}^{\mathrm{since}}={t}_{\mathrm{now}}-{t}_{\mathrm{MW}/{\rm{M}}31\mathrm{infall}}$.

We first examine how the virial-infall times of satellites at z = 0 depend on their mass. Figure 1 shows ${t}_{\mathrm{first}\;\mathrm{infall}}^{\mathrm{since}}$ (left) and ${t}_{\mathrm{MW}/{\rm{M}}31\;\mathrm{infall}}^{\mathrm{since}}$ (right), or z_{first infall} and z_{MW/M31 infall} on the right axes, as a function of satellite M_star, or subhalo M_peak on the top axes.

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For both virial-infall metrics, lower-mass satellites fell in earlier, though significant scatter persists at all masses. This trend with M_peak (or M_star) is a natural result of hierarchical structure formation, for two reasons. First, halos of a given M_peak are more common at later cosmic time. Thus, higher-mass satellites are more likely to have formed, and subsequently fallen in, at later time. Second, satellites with higher M_peak have shorter dynamical-friction lifetimes (for fixed host-halo mass) before they tidally disrupt or merge with the host (Boylan-Kolchin et al. 2008; Jiang et al. 2008; Wetzel & White 2010).

Our lowest-mass (ultrafaint) satellites first fell into any host halo typically $\sim 10\;\mathrm{Gyr}$ ago at $z\sim 1.7$, and they first fell into the MW/M31 halo $\sim 7.5\;\mathrm{Gyr}$ ago at $z\sim 1$. By contrast, our highest-mass satellites (corresponding to the LMC, SMC, NGC 205, M32) have ${t}_{\mathrm{first}\;\mathrm{infall}}^{\mathrm{since}}\sim 6.5\;\mathrm{Gyr}$ (${z}_{\mathrm{first}\;\mathrm{infall}}\sim 0.8$) and ${t}_{\mathrm{MW}/{\rm{M}}31\;\mathrm{infall}}^{\mathrm{since}}\sim 5\;\mathrm{Gyr}$ (z_{MW/M31 infall} $\sim \;0.5$). Thus, satellites first fell into any host halo a few Gyr before they fell into the MW/M31 halo, as we will examine further in Section 4.3. This result is generic for hierarchical structure formation.

Overall, satellite dwarf galaxies at z = 0 typically have evolved as a satellite in a host halo for over half of their entire history, so the host-halo environment typically has had significant time to affect their evolution.

We next explore how the above virial-infall times of satellites depend on their current distance from the MW/M31 host. Previous analyses at higher mass scales in cosmological simulations showed that satellites at smaller distances tend to have fallen in earlier (e.g., Gao et al. 2004; Smith et al. 2012; Oman et al. 2013). This is because (1) R_vir of the host halo was smaller at earlier times, and (2) satellite orbits get dragged to smaller distance over time via dynamical friction. Such a trend for satellites in the LG would be important for several reasons. First, ultrafaint (${M}_{\mathrm{star}}\lesssim {10}^{5}\;\;{M}_{\odot }$) satellites currently are observable only within the inner $\sim 50\;\mathrm{kpc}$ of the MW halo, so it is possible that they had systematically earlier infall times than the median in Figure 1. Second, such a correlation with distance would provide a statistical proxy for an environmental evolutionary sequence (since the time of infall) for the observable satellite population.

Figure 2 shows ${t}_{\mathrm{first}\;\mathrm{infall}}^{\mathrm{since}}$ (top row) and ${t}_{\mathrm{MW}/{\rm{M}}31\;\mathrm{infall}}^{\mathrm{since}}$ (bottom row) as a function of distance to the host's center, d, as scaled to the host's virial radius, R_vir, at z = 0. We compute these quantities in bins of $d/{R}_{\mathrm{vir}}$ for each MW/M31 halo, and using that the median R_vir in ELVIS is $300\;\mathrm{kpc}$, we also show the (approximate) dependence on d along the top axes. For both infall metrics and at all masses, satellites closer to the host fell in earlier, though with significant scatter. Overall, the trend for MW/M31 infall is slightly stronger than for first infall, as expected given that we measure d with respect to the MW/M31 center. The gradient in ${t}_{\mathrm{first}\;\mathrm{infall}}^{\mathrm{since}}$ and ${t}_{\mathrm{MW}/{\rm{M}}31\;\mathrm{infall}}^{\mathrm{since}}$ from $d/{R}_{\mathrm{vir}}=0$ to 1 for massive satellites is 6.5 and $4.5\;\mathrm{Gyr}$, respectively, while for our lowest-mass satellites it is 2.5 and $4\;\mathrm{Gyr}$. Thus, the correlation of infall time with distance is stronger for more massive satellites, because (1) they fell in more recently, making them less smeared out in orbital phase space, and (2) they experience more efficient dynamical friction. For our lowest-mass (ultrafaint) satellites, those in our smallest distance bin, where they are observable, experienced first infall typically $\sim 11\;\mathrm{Gyr}$ ago at $z\sim 2.2$, and they first fell into the MW/M31 halo $\sim 9\;\mathrm{Gyr}$ ago at $z\sim 1.5$, so these are slightly earlier than Figure 1.

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We conclude that a satellite's distance does provide a statistical proxy for its virial-infall time, and therefore the distribution of distances for the satellite population at z = 0 provides a proxy for an environmental evolutionary sequence, especially for more massive satellites. However, note one caveat: despite the correlation with distance, satellites currently near R_vir have been satellites for quite a while, typically $3-8\;\mathrm{Gyr}$, depending on mass. Thus, the satellite population near R_vir is not only a recent-infall population, but rather, it is a superposition of inward- and outward-orbiting satellites, some of which already experienced a pericentric passage. Note that any given satellite spends most of its orbital time near apocenter. (For reference, the virial crossing time, ${R}_{\mathrm{vir}}/{V}_{\mathrm{vir}}$, is $\approx 2\;\mathrm{Gyr}$ at z = 0.)

The virial-infall times in Figures 1 and 2 have important implications for understanding the relative effects of cosmic reionization versus host-halo environment on surviving dwarf galaxies, in particular, whether the effects of these two processes occurred at distinct epochs during the formation histories of these galaxies. In these figures, the dashed line at z = 6 represents the end of cosmic reionization as constrained by various observations (e.g., Robertson et al. 2013, and references therein). Across all masses and distances, none of the satellites at z = 0 were within R_vir of their MW/M31 halo any time during reionization. Furthermore, $\lt 4\%$ were within R_vir of any host halo during reionization. There are regimes where this fraction is somewhat higher, the highest being 10% for satellites at ${M}_{\mathrm{star}}={10}^{5-8}\;{M}_{\odot }$ and $d/{R}_{\mathrm{vir}},\lt 0.1$, but this fraction is typically only a few percent across our range of mass and distance. Thus, essentially none of the dwarf galaxies in the LG were within R_vir of a host halo during reionization, such that they would have experienced strong environmental effects at that time.

To understand this result in more detail, we also examine how close the dwarf galaxies came to a more massive halo during reionization. Thus, we select all satellites in the MW/M31 halos at z = 0 and trace them back to $z\gt 6$, when almost all such dwarfs were isolated (non-satellite) halos. (We are able to track all (sub)halos back to $z\gt 6$, except for 6% of those at ${M}_{\mathrm{star}}\lt {10}^{4}\;\;{M}_{\odot }$, which formed after z = 6.) At all $z\gt 6$ (for which ELVIS contains six snapshots), we then compute the nearest distance, ${d}_{\mathrm{nearest}}$, that each satellite's progenitor came to the center of any neighboring halo that is more massive and thus feasibly could induce environmental effects.

Figure 3 shows the cumulative distribution of ${d}_{\mathrm{nearest}}$ in comoving units (left) and scaled to R_vir of the nearest, more massive halo (right). The thick solid curve shows the average across the paired MW/M31 halos. We show the average for all satellites across our mass range, ${M}_{\mathrm{star}}={10}^{3-9}\;\;{M}_{\odot }$, as we find no significant dependence on satellite mass. The typical ${d}_{\mathrm{nearest}}$ at $z\gt 6$ was large: $3\;\mathrm{Mpc}$ comoving ($\sim 400\;\mathrm{kpc}$ physical), or $500\;{R}_{\mathrm{vir}}$. Moreover, only $\approx 5\%$ of these galaxies came within 1 Mpc comoving, or $100\;{R}_{\mathrm{vir}}$, of a more massive halo. The thin solid curves show each MW/M31 pair, highlighting the factor of ∼2 scatter in these distributions. For reference, the thick dotted curve shows the average for the isolated MW/M31 halos, which we discuss in the Appendix.

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If strong environmental effects (such as star formation quenching) on dwarf galaxies are confined to within R_vir (or even larger) of a host halo at these redshifts, then the results of Figures 1–3 indicate that such environmental processing occurred only at $z\lt 6$ during the histories of satellites at z = 0, and more typically, at $z\lesssim 3$ (for $\approx 84\%$ of all satellites). The properties of the LG support this result, because a strong transition in morphology, star formation, and gas content of dwarf galaxies, as induced by the host halo, occurs only within $\approx 300\;\mathrm{kpc}$ ($\approx {R}_{\mathrm{vir}}$) of the MW or M31.

Given that cosmic reionization ended by z = 6, we thus conclude that the effects of reionization occurred well before those of the host-halo environment for surviving satellites. Specifically, for surviving satellites, the duration between the end of reionization and first crossing within R_vir of a host halo was typically $\gt 2\;\mathrm{Gyr}$ for first infall into any host halo (including group preprocessing) and $\gt 4\;\mathrm{Gyr}$ for first infall into the MW/M31 halo. This result strongly motivates the use of faint and ultrafaint satellites as probes of reionization, e.g., by measuring the (potential) effect of reionization on their star formation histories as derived from their current stellar populations (e.g., Brown et al. 2014; Weisz et al. 2014), if such star formation histories can demonstrate that any individual satellite quenched at $z\gtrsim 6$ or that any common features (such as quenching) occurred at $z\gtrsim 3$ for a population of several satellites (given that $\approx 84\%$ surviving satellites fell into a host halo at $z\lesssim 3$).

Figure 4 (left) shows both of the above preprocessed fractions as a function of satellite M_star or M_peak. First, the red short-dashed curve shows the fraction of satellites that were a satellite in a group at the time of falling into the MW/M31 halo. For our highest-mass satellites, this fraction is relatively low ($\sim 10\%$) but increases significantly to 30% for our lowest-mass satellites. Thus, $\sim 1/3$ of all faint and ultrafaint satellites were in a group when they fell into the MW/M31 halo, in good agreement with the results of Li & Helmi (2008), which was based on a cosmological simulation of a single MW-like halo.

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Second, the blue long-dashed curve shows the fraction of satellites that were a satellite in a group any time before falling into the MW/M31 halo. This fraction is significantly ($\sim 2\times$) higher, because of the large fraction of satellites whose orbits brought them beyond R_vir of their preprocessing group. For our highest-mass satellites, $\sim 30\%$ were preprocessed by a group before joining the MW/M31 halo. Again, this preprocessed fraction increases at lower mass, being $\sim 60\%$ for faint and ultrafaint satellites. Thus, half of all satellite galaxies with ${M}_{\mathrm{star}}\lt {10}^{6}\;{M}_{\odot }$ were preprocessed as a satellite in a group prior to joining the MW/M31 halo.

We also explore how many current satellites in the MW/M31 halo were the central (most massive) galaxy in such an infalling group. That is, we identify satellites in the MW/M31 halo at z = 0 that hosted their own major satellite(s) when they fell into the MW/M31 halo. (By "major," we mean that M_star differs by less than a factor of 10, as detailed in Section 2.3.) Figure 4 (right) shows this fraction via the green long-short-dashed curve, which is 5%–10% across our mass range. This fraction increases only weakly with mass because of the combination of (1) a nearly mass-independent distribution of ${M}_{\mathrm{peak},\mathrm{satellite}}/{M}_{\mathrm{peak},\mathrm{host}}$ in ΛCDM, (2) our power-law ${M}_{\mathrm{star}}-{M}_{\mathrm{peak}}$ relation, and (3) our requirement that ${M}_{\mathrm{star},\mathrm{satellite}}/{M}_{\mathrm{star},\mathrm{host}}\gt 0.1$.

For comparison, Figure 4 (right) also shows the same red short-dashed curve as in the left panel, and the black dot-dashed curve shows the sum of the two curves, indicating the total fraction of satellites that fell into the MW/M31 halo as part of a major group. This overall fraction is significant at 20%–40% across our mass range.

We next explore how the above preprocessed fractions vary with the current distance of satellites from their host. The two panels in Figure 5 show the same two preprocessed fractions as in Figure 4 (left), but as a function of $d/{R}_{\mathrm{vir}}$ at z = 0, similar to Figure 2. Again, we compute these quantities in bins of $d/{R}_{\mathrm{vir}}$ for each MW/M31 halo, though we also show the dependence on d (using the median R_vir across the MW/M31 halos) along the top axes. At any distance, lower-mass satellites are more likely to have been preprocessed. Moreover, at nearly all satellite masses, those closer to the host center are more likely to have been preprocessed, with a nearly $2\times$ increase from $d/{R}_{\mathrm{vir}}=1$ to 0.1 for our lowest-mass satellites. Most likely, this gradient arises because a satellite that fell in as part of a group remained bound to the (more massive) group for some time after infall, so it experienced more efficient dynamical friction that dragged it to the center of the MW/M31 halo more rapidly.

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Overall, given that the faintest galaxies are observable only at small distances within the MW halo, most likely about half of them were a satellite in another group(s) before/during infall into the MW halo.

We next examine in more detail the durations and host-halo masses that satellites at z = 0 experienced during their group preprocessing, in order to understand better its potential impact on their evolution.

Figure 6 (top) shows the distribution of maximum host-halo mass that satellites experienced during group preprocessing as a function of their M_star. The typical preprocessing group had ${M}_{\mathrm{vir}}\sim {10}^{11}\;\;{M}_{\odot }$, with 68% spread of ${10}^{10-12}\;\;{M}_{\odot }$, largely independent of satellite mass, though with scatter to M_vir at lower M_star. Combined with Figure 4 (left), this means that $\sim 25\%$ of all satellites at z = 0 were preprocessed in groups of ${M}_{\mathrm{vir}}\gtrsim {10}^{11}\;\;{M}_{\odot }$, comparable to the LMC or M33.

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The total population of preprocessed satellites at z = 0 originated from typically 30 infalling groups, with most groups containing two to five satellites. However, about half of all preprocessed satellites fell in via the two to three most massive groups (${M}_{\mathrm{vir}}\gtrsim {10}^{11}\;\;{M}_{\odot }$, similar to the LMC or M33), and the most massive infalling group typically brought in ∼25%–30% of all preprocessed satellites, or $\sim 13\%$ of all satellites in total.

However, for half of the preprocessed satellites, their preprocessing host does not survive to z = 0 but instead merges/disrupts within the MW/M31 halo. Thus, surviving preprocessed satellites do not necessarily have their preprocessing host galaxy surviving near them at z = 0; instead, the host galaxy could persist in a disrupted stream configuration. On the other hand, particularly massive (${M}_{\mathrm{peak}}\gtrsim {10}^{11}\;\;{M}_{\odot }$, comparable to the LMC) satellites that do survive to z = 0 typically brought in $\sim 7\%$ of overall satellite dwarf population in the MW/M31 halo (Deason et al. 2015).

Satellites can be preprocessed by the other MW/M31 halo in the pair, if they fell into one of the MW/M31 halos, orbited beyond its R_vir, and then fell into the other MW/M31 halo. However, this accounts for $\lt 2\%$ of all preprocessed satellites across our mass range, in general agreement with Knebe et al. (2011), so this is not a particularly important population.

Figure 6 (bottom) shows the distribution of the duration that satellites spent in a preprocessing host halo. The typical duration was $\sim 1.2\;\mathrm{Gyr}$, with 68% spread of $0.5-3.5\;\mathrm{Gyr}$. At ${M}_{\mathrm{star}}\gt {10}^{7}\;\;{M}_{\odot }$, no satellites were preprocessed longer than $1.8\;\mathrm{Gyr}$, while at ${M}_{\mathrm{star}}\lt {10}^{7}\;\;{M}_{\odot }$, the scatter increases significantly, with some satellites having experienced up to $7\;\mathrm{Gyr}$ of preprocessing. The small durations at ${M}_{\mathrm{star}}\gt {10}^{7}\;\;{M}_{\odot }$ likely arise because those satellites have M_peak that approaches that of their preprocessing host halo, corresponding to shorter dynamical friction lifetimes, so they could not have been preprocessed too long without merging/disrupting.

Overall, most preprocessing occurred within groups of ${M}_{\mathrm{vir}}={10}^{10-12}\;\;{M}_{\odot }$, masses that feasibly could influence satellite galaxies, though environmental effects at these masses remain poorly understood. Furthermore, the typical preprocessing duration was $0.5-3.5\;\mathrm{Gyr}$, comparable to typical timescales over which such satellite dwarf galaxies are quenched environmentally (Fillingham et al. 2015; Wetzel et al. 2015). Thus, we conclude that such group preprocessing before joining the MW/M31 halo is likely an important component in the evolution of satellite dwarf galaxies.

Using the ELVIS suite of cosmological zoom-in dissipationless simulations, we examined the virial-infall histories and group preprocessing of satellites across the observed range of masses for dwarf galaxies: ${M}_{\mathrm{star}}={10}^{3-9}\;\;{M}_{\odot }$. While we examined all 48 MW/M31 halos in ELVIS, we focused on the 10 halo pairs (20 halos total) that most resemble the LG, thus providing good statistics in a realistic cosmic setting. We summarize our primary results as follows.

• a.  
  Virial-infall histories: satellites at z = 0 fell into the MW/M31 halo typically $5-8\;\mathrm{Gyr}$ ago at $z=0.5-1$, though they first fell into any host halo typically $7-10\;\mathrm{Gyr}$ ago at $z=0.7-1.5$. The difference between these infall times arises because of group preprocessing. Satellites at lower mass or closer to the center of the MW/M31 experienced earlier infall times. The latter means that the distribution of distances of satellites at z = 0 provides a statistical proxy for an environmental evolutionary sequence after infall. Overall, current satellites have evolved as satellites within a host halo for over half of their entire history.
• b.  
  Group preprocessing: a large fraction of satellites were a satellite in a group (another host halo), typically of ${M}_{\mathrm{vir}}\sim {10}^{10-12}\;\;{M}_{\odot }$, for a duration of $0.5-3.5\;\mathrm{Gyr}$, before falling into the MW/M31 halo. This group preprocessing is especially common among faint and ultrafaint satellites: at ${M}_{\mathrm{star}}\lesssim {10}^{6}\;\;{M}_{\odot }$, $\approx 30\%$ of all satellites at z = 0 fell into the MW/M31 halo as a satellite in a group, and half of all satellites at z = 0 were in a group any time before falling into the MW/M31 halo. Thus, $\sim 25\%$ of all satellites at z = 0 were preprocessed in groups with ${M}_{\mathrm{vir}}\gtrsim {10}^{11}\;\;{M}_{\odot }$, comparable to the LMC. Satellites closer to the center of the MW/M31 are more likely to have experienced group preprocessing.
• c.  
  Satellite–satellite mergers: group infall drives most (60%–90%) of the satellite–satellite major mergers that occurred after falling into the MW/M31 halos, as we explored in Deason et al. (2014a).
• d.  
  Cosmic reionization: none of the surviving satellite dwarf galaxies were within their MW/M31 halo during reionization ($z\gt 6$), and only $\lt 4\%$ were within the virial radius of any host halo during reionization. Furthermore, the typical distance to the nearest, more massive halo at $z\gt 6$ was $3\;\mathrm{Mpc}$ comoving ($\sim 400\;\mathrm{kpc}$ physical), or $500\;{R}_{\mathrm{vir}}$. Thus, the effects of cosmic reionization versus host-halo environment on the formation histories of surviving dwarf galaxies in the LG occurred at distinct epochs separated typically by $2-4\;\mathrm{Gyr}$, and are separable in time theoretically and, in principle, observationally.

6.2.1. Impact of Group Preprocessing on the Evolution of Dwarf Galaxies

6.2.2. Implications for Observed Associations in the LG

6.2.3. Effects of Numerical Resolution and Baryonic Physics