# Satellite Dwarf Galaxies in a Hierarchical Universe: Infall Histories, Group Preprocessing, and Reionization

Abstract

In the Local Group, almost all satellite dwarf galaxies that are within the virial radius of the Milky Way (MW) and M31 exhibit strong environmental influence. The orbital histories of these satellites provide the key to understanding the role of the MW/M31 halo, lower-mass groups, and cosmic reionization on the evolution of dwarf galaxies. We examine the virial-infall histories of satellites with $${M_{\rm star}}=10^{3-9} {~\mbox{M}_\odot}$$ using the ELVIS suite of cosmological zoom-in dissipationless simulations of 48 MW/M31-like halos. Satellites at $$z=0$$ fell into the MW/M31 halos typically $$5-8 {~\mbox{Gyr}}$$ ago at $$z=0.5-1$$. However, they first fell into any host halo typically $$7-10 {~\mbox{Gyr}}$$ ago at $$z=0.7-1.5$$. This difference arises because many satellites experienced “group preprocessing” in another host halo, typically of $${M_{\rm vir}}\sim 10^{10-12} {~\mbox{M}_\odot}$$, before falling into the MW/M31 halos. Satellites with lower-mass and/or those closer to the MW/M31 fell in earlier and are more likely to have experienced group preprocessing; half of all satellites with $${M_{\rm star}}< 10^6 {~\mbox{M}_\odot}$$ were preprocessed in a group. Infalling groups also drive most satellite-satellite mergers within the MW/M31 halos. Finally, none of the surviving satellites at $$z=0$$ were within the virial radius of their MW/M31 halo during reionization ($$z > 6$$), and only $$< 4\%$$ were satellites of any other host halo during reionization. Thus, effects of cosmic reionization versus host-halo environment on the formation histories of surviving dwarf galaxies in the Local Group occurred at distinct epochs and are separable in time.

# Introduction

Galaxies in dense environments are more likely to have suppressed (quiescent) star-formation rates (SFR), more elliptical/spheroidal/bulge-dominated morphologies, and less cold gas in/around them than galaxies of similar stellar mass, $${M_{\rm star}}$$, in less dense environments. While such environmental effects long have been studied in massive galaxy groups and clusters (for example, Oemler, 1974; Dressler, 1980; Dressler et al., 1983; Balogh et al., 1997; Blanton et al., 2009, for review), the observed effects on the dwarf galaxies of the Local Group (LG), in particular, the satellites within the host halos of the Milky Way (MW) and M31, are even stronger (Mateo, 1998; McConnachie, 2012; Phillips et al., 2014; Slater et al., 2014; Spekkens et al., 2014).

Specifically, the galaxies around the Milky Way (MW) and Andromeda (M31) show a strikingly sharp transition in their properties within $$\approx 300 {~\mbox{kpc}}$$, corresponding to the virial radii, $${R_{\rm vir}}$$, of the halos of the MW and M31 for $${M_{\rm vir}}\approx 10 ^ {12} {~\mbox{M}_\odot}$$ (e.g., Deason et al., 2012; van der Marel et al., 2012; Boylan-Kolchin et al., 2013). Within this distance, galaxies transition from (1) having irregular to elliptical/spheroidal morphologies, (2) having most of their baryonic mass in cold atomic/molecuar gas to having little-to-no detectible cold gas, and (3) being actively star-forming to quiescent (McConnachie, 2012, and references therein). This environmental transition of the population is nearly a complete one, with just a few exceptions. Four gas-rich, star-forming, irregular galaxies persist within the halos of the MW (the LMC and SMC) and M31 (LGS 3 and IC 10). However, the LMC and SMC are likely on their first infall (Besla et al., 2007; Kallivayalil et al., 2013), and given their distances to M31, LGS 3 and IC 10 may be as well. Furthermore, 3 - 4 gas-poor, quiescent, spheroidal galaxies exist just beyond the halos of the MW (Cetus and Tucana) and M31 (KKR 25 and possibly Andromeda XVIII), though the radial velocities of Cetus and Tucana imply that they likely orbited within the MW halo (Teyssier et al., 2012). The fact that almost all of the satellite galaxies within the MW/M31 halos show such strong environmental effects is particularly striking given that, other than KKR 25, all known galaxies at $${M_{\rm star}}< 10 ^ 9 {~\mbox{M}_\odot}$$ that are isolated (not within $$1500 {~\mbox{kpc}}$$ of a more massive galaxy, and thus not strongly influenced by environmental effects) are actively star-forming (Geha et al., 2012) and gas-rich. Thus, the MW and M31 halos exert the strongest observed environmental influence on their galaxy populations of any known systems, making the LG one of the most compelling laboratories to study environmental effects on galaxy evolution.

Several environmental processes within a host halo can play a role in regulating the gas content, star formation, morphology, and eventual tidal distruption of satellite galaxies. Gravitationally, the strong tidal forces of the host halo will strip mass from the satellite (subhalo) from the outside-in (Dekel et al., 2003; Diemand et al., 2007; Wetzel et al., 2010). In addition, the dense collection of satellites within a host halo can drive impulsive gravitational interactions with each other (Farouki et al., 1981; Moore et al., 1998), and satellites can merge with one another (Angulo et al., 2009; Wetzel et al., 2009; Wetzel et al., 2009a; Deason et al., 2014). Moreover, tidal shocking and resonant interactions with the host’s galactic disk can lead to particularly efficient morphological evolution, coring, stripping, and disruption (Mayer et al., 2001; D’Onghia et al., 2010; Zolotov et al., 2012). Hydrodynamically, if the host halo contains thermalized hot gas, this can strip and heat the extended gas from the orbiting satellite subhalo (Balogh et al., 2000; McCarthy et al., 2008), leading to reduced gas cooling/accretion into the satellite’s disk (Larson et al., 1980). More drastically, given a sufficiently high density of hot gas and high orbital velocity, ram-pressure can strip cold gas directly from the satellite’s disk (Gunn et al., 1972; Abadi et al., 1999; Mayer et al., 2006; Chung et al., 2009; Tonnesen et al., 2009). Furthermore, galactic winds driven by feedback within satellite galaxies can allow these environmentel process to operate even more efficiently (for example, Bahé et al., 2015).

Understanding the relative efficiency of the above environmental processes, including the timescales over which they have operated, requires understanding in detail the orbital and virial-infall histories of the current satellite population in the context of the hierarchical structure formation of $$\Lambda$$CDM. While some authors examined the virial-infall times of satellites in cosmological settings (Rocha et al., 2012; Lux et al., 2010), such works used cosmological zoom-in simulations of one or two MW-like halos, which does not model the environment of the MW/M31 pair of the LG or allow for good statistics. In addition, hierarchical growth means that many satellites may have been environmtentally processed in a group before they fell into the MW/M31 halos, which could help to explain the high efficiency and near completeness of the above environmental effects on the satellite population. Several authors explored the importance of this “group preprocessing” on satellites currently in massive groups and clusters (Zabludoff et al., 1998; McGee et al., 2009; Wetzel et al., 2013; Hou et al., 2014). For example, Wetzel et al. (2013) found that the higher fraction of satellites that are quiescent in more massive groups/clusters can arise because the satellites in more massive host halos simply have been satellites longer, driven largely by group preprocessing. However, on mass scales of MW/M31 halos, the impact of group preprocessing on dwarf galaxies remains largely unexplored, in part because the degree to which the above environmental processes operate in groups with $${M_{\rm vir}}\ll 10 ^ {12} {~\mbox{M}_\odot}$$ remains uncertain. Using a cosmological zoom-in simulation of a single MW-like halo Li et al. (2008) found that $$\sim 1 / 3$$ of satellites fell in as part of a group, and using the two Via Lactea simulations, Slater et al. (2013) similarly found that many satellites are organized into small groups with correlated infall.

If some satellites fell in the MW/M31 halos as part of a group, this would have several implications for the subsequent evolution and spatial distribution of the satellites. For instance, group infall may drive the strong observed correlations in phase-space coordinates between the satellites (and streams) in the MW and M31 halos (Lynden-Bell et al., 1995; D’Onghia et al., 2008; Klimentowski et al., 2010), including the disk-like configurations of satellites around the MW and M31 (for example, Libeskind et al., 2005; Lovell et al., 2011; Fattahi et al., 2013; Ibata et al., 2013). Furthermore, group infall can drive mergers between satellites after infall into the MW/M31 halos (for example, Deason et al., 2014).

In addition to the above environmental processes that operate within a host halo, cosmic reionization may have had a lasting impact on formation histories of dwarf galaxies in the LG. In particular, reionization may have heated/removed the gas from low-mass halos whose virial temperatures were below that of the ultra-violet photoionization background, thus quenching star-formation in the lowest-mass galaxies and leaving them as relics of reionization (Gnedin, 2000; Bullock et al., 2000). Many ongoing observational efforts aim to use the current stellar populations of faint and ultra-faint satellites in the LG to test the potential impact that reionization may have had on their star-formation histories at $$z \gtrsim 6$$ (for example, Weisz et al., 2014; Brown et al., 2014). However, a long-standing challenge for such studies is whether one can separate the effects of cosmic reionization from those of the host-halo environment on the formation histories of surviving satellite dwarf galaxies.

Our goal in this work is to examine the orbital and virial-infall histories of the current satellite galaxy population in the LG, in a fully cosmological and hierarchical context, including the impact of group preprocessing and implications for reionization. To examine these questions with good statistics in realistic LG-like environments, we use the ELVIS suite of cosmological zoom-in dissipationless simulations of 48 MW/M31-like halos (Garrison-Kimmel et al., 2014). Specifically, we will address the following questions for the satellites in the halos of the MW and M31:

• When did they fall into the MW/M31 halo, and when did they first fall into any host halo?

• What fraction were within their MW/M31 halo, or any other host halo, during cosmic reionization ($$z > 6$$)?

• What fraction were in a group prior to falling into the MW/M31 halo?

• What role does group infall play in driving mergers between satellites?

# Numerical Methods

\label{sec:method}

## Simulations

\label{sec:simulation}

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 et al., 2011), all with a $$\Lambda$$CDM cosmology based on Wilkinson Microwave Anisotropy Probe WMAP7 (Larson et al., 2011): $$\sigma_8 = 0.801$$, $${\Omega_{\rm matter}}= 0.266$$, $${\Omega_{\rm \Lambda}}= 0.734$$, $$n_s = 0.963$$ and $$h = 0.71$$.

The ELVIS suite contains 48 dark-matter halos of mass similar to the MW or M31 ($${M_{\rm vir}}= 1 - 3 \times 10 ^ {12} {~\mbox{M}_\odot}$$) within a zoom-in volume of radius $$\gtrsim 4\,{R_{\rm vir}}$$ of each halo at $$z = 0$$. Half of these halos are located in zoom-in regions 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 mass to the paired ones. These zoom-in regions come from a suite of larger-volume simulations, each a cube with side length $$70.4 {~\mbox{Mpc}}$$. Within the zoom-in regions, the particle mass is $$1.9 \times 10 ^ 5 M_\odot$$ and the Plummer-equivalent force softening is $$140 {~\mbox{pc}}$$ (comoving at $$z > 9$$, physical at $$z < 9$$). Additionally, three of the isolated halos were run at higher resolution, with particle mass $$2.4 \times 10 ^ 4 M_\odot$$ and force softening $$70 {~\mbox{pc}}$$. 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 only the paired halos, which more accurately capture the environment, assembly history, and massive satellite population (LMC/M33-like satellites) of the LG. We ignore the pairs Siegfried & Roy and Serena & Venus because they contain a massive halo within $$1.2 {~\mbox{Mpc}}$$ that is not representative of the LG (Garrison-Kimmel et al., 2014), so most of our results are based on 10 pairs (20 halos). In the Appendix, we compare our main results for the paired versus isolated halos. 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).

## Finding and tracking (sub)halos

\label{sec:subhalo}

ELVIS identifies dark-matter (sub)halos using the six-dimensional halo finder rockstar (Behroozi et al., 2013) and constructs merger trees using the consistent-trees algorithm (Behroozi et al., 2013a). For each halo that is not a subhalo (see below), we assign a virial mass, $${M_{\rm vir}}$$, and radius, $${R_{\rm vir}}$$, using the evolution of the virial relation from Bryan et al. (1998) for our $$\Lambda$$CDM cosmology. At $$z = 0$$, this corresponds to an overdensity of $$\Delta_{\rm critical} = 97~(\Delta_{\rm matter} = 363)$$ times the critical (matter) density, while at $$z \gtrsim 3$$ it assymptotes to $$\Delta_{\rm critical} \approx \Delta_{\rm matter} \approx 178$$.

We define a “host halo” as an isolated halo that can host subhalos within in, and a “subhalo” as a halo whose center is inside $${R_{\rm vir}}$$ of a more massive host halo. When a (sub)halo passes within $${R_{\rm vir}}$$ of a more massive 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, $${M_{\rm peak}}$$, as the maximum instantaneous mass that a (sub)halo ever reaches along the history of its primary progenitor. For subhalos, $${M_{\rm peak}}$$ almost always occurs before virial infall. As explored in Garrison-Kimmel et al. (2014), the resolution scale of ELVIS does not significantly affect its (sub)halo catalogs at (and even below) $${M_{\rm peak}}> 10 ^ 8 {~\mbox{M}_\odot}$$, the limit that we use in this work.

## Assigning stellar mass to (sub)halos

\label{sec:stellar_mass}

Our goal is to map luminous galaxies to the dark-matter (sub)halos in ELVIS. The relation between stellar mass and (sub)halo mass (or maximum circular velocity) for dwarf galaxies is highly uncertain, likely with significant scatter. This is especially true for our lowest-mass subhalos that (likely) host faint and ultra-faint galaxies; some of these subhalos may 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 (sub)halos in Garrison-Kimmel et al. (2014). This relation is based on that of Behroozi et al. (2013) but is modified at the low-mass end according to the observed stellar-mass function of Baldry et al. (2012). This modification better reproduces the dwarf galaxy population ($${M_{\rm star}}< 10 ^ 9 {~\mbox{M}_\odot}$$) of the LG in ELVIS (Garrison-Kimmel et al., 2014). At these mass scales, $${M_{\rm star}}\propto {M_{\rm peak}}^ {1.92}$$. When possible, we show results as a function of both $${M_{\rm star}}$$ and $${M_{\rm peak}}$$, given the uncertainties of abundance matching at these low masses.

In selecting the stellar-mass ratio for defining “major” groups or mergers in the histories of dwarf galaxies in Sections \ref{sec:preprocessing_v_mass} and \ref{sec:mergers}, 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 (for example, Leauthaud et al., 2012; Hudson et al., 2013), in addition to the lack of observational evidence to suggest otherwise. We define major mergers as those for which the stellar-mass ratio is greater than 0.1. This broadly corresponds to mass ratios at which the lower-mass companion is likely to have significant dynamical effect on the more massive galaxy (for example, Hopkins et al., 2010; Helmi et al., 2012; Yozin et al., 2012) and for which recent mergers are likely to be observable. Given our relation between stellar and (sub)halo mass, this corresponds to $${M_{\rm peak}}$$ ratios $$\gtrsim 0.3$$.

# Virial-Infall Times of Satellites

\label{sec:infall_time}

We start by investigating the virial-infall times of the satellite dwarf galaxy population at $$z = 0$$, to understand how long they have been satellites inside a host halo. This timescale has several important implications. First, it provides insight into how long satellites have experienced environmental processes that cause the observed depletion of gas, quenching of star formation, transition of morphology, and (potentially) stripping of stars, as compared with dwarf galaxies that are not satellites, such as those at the outskirts of the LG. Second, it tells us what fraction of satellites at $$z = 0$$ were satellites within a host halo during the epoch of cosmic reionization. This allow us to understand whether the differing physical effects of reionization and host-halo environment on surviving satellites occurred at distinct epochs in the formation histories of surviving satellites.

## Determining virial infall for satellites

\label{sec:infall_time_definition}

While environmental processes clearly affect satellite galaxies within $${R_{\rm vir}}$$ of the MW/M31 halos, whether such environmental processing occurs in lower-mass host halos ($${M_{\rm vir}}\ll 10 ^ {12} {~\mbox{M}_\odot}$$) 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 $${z_{\rm first\,infall}}$$ or time as $${t_{\rm first\,infall}}$$, with $${t_{\rm first\,infall}^{\rm since}}= t_{\rm now} - {t_{\rm first\,infall}}$$. We also examine “MW/M31 infall”: when a satellite first became a satellite in its host MW/M31 halo. We refer to this as $${z_{\rm MW/M31\,infall}}$$ or $${t_{\rm MW/M31\,infall}}$$, with $${t_{\rm MW/M31\,infall}^{\rm since}}= t_{\rm now} - {t_{\rm MW/M31\,infall}}$$.

## Dependence of virial-infall time on satellite mass

\label{sec:infall_time_v_mass}

We first examine how the virial-infall times of satellites at $$z = 0$$ depend on their mass. Figure \ref{fig:infall.time_v_mass} shows $${t_{\rm first\,infall}^{\rm since}}$$ (top) and $${t_{\rm MW/M31\,infall}^{\rm since}}$$ (bottom), or $${z_{\rm first\,infall}}$$ and $${z_{\rm MW/M31\,infall}}$$ on right axes, as a function of satellite $${M_{\rm star}}$$, or subhalo $${M_{\rm peak}}$$ on the top axes.

For both virial-infall metrics, lower-mass satellites fell in systematically earlier, though significant scatter persists at all masses. Such a trend with $${M_{\rm peak}}$$ (and thus $${M_{\rm star}}$$) is a natural result of hierarchical structure formation, for two reasons. First, halos of a given $${M_{\rm peak}}$$ are more common at later cosmic times, and $${M_{\rm peak}}$$, by its definition, typically remains unchanged for satellites after infall. Thus, higher-mass satellites are more likely to have formed, and subsequently fallen in, at later time. Second, satellites with higher $${M_{\rm peak}}$$ have shorter dynamical friction lifetimes (for fixed host-halo mass) before they tidally disrupt or merge with the host halo (Boylan-Kolchin et al., 2008; Jiang et al., 2008; Wetzel et al., 2010).

Our lowest-mass (ultra-faint) satellites first fell into any host halo typically $$\sim 10 {~\mbox{Gyr}}$$ ago at $$z \sim 1.7$$, and they first fell into the MW/M31 halo $$\sim 7.5 {~\mbox{Gyr}}$$ ago at $$z \sim 1$$. By contrast, our highest-mass satellites (corresponding to the LMC, SMC, NGC 205, M32) have $${t_{\rm first\,infall}^{\rm since}}\sim 6.5 {~\mbox{Gyr}}$$ ($${z_{\rm first\,infall}}\sim 0.8$$) and $${t_{\rm MW/M31\,infall}^{\rm since}}\sim 5 {~\mbox{Gyr}}$$ ($${z_{\rm MW/M31\,infall}}\sim 0.5$$). Thus, satellites at $$z = 0$$ first fell into any host halo $$1.5 - 2.5 {~\mbox{Gyr}}$$ before falling into the MW/M31 halo, a generic outcome of hierarchical structure formation, as we will examine further in Section \ref{sec:preprocessing_duration_mass}.

Overall, satellite dwarf galaxies at $$z = 0$$ typically have evolved as satellites 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.

panel 1

panel 2

\label{fig:infall.time_v_mass}

Time since virial infall for satellites at $$z = 0$$ as a function of their stellar mass, $${M_{\rm star}}$$, or peak halo mass, $${M_{\rm peak}}$$: time since first crossing within $${R_{\rm vir}}$$ of any host halo (top panel) or within $${R_{\rm vir}}$$ of the MW/M31 halo (bottom panel). Curves show median, shaded regions show 68%, 95%, and 99.7% of the distribution. Current satellites have been satellites typically for over half of their history, and lower-mass satellites fell in earlier, though with large scatter. The dotted line at $$z = 6$$ indicates the end of cosmic reionization. During reionization, $$< 4\%$$ of current satellites were a satellite in a host halo, and none were in the MW/M31 halo, demonstrating the effects of reionization and the host-halo environment are separable in time during satellites’ evolutionary histories.

## Dependence of virial-infall time on satellite distance

\label{sec:infall_time_v_distance}

We next explore how the above virial-infall times of satellites depend on their current distance to their MW/M31 host. Previous works examining satellites at higher mass scales in cosmological simulations showed that satellites at smaller distances tend to have fallen in earlier (Gao et al., 2004). This is because (1) $${R_{\rm vir}}$$ 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 of the LG would be important for several reasons. First, ultra-faint ($${M_{\rm star}}\lesssim 10 ^ 5 {~\mbox{M}_\odot}$$) satellites currently are observable only within the inner $$\sim 50 {~\mbox{kpc}}$$ of the MW halo, so it is possible that they had systematically earlier infall times than the median in Figure \ref{fig:infall.time_v_mass}. Second, such a correlation with distance could provide a statistical proxy for an environmental evolutionary sequence (since the time of infall) for the observable satellite population.

Figure \ref{fig:infall.time_v_distance} shows $${t_{\rm first\,infall}^{\rm since}}$$ (top row) and $${t_{\rm MW/M31\,infall}^{\rm since}}$$ (bottom row) as a function of distance to the host’s center, $$d$$, as scaled to the host’s virial radius, $${R_{\rm vir}}$$, at $$z = 0$$. We compute these quanities in bins of $$d / {R_{\rm vir}}$$ for each MW/M31 halo, and using that the median $${R_{\rm vir}}$$ across the MW/M31 halos is $$300 {~\mbox{kpc}}$$, we also show the (approximate) dependence on $$d$$ across the sample along the top axis. For both infall metrics and at all masses, satellites closer to the host center 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 change in $${t_{\rm first\,infall}^{\rm since}}$$ and $${t_{\rm MW/M31\,infall}^{\rm since}}$$ from $$d / {R_{\rm vir}}= 0$$ to 1 for massive satellites is $$6.5$$ and $$4.5 {~\mbox{Gyr}}$$, respectively, while for our lowest-mass satellites it is $$2.5$$ and $$4 {~\mbox{Gyr}}$$. 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 (ultra-faint) satellites, those in our smallest distance bin, where they are observable, experienced first infall typically $$\sim 11 {~\mbox{Gyr}}$$ ago at $$z \sim 2.2$$, and they first fell into the MW/M31 halo $$\sim 9 {~\mbox{Gyr}}$$ ago at $$z \sim 1.5$$, so these are slightly earlier than Figure \ref{fig:infall.time_v_mass}.

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 $$z = 0$$ can provide a proxy for an environmental evolutionary sequence, especially for more massive satellites. However, we note one caveat: despite the correlation with distance, satellites currently near $${R_{\rm vir}}$$ have been satellites for quite a while, on average, for $$3 - 8 {~\mbox{Gyr}}$$, being higher at lower mass. Thus, the satellite population near $${R_{\rm vir}}$$ is not just a recently infalling population, but rather, is a superposition of infalling satellites with those that are at/near apocenter, having already experienced one or more pericentric passages. Note that a given satellite spends most of its orbital time near apocenter. (For reference, the virial crossing time, $${R_{\rm vir}}/ {V_{\rm vir}}$$, is $$\sim 2 {~\mbox{Gyr}}$$ at $$z = 0$$.)

panel 1a
panel 1b
panel 1c
panel 2a
panel 2b

panel 2c

\label{fig:infall.time_v_distance}

Time since virial infall for satellites at $$z = 0$$ as a function of their distance to their host’s center, $$d$$, scaled to the host’s virial radius, $${R_{\rm vir}}$$, at $$z = 0$$: time since first crossing within $${R_{\rm vir}}(z)$$ of any host halo (top panels) or within $${R_{\rm vir}}(z)$$ of the MW/M31 halo (bottom panels). The median $${R_{\rm vir}}$$ for the MW/M31 halos at $$z = 0$$ is $$300 {~\mbox{kpc}}$$. Curves shows the median, shaded regions show 68%, 95%, and 99.7% of the distribution. At all masses, satellites closer to host center fell in earlier, though with significant scatter. Dotted line at $$z = 6$$ indicates the end of cosmic reionization. Even for the lowest-mass (ultra-faint) satellites at the smallest distance bin, where they are observable, $$< 4\%$$ were a satellite in any host halo during reinization, and none were in the MW/M31 halo during reionization.

## Implications for dwarf galaxies during cosmic reionization

\label{sec:reionization}

The virial-infall times in Figures \ref{fig:infall.time_v_mass} and \ref{fig:infall.time_v_distance} have important implications for understanding the relative effects of cosmic reionization versus host-halo environment on surviving satellite dwarf galaxies, in particular, whether the effects of these two processes occurred at distinct epochs during the formation histories of these satellites. In these figures, the dashed line at $$z = 6$$ represents the end of cosmic reionization as constrained by various observations (for example, Robertson et al., 2013, and references therein). Across all masses and distances, none of the satellites at $$z = 0$$ were within $${R_{\rm vir}}$$ of their MW/M31 halo any time during reionization. Furthermore, $$< 4\%$$ were within $${R_{\rm vir}}$$ of any host halo during reionization. There are scales where this fraction is somewhat higher, the highest being 10% for satellites at $${M_{\rm star}}= 10 ^ {5 - 8} {~\mbox{M}_\odot}$$ and $$d / {R_{\rm vir}}< 0.1$$, but this fraction is typically only a few percent across our range of mass and distance.

Thus, essentially none of the satellite dwarf galaxies in the LG were within $${R_{\rm vir}}$$ 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 host halos at $$z = 0$$ and trace them back to $$z > 6$$, when almost all were isolated (non-satellite) halos. (We are able to track all satellite (sub)halos back to $$z > 6$$, except for 6% of those at $${M_{\rm star}}< 10 ^ 4 {~\mbox{M}_\odot}$$, which formed after $$z = 6$$.) At all $$z > 6$$ (for which ELVIS contains 6 snapshots), we then compute the nearest distance, $$d_{\rm nearest}$$, 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 \ref{fig:nearest_distance_reionization} shows the cumulative distribution of $$d_{\rm nearest}$$ in comoving units (top panel) and scaled to $${R_{\rm vir}}$$ of the nearest more massive halo (bottom panel). The thick solid curve shows the average across all paired MW/M31 halos, for all satellites across our mass range, $${M_{\rm star}}= 10 ^ {3 - 9} {~\mbox{M}_\odot}$$. Interestingly, we find no significant dependence of this quantity on satellite mass. The typical $$d_{\rm nearest}$$ at $$z > 6$$ was considerable: $$3 {~\mbox{Mpc}}$$ comoving ($$\sim 400 {~\mbox{kpc}}$$ physical), or $$500 \, {R_{\rm vir}}$$. Moreover, only $$\approx 5\%$$ of these dwarf galaxies came within $$1 {~\mbox{Mpc}}$$ comoving, or $$100 \, {R_{\rm vir}}$$, of a more massive halo. The thin solid curves show the values for each MW/M31 pair, highlighting the factor of $$\sim 2$$ 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. If strong environmental effects (aside from reionization) on dwarf galaxies are confined to within $${R_{\rm vir}}$$ (or even somewhat larger) of a host halo at these redshifts, then the results of Figures \ref{fig:infall.time_v_mass}, \ref{fig:infall.time_v_distance}, and \ref{fig:nearest_distance_reionization} indicate that such environmental processing occurred only at $$z < 6$$ 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, beacuse a strong transition in morphology, star formation, and gas content of dwarf galaxies, as induced by environmental host-halo processing, occurs only within $$\approx 300 {~\mbox{kpc}}$$ ($$\approx {R_{\rm vir}}$$) of the MW or M31.

Given that cosmic reionization ended by $$z = 6$$, we conclude that the effects of reionization occurred well before those of the host-halo environment during the formation histories of surviving dwarf galaxies in the LG. These results strongly support the use of faint and ultra-faint satellites as probes of reionization, for example, by measure its (potential) effects on their star-formation histories as derived from their current stellar populations (for example, Weisz et al., 2014; Brown et al., 2014): any features (such as quenching) in the star-formation histories at $$z \gtrsim 6$$ could not have been caused by the host-halo environment. Moreover, given that most ($$\approx 84\%$$) surviving satellites fell into a host halo much later at $$z \lesssim 3$$, any common features that are measured to have occured at least at $$z > 3$$ for a significant population of satellites in the LG also would provide strong evidence for the effects of reionization.

panel 1.

panel 2.

\label{fig:nearest_distance_reionization}

For all satellites with $${M_{\rm star}}= 10 ^ {3 - 9} {~\mbox{M}_\odot}$$ at $$z = 0$$, cumulative distribution of the distance to the nearest, more massive halo, $$d_{\rm nearest}$$, that they experienced during cosmic reionization ($$z > 6$$). Top panel shows comoving distance, and bottom panel shows this distance scaled to $${R_{\rm vir}}$$ of the nearest halo. Solid thick curve shows average over all satellites in the paired MW/M31 halos, while thin curves shows satellites in each pair, to indicate the pair-to-pair scatter. We find no dependence on satellite mass. The typical distance was $$3 {~\mbox{Mpc}}$$ comoving ($$\sim 400 {~\mbox{kpc}}$$ physical), or $$500 \, {R_{\rm vir}}$$. At these distances, dwarf galaxies in the Local Group at $$z = 0$$ do not show strong environmental influence. These results strongly support that the effects of reionization and host-halo environment occurred at distinct epochs and thus are separable in time during the histories of satellites at $$z = 0$$. For comparison, dotted curve shows the average across the isolated MW/M31 halos, whose satellites experienced $$\sim 1/2$$ the distance (see Appendix).

# Group Infall and Preprocessing

\label{sec:preprocessing}

In the previous section, we showed that many satellite dwarf galaxies first became satellites significantly prior to falling into the MW/M31 halo. Thus, many satellites spent significant time in another host halo, which may environmentally “preprocesse” them prior to their joining the MW/M31 halo. We now explore what fraction of all satellites at $$z = 0$$ were preprocessed as a satellite in another host halo (group) prior to falling into the MW/M31 halo. We examine two such metrics: the fraction of all current satellites that were a satellite in another host halo (1) any time before falling into the MW/M31 halo, or (2) at the time of falling into the MW/M31 halo. The difference between these is driven by “ejected” or “backsplash” satellites that fell into another host halo and then orbited out beyond its $${R_{\rm vir}}$$ before falling inside $${R_{\rm vir}}$$ of the MW/M31 halo. Recent work indicates that these satellites are affected environmentally in similar ways as satellites that remain within $${R_{\rm vir}}$$ (for example, Ludlow et al., 2009; Knebe et al., 2011; Teyssier et al., 2012; Bahé et al., 2013; Wetzel et al., 2014). Thus, we examine both preprocessing metrics.

## Dependence of group preprocessing on satellite mass

\label{sec:preprocessing_v_mass}

Figure \ref{fig:infall.fraction_v_mass} (top) shows both of the above preprocessed fractions as a function of satellite $${M_{\rm star}}$$, or $${M_{\rm peak}}$$ on top axis. First, the red short-dashed curve shows the fraction 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 ultra-faint satellites were in a group when they fell into the MW/M31 halo.

Second, the blue long-dashed curve shows the fraction 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 $${R_{\rm vir}}$$ of their preprocessing group. Thus, 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 ultra-faint satellites. Thus, half of all satellite dwarf galaxies with $${M_{\rm star}}< 10 ^ 6 {~\mbox{M}_\odot}$$ 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 $${M_{\rm star}}$$ differs by less than a factor of 10, as detailed in Section \ref{sec:stellar_mass}). Figure \ref{fig:infall.fraction_v_mass} (bottom) shows this fraction via the green long-short-dashed curve. This fraction is $$5 - 10\%$$ across our mass range and increases only weakly with mass. The dependene on mass is weak because of the combination of (1) a nearly mass-independent distribution of $$M_{\rm peak,\,satellite} / M_{\rm peak,\,host}$$ in $$\Lambda$$CDM, (2) our power-law $${M_{\rm star}}- {M_{\rm peak}}$$ relation, and (3) our requirement that $$M_{\rm star,\,satellite} / M_{\rm star,\,host} > 0.1$$.

For comparison, Figure \ref{fig:infall.fraction_v_mass} (bottom) also shows the same red short-dashed curve as in Figure \ref{fig:infall.fraction_v_mass} (top). The fraction that hosted a satellite is much lower than the fraction that were a satellite, which means that most satellites that fell in as part of a group did so in a host halo that was significantly more massive than itself (see also Figure \ref{sec:preprocessing_duration_mass}).

The black dot-dashed curve in Figure \ref{fig:infall.fraction_v_mass} (bottom) 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.

panel 1

panel 2

\label{fig:infall.fraction_v_mass}

Fraction of all satellites at $$z = 0$$ that experienced various aspects of group preprocessing prior to falling into the current MW/M31 halo, as a function of satellite stellar mass, $${M_{\rm star}}$$, or subhalo peak mass, $${M_{\rm peak}}$$. Top: Fraction that were a satellite in a group any time prior to (blue long-dashed) or at the time of (red short-dashed) falling into the MW/M31 halo. Curves show average over all paired MW/M31 halos, while shaded regions show standard deviation from halo-to-halo scatter. The difference between the two curves is driven by ejected/backsplash satellites that were once within another host halo but then orbited beyond its $${R_{\rm vir}}$$. Lower-mass satellites are much more likely to have been preprocessed in a group: over half of the lowest-mass (ultra-faint) satellites were. Bottom: Red short-dashed curve shows shows same as above, while green long-short-dashed curve shows the fraction that were the central (most massive) galaxy in a group that contained a major satellite (at least 0.1 times the central’s $${M_{\rm star}}$$) at the time of falling into the MW/M31 halo. Black dot-dashed curve show the sum of the two curves.

## Dependence of group preprocessing on satellite distance

\label{sec:preprocessing_v_distance}

We next explore how the above group-preprocessed fractions vary with the current distance of the satellites from their host. Figure \ref{fig:infall.fraction_v_distance} (top and bottom) show the same preprocessed fractions as in Figure \ref{fig:infall.fraction_v_mass} (top), but as a function of $$d / {R_{\rm vir}}$$ at $$z = 0$$, similar to Figure \ref{fig:infall.time_v_distance}. Again, we compute these quanities in bins of $$d / {R_{\rm vir}}$$ for each MW/M31 halo, though we also show the dependence on $$d$$ (using the median $${R_{\rm vir}}$$ across the MW/M31 halos) along the top axis. 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 $$d / {R_{\rm vir}}= 1$$ to 0.1 for low-mass satellites. Most likely, this gradient arises because satellites that fell in as part of a group remained bound to that (more massive) group for some time after infall, so they experienced more efficient dynamical friction that dragged them to the center of the MW/M31 halo more rapidly.

Thus, given that faint and ultra-faint satellite galaxies are observable only at small distances within the MW halo, most likely about half of them were satellites in another group before / during falling into the MW halo.

panel 1

panel 2

\label{fig:infall.fraction_v_distance}

Fraction of all satellites at $$z = 0$$ that were a satellite in another host halo any time prior to (top) or at the time of (bottom) falling into the MW/M31 halo, as a function of their current distance to host center, $$d$$, scaled to the host’s current virial radius, $${R_{\rm vir}}$$. The median $${R_{\rm vir}}$$ for the MW/M31 halos at $$z = 0$$ is $$300 {~\mbox{kpc}}$$. Curves show average over all paired MW/M31 halos in bins of satellite $${M_{\rm star}}$$, and error bars show 68% uncertainty in this fraction for a beta distribution (the halo-to-halo scatter is similar to Figure \ref{fig:infall.fraction_v_mass}). For both group-preprocessing metrics, and at across all masses, satelltes closer to the host center are more likely to have been preprocessed.

## Duration and host-halo mass of group preprocessing

\label{sec:preprocessing_duration_mass}

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 importance on their evolution.

Figure \ref{fig:preprocessing_time_mass_v_mass} (top) shows the distribution of the (maximum) host-halo mass that satellites were in during their group preprocessing as a function of their current $${M_{\rm star}}$$, or subhalo $${M_{\rm peak}}$$. The typical preprocessing host halo had $${M_{\rm vir}}\sim 10 ^ {11} {~\mbox{M}_\odot}$$, with 68% spread of $$10 ^ {10 - 12} {~\mbox{M}_\odot}$$, largely independent of satellite mass, though with scatter to lower host-halo masses at lower $${M_{\rm star}}$$. About half of satellites were preprocessed in a host halo that does not survive to $$z = 0$$, but instead falls into the MW/M31 halo and merges/disrupts, and this accounts for most of the preprocessing hosts with $${M_{\rm vir}}> 10 ^ {11.5} {~\mbox{M}_\odot}$$ in Figure \ref{fig:preprocessing_time_mass_v_mass} (top).

Some of these satellites were preprocessed by the other of the paired MW/M31 halos, that is, fell into one of the MW/M31 halos, orbited beyond its $${R_{\rm vir}}$$, and then fell into the paired MW/M31 halo. However, these satellites account for $$< 2\%$$ of all preprocessed satellites across our mass range, in rough agreement with Knebe et al. (2011). Thus, we conclude that this is not a particularly important population.

Figure \ref{fig:preprocessing_time_mass_v_mass} (bottom) shows the distribution of the time that satellites spent in their preprocessing host halo. The typical preprocessing time was $$\sim 1.2 {~\mbox{Gyr}}$$, with 68% spread of $$0.5 - 3.5 {~\mbox{Gyr}}$$, with weak dependence on satellite mass. However, at $${M_{\rm star}}> 10 ^ 7 {~\mbox{M}_\odot}$$, no satellites were preprocessed longer than $$1.8 {~\mbox{Gyr}}$$, while at $${M_{\rm star}}< 10 ^ 7 {~\mbox{M}_\odot}$$, the scatter increases significantly, with some satellites having experienced up to $$7 {~\mbox{Gyr}}$$ of preprocessing. The small preprocessing durations at $${M_{\rm star}}> 10 ^ 7 {~\mbox{M}_\odot}$$ likely arises because those satellites have $${M_{\rm peak}}$$ that approaches that of their preprocessing host-halo in Figure \ref{fig:preprocessing_time_mass_v_mass} (top), corresponding to shorter dynamical friction lifetimes. Thus, massive satellites could not have been preprocessed too long without merging/disrupting within their preprocessing host.

Overall, most preprocessing occurred within groups of $${M_{\rm vir}}= 10 ^ {10 - 12} {~\mbox{M}_\odot}$$, masses that feasibly could influence satellite dwarfs galaxies, though environmental effects at these masses remain poorly understood. Furthermore, the typical preprocessing duration was $$0.5 - 3.5 {~\mbox{Gyr}}$$, comparable to typical timescales over which satellite dwarf galaxies are environmentally quenched (Wetzel et al., in prep.). 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.

panel 1

\label{fig:preprocessing_time_mass_v_mass}

For satellites that were preprocessed in a group before falling into the MW/M31 halo, the maximum host-halo mass experienced during preprocessing (top) and the total duration of preprocessing (bottom), as a function of satellite stellar mass, $${M_{\rm star}}$$, or subhalo peak mass, $${M_{\rm peak}}$$. Solid curves shows median, shaded regions show 68, 95, 99.7% of the distribution. Most group preprocessing occurred in host halos with $${M_{\rm vir}}= 10 ^ {10 - 12} {~\mbox{M}_\odot}$$, masses at which environmental effects are feasible, though poorly understood. The typical group preprocessing duration was $$0.5 - 3.5 {~\mbox{Gyr}}$$, though some satellites at $${M_{\rm star}}< 10 ^ 7 {~\mbox{M}_\odot}$$ experienced significantly longer duration.

# Group Infall Drives Satellite-Satellite Mergers

\label{sec:mergers}

In Deason et al. (2014), we showed that most ($$> 70\%$$) satellites in the LG experienced a major merger ($${M_{\rm star}}$$ ratio greater than 0.1) during their history. While most mergers occurred prior to falling into the MW/M31 halo, a significant fraction were satellite-satellite mergers after infall. Almost all of the latter occurred rapidly after falling in the MW/M31 halo , which suggests that such mergers occurred between satellites with correlated infall histories (for example, Li et al., 2008; Angulo et al., 2009; Wetzel et al., 2009; Wetzel et al., 2009a), in particular, that were part of the same group at infall. We now demonstrate that group infall drives most satellite-satellite mergers.

Figure \ref{fig:mergers} shows, for all satellites that experienced a major merger after falling into the MW/M31 halo, what fraction occurred between galaxies that fell into the MW/M31 halo in the same group, as a function of the time since the last major merger, $$T_{\rm LMM}$$. To address the limited statistics of major mergers, unlike in the rest of this paper, we combine all 48 paired and isolated MW/M31 halos in ELVIS, and we bin all satellites across $${M_{\rm star}}= 10 ^ {3 - 9} {~\mbox{M}_\odot}$$, given that we do not find any significant dependence on satellite mass.

The majority ($$60 - 90\%$$) of all satellite-satellite major mergers occured between two galaxies that were in the same group when they fell into the MW/M31 halo. Such group infall drives a somewhat lower fraction of mergers at later cosmic times. This likely relates to the larger delay time between MW/M31 infall and merging at later cosmic time (citation not found: Deason2014), which suggests that satellites have more opportunity to experience a “chance” merger with another satellite in the MW/M31 halo at later time.

Overall, in addition to driving preprocessing before falling into the MW/M31 halo, group infall is also an important catalyst for major mergers between satellite galaxies after they fall into the MW/M31 halo.

\label{fig:mergers}

For all satellites at $$z = 0$$ with $${M_{\rm star}}= 10 ^ {3 - 9} {~\mbox{M}_\odot}$$ that experienced a major merger with another satellite after falling into the MW/M31 halo, the fraction of such mergers that fell in as part of the same host halo (group), as a function of the time since the last major merger, $$T_{\rm LMM}$$, or redshift of major merger, $$z_{\rm LMM}$$, on top axis. We do not find any significant dependence on satellite mass. Infalling groups drive the majority ($$60 - 90\%$$) of all satellite-satellite mergers.

# Summary and discussion

\label{sec:summary_discussion}

## Summary

\label{sec:summary}

Using the ELVIS suite of cosmological zoom-in dissipationless simulations, we examined the virial-infall histories and group preprocessing of satellites across the observable range of dwarf galaxy masses, $${M_{\rm star}}= 10 ^ {3 - 9} {~\mbox{M}_\odot}$$. While we examined all 48 MW/M31 halos in ELVIS, we focused on the 20 paired MW/M31 halos that most resemble the Local Group, thus providing good statistics in a realistic cosmic setting. We summarize our primary results as follows.

Virial-infall histories: satellites at $$z = 0$$ fell into the MW/M31 halo typically $$5 - 8 {~\mbox{Gyr}}$$ ago at $$z = 0.5 - 1$$, though they first fell into any host halo typically $$7 - 10 {~\mbox{Gyr}}$$ 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.

Group preprocesssing: a large fraction of satellites were a satellite in a group(another host halo), typically of $${M_{\rm vir}}\sim 10 ^ {10 - 12} {~\mbox{M}_\odot}$$, for a duration of $$0.5 - 3.5 {~\mbox{Gyr}}$$, before falling into the MW/M31 halo. This group preprocessing is especially common among faint and ultra-faint satellites: at $${M_{\rm star}}\lesssim 10 ^ 6 {~\mbox{M}_\odot}$$, $$\approx 30\%$$ of all satellites fell into the MW/M31 halo as a satellite in a group, and half of all satellites were in a group any time before falling into the MW/M31 halo. Satellites closer to the center of the MW/M31 are more likely to have experienced group preprocessing.

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. (2014).

Cosmic reionization: none of the surviving satellties were within their MW/M31 halo during reionization ($$z > 6$$), and only $$< 4\%$$ were within the virial radius of any host halo during reionization. Furthermore, the typical distances to the nearest more massive halo at $$z > 6$$ was $$3 {~\mbox{Mpc}}$$ comoving ($$\sim 400 {~\mbox{kpc}}$$ physical), or $$500 \, {R_{\rm vir}}$$. Thus, the effects of cosmic reionization versus host-halo environment on the formation histories of surviving dwarf galaxies in the Local Group occurred at distinct epochs and are separable in time.

## Discussion

\label{sec:discussion}

### Impact of group preprocessing on the evolution of dwarf galaxies

The significant fraction of satellite dwarf galaxies that experienced group preprocessing may help to explain the near-unity fraction of observed satellites that have spheroidal morphology, little-to-no cold gas, and quiescent star formation. However, this depends on the extent to which the environmental processes that we described in the Introduction operate within low-mass groups of $${M_{\rm vir}}< 10 ^ {12} {~\mbox{M}_\odot}$$. If there is a lower limit in virial mass below which host halos do not significantly affect their satellites, then group preprocessing, even if common, many not be a particularly important regulator of the evolution of dwarf galaxies. Because such low-mass groups necessarily are composed of faint galaxies, few observational works have probed the detailed properties of the satellties of such systems, though there are now ongoing efforts (for example, Stierwalt et al., 2014). Additionally, few theoretical works have examined the details of environmental effects in lower-mass host halos, for example, in hydrodynamic simulations. Based on our results, these would be fruitful areas for future investigations.

### Implications for observed associations of satellite galaxies

Our significant fraction (up to $$1 / 3$$) of satellite dwarf galaxies that fell in as part of the same group agrees well with Li et al. (2008), based on a cosmological simulation of a single MW-like halo. Group infall may help to explain the many oberved associations between satellite galaxies (and stellar streams) within the halos of the MW and M31. While we did not examine in detail the phase-space distribution at $$z = 0$$ of our group-infall satellites, Li et al. (2008) showed that infalling groups can remain coherent and share similar orbital planes for up to $$\sim 8 {~\mbox{Gyr}}$$ (see also, Klimentowski et al., 2010; Sales et al., 2011; Slater et al., 2013), which, given our results, is the typical amount of time that satellites have been within the MW/M31 halo.

Observational evidence for associations between dwarf galaxies in the LG dates back to Lynden-Bell (1982), who demonstrated that the satellites in the MW halo appear situated along two great “streams”: the Magellanic stream and the Fornax-Leo-Sculptor stream. The discovery of faint and ultra-faint ($$L \lesssim 10 ^ 5 L_\odot$$) galaxies around the MW (Willman et al., 2005; Belokurov et al., 2006b; Belokurov et al., 2007a) led to further evidence for such galatic associations. For example, the two ultra-faint galaxies Leo IV and Leo V are separated by $$\sim 3$$ degrees on the sky, with small offsets in both distance and velocity (see Fattahi et al., 2013, for more discussion of such pairs). Moreover, many works continue to explore (and debate) the presence of a planar, disk-like distribution of satellites around both the MW and M31 (for example, Libeskind et al., 2005; Deason et al., 2011; Lovell et al., 2011; Fattahi et al., 2013; Ibata et al., 2013), which could be the result of one (or more) infalling groups. Our results also fully support the likelihood that the SMC was bound to the LMC in a group prior to MW infall (Kallivayalil et al., 2013).

Beyond associations between galaxies, we also note many observed association between galaxies, stellar streams, and/or structures in the stellar halo. For example, (Newberg 2010) showed that the Orphan stellar stream (Grillmair, 2006; Belokurov et al., 2007b) has a similar distance, velocity, and position as Segue 1. Likewise, the proximity of Boötes II, in both position and velocity, with the Sagittarius stream led Koch et al. (2009) to suggest that Boötes II may have been stripped from the more massive Sagittarius dwarf. In addition, Deason et al. (2014)a (see also Belokurov et al., 2009) showed that Segue 2, which is perhaps the least-massive known galaxy (Kirby et al., 2013a), is likely associated with the large, metal-rich Triangulum-Andromeda overdensity, and Kirby et al. (2013b) showed that Segue 2 lies off of the tight mass-metallicity relation for most dwarf galaxies, which may be indicative of group infall. We reiterate that in about half of our cases of group infall, the lower-mass satellite from the group survives in the MW/M31 halo while the more massive (primary) galaxy from the group merges/disrupts, which could lead to such observable associations between (surviving) dwarf galaxies and (disrupted) stellar streams. Overall, the enhanced evidence for associations between the lowest-mass satellites agrees well with our predictions (Figure \ref{fig:infall.fraction_v_mass}), and ongoing/upcoming observations such as the Dark Energy Survey, the Hyper Suprime-Cam Survey, LSST and the Gaia satellite will confirm such associations and/or reveal new ones.

### Effects of resolution and baryonic physics

One potential concern of our results is that the survivability lifetime of a satellite depends on how well the simulation resolves it, which might lead to prematurely merging/disrupting (as compared with a real galaxy) of especially a low-mass satellite that fell in at high redshift, and thus virial-infall times for the surviving population at $$z = 0$$ that are biased to lower redshifts. However, using the three isolated MW/M31 halos in ELVIS that were re-run at $$2 \times$$ higher spatial and $$8 \times$$ higher mass resolution, we checked that the virial-infall times do change change significantly in these higher-resolution runs. This agrees with the resolution tests in Garrison-Kimmel et al. (2014), which demonstrated the completeness of the satellite population at our mass range, $${M_{\rm peak}}> 10 ^ 8 {~\mbox{M}_\odot}$$.

A more significant concern is that ELVIS simulates only the gravitational dynamics of dark matter, and baryonic effects may change the survivability and stellar content of satellite subhalos, in at least two ways. First, we assumed that all subhalos with $${M_{\rm peak}}> 10 ^ 8 {~\mbox{M}_\odot}$$ host luminous galaxies, according to abundance matching against $${M_{\rm peak}}$$, regardless of when the (sub)halos formed. We emphasize that this approach is largely consistent with the observed mass function of satellites in the LG (Garrison-Kimmel et al., 2014), especially if one accounts for observational incompleteness (Tollerud et al., 2008; Hargis et al., 2014), and even if not all subhalos host luminous galaxies, this would not bias our results if it were largely stochastic. However, some recent results from cosmological hydrodynamic simulations (Sawala et al., 2014) suggest that the subhalos that do host luminous galaxies are the ones that formed preferentially earlier, when they had deeper potential wells. If true, then it would shift the virial-infall times of surviving, luminous satellites to have occurred at higher redshifts. Second, the addition of the baryonic disk of the host galaxy can lead to more rapid disruption of satellites through tidal shocking or resonant stripping (Mayer et al., 2001; D’Onghia et al., 2010; Zolotov et al., 2012). If a strong effect, then our dark-matter simulations would overestimate how long satellites survive after infall, and the virial-infall times of surviving satellites would need to shift to lower redshifts. Thus, the combination of all potential baryonic effects could shift our results in either direction, and future work should elucidate these trends with statistical samples of baryonic simulations. We emphasize, though, that we do not expect that these baryonic effects would alter our results regarding reionization.

We thank the Aspen Center for Physics, supported in part by the National Science Foundation, for the hospitality and stimulating environment during the preparation of this paper. We thank Erik Tollerud, Dan Weisz, Laura Sales, and ... for useful discussions. AJD is currently supported by NASA through Hubble Fellowship grant HST-HF-51302.01, awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555.

# Appendix

While we have presented results using just the paired MW/M31 halos in ELVIS, here we compare our main results—virial-infall times and group preprocessed fractions—for satellites in the isolated versus paired MW/M31 halos. This comparison is useful for a number of reasons. First, theoretically, it is interesting to understand the degree to which the larger-scale environment around a MW/M31 halo influences the infall histories of its satellite population. This comparison also informs whether theoretical models need to consider separately the satellite populations of paired versus isolated MW/M31 halos, for example, in order to understand satellites in the LG as opposed to in isolated MW/M31-like galaxies in the local volume.

Figure \ref{fig:infall.time_v_mass_isolated} shows $${t_{\rm first\,infall}^{\rm since}}$$ (top) and $${t_{\rm MW/M31\,infall}^{\rm since}}$$ (bottom) as a function of satellite $${M_{\rm star}}$$, or subhalo $${M_{\rm peak}}$$, similar to Figure \ref{fig:infall.time_v_mass}, but for the isolated MW/M31 halos. For comparison, dashed curves show the median values for the paired MW/M31 halos from Figure \ref{fig:infall.time_v_mass}. While satellites in paired MW/M31 halos first fell into any host halo slightly earlier, any such difference is small compared to the large scatter. Thus, we conclude that the virial-infall times of satellites do not depend significantly on whether their host halo is isolated or paired like the LG.

Similar to Figure \ref{fig:infall.fraction_v_mass} (top), Figure \ref{fig:infall.fraction_v_mass_isolated} shows the fraction of all satellites at $$z = 0$$ that were a satellite in another host halo any time before falling into the MW/M31 halo, or at the time of falling into the MW/M31 halo, as a function of satellite mass. For comparison, the light dashed curves show the averages for the paired MW/M31 halos from Figure \ref{fig:infall.fraction_v_mass} (top). Here, differences between paired versus isolated MW/M31 halos are stronger, such that low-mass satellites are more likely to have been preprocessed if they are in paired MW/M31 halos, at a level comparable to the halo-to-halo standard deviation. This trend reverses slightly at higher mass, but here the difference is much smaller than the large scatter, so we do not consider it significant.

Most likely, the higher preprocessed fractions for satellites in the paired MW/M31 halos arises because, as Garrison-Kimmel et al. (2014) noted, the paired MW/M31 halos have many more neighboring host halos within a few Mpc of them than the isolated MW/M31 halos, because the paired MW/M31 halos (almost by definition) reside in a preferentially higher-mass cosmic region. With more neighboring host halos around, the low-mass halos that end up as satellites in the paired MW/M31 halos are more likely first to have fallen into a neighboring host halo and be preprocessed. However, this difference in preprocessed fraction does not lead to a significant difference in infall times in Figure \ref{fig:infall.fraction_v_mass_isolated}, so while group preprocessing is more prevalent for the paired MW/M31 halos, the duration of this preprocessing is not longer.

Finally, the most significant difference that we find between the satellites in paired versus isolated MW/M31 halos was in Figure \ref{fig:nearest_distance_reionization}: during the epoch of reionization ($$z > 6$$), the progenitors of the satellites in the isolated MW/M31 halos were much ($$\sim 2 \times$$) closer to their nearest neighboring, more massive halo than those in the paired MW/M31 halos. This result may seem counterintuitive, given that the paired MW/M31 halos contain many more neighboring host halos at $$z = 0$$. However, we find that these structures were diluted over a much larger volume at $$z > 6$$ for the paired halos. Specifically, we randomly sub-sample all particles within $${R_{\rm vir}}$$ of each MW/M31 halo at $$z = 0$$ and trace their locations back to $$z > 6$$, finding that the Lagrangian volume that contains all such particles was many ($$2 - 6$$) times larger for the paired MW/M31 halos. Thus, the satellite progenitors from the paired MW/M31 halos had fewer neighboring halos at a given distance at $$z > 6$$ than those from the isolated MW/M31 halos.

panel 1

panel 2.

\label{fig:infall.time_v_mass_isolated}

Same as Figure \ref{fig:infall.time_v_mass}, but for satellites in the 24 isolated MW/M31 halos, which are matched in mass to the LG-like paired MW/M31 halos. For comparison, dashed curves show the median values from the paired halos from Figure \ref{fig:infall.time_v_mass}. We find no significant differences in the virial-infall times of satellites in the paired versus isolated MW/M31 halos.

\label{fig:infall.fraction_v_mass_isolated}

Same as Figure \ref{fig:infall.fraction_v_mass}, but for satellites in the isolated MW/M31 halos, which are matched in mass to the LG-like paired MW/M31 halos. For comparison, light dashed curves show the averages from the paired halos from Figure \ref{fig:infall.fraction_v_mass}. For low-mass satellites, those in the paired MW/M31 halos are more likely to have been preprocessed as a satellite before/while falling into the MW/M31 halo, at a level that is comparable to the standard deviation. For high-mass satellites, any differences are well within the standard deviation.

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