Cosmic M\'enage \`a Trois: The Origin of Satellite Galaxies On Extreme Orbits

We examine the orbits of satellite galaxies identified in a suite of N-body/gasdynamical simulations of the formation of $L_*$ galaxies in a LCDM universe. Most satellites follow conventional orbits; after turning around, they accrete into their host halo and settle on orbits whose apocentric radii are steadily eroded by dynamical friction. However, a number of outliers are also present, we find that ~1/3 of satellites identified at $z=0$ are on unorthodox orbits, with apocenters that exceed their turnaround radii. This population of satellites on extreme orbits consists typically of the faint member of a satellite pair that has been ejected onto a highly-energetic orbit during its first approach to the primary. Since the concurrent accretion of multiple satellite systems is a defining feature of hierarchical models of galaxy formation, we speculate that this three-body ejection mechanism may be the origin of (i) some of the newly discovered high-speed satellites around M31 (such as Andromeda XIV); (ii) some of the distant fast-receding Local Group members, such as Leo I; and (iii) the oddly isolated dwarf spheroidals Cetus and Tucana in the outskirts of the Local Group. Our results suggest that care must be exercised when using the orbits of the most weakly bound satellites to place constraints on the total mass of the Local Group.


INTRODUCTION
The study of Local Group satellite galaxies has been revolutionized by digital imaging surveys of large areas of the sky. More than a dozen new satellites have been discovered in the past couple of years (Zucker et al. 2004Willman et al. 2005;Martin et al. 2006;Belokurov et al. 2006Belokurov et al. , 2007Majewski et al. 2007), due in large part to the completion of the Sloan Digital Sky Survey (York et al. 2000;Strauss et al. 2002) and to concerted cam-⋆ Fellow of the Canadian Institute for Advanced Research. paigns designed to image in detail the Andromeda galaxy and its immediate surroundings (Ibata et al. 2001;Ferguson et al. 2002;Reitzel & Guhathakurta 2002;McConnachie et al. 2003;Rich et al. 2004;Guhathakurta et al. 2006;Gilbert et al. 2006;Chapman et al. 2006, Ibata et al. 2007. The newly discovered satellites have extended the faint-end of the galaxy luminosity function down to roughly ∼ 10 3 L⊙, and are likely to provide important constraints regarding the mechanisms responsible for "lighting up" the baryons in low-mass halos. These, in turn, will serve to validate (or falsify) the various theoretical models attempting to reconcile the wealth of "substructure" predicted in cold dark matter (CDM) halos with the scarcity of luminous satellites in the Local Group (see, e.g. Klypin et al. 1999;Bullock et al. 2000;Benson et al. 2002;Stoehr et al. 2002;Kazantzidis et al. 2004;Kravtsov et al. 2004;Penarrubia et al. 2007).
At the same time, once velocities and distances are secured for the newly-discovered satellites, dynamical studies of the total mass and spatial extent of the Local Group will gain new impetus. These studies have a long history (Little & Tremaine 1987;Zaritsky et al. 1989;Kochanek 1996;Wilkinson & Evans 1999;Evans & Wilkinson 2000;Battaglia et al. 2005), but their results have traditionally been regarded as tentative rather than conclusive, particularly because of the small number of objects involved, as well as the sensitivity of the results to the inclusion (or omission) of one or two objects with large velocities and/or distances (Zaritsky et al. 1989;Kochanek 1996;Sakamoto et al. 2003). An enlarged satellite sample will likely make the conclusions of satellite dynamical studies more compelling and robust.
To this end, most theoretical work typically assumes that satellites are in equilibrium, and use crafty techniques to overcome the limitations of small-N statistics when applying Jeans' equations to estimate masses (see, e.g., Little & Tremaine 1987;Wilkinson & Evans 1999;Evans & Wilkinson 2000). With increased sample size, however, follow enhanced opportunities to discover satellites on unlikely orbits; i.e., dynamical "outliers" that may challenge the expectations of simple-minded models of satellite formation and evolution. It is important to clarify the origin of such systems, given their disproportionate weight in mass estimates.
One issue to consider is that the assumption of equilibrium must break down when considering outliers in phase space. This is because the finite age of the Universe places an upper limit to the orbital period of satellites observed in the Local Group; highspeed satellites have typically large apocenters and long orbital periods, implying that they cannot be dynamically well-mixed and casting doubts on the applicability of Jeans' theorem-inspired analysis tools.
To make progress, one possibility is to explore variants of the standard secondary infall model (Gunn & Gott 1972;Gott 1975;Gunn 1977;Fillmore & Goldreich 1984), where satellites are assumed to recede initially with the universal expansion, before turning around and collapsing onto the primary due to its gravitational pull. This is the approach adopted by Zaritsky & White (1994) in order to interpret statistically the kinematics of observed satellite samples without assuming well-mixed orbits and taking into account the proper timing and phase of the accretion process.
In the secondary infall accretion sequence, satellites initially farther away accrete later, after turning around from larger turnaround radii. The turn-around radius grows with time, at a rate the depends on the mass of the primary and its environment, as well as on the cosmological model. Three distinct regions surround a system formed by spherical secondary infall (see, e.g., Bertschinger 1985;: (i) an outer region beyond the current turnaround radius where satellites are still expanding away, (ii) an intermediate region containing satellites that are approaching the primary for the first time, and (iii) an inner, "virialized" region containing all satellites that have turned around at earlier times and are still orbiting around the primary. To good approximation, the latter region is delineated roughly by the conventional virial radius of a system 1 , rvir; the turnaround radius is of order rta ∼ 3 rvir (see, e.g. White et al. 1993).
We note a few consequences of this model. (a) Satellites outside the virial radius are on their first approach to the system and thus have not yet been inside rvir. (b) Satellites inside the virial radius have apocentric radii that typically do not exceed rvir. (c) The farther the turnaround radius the longer it takes for a satellite to turn around and accrete and the higher its orbital energy. (d) Satellites with extreme velocities will, in general, be those completing their first orbit around the primary. Velocities will be maximal near the center, where satellites may reach speeds as high as ∼ 3 Vvir. (e) Since all satellites associated with the primary are bound (otherwise they would not have turned around and collapsed under the gravitational pull of the primary), the velocity of the highest-speed satellite may be used to estimate a lower limit to the escape velocity at its location and, thus, a lower bound to the total mass of the system.
Hierarchical galaxy formation models, such as the current ΛCDM paradigm, suggest further complexity in this picture. Firstly, although numerical simulations show that the sequence of expansion, turnaround and accretion of satellites described above is more or less preserved in hierarchical models, the evolution is far from spherically symmetric (Navarro et al. 1994;Ghigna et al. 1998;Jing & Suto 2002;Bailin & Steinmetz 2005;Knebe & Wießner 2006). Much of the mass (as well as many of the satellites) is accreted through filaments of matter embedded within sheets of matter formation (see, e.g., Navarro et al. 2004). The anisotropic collapse pattern onto a primary implies that the turnaround "surface" won't be spherical and that the virial radius may not contain all satellites that have completed at least one orbit around the primary (see, e.g., Balogh et al. 2000;Diemand et al. 2007).
More importantly for the purposes of this paper, in hierarchical models galaxy systems are assembled by collecting smaller systems which themselves, in turn, were assembled out of smaller units. This implies that satellites will in general not be accreted in isolation, but frequently as part of larger structures containing multiple systems. This allows for complex many-body interactions to take place during approach to the primary that may result in substantial modification to the orbits of accreted satellites.
We address this issue in this contribution using Nbody/gasdynamical simulations of galaxy formation in the current ΛCDM paradigm. We introduce briefly the simulations in § 2, and analyze and discuss them in § 3. We speculate on possible applications to the Local Group satellite population in §4 and conclude with a brief summary in § 5.

THE NUMERICAL SIMULATIONS
We identify satellite galaxies in a suite of eight simulations of the formation of L * galaxies in the ΛCDM scenario. This series has been presented by Abadi, Navarro & Steinmetz (2006), and follow the same numerical scheme originally introduced by Figure 1. Star particles in one of our simulations, shown at z = 0. Particles are colored according to the age of the star; blue means a star is younger than ≃ 1 Gyr, red that it is older than ≃ 10 Gyr. The large box is 2 r vir (632 kpc) on a side and centered on the primary galaxy. More than 85% of all stars are in the inner regions of the primary, within about ∼ 20 kpc from the center (for more details see Abadi et al. 2006). surround the satellites "associated" with the primary galaxy; i.e., satellites that have been within r vir in the past. Note that a few "associated" satellites lie well beyond the virial boundary of the system. Two of these satellites are highlighted for analysis in Figures 2 and 6. Steinmetz & Navarro (2002). The "primary" galaxies in these simulations have been analyzed in detail in several recent papers, which the interested reader may wish to consult for details (Abadi et al. 2003a,b;Meza et al. 2003Meza et al. , 2005Navarro et al. 2004). We give a brief outline below for completeness.
Each simulation follows the evolution of a small region of the universe chosen so as to encompass the mass of an L * galaxy system. This region is chosen from a large periodic box and resimulated at higher resolution preserving the tidal fields from the whole box. The simulation includes the gravitational effects of dark matter, gas and stars, and follows the hydrodynamical evolution of the gaseous component using the Smooth Particle Hydrodynamics (SPH) technique (Steinmetz 1996). We adopt the following cosmological parameters for the ΛCDM scenario: H0 = 65 km/s/Mpc, σ8 = 0.9, ΩΛ = 0.7, ΩCDM = 0.255, Ω b = 0.045, with no tilt in the primordial power spectrum.
All re-simulations start at redshift zinit = 50, have force resolution of order 1 kpc, and the mass resolution is chosen so that each galaxy is represented on average, at z = 0, with ∼ 50, 000 dark matter/gas particles. Gas is turned into stars at rates consistent with the empirical Schmidt-like law of Kennicutt (1998). Because of this, star formation proceeds efficiently only in high-density regions at the center of dark halos, and the stellar components of primary and satellite galaxies are strongly segregated spatially from the dark matter.
Each re-simulation follows a single ∼ L * galaxy in detail, and resolves as well a number of smaller, self-bound systems of stars, gas, and dark matter we shall call generically "satellites". We shall hereafter refer to the main galaxy indistinctly as "primary" or "host". The resolved satellites span a range of luminosities, down to about six or seven magnitudes fainter than the primary. Each primary has on average ∼ 10 satellites within the virial radius. Figure 1 illustrates the z = 0 spatial configuration of star particles in one of the simulations of our series. Only star particles are shown here, and are colored according to their age: stars younger than ≃ 1 Gyr are shown in blue; those older than ≃ 10 Gyr in red. The large box is centered on the primary and is 2 rvir (632 kpc) on a side. The "primary" is situated at the center of the large box and contains most of the stars. Indeed, although not immediately apparent in this rendition, more than 85% of all stars are within ∼ 20 kpc from the center. Outside that radius most of the stars are old and belong to the stellar halo, except for a plume of younger stars stripped from a satellite that has recently merged with the primary. Satellites "associated" with the primary (see § 3.1 for a definition) are indicated with small boxes. Note that a few of them lie well beyond the virial radius of the primary.
A preliminary analysis of the properties of the simulated satellite population and its relation to the stellar halo and the primary galaxy has been presented in Abadi, Navarro & Steinmetz (2006) and Sales et al (2007, submitted), where the interested reader may find further details. Figure 2. Distance to the primary as a function of time for four satellites selected in one of our simulations. The four satellites are accreted into the primary in two pairs of unequal mass. The heavier satellite of the pair, shown by solid lines, follows a "conventional" orbit: after turning around from the universal expansion, it accretes into the primary on a fairly eccentric orbit which becomes progressively more bound by the effects of dynamical friction. Note that, once accreted, these satellites on "conventional" orbits do not leave the virial radius of the primary, which is shown by a dotted line. The light member of the pair, on the other hand, is ejected from the system as a result of a three-body interaction between the pair and the primary during first approach. One of the ejected satellites shown here is the "escaping" satellite identified in Figure 3; the other is the most distant "associated" satellite in that Figure. The latter is still moving toward apocenter at z = 0, which we estimate to be as far as ∼ 3.5 r vir .

Satellites on conventional orbits
The evolution of satellites in our simulations follows roughly the various stages anticipated by our discussion of the secondary infall model; after initially receding with the universal expansion, satellites turn around and are accreted into the primary. Satellites massive enough to be well resolved in our simulations form stars actively before accretion and, by the time they cross the virial radius of the primary, much of their baryonic component is in a tightly bound collection of stars at the center of their own dark matter halos.
The stellar component of a satellite is thus quite resilient to the effect of tides and can survive as a self-bound entity for several orbits. This is illustrated by the solid lines in Figure 2, which show, for one of our simulations, the evolution of the distance to the primary of two satellites that turn around and are accreted into the primary at different times. As expected from the secondary infall model, satellites that are initially farther away turn around later; do so from larger radii; and are on more energetic orbits. After accretion (defined as the time when a satellite crosses the virial radius of the primary), their orbital energy and eccentricity are eroded by dynamical friction, and these two satellites do not leave the virial radius of the primary, shown by the dotted line in Figure 2. Depending on their mass and orbital parameters, some of these satel-lites merge with the primary shortly after accretion, while others survive as self-bound entities until z = 0. For short, we shall refer to satellites that, by z = 0, have crossed the virial radius boundary at least once as satellites "associated" with the primary.
The ensemble of surviving satellites at z = 0 have kinematics consistent with the evolution described above. This is illustrated in Figure 3, where we show the radial velocities of all satellites as a function of their distance to the primary, scaled to virial units. Note that the majority of "associated" satellites (shown as circles in this figure) are confined within rvir, and that their velocity distribution is reasonably symmetric and consistent with a Gaussian (Sales et al 2007). The most recently accreted satellites tend to have higherthan-average speed at all radii, as shown by the "crossed" circles, which identify all satellites accreted within the last 3 Gyr.
Crosses (without circles) in this figure correspond to satellites that have not yet been accreted into the primary. These show a clear infall pattern outside rvir, where the mean infall velocity decreases with radius and approaches zero at the current turnaround radius, located at about 3 rvir. All of these properties agree well with the expectations of the secondary infall model discussed above.

Three-body interactions and satellites on unorthodox orbits
Closer examination, however, shows a few surprises. To begin with, a number of "associated" satellites are found outside rvir. As reported in previous work (see, e.g., Balogh et al. 2000;Moore et al. 2004;Gill et al. 2005;Diemand et al. 2007), these are a minority (∼ 15% in our simulation series), and have been traditionally linked to departures from spherical symmetry during the accretion process. Indeed, anisotropies in the mass distribution during expansion and recollapse may endow some objects with a slight excess acceleration or, at times, may push satellites onto rather tangential orbits that "miss" the inner regions of the primary, where satellites are typically decelerated into orbits confined within the virial radius. These effects may account for some of the associated satellites found outside rvir at z = 0, but cannot explain why ∼ 33% of all associated satellites are today on orbits whose apocenters exceed their turnaround radius. This is illustrated in Figure 4, where we show a histogram of the ratio between apocentric radius (measured at z = 0; rapo) and turnaround radius (rta). The histogram highlights the presence of two distinct populations: satellites on "conventional" orbits with rapo/rta < 1, and satellites on orbital paths that lead them well beyond their original turnaround radius.
Intriguingly, a small but significant fraction (∼ 6%) of satellites have extremely large apocentric radius, exceeding their turnaround radius by 50% or more. These systems have clearly been affected by some mechanism that propelled them onto orbits substantially more energetic than the ones they had followed until turnaround. This mechanism seems to operate preferentially on low-mass satellites, as shown by the dashed histogram in Figure 4, which corresponds to satellites with stellar masses less than ∼ 3% that of the primary.
We highlight some of these objects in Figure 3, using "filled" circles to denote "associated" satellites whose apocenters at z = 0 exceed their turnaround radii by at least 25%. Two such objects are worth noting in this figure: one of them is the farthest "associated" satellite, found at more than ∼ 2.5 rvir from the primary; the second is an outward-moving satellite just outside the virial radius but with radial velocity approaching ∼ 2 Vvir. The latter, in particular, is an extraordinary object, since its radial velocity alone exceeds Figure 3. Radial velocity of satellites versus distance to the primary. Velocities are scaled to the virial velocity of the system, distances to the virial radius. Circles denote "associated" satellites; i.e., those that have been inside the virial radius of the primary at some earlier time. Crosses indicate satellites that are on their first approach, and have never been inside r vir . Filled circles indicate associated satellites whose apocentric radii exceed their turnaround radius by at least 25%, indicating that their orbital energies have been substantially altered during their evolution. "Crossed" circles correspond to associated satellites that have entered r vir during the last 3 Gyrs. The curves delineating the top and bottom boundaries of the distribution show the escape velocity of an NFW halo with concentration c = 10 and c = 20, respectively. Note that there is one satellite "escaping" the system with positive radial velocity. Solid lines show the trajectories in the r − Vr plane of the two "ejected" satellites shown in figure 2. Filled squares correspond to the fourteen brightest Milky Way satellites, taken from van den Bergh (1999)  the nominal escape velocity 2 at that radius. This satellite is on a trajectory which, for all practical purposes, will remove it from the vicinity of the primary and leave it wandering through intergalactic space.
The origin of these unusual objects becomes clear when inspecting Figure 2. The two satellites in question are shown with dashed lines in this figure; each is a member of a bound pair of satellites (the other member of the pair is shown with solid lines of the same color). During first pericentric approach, the pair is disrupted by the tidal field of the primary and, while one member of 2 The notion of binding energy and escape velocity is ill-defined in cosmology; note, for example, that the whole universe may be considered formally bound to any positive overdensity in an otherwise unperturbed Eistein-de Sitter universe. We use here the nominal escape velocity of an NFW model (Navarro et al. 1996(Navarro et al. , 1997 to guide the interpretation. This profile fits reasonably well the mass distribution of the primaries inside the virial radius, and has a finite escape velocity despite its infinite mass. Certainly satellites with velocities exceeding the NFW escape velocity are likely to move far enough from the primary to be considered true escapers. the pair remains bound and follows the kind of "conventional" orbit described in § 3.1, the other one is ejected from the system on an extreme orbit. The trajectories of these two "ejected" satellites in the r-Vr plane are shown by the wiggly lines in Figure 3.
These three-body interactions typically involve the first pericentric approach of a bound pair of accreted satellites and tend to eject the lighter member of the pair: in the example of Figure 2, the "ejected" member makes up, respectively, only 3% and 6% of the total mass of the pair at the time of accretion. Other interaction configurations leading to ejection are possible, such as an unrelated satellite that approaches the system during the late stages of a merger event, but they are rare, at least in our simulation series. We emphasize that not all satellites that have gained energy during accretion leave the system; most are just put on orbits of unusually large apocenter but remain bound to the primary. This is shown by the filled circles in Figure 3; many affected satellites are today completing their second or, for some, third orbit around the primary.
The ejection mechanism is perhaps best appreciated by inspecting the orbital paths of the satellite pairs. These are shown in Figure 6, where the top (bottom) panels correspond to the satellite pair accreted later (earlier) into the primary in Figure 2. Note that in both cases, as the pair approaches pericenter, the lighter member (dashed lines) is also in the process of approaching the pericenter of its own orbit around the heavier member of the pair. This coincidence in orbital phase combines the gravitational attraction of the two more massive members of the trio of galaxies, leading to a substantial gain in orbital energy by the lightest satellite, effectively ejecting it from the system on an approximately radial orbit. The heavier member of the infalling pair, on the other hand, decays onto a much more tightly bound orbit. Figure 6 also illustrates the complexity of orbital configurations that are possible during these three-body interactions. Although the pair depicted in the top panels approaches the primary as a cohesive unit, at pericenter each satellite circles about the primary in opposite directions: in the y-z projection the heavier member circles the primary clockwise whereas the ejected companion goes about it counterclockwise. After pericenter, not only do the orbits of each satellite have different period and energy, but they differ even in the sign of their orbital angular momentum. In this case it would clearly be very difficult to link the two satellites to a previously bound pair on the basis of observations of their orbits after pericenter.
Although not all ejections are as complex as the one illustrated in the top panels of Figure 6, it should be clear from this figure that reconstructing the orbits of satellites that have been through pericenter is extremely difficult, both for satellites that are ejected as well as for those that remain bound. For example, the massive member of the late-accreting pair in Figure 2 sees its apocenter reduced by more than a factor of ∼ 5 from its turnaround value in a single pericentric passage. Such dramatic variations in orbital energy are difficult to reproduce with simple analytic treatments inspired on Chandrasekhar's dynamical friction formula (Peñarrubia 2007, private communication).

APPLICATION TO THE LOCAL GROUP
We may apply these results to the interpretation of kinematical outliers within the satellite population around the Milky Way (MW) and M31, the giant spirals in the Local Group. Although part of the Figure 4. Distribution of the ratio between the apocentric radius of satellites (measured at z = 0) and their turnaround radius, defined as the maximum distance to the primary before accretion. Note the presence of two groups. Satellites on "conventional" orbits have rapo/rta < 1, the rest have been catapulted into high-energy orbits by three-body interactions during first approach. The satellite marked with a rightward arrow is the "escaping" satellite identified by a dot-centered circle in Figure 3; this system has nominally infinite rapo. The dashed histogram highlights the population of lowmass satellites; i.e., those with stellar masses at accretion time not exceeding 2.6% of the primary's final Mstr. The satellite marked with an arrow is a formal "escaper" for which rapo cannot be computed. discussion that follows is slightly speculative due to lack of suitable data on the three-dimensional orbits of nearby satellites, we feel that it is important to highlight the role that the concomitant accretion of multiple satellites may have played in shaping the dynamics of the dwarf members in the Local Group.

Milky Way satellites
The filled squares in Figure 3 show the galactocentric radial velocity of thirteen bright satellites around the Milky Way and compare them with the simulated satellite population. This comparison requires a choice for the virial radius and virial velocity of the Milky Way, which are observationally poorly constrained.
We follow here the approach of Sales et al (2007), and use the kinematics of the satellite population itself to set the parameters of the Milky Way halo. These authors find that simulated satellites are only mildly biased in velocity relative to the dominant dark matter component: σr ∼ 0.9(±0.2)Vvir, where σr is the radial velocity dispersion of the satellite population within rvir. Using this, we find V MW vir = 109 ± 22 km/s and r MW vir = 237 ± 50 kpc from the observed radial velocity dispersion of ∼ 98 km/s. This corresponds to M MW vir = 7 × 10 11 M⊙, in reasonable agreement with the 1-2 × 10 12 M⊙ estimate of Klypin et al. (2002) and with the recent findings of Smith et al. (2006) based on estimates of the escape velocity in the solar neighbourhood.
Since Leo I dwarf has the largest radial velocity of the Milky Way satellites, we have recomputed the radial velocity dispersion excluding it from the sample. We have found that σr drops from 98 to 82 km/s when Leo I is not taken into account changing our estimation of V MW vir from 109 to 91 km/s, still within the errors of the value previously found. Given the recent rapid growth in the number of known Milky Way satellite one would suspect that the velocity dispersion will significantly increase if more Leo Ilike satellites are detected. However, we notice that given their high velocities they are not expected to remain inside the virial radius for a long time period hence not contributing to the σr computation. Figure 3 shows that, considering V MW vir = 109 km/s, the velocities and positions of all MW satellites are reasonably consistent with the simulated satellite population, with the possible exception of Leo I, which is located near the virial radius and is moving outward with a velocity clearly exceeding Vvir. Indeed, for V MW vir = 109 km/s, Leo I lies right on the escape velocity curve of an NFW profile with concentration parameter similar to those measured in the simulations. This is clearly a kinematical outlier reminiscent of the satellite expelled by three-body interactions discussed in the previous subsection and identified by a dot-centered circle in Figure 3. This is the only "associated" satellite in our simulations with radial velocity exceeding Vvir and located outside rvir.
Could Leo I be a satellite that has been propelled into a highlyenergetic orbit through a three-body interaction? If so, there are a number of generic predictions that might be possible to verify observationally. One is that its orbit must be now basically radial in the rest frame of the Galaxy, although it might be some time before proper motion studies are able to falsify this prediction. A second possibility is to try and identify the second member of the pair to which it belonged. An outward moving satellite on a radial orbit takes only ∼ 2-3 Gyr to reach rvir with escape velocity. Coincidentally, this is about the time that the Magellanic Clouds pair were last at pericenter, according to the traditional orbital evolution of the Clouds (see, e.g., Gardiner & Noguchi 1996;van der Marel et al. 2002).
Could Leo I have been a Magellanic Cloud satellite ejected from the Galaxy a few Gyrs ago? Since most satellites that are ejected do so during first pericentric approach, this would imply that the Clouds were accreted only recently into the Galaxy, so that they reached their first pericentric approach just a few Gyr ago. This is certainly in the spirit of the re-analysis of the orbit of the Clouds presented recently by Besla et al. 2007 and based on new proper motion measurements recently reported by Kallivayalil et al. (2006). In this regard, the orbit of the Clouds might resemble the orbit of the companion of the "escaping" satellite located next to Leo I in Figure 3. The companion is fairly massive and, despite a turnaround radius of almost ∼ 600 kpc and a rather late accretion time (tacc = 10.5 Gyr, see Figure 2), it is left after pericenter on a tightly bound, short-period orbit resembling that of the Clouds today (Gardiner & Noguchi 1996;van der Marel et al. 2002). To compound the resemblance, this satellite has, at accretion time, a total luminosity of order ∼ 10% of that of the primary, again on a par with the Clouds.
We also note that an ejected satellite is likely to have picked up its extra orbital energy through a rather close pericentric passage and that this may have led to substantial tidal damage. This, indeed, has been argued recently by Sohn et al. 2006 on the basis of asymmetries in the spatial and velocity distribution of Leo I giants (but see Koch et al. 2007 for a radically different interpretation).
On a final note, one should not forget to mention another (less exciting!) explanation for Leo I: that our estimate of V MW vir is a substantial underestimate of the true virial velocity of the Milky Way. The arrows in Figure 3 indicate how the position of the MW satel-  (Majewski et al. 2007) and And XII (Chapman et al 2007, submitted)  by ∼ 20% or more would make Leo I's kinematics less extreme, and closer to what would be expected for a high-speed satellite completing its first orbit. This rather more prosaic scenario certainly cannot be discounted on the basis of available data (see, e.g., Zaritsky et al 1989, Kochanek 1996, Wilkinson & Evans 1999

M31 satellites
A similar analysis may be applied to M31 by using the projected distances and line-of-sight velocities of simulated satellites, shown in Figure   shows the orbits in the rest frame of the primary. The coordinate system is chosen so that the angular momentum of the primary is aligned with the z axis. A solid curve tracks the path of the heavier satellite; a dashed line follows the satellite that is propelled into a highly energetic orbit after. become available (And XII, Chapman et al 2007, andAnd XIV, Majewski et al. 2007). As in Figure 3, arrows indicate how the position of M31 satellites would change in this figure if V M31 vir were allowed to vary by ±20%. We notice that the exclusion of And XII and And XIV (the highest velocity satellites within 300 kpc from Andromeda) in the V M31 vir estimation gives ∼ 100 km/s, consistent with the V M31 vir = 138 ± 35 km/s previously found considering all satellites. Projected distances are as if viewed from infinity along the direction joining the Milky Way with M31 and that the sign of the line-of-sight velocity in Figure 5 is chosen to be positive if the satellite is receding from the primary (in projection) and negative otherwise.
There are a few possible outliers in the distribution of M31 satellite velocities: And XIV (Majewski et al 2007), the Pegasus dwarf irregular (UGC 12613, Gallagher et al. 1998), And XII (Chapman et al 2007), and UGCA 092 (labelled U092 in Figure 5, McConnachie & Irwin 2006). And XIV and PegDIG seem likely candidates for the three-body "ejection" mechanism discussed above: they have large velocities for their position, and, most importantly, they are receding from M31; a requirement for an escaping satellite. Note, for example, that And XIV lies very close to the "escaping" satellite (dot-centered symbol in Figure 5) paired to Leo I in the previous subsection. Escapers should move radially away from the primary, and they would be much harder to detect in projection as extreme velocity objects, unless they are moving preferentially along the line of sight. It is difficult to make this statement more conclusive without further knowledge of the orbital paths of these satellites. Here, we just note, in agreement with Majewski et al (2007), that whether And XIV and PegDIG are dynamical "rogues" depends not only on the (unknown) transverse velocity of these galaxies, but also on what is assumed for M31's virial velocity. With our assumed V M31 vir = 138 km/s, neither And XIV nor PegDIG look completely out of place in Figure 5; had we assumed the lower value of 120 km/s advocated by Seigar et al (2006) And XIV would be almost on the NFW escape velocity curve, and would certainly be a true outlier.
High-velocity satellites approaching M31 in projection are unlikely to be escapers, but rather satellites on their first approach. This interpretation is probably the most appropriate for And XII and UGCA 092. As discussed by Chapman et al (2007), And XII is almost certainly farther than M31 but is approaching us at much higher speed (∼ 281 km/s faster) than M31. This implies that And XII is actually getting closer in projection to M31 (hence the negative sign assigned to its V los in Figure 5), making the interpretation of this satellite as an escaping system rather unlikely.
Note, again, that although And XII (and UGCA 092) are just outside the loci delineated by simulated satellites in Figure 5, revising our assumption for V M31 vir upward by 20% or more would render the velocity of this satellite rather less extreme, and would make it consistent with that of a satellite on its first approach to M31. As was the case for Leo I, this more prosaic interpretation of the data is certainly consistent with available data.

SUMMARY AND CONCLUSIONS
We examine the orbits of satellite galaxies in a series of Nbody/gasdynamical simulations of the formation of L * galaxies in a ΛCDM universe. Most satellites follow orbits roughly in accord with the expectations of secondary infall-motivated models. Satellites initially follow the universal expansion before being decelerated by the gravitational pull of the main galaxy, turning around and accreting onto the main galaxy. Their apocentric radii decrease steadily afterwards as a result of the mixing associated with the virialization process as well as of dynamical friction. At z = 0 most satellites associated with the primary are found within its virial radius, and show little spatial or kinematic bias relative to the dark matter component (see also Sales et al 2007).
A number of satellites, however, are on rather unorthodox orbits, with present apocentric radii exceeding their turnaround radii, at times by a large factor. The apocenters of these satellites are typically beyond the virial radius of the primary; one satellite is formally "unbound", whereas another is on an extreme orbit and is found today more than 2.5 rvir away, or ∼ > 600 Mpc when scaling this result to the Milky Way.
These satellites owe their extreme orbits to three-body interactions during first approach: they are typically the lighter member of a pair of satellites that is disrupted during their first encounter with the primary. This process has affected a significant fraction of satellites: a full one-third of the simulated satellite population identified at z = 0 have apocentric radii exceeding their turnaround radii. These satellites make up the majority (63%) of systems on orbits that venture outside the virial radius.
We speculate that some of the kinematical outliers in the Local Group may have been affected by such process. In particular, Leo I might have been ejected 2-3 Gyr ago, perhaps as a result of interactions with the Milky Way and the Magellanic Clouds. Other satellites on extreme orbits in the Local Group may have originated from such mechanism. Cetus (Lewis et al. 2007) and Tucana (Oosterloo et al. 1996) -two dwarf spheroidals in the periphery of the Local Group-may owe their odd location (most dSphs are found much closer to either M31 or the Galaxy) to such ejection mechanism.
If this is correct, the most obvious culprits for such ejection events are likely to be the largest satellites in the Local Group (M33 and the LMC/SMC), implying that their possible role in shaping the kinematics of the Local Group satellite population should be recognized and properly assessed. In this regard, the presence of kinematical oddities in the population of M31 satellites, such as the fact that the majority of them lie on "one side" of M31 and seem to be receding away from it , suggest the possibility that at least some of the satellites normally associated with M31 might have actually been brought into the Local Group fairly recently by M33. Note, for example, that two of the dynamical outliers singled out in our discussion above (And XII and And XIV) are close to each other in projection; have rather similar line-of-sight velocities (in the heliocentric frame And XII is approaching us at 556 km/s, And XIV at 478 km/s); and belong to a small subsystem of satellites located fairly close to M33. The same mechanism might explain why the spatial distribution of at least some satellites, both around M31 and the Milky Way, seem to align themselves on a "planar" configuration (Majewski 1994;Libeskind et al. 2005;Koch & Grebel 2006), as this may just reflect the orbital accretion plane of a multiple system of satellites accreted simultaneously in the recent past (Kroupa et al. 2005;Metz et al. 2007).
From the point of view of hierarchical galaxy formation models, it would be rather unlikely for a galaxy as bright as M33 to form in isolation and to accrete as a single entity onto M31. Therefore, the task of finding out which satellites (rather than whether) have been contributed by the lesser members of the Local Group, as well as what dynamical consequences this may entail, should be undertaken seriously, especially now, as new surveys begin to bridge our incomplete knowledge of the faint satellites orbiting our own backyard.