Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 20 February 2008 (MN LATEX style file v2.2) The Collision Between The Milky Way And Andromeda T. J. Cox⋆ and Abraham Loeb† Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA 20 February 2008 ABSTRACT We use a N–body/hydrodynamic simulation to forecast the future encounter be- tween the Milky Way and the Andromeda galaxies, given current observational con- straints on their relative distance, relative velocity, and masses. Allowing for a com- parable amount of diffuse mass to fill the volume of the Local Group, we find that the two galaxies are likely to collide in a few billion years - within the Sun’s lifetime. During the the interaction, there is a chance that the Sun will be pulled away from its present orbital radius and reside in an extended tidal tail. The likelihood for this outcome increases as the merger progresses, and there is a remote possibility that our Sun will be more tightly bound to Andromeda than to the Milky Way before the final merger. Eventually, after the merger has completed, the Sun is most likely to be scattered to the outer halo and reside at much larger radii (> 30 kpc). The density profiles of the stars, gas and dark matter in the merger product resemble those of elliptical galaxies. Our Local Group model therefore provides a prototype progenitor of late–forming elliptical galaxies. Key words: galaxy:evolution — galaxies:evolution — galaxies:formation — galax- ies:interactions — Local Group — methods:N-body simulations. 1 INTRODUCTION ferred about the Local Group provided a plausible set of assumptions. Nearly 50 years ago Kahn & Woltjer (1959) It is well known that the Milky Way (MW) and Andromeda pioneered the “timing argument,” in which the Milky Way (M31) are the two largest members of the Local Group of and Andromeda are assumed to form within close proximity galaxies. Together with their ∼ 40 smaller companions, the to each other, during the dense early stages of the Universe, Milky Way and Andromeda comprise our galactic neigh- before they were pulled apart by the general cosmological borhood, and as such, represent the nearest laboratory, and expansion. They have subsequently reversed their path and therefore the most powerful tool, to study the formation and are approaching one another owing to their mutual gravi- arXiv:0705.1170v2 [astro-ph] 20 Feb 2008 evolution of galactic structure. tational attraction. According to the timing argument, the Like most extragalactic groups, the Local Group is Milky Way and Andromeda have now traced out nearly a full very likely to be decoupled from the cosmological expan- period of their orbital motion which is governed by Kepler’s sion and is now a gravitationally bound collection of galax- laws. By assuming that the system has no angular momen- ies. This notion is supported by the observed relative mo- tum, and given the current separation, velocity of approach, tion between its two largest galaxies; namely, the Milky and the age of the Universe, the timing argument yields es- Way and Andromeda are moving toward each other at ∼ 12 timates for the mass of the Local Group (> 3 × 10 M⊙), 120 km s−1(Binney & Tremaine 1987). Unfortunately, this the semi–major axis of the orbit (< 580 kpc), and the motion alone does not indicate whether the Local Group time of the next close passage (> 4 Gyr) (see Sec. 10.2 of is bound or not. The unknown magnitude of Andromeda’s Binney & Tremaine 1987). transverse velocity adds uncertainty into the present day or- bital parameters and therefore the past and future evolution While the seminal results of Kahn & Woltjer (1959) of the Local Group. were an early indication of the large mass–to–light ratio in Barring the uncertain transverse velocity of An- the Local Group and therefore the presence of dark matter, dromeda, a considerable amount of information can be in- they also began a nearly five decade long quest to under- stand the past, present, and future of our Local Group. In particular, a number of studies have extended the original ⋆ [email protected] timing argument by allowing for various angular momenta, † [email protected] by including more realistic or time–dependent mass distri- c 0000 RAS 2 Cox & Loeb butions, by adding the effects of mass at scales beyond that model for the Local Group in §2 that satisfies all observa- of the Local Group, or testing its validity using numerical tional constraints. We then evolve this model using a self- simulations (see, e.g., Peebles et al. 1989; Fich & Tremaine consistent N-body/hydrodynamic simulation, as described 1991; Valtonen et al. 1993; Peebles 1994; Peebles et al. 2001; in §3. The generic properties of the merger, including the Sawa & Fujimoto 2005; Loeb et al. 2005; Li & White 2007; merger timescale, the possible evolution of our Solar Sys- van der Marel & Guhathakurta 2007). tem, and properties of the merger remnant, are outlined in One of the most intriguing developments stemming §4. Finally, we conclude in §5. from the various studies of the Local Group is an estimate of the transverse velocity of Andromeda. By employing the ac- tion principle to the motions of galaxies within and near 2 A MODEL OF THE LOCAL GROUP (< 20 Mpc) the Local Group, Peebles et al. (2001) con- cluded that the transverse velocity of Andromeda is less The distribution of mass within our Local Group of galaxies than 200 km s−1. Using the well measured transverse ve- has been a long–standing question in astrophysics. It is clear locity of M33 (Brunthaler et al. 2005) and numerical sim- that much of the matter is associated with the two largest ulations that tracked the potential tidal disruption during galaxies in the Local Group: the Milky Way and Andromeda. M33’s past encounters with Andromeda, Loeb et al. (2005) Moreover, these two spiral galaxies are likely to be embedded found an even smaller estimate, ∼ 100 km s−1, for the trans- in an ambient medium of dark matter and gas. verse velocity. While future astrometric observations using 1 2 SIM and GAIA will be able to accurately measure the 2.1 The Milky Way and Andromeda proper motion of Andromeda, the low values favored by these papers suggests that the Local Group is indeed a grav- There are a number of different models for both the Milky itationally bound system. Way and Andromeda galaxies (see, e.g., Klypin et al. 2002; Provided that the Local Group is gravitationally bound, Widrow & Dubinski 2005; Seigar et al. 2006, and reference and that the Milky Way and Andromeda are heading to- therein). These studies generally enlist a myriad of obser- wards each other, one must admit the possibility that they vational data to infer the distribution of baryons, while the will eventually interact and merge. This outcome appears dark matter, which dominates the gravitational potential, inevitable given the massive halos of dark matter that likely is set to match distributions extracted from cosmological N- surround the Milky Way and Andromeda. Numerical exper- body simulations (e.g., Navarro et al. 1996). Together, these iments have robustly concluded that dark matter halos can models specify the total mass distribution out to the virial exert significant dynamical friction, and are sponges that radius (∼ 200 − 300 kpc). soak up energy and angular momentum leading to a rapid In our model of the Local Group we start by adopting merger (Barnes 1988). the models for the Milky Way and Andromeda favored by Even though the eventual merger between the Milky Klypin et al. (2002). Within these models, the baryons are Way and Andromeda is common lore in Astronomy, the contained entirely within the rotationally supported expo- merger process has not been addressed by a comprehen- nential disk and central bulge. These components are then sive numerical study. The one exception is a paper by surrounded by a massive dark–matter halo, which has nearly Dubinski et al. (1996) that presented a viable model for 20 times the mass as the baryons, as specified by the mass the Local Group and numerically simulated the eventual fractions, mb and md, defined as the bulge and disk mass, re- merger between the Milky Way and Andromeda. However, spectively, divided by the total mass. The exponential disk, Dubinski et al. (1996) utilized this Local Group model and of radial disk scale radius Rd, also contains a set fraction f its numerical evolution to study the production of tidal tails of its mass in collisional gas that can cool and form stars. during such an encounter and the possibility to use the struc- Both the bulge and dark halo components are assumed to ture of this tidal material to probe the dark matter poten- follow the Hernquist (1990) profile. The bulge scale radius tial. While the study by Dubinski et al. (1996) provided the a is fixed to be 20% of the radial disk scale radius Rd. The first enticing picture of the future encounter between the dark–matter profile is defined by its concentration c, spin Milky Way and Andromeda, (for a more recent and higher parameter λ, and total virial mass M200 and virial circu- resolution version of this simulation, see Dubinski 2006), it lar velocity V200 (at the radius r200 where the average inte- was neither designed to detail the merger dynamics includ- rior density is 200 times the critical cosmic density today, −29 −3 ing intergalactic material, nor outline the possible outcomes rhocrit = 10 g cm ), which are all listed in Table 1. for the dynamics of our Sun, nor quantify properties of the The numerical construction of these models employs meth- merger remnant.