Galaxy interaction and transformation Houjun Mo April 13, 2004 A lot of mergers expected in hierarchical models. The main issues: The phenomena of galaxy interaction: tidal tails, mergers, starbursts When and where does galaxy interaction most likely to occur The properties of merger remnants
Tidal interaction and tidal radius When an extended system (galaxy) moves in the gravitational potential of another object, the system experiences a tidal force which tends to tear the system apart. Consider a satellite system with mass m of radius r which is on a circular orbit of radius D in the potential well of a point mass M. The accelerations: a = GM/D 2 (at the center of m) GM/(D + r) 2 GM/(D r) 2 (farthest end) (nearest end)
Assuming r D, the acceleration difference is a = 2GMr/D 3 (between the two ends), which tends to tear the material apart from the center. The binding force per unit mass on the two ends of m is Gm/r 2. a = Gm/r 2 defines a tidal radius: r t = (m/2m) 1/3 D. A more rigorous derivation gives: [ ] 1/3 m r t = D. M(3 + m/m) If the radius of the satellite is larger than r t, the material outside r t may be stripped by the tidal force of M.
Tidal tails Tidal force involved in close encounters of spinning galaxies may eject stars into arcing trajectories, leading to the formation of tidal tails. But tidal tails are more prominent in prograde encounters than in retrograde ones.
Retrograde Prograde
Prograde encounter is more violent because of the resonant acceleration. The orbital frequency of a ring of radius r is ω ring = GM/r 3, whereas the angular velocity of the line joining the two massive particles at pericenter is ω orb = [ ] 1/2 2GM(1 + e), D 3 min where e is the eccentricity of the orbit and D min is the minimum separation of the two massive particles. If ω orb = ω ring, i.e., for a ring with radius r = D min /[2(1 + e)] 2/3, and if the encounter is prograde, then a test particle in the ring is in resonance with the tidal acceleration.
Self-consistent simulations of spinning galaxies Disk stars have mass, and disk is embedded in extended dark matter halos. confirm the importance of mutual alignment of spin and orbital angular momentum in making prominent tidal tails demonstrate that interpenetrating encounters from parabolic orbits generally leads to mergers of galaxies within a few dynamical time. This happens because the lauching of tidal tails (now with mass) is at the expense of the orbital energy, which causes the orbit of the galaxies to decay.
Dynamical Friction As an object moves through a sea of particles, it accelerates the surrounding particles, and so the number density of particles down stream is higher than that up stream, leading to a net drag force (dynamic friction) on the object.
Chandrasekhar dynamical friction formula Consider the encounter of an object of mass M with a particle with mass m (the standard gravitational scattering problem). The total change is given by δv M = δv M + δv M. If M goes through a homogeneous sea of particles, δv M = 0. scattering with impact parameter b and velocity V 0, we have For each δv M = 2mV [ 0 1 + m + M b 2 V0 4 ] 1 G 2 (M + m) 2
If the number density of particles (stars) with velocity v m is f (v m )d 3 v m, the rate of encounters of M with such stars and with impact parameters in the range b b+db is 2πbdb v 0 f (v m )d 3 v m. The rate of change in v M due to encounters with these stars is then ( ) dvm dt v m d 3 v m = V 0 f (v m )d 3 v m bmax 0 v M 2πbdb = 2πln ( 1 + Λ 2) G 2 m(m + M) f (v m )d 3 v m (v m v M ) v m v M 3, (1) where Λ b maxv 2 0 G(M+m), b max considered. is the largest impact parameter that needs to be
Assuming that the distribution of v m is isotropic, the rate of change in v M due to encounters with stars of all velocities can be obtained by integrating over v m. Note that this is equivalent to finding the gravitational field at position v M generated by the mass density 4πln(Λ)G 2 m(m + M) f (v m ). The result is dv M dt = 16π 2 lnλg 2 m(m + M) v M v 3 M f (v m )v 2 m dv m. This is the Chandrasekhar dynamical friction formula. ( ) If f (v m ) is Maxwellian: f (v) = n 0 exp v2, then (2πσ 2 ) 3/2 2σ 2 dv M dt where X v M /( 2σ). = 4πlnΛG2 (m + M)ρ v 3 M [ erf(x) 2X π e X2 ]v M,
Dynamical friction in dark halos As a simple application, let us consider a satellite on circular orbit in the potential of a halo of singular isothermal sphere: ρ 0 (r) = Vc 2 /(4πGr 2 ). For an isothermal sphere, σ = V c / 2 and so X = 1. Under the assumption that M m the dynamical friction force experienced by the satellite at radius r is F = 0.428lnΛ GM2 r 2. This force is always tangential, and so the rate of change in the angular momentum L is dl dt = Fr M. Since L = rv c, the radius of the orbit r changes with time as r dr dt = 0.428GM lnλ. V c
For an initial orbit with radius r i, the time for M sink to the halo center is t df = 1.17 ri 2V c lnλ GM = 1.17 ( ri lnλ R h ) 2 ( Mh M ) Rh V c. If r i R h, t df 1.17 ( ) Mh 1 ln(m h /M) M 10H(z), where we have used R h /V c = 1/10H(z). Thus, the dynamical friction timescale is longer than the age of the universe for M/M h < 30.
Criterion for Mergers Galaxy Merging What kind of encounters are likely to lead to the merger of two galaxies? A simple case: two identical spherical galaxies. of mass M and median radius r med. The internal mean-square velocity is v 2 0.4GM/r med. Such an encounter is specified by E orb (the specific orbital) and L (the specific angular momentum) in units derived from v 2 and r med : Ê E orb (1/2) v 2 and ˆL L v 2 1/2 r med. Each encounter is then associated with a point in the (Ê, ˆL) plane which can be devided into different reagions
Orbits in the upper-left region are forbidden, because for a given orbital energy the largest possible angular momentum is that of circular orbit. Encounters with too high orbital energy and too high orbital angular momentum cannot lead to a merger. Mildly hyperbolic orbits can lead to a merger if the orbital angular momentum is sufficiently low.
Merger requires low Ê, i.e. E orb < v 2 /2 (or σ 2 < v 2 /2) and low ˆL (large r med ). Conclusion 1: Galaxies can merge quickly if they are in systems with velocity dispersion comparable to the internal velocity dispersion of the individual galaxies. Conclusion 2: Massive, extended halos can merger more easily than their central galaxies
Structure of Merger Remnants Major mergers of galaxies are expected to be accompanied by violent changes in the gravitational potential of the system. Because of violent relaxation, the merged system generally relax to form a smooth object near the center of the system, with some irregular structure at large radii. The properties of such merger remnants are important to understand. If we know how merger remnants behave, we can look for merger signatures and estimate how many mergers have occurred during the history of the universe. More importantly, the study of the structure of merger remnants can help us to understand what kind of galaxies may have formed by galaxy merging.
Simulation results Being faint, merging structures are in general difficult to observe. Numerical simulations are used to understand the properties of merger remnants. Some of the most important results obtained are 1. Major mergers of galaxies generally lead to elliptical-like remnants, with some irregular structures in the outer regions. Depending on the orbital geometry of the merger, the remnant can either be prolate or oblate. In general, mergers of two equal-mass disks lead to rounder remnants if the spins of the merging progenitors are more tilted relative to the orbital angular momentum. Highly flattened remnants can be produced in prograte and retrograde encounters. 2. The remnant of a major merger generally rotates slowly in the inner region but fast in the outer part. This happens because dynamic friction can transfer angular momentum from particles with high binding energy to the ones with low binding energy. If merging galaxies have extend massive haloes, the
effective transfer of angular momentum from the merging galaxies to dark matter generally leads to slowly-rotating remnants, and so the inner part of such a remnant is supported by velocity dispersion. 3. The final density profiles of merger remnants in projection are well fitted by the R 1/4 -law profiles over a large radial interval.
Transformation of Galaxies in Clusters Although galaxy-galaxy mergers should not be frequent in clusters of galaxies, cluster environment may play an important role in transforming the morphologies of their member galaxies. Clusters of galaxies are the largest virialized systems in the universe, with masses of about 10 14 10 15 M, and velocity dispersions of about 1000kms 1. Many clusters are also found to contain large amount of hot X-ray gas. Thus, galaxies in a cluster can be affected by the cluster environment in three different ways: ram-pressure stripping of their gas components by the hot ICM; encounter with other member galaxies and cluster substructures; tidal interactions with the global cluster potential.
Galaxy Interaction and Starbursts So far only the interactions of gas-free galaxies are discussed. In many cases, merging progenitors may contain gas. For example, mergers of present disk galaxies which contain cold gas; high-redshift protogalaxies. It is important to understand how gas behaves. bbbbbb A parabolic encounter of two gas-rich disk galaxies. The stellar distribution is shown on the left; each frame is about 80 96 kpc. Times (-60, 60, 150, 300, 420 Myr, from top to bottom) are given with respect to pericenter at t = 0. Hot gas is shown in the middle, color codes temperature. Cool gas is shown on the right.
Because of tidal interaction, merger induces non-axisymmetric structure in the center. The gas and stars have different response to the tidal force, and gas and stellar structures have different phases. This phase difference gives rise to torques that can effectively remove angular momentum from the gas. The gas then flows towards the central region, forming a dense gas concentration in the core of the merger remnant. The surface density of the gas core in the merger remnant is in general many orders of magnitudes higher than the surface density of the pregenitors. Since Σ Σ 1.4 gas, intense star formation in the center of a gas merger. This is reminiscent of that for starburst galaxies. There are many reasons to believe that many starbursts are produced by galaxy interaction.
Starbursts short time scale for star formatio: 10 7-10 8 yr, powered by massive young stars. large star formation rate per unit area, compact ( 1kpc). high star formation rate: a powerful starburst may have a SFR 100-1000M yr 1