1. Galaxy Formation and Evolution, Mo, van den Bosch & White, 2010 Galactic Dynamics, Binney & Tremaine 2008

2. Introduction Galaxy interactions are frequent in the hierarchical scenario of galaxy formation. They play important in the evolution of the star formation and morphology of galaxies. How to investigate them?

3. Galaxy interactions High-speed encounters, tidal heating Tidal stripping Dynamical friction Galaxy merging Galaxies in clusters Harassment Cannibalism Ram-pressure stripping Strangulation

4. Energy change of a particle q: Energy change of the system S: This energy is transferred to potential energy, which becomes less negative, implying that the system S is tidally heated and expands.

5. Tidal radius: The radius where the tidal forces exceed the binding forces. For a sub system of mass m moving on an orbit r in an extended host system of mass M: The unbound mass outside r t are stripped gradually. (Gan et al. 2010)

6. The stripped stars move on roughly the same orbit as the satellite galaxy, forming an either trail or lead stream (minor mergers). All stars along the stream have similar orbital energy, it can be used to constrain the gravitational potential of their host system (Milky Way). tidal tail is usually refered to the structures formed by tidally stripped stars in major mergers. Sagittarius stream Tidal tail formed by NGC 4038 and NGC 4039

7. As an object M moves through a sea of particles, the particles passing by are accelerated towards the object. As a result, the particle number density behind the object is higher than that in front of it, and the net effect is a drag force (dynamical friction) on the object. The satellite halos sink to the host system center due to dynamical friction within a merging timescale (Colpi et al., 1999; Boylan-Kolchin et al., 2008; Jiang et al., 2008).

8. Evolution of the orbital angular momentum of a satellite halo (Gan et al. 2010). A: tidal stripping efficiency Mass loss due to tidal stripping weaken the effect of dynamical friction.

9. The merging processes typically are treated with simulation. The violent relaxation plays an important role during the relaxation of the merger remnant. The remnant typically has little resemblance to its progenitors in major merger, while not in minor merger. Disks that accrete small satellites typically survive but can undergo considerable thickening (disk heated). Major mergers that involve one or more disk galaxies tend to create tidal tails. The gas-rich merger (wet merger), in general, triggers new starburst and AGN activity.

10. Harassment Cannibalism Ram pressure stripping Strangulation High density in mass and number High speed Hot gas (ICM) Phoenix clusters simulation

11. The cluster galaxies have typically high velocity and suffer frequent encounters. The cumulative effect of multiple high-speed impulsive encounters is generally referred to as galaxy harassment. The fragile disks of late-type (Sc-Sd) spiral galaxies can be almost entirely destroyed by harassment. The disks lose very substantial amounts of mass. The bound stars are also heated, which transforms the disk into spheroidal component. Dwarf ellipticals are ubiquitous in clusters. For more compact early-type (Sa-Sb) disk galaxies, they can be significantly heated and become more easily to be stripped by tides or ram pressure.

12. A galaxy will sink to the cluster center if the dynamical friction time is sufficiently short. This galaxy merged with the central galaxy and this process is called galactic cannibalism. Cannibalism causes a mass increase of the central galaxy, and a depletion of massive satellite galaxies. Hence, it causes an increase of the magnitude difference between the first and second brightest galaxies in cluster: ΔM 12 The magnitude gap ΔM 12 can be used as a measure for the dynamical age of the cluster. The T df is determined by various factors.

13. A ram pressure is just like one feels wind drag when cycling. Gas stripping occurs where the pressure exceeds the binding force per unit area. Ram-pressure stripping may be efficient and quench star formation in satellite galaxy. But there are still debate. Only the gas at relatively large galactocentric radii is being stripped. The remaining non-stripped gas may actually be compressed by the ram pressure, giving rise to enhanced star formation. The stripped gas may remain bound to the galaxy, fall back and induce a later starburst. (Font et al. 2008)

14. The outer parts of a satellites gas are stripped. Star formation may continue at inner parts but the gas consumption time scale is short (1-5Gyr). A gas reservoir surround the satellite: hot gas just falling; gas shocked to high temperature; reheated and expelled gas by feedback. The gas reservoir is hot and loosely bound to the satellite, so it is fairly easily stripped off, either by tides or by ram pressure. If a large fraction of gas is stripped off from a satellite after it is accreted into the cluster, its star formation rate will decline gradually and this is called strangulation. The strangulation is believed to be responsible for the morphology-density relation. The motion of satellite after accretion is determined by various factors.

15. The morphology–distance relation in Abell cluster. (Park & Hwang 2009) C3: 20.5 > M r > 22.5 C2: 19.0 > M r > 20.5 C1: 17.0 > M r > 19.0

16. Galaxy interactions are of diversity and complicated, especially in clusters. The relative effects of various interactions need to be analyzed statistically based a large sample of evolving galaxies. It may be a way out to examine the magnitude gap and morphology-density relation, following the hierarchical growth of cluster.