Modeling the dynamical friction timescale of a sinking satellite

1. Modeling the dynamical friction timescale of a sinking satellite Gan, Jianling/甘建铃 Korea Astronomy and Space Science Institute Shanghai Astronomical Observatory Collaborator: Kang, Xi/康熙 Purple Mountain Observatory 2010, RAA, 10, 1242

2. Motivation • The merger between halos is an important process in the formation and evolution of galaxy. • How long it needs for a satellite halo merging with the host halo center? • Merging timescale is also called dynamical friction timescale (Tdf ). • Many studies have been dedicated to deriving Tdf but debated on an accurate form of Tdf . • What determines the dynamical friction timescale? 2010, RAA, 10, 1242

3. Previous Results I: point mass • Initial orbital parameters: η, orbital energy; ε, orbital circularity; Rm=M/m, mass ratio between the host and satellite halo. • Binney & Tremaine (1987, BT87): Tdf for a satellite starting with a circular; • Lacey & Cole (1993, LC93): Taking into account the dependence on the orbital circularity; • The both consider satellite as a rigid object (point mass).

4. Previous Results II: live satellite Colpi et al. (1999, C99): N-body simulations Boylan-Kolchin(2008, BK08): N-body simulations Jiang et al. (2008, J08): SPH simulations.

5. Previous results III: Comparison • Tdfdecreases with satellite mass • Tdf increases with orbital angular momentum (ε). • T03 agrees well with LC93 for large satellites (Rm-1<0.1), but disagrees for small satellites. • Tdfof BK08 and J08 are longer than those of T03 and LC93. • Tdf of BK08 exhibit a steeper dependence on ε than other results. • What contributes to these discrepancies?

6. Model Contents The decay of subhalo orbital angular momentum and energy due to dynamical friction; The subhalo mass loss due to tidal stripping; The subhalo mass redistribution due to tidal heating.

7. Dynamical friction:decreases the orbital energy and angular momentum of the subhalo • Chandrasekhar dynamical friction (Binney & Tremaine 1987) • Fdf∝m2，opposes to the motion. • lnΛ：Coulomb logarithm

8. Tidal stripping: decreases the subhalo mass Tstrip: stripping timescale; A:tidal stripping efficiency Tidal radius（Von Hoerner 1957; King 1962; Taylor & Babul 2001）:

9. Tidal heating: changes the subhalo density profile Fitting formula from Hayashi et al. (2003): reduction in central density truncation radius

10. Results • Definition (Tdf): The time interval between accretion and the epoch of merging, when the satellite halo loses all of its angular momentum.

11. Dependence of Tdfon the tidal stripping efficiency A • Tdf depends strongly on A (tidal stripping efficiency), Tdf increases with A. • Stronger tidal stripping lead to more mass loss and subhalo suffer weaker dynamical friction

12. Interpreting the discrepancies of previous results • LC93 considers satellite as rigid object • T03 considers tidal stripping for small satelliteonly (Rm-1<0.1) • J08and BK08 consider a stronger effect of tidal stripping than T03 and LC93 • in T03，A=1.0；in BK08，A≈2.0

13. Dependence of Tdf on orbital circularityε Minor merger, power law, Colpi et al. (1999): Major merger, exponential law, Boylan-Kolchin et al (2008): • The dependence of Tdfon the orbital circularity is mainlydetermined by the distribution of mass ratio between the satellite and host halo.

14. Summary Thank you! 2010, RAA, 10, 1242 We study the physical processes governing the dynamical timescale (merging timescale). The treatment of mass loss from the satellite by tidal stripping dominates the behavior of Tdf . The dependence on ε is determined by the model/simulation sample, in which the mass ratio between the satellite and host halo is crucial.