Dynamical mass segregation near massive black holes

1. Clovis Hopman Leiden Observatory Dynamical mass segregation near massive black holes Shanghai, October 2009

2. Outline • Motivation • Understanding the physics: duo-mass systems • The Galactic center: steady state? • Applications

3. Motivation • General: knowledge of the stellar content of galactic nuclei • Dynamics in inner cusp may be dominated by unobservable stellar black holes; this may have determined the distribution of the S-stars (see talk by Perets) • Gravitational wave inspirals originate close to the black hole

4. Distribution of single mass stellar population around a black hole Assumptions: Stars much lighter than MBH Fixed velocity dispersion σ and density profile far away from MBH Steady state Solution only valid within radius of influence rh=GM/σ2 Genzel et al. (2003) Single mass solution: “Cusp” (Bahcall & Wolf 1976)

5. Dynamical friction v F Motion of heavy object induces over-density of stars behind it As a result, the star slows down and spirals in The effect is stronger for heavy stars than for light ones: mass-segregation

6. Duo-mass systems Bahcall & Wolf (1977) Interaction terms Steady state requires dQ/dx=0. But in the special single mass case that M=M', it holds that Q(x)=0, known as the zero-flow solution In that case, theoretical limit of αH<2 (Bahcall & Wolf 1976)

7. Duo-mass systems Equal mass stars Many very heavy stars Rare very massive stars = 2.75 > 2 “Strong Mass-segregation” (Alexander & Hopman 2009)

8. Strong mass-segregation Steady-state Dynamical friction limit: no zero-flow solution

9. α - 3/2 Duo-mass systems Strong mass-segregation regime Zero-flow limit (Bahcall & Wolf 1977) Alexander & Hopman (2009) See also Murphy et al. (1993), Baumgardt et al. (2004), Freitag et al. (2006) For analysis with continuous mass-function, see Keshet, Hopman & Alexander (2009)

10. Galactic center: Steady state? Late type stars appear to have a core within 0.5 pc (Buchholz et al. 2009; Do et al. 2009; Bartko et al. 2009) Within 0.5 pc, ρ~r-α, α<1 Possibility: Galactic center not relaxed? (Merritt 2009) Merritt (2009); Buchholz et al. (2009)

11. Galactic center: Steady state? Preto & Amaro-Seoane (2009) Steady state with strong mass-segregation reached in 0.2 relaxation times

12. Gravitational Waves Inspiral rate of stars onto MBHs dominated by stellar BHs due to mass-segregation. Hopman & Alexander (2006) Inspiral rate dominated by MBHs less than 4e6 Msun (Hopman 2009, Gair 2009). Relaxation time ~ M5/4 Steady state not an issue. Test for black holes in Galactic center: LISA may see 1 GW burst / yr (Toonen et al. 2009)

13. Cusp-disk interactions The eccentricity instability depends on mass and slope of cusp Madigan, Levin & Hopman (2009)

14. Resonant relaxation and S-stars Rauch & Tremaine (1996); Hopman & Alexander (2006); Perets et al. (2009); Madigan et al. (2009, in prep.) Only if inner 0.01 pc dominated by stellar black holes, resonant relaxation operates fast enough to affect eccentricity of S-stars Perets et al. (2009)

15. Conclusions • Dynamical friction drives BHs close to MBH • Strong mass-segregation with slopes steeper than -2 possible • Not clear whether Galactic center in steady state; there appears to be a “hole” • Gravitational wave sources dominated by BHs • S-stars evolve dynamically through resonant relaxation only with enough BHs