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Dynamical mass segregation near massive black holes

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Leiden Observatory

Dynamical mass segregation near massive black holesShanghai, October 2009

Outline

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

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

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)

Dynamical friction black hole

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

Duo-mass systems black hole

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)

Duo-mass systems black hole

Equal mass stars

Many very heavy stars

Rare very massive stars

= 2.75 > 2

“Strong Mass-segregation” (Alexander & Hopman 2009)

α black hole - 3/2

Duo-mass systemsStrong 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)

Galactic center: Steady state? black hole

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)

Galactic center: Steady state? black hole

Preto & Amaro-Seoane (2009)

Steady state with strong mass-segregation reached in 0.2 relaxation times

Gravitational Waves black hole

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)

Cusp-disk interactions black hole

The eccentricity instability depends on mass and slope of cusp

Madigan, Levin & Hopman (2009)

Resonant relaxation and S-stars black hole

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)

Conclusions black hole

- 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

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