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Clovis Hopman Leiden Observatory. Dynamical mass segregation near massive black holes. Shanghai, October 2009. Outline. Motivation Understanding the physics: duo-mass systems The Galactic center: steady state? Applications. Motivation.

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Clovis hopman leiden observatory

Clovis Hopman

Leiden Observatory

Dynamical mass segregation near massive black holes

Shanghai, October 2009


Outline
Outline

  • Motivation

  • Understanding the physics: duo-mass systems

  • The Galactic center: steady state?

  • Applications


Motivation
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
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
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
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 systems1
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)


Strong mass segregation
Strong mass-segregation black hole

Steady-state

Dynamical friction limit: no zero-flow solution


Duo mass systems2

α black hole - 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)


Galactic center steady state
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 state1
Galactic center: Steady state? black hole

Preto & Amaro-Seoane (2009)

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


Gravitational waves
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
Cusp-disk interactions black hole

The eccentricity instability depends on mass and slope of cusp

Madigan, Levin & Hopman (2009)


Resonant relaxation and s stars
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
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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