dynamical evolution of stars near massive black holes · dynamical evolution of stars near massive...

Dynamical Evolution of Stars Near Massive Black Holes

Dynamical Evolution of StarsNear Massive Black Holes

Tal Alexander

Weizmann Institute of Science


Introduction

Introduction

I Evolution of isolated starsB Fixed by initial (internal) conditions (Mass, abundances, spin)

I Galactic center environmentB Central MBH (mass sink, tidal field)

B Extreme stellar densityB High velocity collisions

I Evolution of stars near a MBHB Modified by strong gravitational interactions (dynamical history)

B Stochastic evolution (different stars—different histories)

B Long-term evolution uncertain (complex stellar structure physics)

B Short-term energetic destruction (GW inspiral, tidal disruption)

I Stellar evolution coupled with dynamical evolution


Extreme stellar dynamics

Extreme stellar density

Genzel et al. 2003; Schödel et al 2006

ρGC(<1 mpc)∼108 M�pc−3∼109ρ� I tcoll < t?, vcoll >vesc


Extreme stellar dynamics

Star-star interactions

Collisional destruction Tidal spin-up

10

100

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

L K [

L Ko]

p [arcsec]

0.001

0.01

0.1

1

0.1Fr

actio

n of

bre

akup

rota

tion

r [pc]

TotalMS-MSMS-WDMS-NSMS-BH

Alexander 1999 (new data: Ott & Trippe 2005) Alexander & Kumar 2001


Strong star-MBH interactions


Direct infall Absorption / Annihilation

Feeding, Tidal disruption, detonation, flares Γinfall

Inspiral Meta-stable decay vs collisional ionization

Tidal scattering Deep inelastic scattering

3-body exchange Charge exchange

Alexander & Livio 2001; Alexander & Hopman 2003; Alexander & Morris 2003; Alexander & Livio 2004




Direct infall Absorption / AnnihilationΓinfall

Inspiral Meta-stable decay vs collisional ionization

Gravity waves, Tidal capture (“Squeezars”) Γinspiral∼10−2Γinfall








Inspiral Meta-stable decay vs collisional ionizationΓinspiral∼10−2Γinfall


“Weird” stars Γscatter(< r)∼Γinfall

h(r/q)δ − 1

i∼O(Γinfall )







Inspiral Meta-stable decay vs collisional ionizationΓinspiral∼10−2Γinfall

Tidal scattering Deep inelastic scatteringΓscatter(< r)∼Γinfall

h(r/q)δ − 1

i∼O(Γinfall )


Orbital capture

Σ'»

1+A2M?(m+M•)

mM•V 2

–| {z }

Grav. focusing

B„

M•+M?

m+M•+M?

«2πa2

| {z }Capture radius

"„M?

M•

«7/4 „m+M•

m+M?

«1/4#

| {z }Phase space volume




Loss-cone replenishment

Jlc /Jc

Kick regime

Diffusion regime(small r, high E)

(large r, low E)

Change per period

ScattererHills 1975Frank & Rees 1977Lightman & Shapiro 1977Cohn & Kulsrud 1978Shapiro & Marchant 1978

• 2-body relaxation Γ∼ n?/ log(Jc/Jlc)trelax

B Slow diffusion into the loss-cone

• Is faster relaxation possible?B Non-spherical potentials Magorrian & Tremaine 1999

B Chaotic orbits Norman & Silk 1983Gerhard & Binney 1985Merritt & Poon 2004


Beyond 2-body stellar relaxation

Resonant relaxation

Stationary ellipses in point mass potential

Planar rosettes inspherical potential

Effect on perturbed starPerturbing stars

Scalar resonant relaxation

Vector resonant relaxation

Rauch & Tremaine 1996



Resonant relaxation near the Galactic black hole

10−3 10−2 10−1 1a (pc)

101

102

103

104

t (M

yr)

TNR

T_ s

RR TvRR

Star disks

S- stars

GW sources

Relaxed giants

Hopman & Alexander 2006



Accelerated relaxation by massive perturbers

Large-angle deflection: v2 ∼ 2GM/rc Obs. MPs in central 100 pc

Deflection rate: Γ∼nvr2c ∼nM2/v3 ∼ 108 stars of 1 M�

(Zhao, Haehnelt & Rees 2002) ∼ 102 MPs of 103−5 M�Example:`nM2´

GMC∼3×103 `

nM2´?

Perets, Hopman & Alexander 2006

GMC

cluster

Massive perturbersaccelerate relaxation inthe Galactic Center andplausibly in late-typegalaxies generally.



Massive perturbers in the Galaxy

0.001 0.004 0.01 0.04 0.1 0.4

0.1

1

10

Semi Major Axis (pc)

No. o

f MS

B−St

ars

GMC1

GMC2Clusters

Stars

Observed

First results:

• Exchange capture ofyoung stars near SgrA?

(Gould & Quillen 2003)

• Steady supply of high-v stars

B Tens of v >500 km/s, 3-5 M�stars, tens of kpc from GC

• Rapid binary MBH mergers

B 2×106 M� + 2×106 M�merger in Galactic Centerin <109 yr

Perets, Hopman & Alexander 2006, in prep.


Summary

Summary

I Stellar evolution near a MBH is an interplay of

B Initial conditionsB Dynamical history

I A high density cusp near a MBH

B Frequent star-star interactionsB Large reservoir for star-MBH interactions

I Fast relaxation is key to star-MBH interactions

B Resonant relaxation near MBHB Massive perturbers far from MBH


Summary

Accelerated binary MBH merger

0 1 2 3 4 5 60.001

0.01

0.1

1

Time (108 yrs)

Sem

i Maj

or A

xis

(pc)

10−5 10−4 10−3 10−2 10−1 100104

106

108

1010

1012

1014

Semi Major Axis (pc)Co

ales

cenc

e Ti

me

(yea

rs) GW

Scattering

Perets, Hopman & Alexander 2006

dynamical evolution of stars near massive black holes · dynamical evolution of stars near massive...

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