Relativistic loss-cone dynamics: Implications for the ...snaoz/Aspen16/Slides/aspen16.pdf ·...

Relativistic loss-cone dynamics: Implications for the Galactic Center

Relativistic loss-cone dynamics:Implications for the Galactic Center

Tal Alexander

Weizmann Institute of Sciencelo

g1

0 a

/mpc

log10 j

LSO

GW timescales

GW Separatrix

aGW

RR>NR contour

AI contour

MW S-stars

-1

0

1

2

3

-3 -2.5 -2 -1.5 -1 -0.5 0

RR > NR

RR < NR

MBH

GW

Plunge

Bar-Or & TA 2015


Getting stars to the MBH

The stellar dynamical loss-cone problem:

How do stars in a galactic nucleus interact strongly with a massive black

hole (MBH) and/or fall into it, and at what rates?

��

��

Scatterers

Test star

"Loss cone"

BH and "strong interaction zone"

Implications

Plunge processes:Tidal disruption �ares1,2, tidal detonation3,tidal scattering 4, gravitational wave (GW) �ares

Inspiral processes:GW extreme mass ratio inspirals (EMRIs) 1,2,5,tidal squeezars 6, accretion disk capture

Exotic stellar populations near MBHs 7,8,9

MBH+stars formation and evolution 10,11,12,13

How do galactic nuclei randomize and relax?

1:TA & Hopman 2003 2:Bar-Or & TA 2015 3: TA 2005 4:TA & Livio 2001 5:Hopman & TA 2005, 2006a, 2006b 6:TA & Morris 2003 7:TA 1999

8:TA & Livio 2004 9:Perets, Hopman & TA 2007 10:TA & Hopman 2009 11:TA & Kumar 2001 12:Bar-Or & TA 2014 13:Bregman & TA 2012



Randomization by relaxation

Relaxation near a MBHNon-coherent relaxation (NR: E , J) Resonant relaxation (RR: J)

Point�point interactions Orbit-orbit interactions

��

��

Scatterers

Test star

"Loss cone"

BH and "strong interaction zone"

Stationary ellipses

in point mass potential

Planar rosettes in

spherical potential

Effect on perturbed starPerturbing stars

Scalar resonant relaxation

Vector resonant relaxation

Rauch & Tremaine 1996

Q = M•/M?

TNR ∼ [Q2P /N?]/ logQ TRR ∼ [Q2P/N?]P/tcoh1/ logQ: relaxation boost from close encounters P/tcoh: relaxation boost from long coherence

Near MBH: TRR/TNR ∼ logQ(P/tcoh)� 1

Fast evolution to J → 0: Strong interaction with the MBH




The �classical� (pre-RR) loss-cone: Plunge vs inspiral

Loss primarily by by J-relaxation: TJ ∼ j2TE j = J/Jc (E)

short P

long P

ciscolog a

log a

Plunge

log J/Jclog J /Jlc

J−scattering

E,J−scattering

short P

long P

crit

isco log J/Jlog a

log a

log a

cclog J /Jlc

Inspiral

Plunge

Detectable GW

J−scattering

Dissipation

(Lightman & Shapiro 1977; Cohn & Kulsrud 1978) (TA & Hopman 2003; Hopman & TA 2005)

Γplunge∼ N?(< rh)/ 〈log(Jc/Jlc)TE 〉 Γinspiral ∼ N? [< rcrit(TE )] /〈log(Jc/Jlc)TE 〉

Γinspiral ∼ O(0.01)Γplunge




The �danger� of unquenched RR: No inner cusp(No GR stars, no GW EMRIs, no . . . )

The �fortunate coincidence� conjecture:(Hopman & TA 2006)

I Unquenched, RR drives all stars toplunge orbits (no EMRIs!).

I O(β2j−2) GR in-plane Schwarzschildprecession becomes signi�cant beforeO(β5/2j−7Q−1) GW dissipation.

I GR precession quenches RR and allowsEMRIs to proceed unperturbed,decoupled from the background stars.

(Bar-Or & TA 2015)

log

10(a

/mpc)

log10(j)

log10(d2n/dlgj dlga)

-0.5 <

-1.0 < -0.5

-1.5 < -1.0

-2.0 < -1.5

-2.5 < -2.0

-3.0 < -2.5

-3.5 < -3.0

-4.0 < -3.5

-4.5 < -4.0

-5.0 < -4.5

-5.5 < -5.0

<-5.5

LSO

GW

inspiral

plunge

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

-3 -2.5 -2 -1.5 -1 -0.5 0

nsnap=24982944 np=10469 ni=0

Rp= 8.0e-04 1/yr

Ri= 0.0e+00 1/yr

−2.5 −2.0 −1.5 −1.0 −0.5log10(J/Jc)

−2

−1

0

1

2

3log 1

0(a/m

pc) RR > NR

Last Stable Orbit


Results

The relativistic loss-conelo

g1

0 a

/mp

c

log10 j

LSO

GW timescales

GW Separatrix

aGW

RR>NR contour

AI contour

MW S-stars

-1

0

1

2

3

-3 -2.5 -2 -1.5 -1 -0.5 0

RR > NR

RR < NR

MBH

GW

Plunge

The η-formalism

Stellar dynamics in the presence of correlated noise

(Ben Bar-Or's talk)

• Adiabatic invariance(?) quenches RR at low-j

• NR dominates evolution on long time scales

• Dynamical modeling of the relativistic loss-cone

E�ective RR di�usion that express correlated noise and secular

precessions, together with NR di�usion and GW dissipation,

provide a powerful scalable Monte Carlo tool for modeling

long-term dynamics and loss-rates of galactic nuclei in the

realistic N? � 1 limit(†).

? Correct form and interpretation of the �Schwarzschild Barrier�(Merritt, TA, Mikkola & Will 2011).

† Validated against N-body results in the low-N?regime.

(Bar-Or & TA 2015)


Results

GW EMRI and tidal disruption rates in steady statelo

g10(a

/mpc)

log10(j)

log10(d2n/dlgj dlga)

-0.5 <

-1.0 < -0.5

-1.5 < -1.0

-2.0 < -1.5

-2.5 < -2.0

-3.0 < -2.5

-3.5 < -3.0

<-3.5

LSO

GW

AI contour

DC contour

inspiral

plunge

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

-3 -2.5 -2 -1.5 -1 -0.5 0

nsnap=24984314 np=9625 ni=29

Rp= 7.4e-04 1/yr

Ri= 2.2e-06 1/yr

ma

xa

/a

R (NR+RR) / R (NR) pp

102 103 104 105 106 107 108 109 1010

M•/M⊙

10−7

10−6

10−5

10−4

10−3

10−2

Rat

e[1

/yr]

Plunges

Inspirals

MC data without RRMC data with RR

Galactic nucleus model (�MWEG�)

• GR+mass precession

• GW+NR+RR

• Smooth noise+mass quenching

• Adiabatic invariance saves EMRIs:

�Fortunate coincidence� validated.


Results

Puzzles of the Galactic center:Origin of the S-stars? Where's the old stellar cusp?

Incomingscatteredbinary

Captured star

EjectedHyper−Velocity Star

Efficient scattering by massive perturbers(Perets, Hopman & TA 2007)

(Hills 1991)

log

10 a

/mp

c

log10 j

LSO

Tidal disruption

RR>NR contour

AI contour

MW S-stars (observed)

Binary capture model jiDisk origin model ji

-1

0

1

2

3

-3 -2.5 -2 -1.5 -1 -0.5 0

RR > NR

RR < NR

MBH

TD

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

CD

F[P

(>j o

bs)]

P(>jobs)

Cusp TBC PKS=0.40 ± 0.10

Cusp Disk PKS=0.10 ± 0.05

Core TBC PKS=6e-9 ± 1e-7

Core Disk PKS=1e-3 ± 1e-2

Blue giants

Compact remnants

Red giants

B dwarfs

Faint low−mass stars

Warped disk(s)

GMC

[Binaries?]

[Disrupted cluster + IMBH?]

S−cluster

[Dark cluster?]

Molecularclumps

~0.5 pc

~0.04 pc

10−100 pcr_infl ~2 pc

~1.5 pc

Sabsovich, Bar-Or & TA 2016, in prep.

Conclusions: 1. RR is essential for S-stars post-capture/migration randomization.

Disk formation and migration (Levin 2007) 2. Best �t model: Tidal capture in dense old cusp of stellar remnants.


Results

The hunt for relativistic stars for testing strong gravity1,2,3

I Option 1: No old cusp in inner Galactic center (inner RG cusp missing4,5,6)

I All young stars inside . 0.01 pc observed�none strongly relativistic.

I Low stellar density ⇒ very slow dynamical evolution.

I ⇒ No local stellar targets for tests of strong GR.

I Option 2: Dark cusp of stellar remnants + old stars further out

I Rapid e-evolution (RR), but slower a-evolution (NR).

I Stellar destruction (T ? ∼ 5× 107 yr) faster than TE at O(1 pc).I Strong depletion of local strongly relativistic stars.

I Option 3: Dark cusp of stellar remnants + tidally-captured stars

I Low-mass equivalents of S-stars / Hyper-velocity B-stars.

I Fast, continuous supply rate if scaled by S-stars.

1:Zucker, TA, Gillessen et al 2006 2:Will 2008 3:Merritt, TA, Mikkola & Will 2010 4:Buchholz et al 2009 5:Do et al 2009 6:Bartko et al 2010


Results

Evolution of tidally-captured relativistic stars in a dark cusp

Orbital evolution of captured stars with NR+RR+GW+tides+collisions

1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 3.0e+02 yr

µas/yr 1 5 10

S 0.0004 0.0003 0.0002

J 0.0002 0.0001 8e-05

Q 4e-05 2e-05 6e-06

Sabsovich, Bar-Or & TA, 2016, in prep.


Results



1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 1.0e+03 yr

µas/yr 1 5 10

S 0.003 0.002 0.001

J 0.001 0.0006 0.0004

Q 0.0002 9e-05 3e-05



Results



1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 3.0e+03 yr

µas/yr 1 5 10

S 0.008 0.005 0.004

J 0.004 0.002 0.001

Q 0.0008 0.0003 0.0001



Results



1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 1.0e+04 yr

µas/yr 1 5 10

S 0.03 0.02 0.01

J 0.01 0.007 0.005

Q 0.003 0.0009 0.0003



Results



1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 3.0e+04 yr

µas/yr 1 5 10

S 0.09 0.05 0.04

J 0.04 0.02 0.01

Q 0.008 0.002 0.0007



Results



1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 1.0e+05 yr

µas/yr 1 5 10

S 0.3 0.2 0.1

J 0.1 0.07 0.05

Q 0.03 0.006 0.001



Results



1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 3.0e+05 yr

µas/yr 1 5 10

S 0.7 0.5 0.4

J 0.3 0.2 0.1

Q 0.06 0.01 0.002



Results



1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 1.0e+06 yr

µas/yr 1 5 10

S 2 1 1

J 0.9 0.5 0.3

Q 0.1 0.02 0.003



Results



1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 3.0e+06 yr

µas/yr 1 5 10

S 5 3 2

J 2 1 0.6

Q 0.2 0.03 0.004



Results



1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 1.0e+07 yr

µas/yr 1 5 10

S 1e+01 5 4

J 3 2 0.9

Q 0.3 0.03 0.004



Results



1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 3.0e+07 yr

µas/yr 1 5 10

S 2e+01 8 6

J 5 2 1

Q 0.3 0.04 0.005



Results



1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 1.0e+08 yr

µas/yr 1 5 10

S 4e+01 1e+01 8

J 6 2 1

Q 0.4 0.04 0.005



Results



1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 3.0e+08 yr

µas/yr 1 5 10

S 5e+01 2e+01 9

J 7 2 1

Q 0.4 0.04 0.005



Results



1

5

10

1

5

10

1

5 µas/yr10

-3 -2.5 -2 -1.5 -1 -0.5 0

log10(1-e)

-1.5

-1

-0.5

0

0.5

1

1.5

log

10(P

/yr)

-10

-8

-6

-4

-2

0

TD THQ2

J

S

t = 1.0e+09 yr

µas/yr 1 5 10

S 5e+01 2e+01 9

J 7 2 1

Q 0.4 0.04 0.005



Summary

Summary

I Theoretical results (more in Ben Bar-Or's talk)

I NR, RR, GW dissipation and secular precession can be treatedanalytically as e�ective di�usion with correlated noise.

I The steady state depends mostly on NR, which erases AI.

I General applications

I Relativistic loss-cone modeling of galactic nuclei in N? � 1 limit.

I Plunge / EMRI rates and branching ratios.

I Implications for the Galactic Center

I Origin of S-stars: Dark cusp + binary capture favored.

I O(100) captured low-mass relativistic stars may exist in GC, butstrongly relativistic orbits suppressed by tidal interaction with MBH.

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