Stellar Dynamical Processes Steinn Sigurdsson Penn State 18 Nov - - PowerPoint PPT Presentation

18 Nov 2002 MBHCoal ’02

Stellar Dynamical Processes

Steinn Sigurdsson Penn State

18 Nov 2002 MBHCoal ’02

”Hard Binaries”

• Problem of transiting from the “dynamical

friction dominated’’ regime to the “gravitational radiation’’ dominated regime

• Obvious channel is super−elastic scattering
• ff individual stars in the “background’’
• Do we get from rh to rgrav−rad in less than

Hubble time? In ~ 108 years or some longer timescale?

18 Nov 2002 MBHCoal ’02

How hard is hard

• Normal 3−body definition :

– E* > GM1M2/a – Here M1

–

–

–

–

– vej ~ 1/4 vorb

18 Nov 2002 MBHCoal ’02

Reality Bites

• We see SMBH in galaxies
• We see mergers of galaxies
• We see very few obvious binary SMBH
• Do they merge: (BBR ‘80)?

– Need ~ 8 halfings of semi−major axis − so refill the loss−cone several times – Or e > 0.9 after few halfings

18 Nov 2002 MBHCoal ’02

Initial Problem

• Initial Condition:

two black holes − mass function, associated nucleus of stars, accretion disk two galaxies − density, dispersion, shape, f(E,J,I3) relaxed? Undergoing violent relaxation? gas! (stellar mass function, ongoing star formation)

18 Nov 2002 MBHCoal ’02

Dynamical Friction end−point

• From merger scenarios we need three key

pieces of information:

– Mass ratio (distribution) of SMBH – “Initial eccentricity” of the orbit at the point the binary becomes hard. Circularization? No…! – Velocity distribution of inner part of merged galaxy, including isotropy – dyn. fric. depends on density gradient and dispersion profile

18 Nov 2002 MBHCoal ’02

Loss−Cone Depletion

• Run out of stars
• Replace by:

– Diffusion – Pinhole scattering, dynamical “walking” in J due to eg

triaxiality, fluctuating potential

– BH wandering − super−elastic scattering, restoring

force?

– Star formation? Clusters?? – Or fail. Binary “hangs up”. Should then see many

SMBH with O(0.01−1) pc separation

18 Nov 2002 MBHCoal ’02

History

• Roos: merger possible if galaxies cuspy, sees

de/dt > 0 for large initial e

• Mikkola & Valtonen: de/dt depends on initial e

and f(v)

• Vecchio et al: de/dt > 0; Governato et al: initial

SMBH binary too wide to harden

• Fukushige et al: initial e is high
• Phinney & Villumsen: initial small e remains

small

18 Nov 2002 MBHCoal ’02

Modern age

• Quinlan ‘96; Quinlan & Hernquist ‘97:

– de/dt > 0 for high initial e – In Jaffe and Plummer N−body models, e 0 including

initially anisotropic models

• Zier & Biermann ‘01: efficient dJ/dt, assume

initial zero eccentricity, massive cluster

• Milosavljevic & Merritt ‘01: e 0
• Hemsendorf et al ‘02: e grows − numerical

effect?

• Aarseth ‘02: e grows! See this meeting…

18 Nov 2002 MBHCoal ’02

Eccentric behaviour

• Can we take away J faster than E?
• How.
• Does it help enough to matter?

– tgr a4 f(e) − f(e) ~ 2(1−e2)7/2 – If final e >~ 0.9 then we don’t need to harden through the difficult last stages through further

• encounters. We must resolve this issue and

whether it is initial condition dependent or not.

18 Nov 2002 MBHCoal ’02

3−body interactions

• Hyperbolic scattering leads to small, analytically

predictable changes in eccentricity

• Resonances can transfer more J at given E, dominate de/dt

at near parabolic encounters (Kozai pumping?)

• Enhanced tidal disruption, and stellar coalescence!

18 Nov 2002 MBHCoal ’02

18 Nov 2002 MBHCoal ’02

e(t)

• Quinlan & Hernquist ‘97 − N−body model
• Hemsendorf et al ‘02 − N−body model

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18 Nov 2002 MBHCoal ’02

Eccentricity

• e(N) for scattering
• Low J scatterers
• High J scatterers
• m/M = 0.001

Note largish jumps in eccentricity especially at high eccentricity Resonance dominated, small N a concern

18 Nov 2002 MBHCoal ’02

18 Nov 2002 MBHCoal ’02

More scatterings

18 Nov 2002 MBHCoal ’02

Not just what you do, but how you do it…

• If high J* matters, then diffusion vs pinhole

filling matters a lot. Shape and f(E,J) matters.

• Can violent relaxation, triaxiality, or large scale

coarseness be significant?

• BH wandering from super−elastic recoil (cf

Merritt). Deplete core implies no restoring force and large wandering amplitude.

• Star formation and dissipation?

18 Nov 2002 MBHCoal ’02

When gravity fails

• Gas dynamics: BBR noted that if we wait long enough gas

will arrive.

• If AGN for ~ Salpeter time, then Mgas ~ M at radius r <

tS( cS ) ~ few pc or less

• BH spin flip (cf Wilson & Colbert ‘95)

–

–

• If gas fails, we will merge again. Full blown 3−body interactions and recoil.
• Residual worry: grav rad recoil ejects BH at coalescence

18 Nov 2002 MBHCoal ’02

What do we know

• N−body simulations are scale free
• Still somewhat N limited
• Absolute low mass mergers probably easier
• M2 << M1 with large and little gas in primary

is where we should worry about hang−up −− “2nd” or “3rd” merger in clusters

• If there is post merger accretion with M >>

Minitial then coalescence is easier then we

• predict. Need to understand pre/post accretion

history

18 Nov 2002 MBHCoal ’02

Conclusions

• There is no conclusion
• We need to establish whether stellar dynamics

can transit BH binaries through the loss−cone, and whether that is the actual process of transition.

• Limited by N, initial conditions, and

understanding what approximations are adequate.

• Must understand de/dt , explore mass ratios

further