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

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 off 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 m* – More useful to consider v * << vorb – Or a < rh = GM/ 2 – So when enclosed mass in stars ~ M then we’re in interesting regime – can eject N*~ O(M/m) and shrink a by ~ 2 – 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 a 4 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 18 Nov 2002 MBHCoal ’02

18 Nov 2002 MBHCoal ’02

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 18 Nov 2002 MBHCoal ’02 Resonance dominated, small N a concern

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) – spin up during coalescence due to accretion? – GPS sources??? • 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 18 Nov 2002 MBHCoal ’02