Capture of Stars by Supermassive Black Holes J.A. de Freitas Pacheco T. Regimbau C. Filloux Observatoire de la Côte d’Azur

Main Ideas (dynamics of black holes in globular clusters and …how to power QSOs) J.N. Bahcall & R.A. Wolf – ApJ 209, 214, 1976 J.N. Bahcall & R.A. Wolf – ApJ 216, 883, 1977 A.P. Lightman & S.L. Shapiro – ApJ 211, 244, 1977 D. Hils & P. Bender – ApJ 445, L7, 1995 S. Sigurdsson & M. Rees – MNRAS 284, 318, 1997 M. Freitag – ApJ 583, L21, 2003 C. Hopman & T. Alexander – ApJ 629, 362, 2005 C. Hopman & T. Alexander – astro-ph/

r*r* Within the ’’influence region’’: a)bound stars b) ’’unbound’’ stars with high excentric orbits Non-resonant relaxation: Resonant relaxation: define t  as the timescale required to change the argument of the periapse by . Then RR relaxation – mechanism deflecting stars into loss-cone orbits

’’Loss Cone’’ Theory - Basic Features - Collisions leading to important variations in energy & angular momentum per orbital period  direct capture if J < J crit (loss cone) ; stars are tidally disrupted if J crit  (GM BH r t ) 1/2 Consumption rate at r crit balanced by collisions at r * Stars in tightly bound orbits  diffusion in J-espace with a small step size  J per orbital period (lost of angular momentum mainly by emission of gravitational waves) Steady flow possible if t R at r * is less than ~ 12 Gyr.

Tidal Disruption Critical Black Hole Masses Type Mass (in M  ) RadiusBlack Hole Mass ND stars R  1.3  10 8 M  white dwarfs km 6.1  10 5 M  neutron stars km 17 M 

Which stars will inspiral into the BH ? only tightly bound orbits an upper limit for the semi-major axis can be derived by equating the inspiral timescale t gw to the non-resonant timescale (Hopman & Alexander 2005)

The (Inspiral) Capture Rate (Hopman & Alexander 2006)

Theoretical fraction of compact objects – Mean population age = 12 Gyr

The Stellar Density by inverting an Abel integral:

The Galactic Center The central BH  M BH = 2.8  10 6 M  ;  1D = 112 ±14 km/s Consistent with simulations by Freitag 2003

Capture Rates for E+S0 Galaxies Notice that Gair et al derived   M BH 3/8 but assumed that galaxies have isothermal cores!

Redshift Espace Probed by LISA S/N = 5

The Expected Number of Events

Upper and Lower Mass Limits * Lower limit - lowest observed mass black hole  1.4  10 6 M  (in M32) - negative searches for intermediate mass black holes - upper limits for M33 (3  10 3 M  ) and NGC 205 (3.8  10 4 M  ) - indirect evidence for IMBH in NLSeyf1 (8   10 6 M  )

Results Conservative Estimate – M min = 1.4  10 6 M  Total number of events (one year) = 9 (7-8 white dwarfs and 1-2 neutron stars/black holes) E/S0 = 54% Sa/Sb = 27% Sc = 19% Optimistic Estimate – M min = 2  10 5 M  Total number of events (one year) = 579 (274 black holes, 194 neutron stars and 111 white dwarfs) E/S0= 53% Sa/Sb = 21% Sc = 26%

Current Investigations Evolutionary effects: growth and mass distribution Coalescences at high z GW background from SMBH in formation at z > 4-5 Improvements in the capture rate – diffusion in both E, J espace Captures of non-degenerate stars by SMBH with masses higher than ~ few 10 8 M 