1. Probing Dormant Massive Black Hole Binaries at Galactic Nuclei Fukun Liu Astronomy Department & KIAA, Peking University, Beijing, China Probing Strong Gravity Near BHs 15-18 Feb., 2010 Collaborators: Xian Chen (PKU), Shuo Li (PKU), John Magorrian (Oxford), Piero Madau (UCSC), Alberto Sesana (PSU/AEI) KIAA-PKU

2. Evolution timescale DistanceDistance Dynamical Friction Gravitational Wave Radiation 1.1 、 Massive black hole binaries (MBHBs) and their observational evidences in gaseous environments Begelmann et al. 1980 Stefanie Komossa’ talk Most MBHBs in galactic nuclei may be quiescent: How to probe them? ~1pc

3. BH M BH r g (Komossa & Bade 1999, Halpern et al. 2004, Esquej et al. 2008, Gezari et al. 2009) A star tidally disrupted by a massive black hole (MBH): bound part of the fluids falling back and leading transient accretion onto MBHs (Hills, 1975,Rees 1988, Phinney 1989, Evans & Kochanek 1989, Lodato et al. 2009, etc) 1.2 、 Probing dormant MBHBs in galactic nuclei Spherical two-body relaxation:  10 -5 yr -1 (Wang & Merritt, 2004) (Komossa 2004)

4. BH 2.1 、 Effects of MBHBs on tidal disruption rates: unbound stars Methods: (Chen, Liu, & Magorrian, 2008) The interaction of stars and MBHBs: scattering experiments Refilling of stars: spherical two-body relaxation 51 elliptical galaxies with known BH & bulge masses Tidal disruption rates of unbound stars by MBHBs: ~10 -7 yr -1 Single BHPrimary BH Secondary BH

5. A newly formed binary surround by bound stellar cusp: stars in chaotic region (a/3 < a * < 3a): scattering into the tidal radius of MBHs during procedure to obtain escapable velocity stars in stable region (a * < a/3): secular periodic oscillation of eccentricity to a very high value (e * ~1) – Kozai effect Close-encounter cross-section: stars with a/2 < a * < 2a 2.2 、 Effects of MBHBs on tidal disruption rates: bound stars (Chen, Madau, Sesana, Liu, 2009) The orbit of a star: a * = 1.2a, and e * = 0.5; M BH = 10 7 M ☉, q=1/81, a=a h N=10 5

6. A complete picture for the stellar disruption rate in MBHBs: 3 Phases Phase I: shortly after MBHBs becoming bound, high rate, short duration (Kozai timescale)Phase I: shortly after MBHBs becoming bound, high rate, short duration (Kozai timescale) Phase II: after the initial stellar cusp is destroyed, low rate, long duration (until BHs coalesce) Phase II: after the initial stellar cusp is destroyed, low rate, long duration (until BHs coalesce) Phase III: after BHs coalesce, recovering, relaxation timescale (Merritt & Wang 2005) Phase III: after BHs coalesce, recovering, relaxation timescale (Merritt & Wang 2005) Tidal disruption rate of bound stars: Peak rate: ~10 -1 yr -1, insensitive to e or q Very sensitive to the cusp density profile During time: t~ 10 5 yr Isothermal cusp Shallower cusp I

7. Numerical Simulation Investigating the influence of MBHBs on the orbits of the tidally disrupted gas elements and their falling-back Interaction between gas debris elements: negligible before they fall back to a few tidal radius because pressure of debris gas p  0 (Evans & Kochanek, 1989) Debris gas returning to the tidal radius: rapid circularization (interaction/shocks) and accretion onto MBH (Rees 1988, etc) 3. Effects of MBHBs on tidal flares: Interruption (Liu, Li, Chen, 2009, ApJL) The debris fluid elements with a gas < a b /3 : stable orbits & falling back to the tidal disruption radius a gas > a b /3 : chaotic & significant change on dynamical time scale

8. Simulations: N=10 7 particles Parameters: M BH =10 7 M ☉, q=m BH /M BH = 0.1, a b =10 4 r G Interruption at time: T tr ~ 0.25 T b T tr /T b : insensitive to the MBHB parameters: a b and q T tr / T b ~0.15-0.5: Depending on the orbit parameters of the disrupted star  : the inclination angle between the orbital planes  : the longitude of ascending node  : the argument of pericenter

9. X-ray flares at center of local quiescent galaxies: consistent with falling-back model (Komossa, 2004) Flare followed by extremely low upper limit: MSBHB in RXJ1624+75 ?? 4) 、 Applications: preliminary results (?) Chen, Liu, Magorrian 2008 0.4 0.00.8 Preliminary survey: tidal disruption candidates in inactive galaxies (Komossa 2002, Donley et al. 2002, Gezari et al. 2006) flare rates vs binary fraction

10. Conclusions   Rich electro-magnetic signature from dormant MBHBs in galactic nuclei   The tidal disruption rates of bound stars could temporarily be enhanced to ~ 0.1-1 yr -1   The tidal disruption rates of unbound stars could be depressed to 10 -7 yr -1 (~10 -5 yr -1 for single MBH)   The tidal flare of stars would be interrupted by MBHBs   A quiescent MBHB (a b ~10 3 r g ) emitting strong gravitational wave can be identified by detecting tidal flares with abrupt drop/interruption at time of a few months