Gas Driven Supermassive Black Hole Binaries: periodic quasar variability and the gravitational wave background Bence Kocsis (CFA) Einstein Symposium, 10/26/2009

Galaxies merge  ignite quasars  black holes merge AGN variability surveys and Pulsar Timing Arrays detects them

Evolution of binaries 1. Collisionless damping (~kpc; “dynamical friction”, “Landau damping”) 2. 3-body encounters with stars (~ 1 pc) Gas driven migration (~0.1 pc, “Type II migration”) 4. Gravitational waves (~0.01 pc) Note: sub-parsec SMBH binaries ~ weeks – months orbital periods ~ 10 3 – 10 4 km/s velocity

Evolution of binaries 1. Collisionless damping (~kpc; “dynamical friction”, “Landau damping”) 2. 3-body encounters with stars (~ 1 pc) Gas driven migration (~0.1 pc, “Type II migration”) 4. Gravitational waves (~0.01 pc) Note: sub-parsec SMBH binaries ~ weeks – months orbital periods ~ 10 3 – 10 4 km/s velocity Number of binaries reduced at corresponding separation due to gas!

Within the last pc Cuadra et al. 2009; see also Ivanov et al. 1999; Armitage & Natarayan 2002, 2005; MacFadyen & Milosavljevic 2008; Thin gaseous disk Disk aligns with binary plane (Bardeen & Peterson 1975, Ivanov et al. 1999) Binary evacuates cavity (Artymowicz & Lubov 1994) 4. “Type II migration”) 4. Viscous decay ( “Type II migration”) Secondary dominated Disk dominated Gravitational Wave driven evolution

Within the last pc Cuadra et al. 2009; see also Ivanov et al. 1999; Armitage & Natarayan 2002, 2005; MacFadyen & Milosavljevic 2008; Accretion Rate Thin gaseous disk Disk aligns with binary plane (Bardeen & Peterson 1975, Ivanov et al. 1999) Binary evacuates cavity (Artymowicz & Lubov 1994) 4. “Type II migration”) 4. Viscous decay ( “Type II migration”) Secondary dominated Disk dominated Gravitational Wave driven evolution

Within the last pc Haiman, Kocsis, Menou, 2009, ApJ, 700, 1952 Residence Time Thin gaseous disk Disk aligns with binary plane (Bardeen & Peterson 1975, Ivanov et al. 1999) Binary evacuates cavity (Artymowicz & Lubov 1994) 4. “Type II migration”) 4. Viscous decay ( “Type II migration”) Secondary dominated Disk dominated Gravitational Wave driven evolution

Within the last pc Haiman, Kocsis, Menou, 2009, ApJ, 700, 1952 Residence Time Thin gaseous disk Disk aligns with binary plane (Bardeen & Peterson 1975, Ivanov et al. 1999) Binary evacuates cavity (Artymowicz & Lubov 1994) 4. “Type II migration”) 4. Viscous decay ( “Type II migration”) Secondary dominated Disk dominated Gravitational Wave driven evolution

Detecting Decaying binaries Optimistic Assumptions: binary is producing bright emission (~30% L edd ) non-negligible fraction (~10%) of this emission is variable clearly identifiable period t var ~ t orbit in-spiraling binary = periodically variable quasar Identifying such binaries statistically? fraction of quasars with period t var = (1+z) t orb f var = t res / t Q

Requirements for an (optical) survey for finding periodic variable sources Require: ≥ 100 t var ≤ 1 yr ≥ 5 t var ≤ 20 wk Assume: f Edd = 0.3 f var = 0.1 t Q = 10 7 yr Hopkins et al. z=2 Conclude: wide survey best to probe GW-decay disk physics at i~26.5 Haiman, Kocsis, Menou, 2009, ApJ, 700, 1952

Earth Pulsar Time Intensity Pulsar Timing Arrays

PPTA (Parkes pulsar timing array)‏ LEAP (large European array for pulsars)‏ NanoGrav (north American nHz observatory for gravitational waves)‏

GW background for PTAs Characteristic gravitational wave (GW) signal Characteristic gravitational wave (GW) signal Merger history Merger history   Millennium Run (Springel et al. 2005; Sesana et al. 2009) “Residence time” at sub-pc scales “Residence time” at sub-pc scales   From our previous plot Millennium Run

Gravitational Waves for PTAs Gas OFFGas ON Contribution of individual sources Unresolved background Total signal Spectrum averaged over 1000 Monte Carlo realizations Kocsis & Sesana (2009)

Summary SMBH binaries, gas/GW driven dynamics SMBH binaries, gas/GW driven dynamics AGN surveys Look for week-month year periodic variability Look for spectral features ~ several x 1,000 km/s Pulsar Timing Arrays Gas suppresses the stochastic background Individually resolvable sources remain

Higher signal variance: impossible to characterize the slope of the background a priori Statistics of resolvable sources basically unaffected

GW background for PTAs Characteristic gravitational wave (GW) signal Characteristic gravitational wave (GW) signal This depends on This depends on Merger history  Merger history  Millennium Run (Springel et al. 2005; Sesana et al. 2009) “Residence time” at subparsec scales “Residence time” at subparsec scales   From our previous plot Millennium Run

Millennium simulation (Springel et al. 2005) N-body numerical simulation of halo hierarchy Semi-analytical models for galaxy formation and evolution We extract catalogs of merging galaxies and populate them with sensible MBH prescriptions SMBH Merger history

Cartoon Model of Binary + Gas evolution a. Gas cools and settles into a thin circumbinary disk b. Disk aligned with binary orbital plane b. Disk aligned with binary orbital plane (Bardeen & Peterson 1975, Ivanov et al. 1999) c. Torques from binary evacuate central cavity c. Torques from binary evacuate central cavity r ~ 2a (Artymowicz & Lubov 1994) d. Orbit decays due to torques and viscosity, gas follows i. Analogous to Type – II planetary migration ii. When local disk mass < binary mass  migration slows down e. becomes shorter than when e. t GW becomes shorter than t vis when r ~ 100 R S

Punctured disk