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					            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)
3.   Gas driven migration (~0.1 pc, “Type II migration”)
4.   Gravitational waves (~0.01 pc)
                            Note: sub-parsec SMBH binaries
                                     ~ weeks – months orbital periods
                                     ~ 103 – 104 km/s velocity
            Evolution of binaries
1.   Collisionless damping (~kpc; “dynamical friction”,
     “Landau damping”)
2.   3-body encounters with stars (~ 1 pc)
3.   Gas driven migration (~0.1 pc, “Type II migration”)
4.   Gravitational waves (~0.01 pc)
                            Note: sub-parsec SMBH binaries
                                     ~ weeks – months orbital periods
                                     ~ 103 – 104 km/s velocity


            Number of binaries reduced at
          corresponding separation due to gas!
                      Within the last pc
                                                    1.   Thin gaseous disk
                                                    2.   Disk aligns with binary
                                                         plane (Bardeen & Peterson 1975,
                                                         Ivanov et al. 1999)
                                                    3.   Binary evacuates cavity
                                                         (Artymowicz & Lubov 1994)
                                                    4.   Viscous decay (“Type II
                                                         migration”)
                                                         1. Secondary dominated
                                                         2. Disk dominated

                                                    5.   Gravitational Wave
                                                         driven evolution

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

                                                         5.   Gravitational Wave
                                                              driven evolution


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

                                              5.   Gravitational Wave
                                                   driven evolution



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

                                              5.   Gravitational Wave
                                                   driven evolution



Haiman, Kocsis, Menou, 2009, ApJ, 700, 1952
     Detecting Decaying binaries

   Optimistic Assumptions:
       binary is producing bright emission (~30% Ledd)
       non-negligible fraction (~10%) of this emission is
        variable
       clearly identifiable period tvar~ torbit
       in-spiraling binary = periodically variable quasar
   Identifying such binaries statistically?
       fraction of quasars with period tvar = (1+z) torb
                        fvar = tres / tQ
      Requirements for an (optical) survey
      for finding periodic variable sources
                                                 Require:
                                                  ≥ 100 sources @ tvar≤ 1 yr
                                                  ≥ 5 sources @ tvar≤ 20 wk

                                                 Assume:
                                                      • fEdd= 0.3
                                                      • fvar = 0.1
                                                      • tQ = 107 yr
                                                       • Hopkins et al. QSOLF @ z=2
                                                 Conclude:
                                                      • wide survey best
                                                        to probe GW-decay
                                                      • disk physics at i~26.5

Haiman, Kocsis, Menou, 2009, ApJ, 700, 1952
                   Pulsar Timing Arrays




                            Pulsar
Intensity




                                     Earth

            Time
PPTA (Parkes pulsar timing array)




                               NanoGrav (north American nHz
                               observatory for gravitational waves)




  LEAP (large European array
  for pulsars)
                                                   Millennium Run
        GW background for
             PTAs
   Characteristic gravitational wave
    (GW) signal

       Merger history
          Millennium Run (Springel et al. 2005;
           Sesana et al. 2009)


       “Residence time” at sub-pc scales
          From our previous plot
       Gravitational Waves for PTAs
               Gas OFF                                      Gas ON
                                                             Kocsis & Sesana (2009)




Contribution of    Unresolved                  Spectrum averaged over 1000
individual sources background   Total signal   Monte Carlo realizations
                       Summary
   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
                                        Statistics of resolvable
                                   sources basically unaffected




Higher signal variance:
impossible to characterize the
slope of the background a priori
                                                      Millennium Run

     GW background for
          PTAs
   Characteristic gravitational wave (GW) signal




   This depends on
        Merger history  Millennium Run
         (Springel et al. 2005; Sesana et al. 2009)
        “Residence time” at subparsec scales
            From our previous plot
                     SMBH Merger history
   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
     Cartoon Model of Binary + Gas evolution

a.        Gas cools and settles into a thin circumbinary disk
b.        Disk aligned with binary orbital plane
                           (Bardeen & Peterson 1975, Ivanov et al. 1999)
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.        tGW becomes shorter than tvis when r ~ 100 RS
Punctured disk

				
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