Gravitational radiation from Massive Black Hole Binaries Andrew Jaffe PTA “Focus group” — PSU/CGWP 22 July D. Backer, D. Dawe, A. Lommen

Gravitational Radiation from MBH Binaries  Ingredients:  Galaxy mergers & MBH assembly  Black Hole Demographics  Galactic dynamics & the Final Parsec Problem  GW waveforms  ⇒ Stochastic Background of MBH Binary GWs

Model Universe of MBH Binaries D. Backer

GWs from MBH Mergers □ Massive Black Holes in nearby galaxies...  MBH demographics from kinematics □... and high z (AGN) □ Modern galaxies are the result of mergers  Ellipticals from major mergers □ → MBH binaries ubiquitous □ Quickly driven to center of daughter galaxy by Dynamical Friction, followed by... □...Gravitational-Radiation-driven coalescence  IF they get close enough...

Observational Calibration Theoretical Understanding Open Questions  z=0 MBH Demographics  Luminous Galaxy merger rate at z~0 (z~1?)  Epoch of reionization 6<z<20 (?)  Halo Merger Rates  Dynamical Friction to ~1pc  GW radiation regime  MBH Merger rates  Final PC problem?  Naked MBHs?  Epoch of MBH formation

Binary MBH GW Spectrum □ Merger rate + Mass function + GWs:  N(z, f, M 1, M 2 ) df  φ 1 φ 2 R(z)C[Ω, z] M -5/3 f -8/3 df/f h c 2 (f) = f ∫dz dM 1 dM 2 h 2 (z,M) N(z, f, M 1, M 2 ) =  ( M /10 8 M ⊙ ) 5/3  (f/yr -1 ) -4/3 I h (see also Phinney 2002) nb. integral separates: φ(M) f -8/3 I(z) Stochastic (mean- square) M =(M 1 M 2 ) 3/5 /(M 1 +M 2 ) 1/5

Gravitational Radiation from MBH Binaries  GWs from ~Kepler motion: weak-field GR  P~1 yr for 10 9 M ⊙ at 0.01 pc  h c (f) ~ μ (M f ) 2/3 r -1 (& redshift to z=0 )  h~ for 10 9 M ⊙ at 1 Gpc for f=1/yr  long lifetime at P~ months-year  Pulsar Timing (Kaspi et al 1994; Rajagopal & Romani 1995; Thorsett & Dewey 1997)

GWs from MBH Binaries  Orbits circularized quickly (dynamics and/or GW)  h rms (f )~μ (M f ) 2/3 r -1 ~ M 5/3 chirp  (stochastic sum over population)  Cosmology, mass, frequency dependence 10 9 M ⊙ & 10 8 M ⊙, P = 1 yr

Binary formation and Dynamics: Approaching the problem  Pioneers:  Begelman Blandford & Rees  Haehnelt & Kauffmann  Rajagopal & Romani  Analytic (e.g., Backer & J)  Explicit calculations of MBH binary/galaxy dynamics (Dawe & J)  Semi-analytic (Extended Press-Schechter formalism)  Menou et al ( )  Wyithe & Loeb ( )  Enoki et al ( )  From Halos - Galaxies (baryons):  Sesana et al ( , )  Some explicit MBH binary/galaxy dynamics

MBH Coalescence: Galaxy merger rate  Binary MBH formation driven by Galaxy mergers  Poorly-measured even at moderate z Enoki et al 2005

MBH Growth  Coalescence dominates dM/dt for z<1  From Halos to MBHs  Gas physics  Heating, cooling, star formation  Accretion Enoki et al 2005

Massive Black Hole Demographics  Roughly, M  ≈ M sph  M  ≈ 10 8 M ⊙ ( σ / 200km/s) 4.72  Implies accretion- dominated growth? (Silk & Rees)  How to maintain in the presence of mergers?  (Magorrian et al, Gebhardt et al, Ferrarese & Merritt, Tremaine et al)  Traces merger history and/or potential depth?  High z?  AGN activity (McClure & Dunlop)

MBH Mass function □ MBH Demographics roughly constant over large z range □ Conversion of AGN to normal galaxies Ferrarese 2002

MBH Binary dynamics  Dynamical friction (&c.) drags black holes to center  t DF ≈ Myr (M  /10 8 M ⊙ ) -1, Binary hardens  loss cone is depleted, GW timescale still >>H 0 -1  Need to get to a~0.02 pc, P~30 yr  Stellar Dynamics difficult (Yu 2001; Milosavljevic & Merritt 2002;...)  Gas dynamics? (Gould & Rix 2000; Armitage & Natarajan 2002)  “Wandering”? 3-body interactions?  GW energy loss until final inspiral (~1 day)  Successful inspiral or many MBH binaries?  too close to observe?  Absence of evidence or evidence of absence?  Need evidence of post-merger binary activity (e.g., Merritt & Ekers 2002 “X” sources; dual-nucleus Chandra source;...)

Life cycle of a MBH Binary

Dynamics and the low-f cutoff  Losing energy to stars/gas/galaxy prior to GW regime Sesana et al 2004

The final parsec problem  Binary “hung up” before GW regime — energy-loss timescale >> Hubble time H -1  (nb also need to take delay into account when not << H -1 ) Sesana et al 2004 instantaneous Delayed

Timescales and the final pc problem  Need careful accounting of MBH Binary dynamics  (and galaxy merger/coalescence delay)

Contributions to the GW spectrum Enoki et al 2005

Coalescence and the high-f cutoff  Quasi-Newtonian until Innermost Stable Circular Orbit.  Enoki et al: high-f cutoff bend at ~10 -6 Hz  Feeds into LISA rate Sesana et al 2004 Enoki et al 2005

Stochastic GW Background

Gravitational Waves from LISA  See some fraction of total event rate (only sensitive to events in-band: M ~ 10 5 M ⊙ /(1+z)  nb. lighter MBHs inevitably more common at higher z  Individual events, not stochastic background  Hughes 2001 for parameter extraction

MBH Binaries at z=1: LISA Signal

Future Work □ Full calculation/measurement of Galaxy (MBH) merger rate  Crucial especially for LISA event rate  Use n-body, Press-Schecter, merger trees  Measurement of high-z merger rate  (DEEP2)  Detection of binary MBHs □ Galactic Dynamics: the final parsec problem □ Pulsar Timing Array

Conclusions □ Massive Black Hole Binary coalescence rate depends on merger rate, Black Hole demographics, galactic dynamics  Major uncertainties in all of these, esp. at high z □ µhz - nHz “Newtonian” regime potentially observable via Pulsar Timing □ Final coalescence are brightest GW events; observable via LISA