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Gravitational radiation from Massive Black Hole Binaries

Gravitational radiation from Massive Black Hole Binaries. Andrew Jaffe PTA “Focus group” — PSU/CGWP 22 July 2005 + D. Backer, D. Dawe, A. Lommen. Gravitational Radiation from MBH Binaries. Ingredients: Galaxy mergers & MBH assembly Black Hole Demographics

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Gravitational radiation from Massive Black Hole Binaries

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  1. Gravitational radiation from Massive Black Hole Binaries Andrew Jaffe PTA “Focus group” — PSU/CGWP 22 July 2005 + D. Backer, D. Dawe, A. Lommen

  2. Gravitational Radiationfrom MBH Binaries • Ingredients: • Galaxy mergers & MBH assembly • Black Hole Demographics • Galactic dynamics & the Final Parsec Problem • GW waveforms • ⇒ Stochastic Background of MBH Binary GWs

  3. Model Universe of MBH Binaries D. Backer

  4. 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...

  5. Binary MBH GW Spectrum • Merger rate + Mass function + GWs: • N(z, f, M1, M2) df φ1φ2 R(z)C[Ω, z] M-5/3 f-8/3df/fhc2(f) = f∫dz dM1 dM2h2(z,M) N(z, f, M1, M2)= (M /108M⊙)5/3 (f/yr-1)-4/3 Ih(see also Phinney 2002)nb. integral separates: φ(M) f -8/3 I(z) Stochastic (mean-square) M=(M1M2)3/5/(M1+M2)1/5

  6. Gravitational Radiationfrom MBH Binaries • GWs from ~Kepler motion: weak-field GR • P~1 yr for 109M⊙ at 0.01 pc • hc(f) ~ μ (Mf )2/3r-1 (& redshift to z=0) • h~10-15 for 109M⊙ at 1 Gpc forf=1/yr • long lifetime at P~months-year • Pulsar Timing (Kaspi et al 1994; Rajagopal & Romani 1995; Thorsett & Dewey 1997)

  7. 109M⊙ & 108M⊙, P = 1 yr GWs from MBH Binaries • Orbits circularized quickly (dynamics and/or GW) • hrms(f )~μ(M f )2/3r-1~ M5/3chirp • (stochastic sum over population) • Cosmology, mass, frequency dependence

  8. 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 (0101196) • Wyithe & Loeb (0211556) • Enoki et al (0404389) • From Halos - Galaxies (baryons): • Sesana et al (0401543, 0409255) • Some explicit MBH binary/galaxy dynamics

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

  10. MBH Growth • Coalescence dominates dM/dtfor z<1 • From Halos to MBHs • Gas physics • Heating, cooling, star formation • Accretion Enoki et al 2005

  11. Massive Black Hole Demographics • Roughly, M ≈ 0.003 Msph • M≈ 108M⊙(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)

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

  13. MBH Binary dynamics • Dynamical friction (&c.) drags black holes to center • tDF ≈ Myr (M/108 M⊙)-1,Binary hardens • loss cone is depleted, GW timescale still >>H0-1 • 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; ...)

  14. Life cycle of a MBH Binary

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

  16. 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 Delayed instantaneous

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

  18. Contributions to the GW spectrum Enoki et al 2005

  19. 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

  20. Stochastic GW Background

  21. Gravitational Waves from LISA • See some fraction of total event rate (only sensitive to events in-band:M ~ 105M⊙/(1+z) • nb. lighter MBHs inevitably more common at higher z • Individual events, not stochastic background • Hughes 2001 for parameter extraction

  22. MBH Binaries at z=1:LISA Signal

  23. 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

  24. 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

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