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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 - PowerPoint PPT Presentation
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Gravitational radiation from Massive Black Hole Binaries
Andrew JaffePTA “Focus group” — PSU/CGWP
22 July 2005
+ D. Backer, D. Dawe, A. Lommen
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
Model Universe of MBH Binaries
Gravity waves
MBHdemographics
MBH BinaryDynamics
Galaxy MergerRates
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
1φ
2 R(z)C[Ω, z] M-5/3 f -8/3df/f
hc2(f) = f ∫dz dM
1 dM
2 h2(z,M) N(z, f, M
1, M
2)
= (M /108M⊙)5/3 (f/yr-1)-4/3 Ih
(see also Phinney 2002)
nb. integral separates: φ(M) f -8/3 I(z)
MBHMass fn Merger rate Cosmology GW Timescale
€
Ih =R z( )R0
∫ dz
E z( ) 1+z( )4 / 3
Stochastic (mean-square) M=(M1M2)3/5/(M1+M2)1/5
Gravitational Radiationfrom MBH Binaries
GWs from ~Kepler motion: weak-field GR P~1 yr for 109 M⊙ at 0.01 pc
hc(f) ~ μ (M f )2/3 r-1 (& redshift to z=0)
h~10-15 for 109 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)
hrms
(f )~μ (M f )2/3 r-1
~ M5/3chirp
(stochastic sum over population)
Cosmology, mass, frequency dependence
109 M⊙ & 108 M⊙, P = 1 yr109 M⊙ & 108 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 (0101196) Wyithe & Loeb (0211556) Enoki et al (0404389)
From Halos - Galaxies (baryons): Sesana et al (0401543, 0409255)
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≈ 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)
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/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; ...)
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
instantaneousDelayed
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
Kaspi et al 1994Lommen 2002
ProspectivePTA limits
Monte Carlorealizations
Early activity,High, low
merger-ratemodels
Low-f cutoff due toMBH Dynamics
(Dawe & Jaffe 2003)
Gravitational Waves from LISA
See some fraction of total event rate (only sensitive to events in-band:
M ~ 105 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