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