Gravitational Waves from Massive Black-Hole Binaries Stuart Wyithe (U. Melb) NGC 6420

Outline The black-hole - galaxy relations. Regulation of growth during quasar phase. The quasar luminosity function. Evolution of the BH mass function. Rate of gravity wave detection (LISA). The gravity wave back-ground. The occupation fraction of SMBHs in halos and GW predictions.

Black Hole - Galaxy Relations Ferrarese (2002)

Quasar hosts at high z are smaller than at z=0 (Croom et al. 2004). The Black Hole-Bulge Relationship

Radio quiet QSOs conform to the M bh - * with little dependence on z (Shields et al. 2002).

Three assumptions: One quasar episode per major merger. Accretion at Eddington Rate with median spectrum. Hypothesis: Black-Hole growth is regulated by feedback over the dynamical time. Model Quasar Luminosity Function Wyithe & Loeb (ApJ 2003) This hypothesis provides a physical origin for the Black-Hole mass scaling. The dynamical time is identified as the quasar lifetime.

Wyithe & Loeb (ApJ 2003;2004) Model Quasar Luminosity Function. clustering of quasars The black-hole -- dark matter halo mass relation agrees with the evolution of clustering. The galaxy dynamical time reproduces the correct number of high redshift quasars.

Properties of Massive BHs Ubiquitous in galaxies >10 11 M solar at z~0. Tight relation between M bh and  * (or v c, M halo ). Little redshift evolution of M bh ~f( * ) to z~3. Feedback limited growth describes the evolution of quasars from z~2-6. Massive BHs (M bh >10 9 M solar ) at z>6. Is formation via seed BHs at high z or through continuous formation triggered by gas cooling? What is the expected GW signal?

Evolution of Massive BHs Were the seeds of super- massive BHs the remnant stellar mass BHs from an initial episode of metal free star formation at z~20?

The BH seeds move into larger halos through hierachical merging.

Evolution of Massive BHs Is super-massive BH formation ongoing and triggered by gas cooling inside collapsing dark- matter halos?

BH Evolution Triggered by Gas Cooling Prior to reionization, cooling of gas inside dark- matter halos is limited by the gas cooling thresh-hold (10 4 K for H). Following reionization the infall of gas into dark-matter halos is limited by the Jeans Mass. High z Reionisation Low z

Reionization may affect BH formation in low mass galaxies as it does star formation.

Merging Massive BHs Satellite in a virialized halo sinks on a timescale (Colpi et al. 1999) Allow at most one coalescence per t sink. BBHs in some galaxies will converge within H -1 Coalescence more rapid in triaxial galaxies. Brownian motion of a binary black hole results in a more rapid coalescence. We parameterise the hard binary coalescence efficiency by  mrg.

LISA GW Event Rate (h c > at f c =10 -3 Hz) An event requires the satellite galaxy to sink, rapid evolution through hard binary stage, and a detectable GW signal.

Number counts resulting from BH seeds

Number counts resulting from continuous BH formation

Characteristic Strain Spectrum h spec < (current) h spec < (PPTA) Jenet et al. (2006)

Ferrarese (2002):  0 = =5.5 WL (2002):  0 = =5.0 h spec is Sensitive to the M bh -v c Relation

Sesna et al. (2004) Massive Black-Holes at low z Dominate GW Back Ground

Black-Hole Mass-Function The halo mass-function over predicts the density of local SMBHs. Most GWBG power comes from z<1-2.

Model Over-Predicts Low-z Quasar Counts at High Luminosities

Galaxy Occupation Fraction The occupation fraction is the galaxy LF / halo MF Assume 1 BH/galaxy

Reduced GW Background Inclusion of the occupation fraction lowers the predicted GW background by 2 orders of magnitude.

Conclusions The most optimistic limits on the spectrum of strain of the GW back-ground are close to expected values. Tighter limits or detection of the back-ground may limit the fraction of binary BHs. Allowance should be made for the occupation of SMBHs in halos, which lower estimates of the GW background based on the halo mass function by 2 orders of magnitude. Models are very uncertain! PTAs will probe the evolution of the most massive SMBHs at low z.

Limits on the GW Back-Ground Pulsar Timing arrays limit the energy density in GW.  gw h 2 <2x10 -9 (Lommen 2002)

Atomic hydrogen cooling provides the mechanism for energy loss that allows collapse to high densities. This yields a minimum mass in a neutral IGM. Minimum Halo Mass for Star formation

Assume gas settles into hydrostatic equilibrium after collapse into a DM halo from an adiabatically expanding IGM. This yields a minimum mass in an ionized IGM. Minimum Halo Mass for Baryonic Collapse

(Dijkstra et al. 2004) A minimum mass is also seen in simulations. The minimum mass is reduced at high redshift. Minimum Halo Mass for Baryonic Collapse z=11 z=2

Median Quasar Spectral Energy Distribution Elvis et al. (1994); Haiman & Loeb (1999) The median SED can be used to compute number counts. The SED can also be used to convert low luminosity X- ray quasar densities to low luminosity optical densities.

Binary BH Detection by LISA Hz Hz

Black-holes at high z accrete near their Eddington Rate

A BBH in a pair of Merging Galaxies (NGC 6420; Komossa et al. 2003)

Gravitational Waves from BBHs The observable is a strain amplitude In-spiral due to gravitational radiation.

Merger Rates for DM Halos k   crit (z) Large MSmall M Time Lacey & Cole (1993)

The Press-Schechter Mass Function Z=30 Z=0

Reionization may affect BH formation in low mass galaxies as it does starformation.

Binary Evolution Timescales (Yu 2002) BBHs in some galaxies will converge within H -1 Coalescence more rapid in triaxial galaxies. Residual massive BH binaries have P>20yrs and a>0.01pc.

Merging Massive BHs Satellite in a virialized halo sinks on a timescale (Colpi et al. 1999) Allow at most one coalescence during the decay plus coalescence times.

Reduced Event Rate Inclusion of the occupation fraction lowers the predicted event rate by an order of magnitude.