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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 5/3 M bh M halo v c5 Ferrarese (2002) The Black Hole-Bulge Relationship • 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 Mbh-* with little dependence on z (Shields et al. 2002). Model Quasar Luminosity Function • One quasar episode per major merger. Three assumptions: • Accretion at Eddington Rate with median spectrum. • Hypothesis: Black-Hole growth is regulated by feedback over the dynamical time. This hypothesis provides a physical origin for the Black-Hole mass scaling. 5 5/3 M bh vcir Mhalo 1 z 5/2 The dynamical time is identified as the quasar lifetime. (L B ,z) 0.5M halo 0 dn ps d2Nmerge 3 t dyn dMhalo (M halo M halo ) 3 5 5.7 10 d( M halo M halo ) dMhalodt Wyithe & Loeb (ApJ 2003) Model Quasar Luminosity Function. • 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. clustering of quasars Wyithe & Loeb (ApJ 2003;2004) Properties of Massive BHs • Ubiquitous in galaxies >1011Msolar at z~0. • Tight relation between Mbh and * (or vc, Mhalo). • Little redshift evolution of Mbh~f(*) to z~3. • Feedback limited growth describes the evolution of quasars from z~2-6. • Massive BHs (Mbh>109Msolar) 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 supermassive 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 darkmatter halos? BH Evolution Triggered by Gas Cooling • Prior to reionization, cooling of gas inside darkmatter halos is limited by the gas cooling thresh-hold (104K for H). • Following reionization the infall of gas into dark-matter halos is limited by the Jeans Mass. • High z -3/2 1 z 10 8 M solar 20 Low z Reionisation 1 z 1010 10 -3/2 Tvir 5 M solar 10 K • 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) 1 M M t sink 0.25H M • Allow at most one coalescence per tsink. • 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 (hc>10-22 at fc=10-3Hz) d2Ngw dtdz 0 dM dMM,M,fc ,hc ,z Sz, M bh ,M bh M 0 dn bh 2 dn bh dN d V mrg d M 4 dM d Mdt M dn ps 1 z dzd d M 2 • 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 Sh (f) 0 dh 0 2 d d V 2 dz h (z)4 dhdf dzd • hspec<10-14 (current) • hspec<10-15.5 (PPTA) Jenet et al. (2006) hspec (f) fS h (f) hspec is Sensitive to the Mbh-vc Relation 2 3 M halo M bh 1.20 12 10 M halo Ferrarese (2002): 0=10-5.0 =5.5 WL (2002): 0=10-5.4 =5.0 Massive Black-Holes at low z Dominate GW Back Ground Sesna et al. (2004) 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. • gwh2<2x10-9 1 dρ GW ΩGW (f) ρ crit dlnf (Lommen 2002) Minimum Halo Mass for Star formation • Atomic hydrogen cooling provides the mechanism for energy loss that allows collapse to high densities. • This yields a minimum mass in a neutral IGM. M min 3 2 1 z 10 M solar 10 8 Minimum Halo Mass for Baryonic Collapse • Assume gas settles into hydrostatic equilibrium after collapse into a DM halo from an adiabatically expanding IGM. 3 2 6 Tvir b b 1 1 1 5 T b Tvir 17.2T (b 100) • This yields a minimum mass in an ionized IGM. 3 M min 1 z 2 5 10 M solar 10 9 Minimum Halo Mass for Baryonic Collapse z=11 QuickT ime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. Qui ckTime™ and a TIFF (Uncompres sed) decompressor are needed to see this picture. z=2 • A minimum mass is also seen in simulations. The minimum mass is reduced at high redshift. QuickT ime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. QuickT ime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. (Dijkstra et al. 2004) 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 Xray quasar densities to low luminosity optical densities. Binary BH Detection by LISA 107 106 105 104 10-3.5Hz 10-1.5Hz Black-holes at high z accrete near their Eddington Rate 2π 2 3 ΩGW (f) f S h (f ) 2 3H 0 A BBH in a pair of Merging Galaxies (NGC 6420; Komossa et al. 2003) Gravitational Waves from BBHs • The observable is a strain amplitude M bh ΔM bh f 2/3 20 16 hc 10 10 1/3 R(z) M bh ΔM bh • In-spiral due to gravitational radiation. P t P 10 P 1sec 5 5/3 Merger Rates for DM Halos d2N (M) dMdt crit(z) Large M Time Small M k 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) t decay rvir 1.2 vc M ΔM ε 0.4 ΔM ln M ΔM e ΔM M ΔM 0.25H ΔM 1 • 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.