Gravitational Waves from Massive Black-Hole Binaries

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

2. 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.

3. Black Hole - Galaxy Relations Ferrarese (2002)

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

5. The Black Hole-Bulge Relationship • Radio quiet QSOs conform to the Mbh-* with little dependence on z (Shields et al. 2002).

6. Model Quasar Luminosity Function • 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. Three assumptions: 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)

7. 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)

8. Properties of Massive BHs • Ubiquitous in galaxies >1011Msolar at z~0. • Tight relation between Mbhand * (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?

9. 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?

10. The BH seeds move into larger halos through hierachical merging.

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

12. High z Low z Reionisation BH Evolution Triggered by Gas Cooling • Prior to reionization, cooling of gas inside dark-matter 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.

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

14. Merging Massive BHs • Satellite in a virialized halo sinks on a timescale (Colpi et al. 1999) • 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.

15. An event requires the satellite galaxy to sink, rapid evolution through hard binary stage, and a detectable GW signal. LISA GW Event Rate (hc>10-22 at fc=10-3Hz)

16. Number counts resulting from BH seeds

17. Number counts resulting from continuous BH formation

18. Characteristic Strain Spectrum • hspec<10-14 (current) • hspec<10-15.5 (PPTA) Jenet et al. (2006)

19. hspec is Sensitive to the Mbh-vc Relation Ferrarese (2002): 0=10-5.0 =5.5 WL (2002): 0=10-5.4 =5.0

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

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

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

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

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

25. 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.

30. Limits on the GW Back-Ground • Pulsar Timing arrays limit the energy density in GW. • gwh2<2x10-9 (Lommen 2002)

31. 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.

32. Minimum Halo Mass for Baryonic Collapse • 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.

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

34. 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.

35. 107 106 105 10-3.5Hz 10-1.5Hz Binary BH Detection by LISA 104

36. Black-holes at high z accrete near their Eddington Rate

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

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

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

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

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

42. 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.

43. 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.

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