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Gravitational Waves from Massive Black-Hole Binaries

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).

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Gravitational Waves from Massive Black-Hole Binaries

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  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.

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

  27. 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.

  28. 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.

  29. 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)

  30. 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.

  31. 107 106 105 10-3.5Hz 10-1.5Hz Binary BH Detection by LISA 104

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

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

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

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

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

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

  38. 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.

  39. 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.

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

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