Gravitational Waves from Massive BlackHole Binaries

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Gravitational Waves from Massive Black-Hole
Binaries

• Stuart Wyithe (U. Melb)

NGC 6420
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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.

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Black Hole - Galaxy Relations
Ferrarese (2002)
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The Black Hole-Bulge Relationship

• Quasar hosts at high z are smaller than at z0
  (Croom et al. 2004).

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The Black Hole-Bulge Relationship

• Radio quiet QSOs conform to the Mbh-? with
  little dependence on z (Shields et al. 2002).

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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)
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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 20032004)
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Properties of Massive BHs

• Ubiquitous in galaxies gt1011Msolar at z0.
• Tight relation between Mbh and ? (or vc, Mhalo).
• Little redshift evolution of Mbhf(?) to z3.
• Feedback limited growth describes the evolution
  of quasars from z2-6.
• Massive BHs (Mbhgt109Msolar) at zgt6.
• Is formation via seed BHs at high z or through
  continuous formation triggered by gas cooling?
• What is the expected GW signal?

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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 z20?

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

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Evolution of Massive BHs

• Is super-massive BH formation ongoing and
  triggered by gas cooling inside collapsing
  dark-matter halos?

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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.

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

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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.

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LISA GW Event Rate (hcgt10-22 at fc10-3Hz)

• An event requires the satellite galaxy to sink,
  rapid evolution through hard binary stage, and a
  detectable GW signal.

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Number counts resulting from BH seeds
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Number counts resulting from continuous BH
formation
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Characteristic Strain Spectrum

• hspeclt10-14 (current)
• hspeclt10-15.5 (PPTA)

Jenet et al. (2006)
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• hspec is Sensitive to the Mbh-vc Relation

Ferrarese (2002) ?010-5.0 ?5.5
WL (2002) ?010-5.4 ?5.0
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Massive Black-Holes at low z Dominate GW Back
Ground
Sesna et al. (2004)
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Black-Hole Mass-Function

• The halo mass-function over predicts the density
  of local SMBHs.
• Most GWBG power comes from zlt1-2.

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Model Over-Predicts Low-z Quasar Counts at High
Luminosities
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Galaxy Occupation Fraction

• The occupation fraction is the galaxy LF / halo
  MF
• Assume 1 BH/galaxy

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Reduced GW Background

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

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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.

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Limits on the GW Back-Ground

• Pulsar Timing arrays limit the energy density in
  GW.
• ?gwh2lt2x10-9

(Lommen 2002)
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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.

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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.

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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)
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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.

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Binary BH Detection by LISA
104
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Black-holes at high z accrete near their
Eddington Rate
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A BBH in a pair of Merging Galaxies (NGC 6420
Komossa et al. 2003)
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Gravitational Waves from BBHs

• The observable is a strain amplitude
• In-spiral due to gravitational radiation.

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Merger Rates for DM Halos
Time
Large M
Small M
Lacey Cole (1993)
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The Press-Schechter Mass Function
Z0
Z30
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• Reionization may affect BH formation in low mass
  galaxies as it does starformation.

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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 Pgt20yrs and
  agt0.01pc.

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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.

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Reduced Event Rate

• Inclusion of the occupation fraction lowers the
  predicted event rate by an order of magnitude.