Realistic Rates for the Detection of Supermassive Black Hole coalescence by LISA

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Realistic Rates for the Detection of Supermassive
Black Hole coalescence by LISA

• Kirsty Rhook
• Stuart Wyithe
• (University of Melbourne)

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Plan

• The existence of SMBHs
• Binary Black Hole Coalescence
• Detection of Inspiral and Ringdown phases
• Cosmological rates of SMBH coalescence
• Mbh-Mhalo relationship
• SMBH occupation fraction
• Predicted detection rates

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The existence of SMBH

• Keplerian rotation curves of stars in nearby
  galaxies give direct dyanamical evidence for
  nuclear BHs with mass 106 - 109 Msolar
• Estimates using the relationship between BH mass
  and bulge mass yield nuclear BH masses as low as
  105 Msolar
• Estimates the mass of the black holes that power
  quasars
• Luminous quasars powered by 109 Msolar mass BHs
  exist as early as zlt6.
• Nuclear BH as small as 105 Msolar may power
  low-luminosity AGN

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Binary Black Hole Coalescence

• SMBHs sink to centre of merged system via
  dynamical friction
• Form a bound binary
• Binary hardens due to 3-body interactions with
  stars
• (possible bottleneck)
• At a critical (binary characteristic dependent)
  separation energy loss becomes dominated by
  gravitational radiation
• Rapid coalescence
• Efficiency depends on orbital parameters of
  halos, stellar distribution, relative BH mass

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Gravitational waves

• Weak field limit to Einsteins field equations
  predict perturbations in space-time that travel
  at c
• 2 independent plane polarised wave solutions

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Laser Interferometer Space Antennae (LISA)
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Gravitational waves from SMBH coalescence

• Inspiral phase slow adiabatic inspiral
• frequency and strain increase in time
• waveform depends on binary masses, initial
  frequency, distance to binary (z cosmology)
• Ringdown phase quadrupole distortion to rotating
  (Kerr) black hole
• expand in quadrupole spheroidal modes
• assume energy is radiated in l2, m2 mode only
• waveform is an exponentially damped sinusoid
  depending on binary mass, spin and distance

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LISAs threshold sensitivity
Threshold strain
LISAs threshold sensitivity
Detected gravitational wave frequency
(Hz)
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Signal to Noise Ratios
SNR
Ringdown / Inspiral SNR
Coalescing BH mass
(Msolar)
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Merger and Coalescence Rates

• Extended Press-Schechter gt rate of major halo
  mergers
• Weight by
• Press-Schechter abundance of dark matter halos
• Fraction of halo pairs that both host SMBHs
• Probability for detection of coalescence lt?gt
• (event rate -gt detectable event rate)
• Scales linearly with the (mean) efficiency of
  SMBH coalescence.

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Merger and Coalescence rates

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The Mbh-Mhalo Relationship

• Measurements of
• local galaxies (spiral and bulge) (Ferrarese
  2002) and
• radio-quiet AGN out to z 3 (Shields et al.
  2003)
• Dynamics in outer regions of local galaxies
  
• gt the mass of a BH depends on the depth of the
  gravitational potential well provided by the host
  halo

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The SMBH Occupation Fraction
SMBH Occupation fraction

• Recast Press-Schechter in terms of an observable
  dynamical variable vcool.
• Weak lensing studies gt
• vcool 1.8 vvir Mvir1/3
• Assume all galaxies in halos above a critical
  virial temperature host a SMBH

Maximum circular velocity (km/s)
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The minimum SMBH mass

• Pre-reionisation gas cannot cool (within a
  Hubble time) in halos with Tvir lt 104K.
• Post-reionisation the temperature of the IGM
  inhibits infall into halos with Tvir lt 2x105K.
• Constraints for SMBH formation may be much more
  stringent local SMBHs reside in halos with Tvir
  gt 105.4K.

• Minimum virial temperature gt minimum halo mass
  that may host SMBH formation
• ..and in turn, specify a (redshift independent)
  lower limit to the smallest SMBH that may form
• Mbh,min 15 Msolar (zltzreion)
• Mbh,min 1.4x104 Msolar (zgtzreion)

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Event-rate predictions
Detections per year
Minimum black hole mass (Msolar)
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Redshift distribution of events
Ringdown
Inspiral
Events/year/dz
z
Red shift
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Summary

• LISA will detect coalescence between BHs as
  massive as 109 Msolar in the ringdown phase
• We have made an empirically motivated estimate of
  the maximum (assuming efficient coalescence)
  event rate of SMBH coalescence detectable by LISA
• Predictions decay rapidly with minimum SMBH mass
  that may form
• If all black holes are more massive than those in
  local galaxies (105 Msolar)
• 15 detections per year
• If most black holes are more massive than those
  that power quasars at z 3 (107 Msolar)
• lt 10-3 detections per year