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

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


1
Realistic Rates for the Detection of Supermassive
Black Hole coalescence by LISA
  • Kirsty Rhook
  • Stuart Wyithe
  • (University of Melbourne)

2
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

3
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

4
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

5
Gravitational waves
  • Weak field limit to Einsteins field equations
    predict perturbations in space-time that travel
    at c
  • 2 independent plane polarised wave solutions

6
Laser Interferometer Space Antennae (LISA)
7
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

8
LISAs threshold sensitivity
Threshold strain
LISAs threshold sensitivity
Detected gravitational wave frequency
(Hz)
9
Signal to Noise Ratios
SNR
Ringdown / Inspiral SNR
Coalescing BH mass
(Msolar)
10
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.


11
Merger and Coalescence rates

12
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


13
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)
14
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)


15
Event-rate predictions
Detections per year
Minimum black hole mass (Msolar)
16
Redshift distribution of events
Ringdown
Inspiral
Events/year/dz
z
Red shift
17
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
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