Measuring SMBH parameters with LISA

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Measuring SMBH parameters with LISA
Emanuele Berti Washington University in Saint
Louis
EB, A. Buonanno, C.Will, PRD 71, 124008 (2005)
inspiral EB, V.Cardoso, C.Will, PRD 73, 064030
(2006) ringdown EB, astro-ph/0602470 event
rates, open issues (spins, eccentricity..)

(Kip Thorne)
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Inspiral (circular) Post-Newtonian waveforms
Spin-orbit, 1.5PN
Spin-spin, 2PN
Brans-Dicke dipole radiation - best bounds
from NS-IMBH systems
Massive graviton D-dependent delay in wave
propagation Best bounds from SMBH binaries
(Psaltis talk)
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Ringdown black hole spectroscopy
wlmnwRiwI2pfi/t
f 0.012 (106Msun)/M Hz t 55 M/(106Msun) s

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Spectroscopy of Kerr black holes

Modes always come in pairs reflection symmetry m
-m wR - wR
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GR tests from ringdown waves
One-mode detection if we know which mode we are
detecting (eg. lm2) measure of black holes
mass and angular momentum
f(M,j), t(M,j) M(f,t), j(f,t)
(Echeverria, Finn) Multi-mode detection First
mode yields (M,j) In GR Kerr quasinormal
frequencies depend only on M and j second mode
yields test that we are observing a Kerr black
hole (Dreyer et al.) Under reasonable
assumptions, the test requires SNR10-100 (EB,
Cardoso Will) Test similar in nature to
multipolar mapping with EMRIs
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SNR for inspiral and ringdown
10000 _at_ z0.54
300 _at_ z10
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Parameter estimation
Gravitational-wave signal described by parameters
li Inspirallimasses, spins, sky location,
orbital orientation.. Ringdown liBH mass,
angular momentum, spin orientation, sky
location.. In the limit of high SNR, errors have
a Gaussian distribution
where the Fisher matrix
Errors on and correlations between parameters
are given by the correlation matrix
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SMBH merger history Msource(z), Jsource(z)
LISA only measures redshifted combinations of
masses and spins, of the form M(1z)Msource
J(1z)2Jsource Measuring luminosity distance
DL(z,cosmology) and assuming cosmology is known,
find z(DL) and remove degeneracy Holz Hughes
lensing errors usually larger, need EM
counterparts
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Errors on single-mode detection with LISA
DL3Gpc, erd3
Errors scale as SNR-1erd-1/2
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Summary

• Inspiral and ringdown both detectable out to
  very large z
• SMBH binary inspiral both masses within lt
  0.1, DL within 1-10
• approximate sky location, need EM
  counterpart
• SMBH ringdown both mass and spin determined
  within lt 0.1
• possible tests of the Kerr
  nature of the source
• Needed astrophysical input for optimal data
  analysis before LISA flies
• event rate (Volonteri, Haenhelt, Koushiappas)
  few events or background?
• eccentricity (Spurzem, Colpi, Makino) higher
  frequency harmonics, could see higher-mass BHs
• spin (Volonteri, Shapiro) precession induced
  amplitude modulations
• Spin and eccentricity complicate waveform and
  data analysis,
• but this is good more information, better tests
  of GR

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Eccentricity and high-order PN corrections

• (Plot by Jim Shifflett)
• For SMBH-IMBH binaries
• 1) high-order harmonics
• have large relative SNR
• 2) high-order PN terms
• contribute many cycles
• even for zero eccentricity
• Mixed PN-perturbative approach?

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Graviton Compton wavelength
Will 98 (LIGO and LISA), Will Yunes 04 (LISA
SCG, angle-average, no spins)
Binary at DL3 Gpc (z0.5) Solar system
bound (Yukawa-term deviations from Keplers third
law) lg3x1012 km Bound from galaxy
clusters lg6x1019 km
Alternatives Sutton Finn 02 (binary pulsars)
Cutler, Hiscock Larson 03 (GW phase vs.
orbital phase) Jones 04 (eccentricity)
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SMBH binary formation and event rates
1) Black holes sink to the center by dynamical
friction 2) Gravitational slingshot interactions
(or gas accretion) increase the binarys binding
energy 3) Gravitational radiation drives binary
to merger eccentric binaries coalesce faster 4)
Gravitational-wave recoil for unequal-mass
binaries may kick BHs out of the host galaxy
Bottom line maybe 10 events/year at 2ltzlt6
possible SMBH background! Matsubayashi et al.,
Miller, Portegies-Zwart et al. (05) a few, or up
to 100 IMBH-SMBH/yr (1000106 Msun)