applying numerical relativity and eob to black hole binary observation sean mcwilliams nasa goddard...
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Applying Numerical Relativity and EOB to Black Hole Binary
Observation
Sean McWilliamsNASA Goddard Space Flight Center
University of MarylandCollaborators: John Baker, Joan Centrella, Bernard Kelly, Jim Van Meter, Alessandra Buonanno, Yi Pan
10 August 2007
10 August 2007 Sean T. McWilliams UMD/NASA GSFC
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In this talk…• Creating optimal hybrid NR-PN waveforms
via phase evolution comparisons
• Using our hybrid waveform to investigate overall detectability for LIGO, Advanced LIGO, and LISA
• Using EOB to fit an analytic waveform to the numerical merger, comparing the fit to other PN methods in the late inspiral
• What’s next
10 August 2007 Sean T. McWilliams UMD/NASA GSFC
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Phase comparisons
Out of sync In sync
• Waveforms evolve out of sync in phase and frequency• δφ depends on what time you set the waveforms to be equal
Calculating δφ vs. frequency does not yield the same results as calculating vs. time over a particular time interval.
10 August 2007 Sean T. McWilliams UMD/NASA GSFC
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08.0cMNRcPNc Md
d
Md
d
)(
)(
)(
)(
5.3
• For data analysis, we construct a “best guess” waveform with a PN inspiral and NR merger
• We find
for , or t = -328M (circled below)
10 August 2007 Sean T. McWilliams UMD/NASA GSFC
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Example signals for LIGO and Advanced LIGO
)(~
)( fhffhchar )(5)( ffSfh nrms
10 August 2007 Sean T. McWilliams UMD/NASA GSFC
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Example signals for LISA
10 August 2007 Sean T. McWilliams UMD/NASA GSFC
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Horizon of detectabilityHow close does an average oriented, average sky location LIGO
source need to be to have an SNR of 8, i.e. to be detectable?
10 August 2007 Sean T. McWilliams UMD/NASA GSFC
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SNR vs. nonred-shifted mass and
redshift for Advanced LIGO and LISA
• 10s to 100s of mergers per year seen by LISA for 104 MSun < M < 106 MSun
(Sesana et al. 2007) • >10 mergers/year for M =
~103 MSun by AdLIGO and LISA (Fregeau et al. 2006), but rates are far less certain
Advanced LIGO
LISA
10 August 2007 Sean T. McWilliams UMD/NASA GSFC
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Example of a simulated LISA signal
Michelson single arm X observable for two 105 MSun black holes (as measured in the binary COM frame) at z=15. The response
function for the example’s sky location is close to the average, but this signal is optimally oriented, so the
sky- and orientation-averaged SNR~300 is
roughly a factor sqrt(5) less than the true SNR for
this signal
10 August 2007 Sean T. McWilliams UMD/NASA GSFC
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Matching NR
and EOB
4:11:1
h+ for 4:1 mass ratio, summed through l=4,
evaluated at =/3
The EOB model includes a
phenomeno-logical 4PN term in the effective potential A(r), and 3 QNMs
attached at the peak orbital
frequency and tuned to the Mf and af from the
numerical simulations.
See Yi Pan’s talk tomorrow, 5:10, in
Thomas 216 for more EOB-NR details
10 August 2007 Sean T. McWilliams UMD/NASA GSFC
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PN late inspiral comparison
1:1 4:1
All PN flavors are compared to Tt3, which uses PN-expanded phase as a function of time. T re-expands the energy balance
equation in powers of orbital frequency. Tt1 solves energy balance numerically without re-expanding flux or energy.
10 August 2007 Sean T. McWilliams UMD/NASA GSFC
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Plans for future work include
• Testing LIGO burst and inspiral algorithms by injecting NR-PN hybrid waveforms into the data.
• Performing studies of parameter estimation using NR waveforms with Advanced LIGO and LISA.
• Constructing templates for signal detection and parameter estimation investigations using NR runs and the EOB formalism which will incorporate spin effects.