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Applying Numerical Relativity and EOB to Black Hole Binary Observation

This talk discusses the application of numerical relativity and the effective one-body (EOB) approach in investigating the detectability of black hole binary mergers by LIGO, Advanced LIGO, and LISA. It also explores the use of EOB to fit analytical waveforms to numerical mergers and compares the results to other post-Newtonian methods.

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Applying Numerical Relativity and EOB to Black Hole Binary Observation

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  1. Applying Numerical Relativity and EOB to Black Hole Binary Observation Sean McWilliams NASA Goddard Space Flight Center University of Maryland Collaborators: John Baker, Joan Centrella, Bernard Kelly, Jim Van Meter, Alessandra Buonanno, Yi Pan 10 August 2007

  2. 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 Sean T. McWilliams UMD/NASA GSFC

  3. Phase comparisons Calculating δφvs. frequency does not yield the same results as calculating vs. time over a particular time interval. • Waveforms evolve out of sync in phase and frequency • δφ depends on what time you set the waveforms to be equal Out of sync In sync Sean T. McWilliams UMD/NASA GSFC

  4. For data analysis, we construct a “best guess” waveform with a PN inspiral and NR merger • We find for , or t = -328M (circled below) Sean T. McWilliams UMD/NASA GSFC

  5. Example signals for LIGO and Advanced LIGO Sean T. McWilliams UMD/NASA GSFC

  6. Example signals for LISA Sean T. McWilliams UMD/NASA GSFC

  7. Horizon of detectability How close does an average oriented, average sky location LIGO source need to be to have an SNR of 8, i.e. to be detectable? Sean T. McWilliams UMD/NASA GSFC

  8. SNR vs. nonred-shifted mass and redshift for Advanced LIGO and LISA LISA Advanced LIGO • 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 Sean T. McWilliams UMD/NASA GSFC

  9. 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 Sean T. McWilliams UMD/NASA GSFC

  10. Matching NR and EOB 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. 1:1 4:1 h+ for 4:1 mass ratio, summed through l=4, evaluated at q=p/3 See Yi Pan’s talk tomorrow, 5:10, in Thomas 216 for more EOB-NR details Sean T. McWilliams UMD/NASA GSFC

  11. 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. Sean T. McWilliams UMD/NASA GSFC

  12. 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. Sean T. McWilliams UMD/NASA GSFC

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