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. Sean T. McWilliams UMD/NASA GSFC 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

3. 10 August 2007Sean T. McWilliams UMD/NASA GSFC 3 Phase comparisons Out of syncIn 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.

4. 10 August 2007Sean 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)

5. 10 August 2007Sean T. McWilliams UMD/NASA GSFC 5 Example signals for LIGO and Advanced LIGO

6. 10 August 2007Sean T. McWilliams UMD/NASA GSFC 6 Example signals for LISA

7. 10 August 2007Sean 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?

8. 10 August 2007Sean T. McWilliams UMD/NASA GSFC 8 SNR vs. nonred- shifted mass and redshift for Advanced LIGO and LISA 10s to 100s of mergers per year seen by LISA for 10 4 M Sun < M < 10 6 M Sun (Sesana et al. 2007) >10 mergers/year for M = ~10 3 M Sun by AdLIGO and LISA (Fregeau et al. 2006), but rates are far less certain Advanced LIGO LISA

9. 10 August 2007Sean T. McWilliams UMD/NASA GSFC 9 Example of a simulated LISA signal Michelson single arm X observable for two 10 5 M Sun 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. 10 August 2007Sean T. McWilliams UMD/NASA GSFC 10 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 M f and a f from the numerical simulations. See Yi Pan’s talk tomorrow, 5:10, in Thomas 216 for more EOB-NR details

11. 10 August 2007Sean T. McWilliams UMD/NASA GSFC 11 PN late inspiral comparison 1:14:1 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.

12. 10 August 2007Sean 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.