LIGO Document P1500263-v21

Directly comparing GW150914 with numerical solutions of Einstein’s equations for binary black hole coalescence

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20 Jun 2016, 10:53
We compare GW150914 directly to simulations of coalescing binary black holes in full general relativity, in- cluding several performed specifically to reproduce this event. Our calculations go beyond existing semianalytic models, because for all simulations – including sources with two independent, precessing spins – we perform comparisons which account for all the spin-weighted quadrupolar modes, and separately which account for all the quadrupolar and octopolar modes. Consistent with the posterior distributions reported in LVC-PE[1] (at 90% confidence), we find the data is compatible with a wide range of nonprecessing and precessing simulations. Fol- lowup simulations performed using previously-estimated binary parameters most resemble the data, even when all quadrupolar and octopolar modes are included. Comparisons including only the quadrupolar modes con- strain the total redshifted mass Mz [64 − 82M⊙], mass ratio q = m2/m1 ∈ [0.6, 1], and effective aligned spin χeff ∈ [−0.3, 0.2] [χeff = (S1/m1 + S2/m2) · Lˆ /M]. Including both quadrupolar and octopolar modes, we find the mass ratio is even more tightly constrained. Even accounting for precession, simulations with extreme mass ratios and effective spins are highly inconsistent with the data, at any mass. Several nonprecessing and precess- ing simulations with similar mass ratio and χeff are consistent with the data. Though correlated, the components spins (both in magnitude and directions) are not significantly constrained by the data: the data is consistent with simulations with component spin magnitudes a1,2 up to at least 0.8, with random orientations. Further detailed followup calculations are needed to determine if the data contains a weak imprint from transverse (precessing) spins. For nonprecessing binaries, interpolating between simulations, we reconstruct a posterior distribution consistent with previous results. The final black hole’s redshifted mass is consistent with Mf,z between 64.0−73.5M⊙ and the final black hole’s dimensionless spin parameter is consistent with af =0.62−0.73. As our approach invokes no intermediate approximations to general relativity and can strongly reject binaries whose radiation is inconsistent with the data, our analysis provides a valuable complement to LVC-PE[1].
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