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

We compare GW150914 directly to simulations of coalescing binary black holes in full general relativity,including several performed specifically to reproduce this event. Our calculations go beyond existingsemianalytic 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 separatelywhich account for all the quadrupolar and octopolar modes. Consistent with the posterior distributionsreported by Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016)] (at the 90% credible level), we find the dataare compatible with a wide range of nonprecessing and precessing simulations. Follow-up simulationsperformed using previously estimated binary parameters most resemble the data, even when all quadrupolarand octopolar modes are included. Comparisons including only the quadrupolar modes constrain the totalredshifted mass Mz ∈ ½64 M⊙ − 82 M⊙, mass ratio 1=q ¼ m2=m1 ∈ ½0.6; 1, and effective aligned spinχeff ∈ ½−0.3; 0.2, where χeff ¼ ðS1=m1 þ S2=m2Þ · L ˆ =M. Including both quadrupolar and octopolarmodes, we find the mass ratio is even more tightly constrained. Even accounting for precession, simulationswith extreme mass ratios and effective spins are highly inconsistent with the data, at any mass. Severalnonprecessing and precessing simulations with similar mass ratio and χeff are consistent with the data.Though correlated, the components’ spins (both in magnitude and directions) are not significantlyconstrained by the data: the data is consistent with simulations with component spin magnitudes a1;2 upto at least 0.8, with random orientations. Further detailed follow-up calculations are needed to determine ifthe data contain a weak imprint from transverse (precessing) spins. For nonprecessing binaries, interpolatingbetween simulations, we reconstruct a posterior distribution consistent with previous results. The final blackhole’s redshifted mass is consistent with Mf;z in the range 64.0 M⊙ − 73.5 M⊙ and the final black hole’sdimensionless spin parameter is consistent with af ¼ 0.62–0.73. As our approach invokes no intermediateapproximations to general relativity and can strongly reject binaries whose radiation is inconsistent with thedata, our analysis provides a valuable complement to Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016)].