Including higher order multipoles in gravitational-wave models for precessing binary black holes

Abstract

Estimates of the source parameters of gravitational-wave (GW) events produced by compact binary mergers rely on theoretical models for the GW signal. We present the first frequency-domain model for the inspiral, merger, and ringdown of the GW signal from precessing binary black hole systems that also includes multipoles beyond the leading-order quadrupole. Our model, PhenomPv3HM, is a combination of the higher-multipole nonprecessing model PhenomHM and the spin-precessing model PhenomPv3 that includes two-spin precession via a dynamical rotation of the GW multipoles. We validate the new model by comparing to a large set of precessing numerical-relativity simulations and find excellent agreement across the majority of the parameter space they cover. For mass ratios $<5$ the mismatch improves, on average, from $\ensuremath{\sim}6%$ to $\ensuremath{\sim}2%$ compared to PhenomPv3 when we include higher multipoles in the model. However, we find mismatches $\ensuremath{\sim}8%$ for a mass-ratio-6 and highly spinning simulation. We quantify the statistical uncertainty in the recovery of binary parameters by applying standard Bayesian parameter estimation methods to simulated signals. We find that, while the primary black hole spin parameters should be measurable even at moderate signal-to-noise ratios (SNRs) $\ensuremath{\sim}30$, the secondary spin requires much larger SNRs $\ensuremath{\sim}200$. We also quantify the systematic uncertainty expected by recovering our simulated signals with different waveform models in which various physical effects---such as the inclusion of higher modes and/or precession---are omitted and find that even in the low-SNR case ($\ensuremath{\sim}17$) the recovered parameters can be biased. Finally, as a first application of the new model we analyze the binary black hole event GW170729. We find larger values for the primary black hole mass of ${58.25}_{\ensuremath{-}12.53}^{+11.73}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ (90% credible interval). The lower limit ($\ensuremath{\sim}46\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$) is comparable to the proposed maximum black hole mass predicted by different stellar evolution models due to the pulsation pair-instability supernova (PPISN) mechanism. If we assume that the primary black hole in GW170729 formed through a PPISN, then out of the four PPISN models we consider only the model of Woosley [1] is consistent with our mass measurements at the 90% confidence level.