Detection and characterization of spin-orbit resonances in the advanced gravitational wave detectors era

Abstract

In this paper, we test the performance of templates in detection and characterization of Spin-orbit resonant (SOR) binaries. We use precessing SEOBNRv3 waveforms as well as {\it four} numerical relativity (NR) waveforms to model GWs from SOR binaries and filter them through IMRPhenomD, SEOBNRv4 (non-precessing) and IMRPhenomPv2 (precessing) approximants. We find that IMRPhenomD and SEOBNRv4 recover only $\sim 70\%$ of injections with fitting factor (FF) higher than 0.97 (or 90\% of injections with $\mathrm{FF}>0.9$).However, using the sky-maxed statistic, IMRPhenomPv2 performs magnificently better than their non-precessing counterparts with recovering $99\%$ of the injections with FFs higher than 0.97. Interestingly, injections with $\hat{I}”\ddot{I}•=180^{\circ }$ have higher FFs ($\hat{I}”\ddot{I}•$ is the angle between the components of the black hole spins in the plane orthogonal to the orbital angular momentum) as compared to their $\hat{I}”\ddot{I}•=0^{\circ }$ and generic counterparts. This implies that we will have a slight observation bias towards $\hat{I}”\ddot{I}•=180^{\circ }$ SORs while using non-precessing templates for searches. All template approximants are able to recover most of the injected NR waveforms with FFs $>0.95$. For all the injections including NR, the error in estimating chirp mass remains below $<10\%$ with minimum error for $\hat{I}”\ddot{I}•=180^{\circ }$ resonant binaries. The symmetric mass ratio can be estimated with errors below $15\%$. The effective spin parameter $\ddot{I}{‡}_{\mathrm{eff}}$ is measured with maximum absolute error of 0.13. The in-plane spin parameter $\ddot{I}{‡}_p$ is mostly underestimated indicating that a precessing signal will be recovered as a relatively less precessing signal. Based on our findings, we conclude that we not only need improvements in waveform models towards precession and non-quadrupole modes but also better search strategies for precessing GW signals.

27 pages, 15 figures. Abstract shortened due to word limit