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

Spin-orbit resonances have important astrophysical implications as the evolution and subsequent coalescence of supermassive black hole binaries in one of these configurations may lead to low recoil velocity of merger remnants. It has also been shown that black hole spins in comparable mass stellar-mass black hole binaries could preferentially lie in a resonant plane when their gravitational waves (GWs) enter the advanced LIGO frequency band [1]. Therefore, it is highly desirable to investigate the possibility of detection and subsequent characterization of such GW sources in the advanced detector era, which can, in turn, improve our perception of their high mass counterparts. The current detection pipelines involve only nonprecessing templates for compact binary searches whereas parameter estimation pipelines can afford to use approximate precessing templates. In this paper, we test the performance of these templates in detection and characterization of spin-orbit resonant binaries. We use fully precessing time-domain SEOBNRv3 waveforms as well as four numerical relativity (NR) waveforms to model GWs from spin-orbit resonant binaries and filter them through IMRPhenomD, SEOBNRv4 and IMRPhenomPv2 approximants. We find that the nonprecessing approximants IMRPhenomD and SEOBNRv4 recover only $\ensuremath{\sim}70%$ of injections with fitting factor (FF) higher than 0.97 (or 90% of injections with $\mathrm{FF}>0.9$). This loss in signal-to-noise ratio is mainly due to the missing physics in these approximants in terms of precession and nonquadrupole modes. However, if we use a new statistic, i.e., maximizing the matched filter output over the sky-location parameters as well, the precessing approximant IMRPhenomPv2 performs magnificently better than their nonprecessing counterparts with recovering 99% of the injections with FFs higher than 0.97. Interestingly, injections with $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}=180\ifmmode^\circ\else\textdegree\fi{}$ have higher FFs ($\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}$ is the angle between the components of the black hole spins in the plane orthogonal to the orbital angular momentum) as compared to their $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}=0\ifmmode^\circ\else\textdegree\fi{}$ and generic counterparts. This is because $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}=180\ifmmode^\circ\else\textdegree\fi{}$ binaries are not as strongly precessing as $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}=0\ifmmode^\circ\else\textdegree\fi{}$ and generic binaries. This implies that we will have a slight observation bias towards $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}=180\ifmmode^\circ\else\textdegree\fi{}$ and away from $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}=0\ifmmode^\circ\else\textdegree\fi{}$ resonant binaries while using nonprecessing templates for searches. Moreover, all template approximants are able to recover most of the injected NR waveforms with FFs $>0.95$. For all the injections including NR, the systematic error in estimating chirp mass remains below $<10%$ with minimum error for $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}=180\ifmmode^\circ\else\textdegree\fi{}$ resonant binaries. The symmetric mass-ratio can be estimated with errors below 15%. The effective spin parameter ${\ensuremath{\chi}}_{\mathrm{eff}}$ is measured with maximum absolute error of 0.13. The in-plane spin parameter ${\ensuremath{\chi}}_{p}$ 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 nonquadrupole modes but also better search strategies for precessing GW signals.

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