Measuring neutron star tidal deformability with Advanced LIGO: A Bayesian analysis of neutron star-black hole binary observations

Abstract

The pioneering discovery of gravitational waves (GWs) by Advanced LIGO has ushered us into an era of observational GW astrophysics. Compact binaries remain the primary target sources for GW observation, of which neutron star-black hole (NSBH) binaries form an important subset. GWs from NSBH sources carry signatures of (a) the tidal distortion of the neutron star by its companion black hole during inspiral, and (b) its potential tidal disruption near merger. In this paper, we present a Bayesian study of the measurability of neutron star tidal deformability ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}\ensuremath{\propto}(R/M{)}_{\mathrm{NS}}^{5}$ using observation(s) of inspiral-merger GW signals from disruptive NSBH coalescences, taking into account the crucial effect of black hole spins. First, we find that if nontidal templates are used to estimate source parameters for an NSBH signal, the bias introduced in the estimation of nontidal physical parameters will only be significant for loud signals with signal-to-noise ratios greater than $\ensuremath{\simeq}30$. For similarly loud signals, we also find that we can begin to put interesting constraints on ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}$ (factor of 1--2) with individual observations. Next, we study how a population of realistic NSBH detections will improve our measurement of neutron star tidal deformability. For an astrophysically likely population of disruptive NSBH coalescences, we find that 20--35 events are sufficient to constrain ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}$ within $\ifmmode\pm\else\textpm\fi{}25%--50%$, depending on the neutron star equation of state. For these calculations we assume that LIGO will detect black holes with masses within the astrophysical mass gap. In case the mass gap remains preserved in NSBHs detected by LIGO, we estimate that approximately 25% additional detections will furnish comparable ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}$ measurement accuracy. In both cases, we find that it is the loudest 5--10 events that provide most of the tidal information, and not the combination of tens of low-SNR events, thereby facilitating targeted numerical-GR follow-ups of NSBHs. We find these results encouraging, and recommend that an effort to measure ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}$ be planned for upcoming NSBH observations with the LIGO-Virgo instruments.