Leveraging gravitational-wave memory to distinguish neutron star--black hole binaries from black hole binaries

In the observation of gravitational waves (GWs) from a compact binary coalescence system where the mass of one of the companions is $\leq 5~M_{\odot}$ the nature of the object is ambiguous until the measurements of tidal effects give evidence for the presence of a neutron star (NS) or a low mass black hole (BH). The relevance of tidal effects in a neutron star--black hole (NSBH) binary system depends crucially upon the mass and the spin of the companion BH. These effects become important predominantly when the binary system is of comparable mass and/or has large aligned spins. Depending upon the masses and spins the NS can even get tidally disrupted before the innermost stable circular orbit (ISCO) is reached. The gravitational-wave signatures of various tidal effects are encoded in the phasing of the signal and in the case of tidal disruption an abrupt cutoff of the signal amplitude occurs. In this work we show that tidal effects can also be captured by the nonlinear memory of the GW signal. Although small in amplitude, nonlinear memory is present at low frequency in contrast to the oscillatory GW signal. We introduce nonlinear memory in the NSBH and binary black hole (BBH) waveform models and show how the addition of memory aids in distinguishing NSBH systems from BBH systems for a larger part of the parameter space. We discuss the recently detected events of interest by LIGO-Virgo and provide the future prospects for the third generation detectors where nonlinear memory can play a crucial role in inferring the nature of the coalescence as BBH or NSBH from its GW signal alone.