Extracting equation of state parameters from black hole-neutron star mergers: Nonspinning black holes

The late inspiral, merger, and ringdown of a black hole-neutron star (BHNS) system can provide information about the neutron-star equation of state (EOS). Candidate EOSs can be approximated by a parametrized piecewise-polytropic EOS above nuclear density, matched to a fixed low-density EOS; and we report results from a large set of BHNS inspiral simulations that systematically vary two parameters. To within the accuracy of the simulations, we find that, apart from the neutron-star mass, a single physical parameter $\ensuremath{\Lambda}$, describing its deformability, can be extracted from the late inspiral, merger, and ringdown waveform. This parameter is related to the radius, mass, and $\ensuremath{\ell}=2$ Love number, ${k}_{2}$, of the neutron star by $\ensuremath{\Lambda}=2{k}_{2}{R}^{5}/3{M}_{\mathrm{NS}}^{5}$, and it is the same parameter that determines the departure from point-particle dynamics during the early inspiral. Observations of gravitational waves from BHNS inspiral thus restrict the EOS to a surface of constant $\ensuremath{\Lambda}$ in the parameter space, thickened by the measurement error. Using various configurations of a single Advanced LIGO detector, we find that ${\ensuremath{\Lambda}}^{1/5}$ or equivalently $R$ can be extracted to 10--50% accuracy from single events for mass ratios of $Q=2$ and 3 at a distance of 100 Mpc, while with the proposed Einstein Telescope, EOS parameters can be extracted to accuracy an order of magnitude better.