Extracting equation of state parameters from black hole-neutron star mergers: aligned-spin black holes and a preliminary waveform model

Information about the neutron-star equation of state is encoded in the waveform of a black hole-neutron star system through tidal interactions and the possible tidal disruption of the neutron star. During the inspiral this information depends on the tidal deformability Lambda of the neutron star, and we find that Lambda is the best measured parameter during the merger and ringdown as well. We performed 134 simulations where we systematically varied the equation of state as well as the mass ratio, neutron star mass, and aligned spin of the black hole. Using these simulations we have developed an analytic representation of the full inspiral-merger-ringdown waveform calibrated to these numerical waveforms, and we use this analytic waveform to estimate the accuracy to which Lambda can be measured with gravitational-wave detectors. We find that although the inspiral tidal signal is small, coherently combining this signal with the merger-ringdown matter effect improves the measurability of Lambda by a factor of ~3 over using just the merger-ringdown matter effect alone. However, incorporating correlations between all the waveform parameters then decreases the measurability of Lambda by a factor of ~3. The uncertainty in Lambda increases with the mass ratio, but decreases as the black hole spin increases. Overall, a single Advanced LIGO detector can measure Lambda for mass ratios Q = 2--5, black hole spins J_BH/M_BH^2 = -0.5--0.75, neutron star masses M_NS = 1.2M_sun--1.45M_sun, and an optimally oriented distance of 100Mpc to an uncertainty of ~10%--100%. For the proposed Einstein Telescope, the uncertainty in Lambda is an order of magnitude smaller.