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 $\mathrm{\ensuremath{\Lambda}}$ of the neutron star, and we find that the best-measured parameter during the merger and ringdown is consistent with $\mathrm{\ensuremath{\Lambda}}$ 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 develop an analytic representation of the full inspiral-merger-ringdown waveform calibrated to these numerical waveforms; we use this analytic waveform and a Fisher matrix analysis to estimate the accuracy to which $\mathrm{\ensuremath{\Lambda}}$ 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 $\mathrm{\ensuremath{\Lambda}}$ by a factor of $\ensuremath{\sim}3$ over using just the merger-ringdown matter effect alone. However, incorporating correlations between all the waveform parameters then decreases the measurability of $\mathrm{\ensuremath{\Lambda}}$ by a factor of $\ensuremath{\sim}3$. The uncertainty in $\mathrm{\ensuremath{\Lambda}}$ increases with the mass ratio, but decreases as the black hole spin increases. Overall, a single Advanced LIGO detector can only marginally measure $\mathrm{\ensuremath{\Lambda}}$ for mass ratios $Q=2\char21{}5$, black hole spins ${J}_{\mathrm{BH}}/{M}_{\mathrm{BH}}^{2}=\ensuremath{-}0.5\char21{}0.75$, and neutron star masses ${M}_{\mathrm{NS}}=1.2{M}_{\ensuremath{\bigodot}}\char21{}1.45{M}_{\ensuremath{\bigodot}}$ at an optimally oriented distance of 100 Mpc. For the proposed Einstein Telescope, however, the uncertainty in $\mathrm{\ensuremath{\Lambda}}$ is an order of magnitude smaller.