Inferring physical properties of stellar collapse by third-generation gravitational-wave detectors

Galactic core-collapse supernovae are among the possible sources of gravitational waves. We investigate the ability of gravitational-wave observatories to extract the properties of the collapsing progenitor from the gravitational waves radiated. We use simulations of supernovae that explore a variety of progenitor core rotation rates and nuclear equations of state and examine the ability of current and future observatories to determine these properties using gravitational-wave parameter estimation. We use principal component analysis of the simulation catalog to determine the dominant features of the waveforms and create a map between the measured properties of the waveform and the physical properties of the progenitor. We use Bayesian parameter inference and the parameter map to calculate posterior probabilities for the physical properties given a gravitational-wave observation. We estimate the ratio of the progenitor's core rotational kinetic energy to potential energy ($\beta$) and the post bounce oscillation frequency. For a supernovae at the distance of the galactic center (8.1 kpc) with $\beta = 0.02$ our method can estimate $\beta$ with a $90\%$ credible interval of $0.004$ for Advanced LIGO, improving to $0.0008$ for Cosmic Explorer. We demonstrate that if the core is rotating sufficiently rapidly for a signal observed by Cosmic Explorer, our method can also extract the post bounce oscillation frequency of the protoneutron star to a precision of within $5$~Hz ($90\%$ credible interval) allowing us to constrain the nuclear equation of state. For a supernovae at the distance of the Magellanic Clouds (48.5 kpc) Cosmic Explorer's ability to measure these parameters decreases slightly to $0.003$ for rotation and $11$~Hz for the postbounce oscillation frequency ($90\%$ credible interval). Sources in Magellanic Clouds will be too distant for Advanced LIGO to measure these properties.