Bayesian inference from gravitational waves in fast-rotating, core-collapse supernovae

Core-collapse supernovae (CCSNe) are prime candidates for gravitational-wave detectors. The analysis of their complex waveforms can potentially provide information on the physical processes operating during the collapse of the iron cores of massive stars. In this work we analyze the early-bounce rapidly rotating CCSN signals reported in the waveform catalog of Richers et al. 2017. This catalog comprises over 1800 axisymmetric simulations extending up to about 10 ms of postbounce evolution. It was previously established that for a large range of progenitors, the amplitude of the bounce signal, $D·\Delta h$, is proportional to the ratio of rotational-kinetic energy to potential energy, $T/\left|W\right|$, and the peak frequency, $f_{\mathrm{peak}}$, is proportional to the square root of the central rest-mass density, $\sqrt{{\rho }_c}$. In this work, we exploit these relations to suggest that it could be possible to use such waveforms to infer protoneutron star properties from a future gravitational wave observation, but only if the distance and inclination are well known and the rotation rate is sufficiently low. Our approach relies on the ability to describe a subset of the waveforms in the early postbounce phase in a simple form—a master waveform template—depending only on two parameters, $D·\Delta h$ and $f_{\mathrm{peak}}$. We use this template to perform a Bayesian inference analysis of waveform injections in Gaussian colored noise for a network of three gravitational wave detectors formed by Advanced LIGO and Advanced Virgo. We show that, for a Galactic event ($D\sim 10\mathrm{kpc}$), it is possible to recover the peak frequency and amplitude with an accuracy better than 10% for $\sim 80\%$ and $\sim 60\%$ of the signals, respectively, given known distance and inclination angle. However, inference on waveforms from outside the Richers catalog is not reliable, indicating a need for carefully verified waveforms of the first 10 ms after bounce of rapidly rotating supernovae of different progenitors with agreement between different codes.