Measuring the angular momentum distribution in core-collapse supernova progenitors with gravitational waves

The late collapse, core bounce, and the early postbounce phase of rotating core collapse leads to a characteristic gravitational wave (GW) signal. The precise shape of the signal is governed by the interplay of gravity, rotation, nuclear equation of state (EOS), and electron capture during collapse. We explore the detailed dependence of the signal on total angular momentum and its distribution in the progenitor core by means of a large set of axisymmetric general-relativistic hydrodynamics core-collapse simulations, in which we systematically vary the initial angular momentum distribution in the core. Our simulations include a microphysical finite-temperature EOS, an approximate electron capture treatment during collapse, and a neutrino leakage scheme for the postbounce evolution. Our results show that the total angular momentum of the inner core at bounce and the inner core's ratio of rotational kinetic energy to gravitational energy $T/|W|$ are both robust parameters characterizing the GW signal. We find that the precise distribution of angular momentum is relevant only for very rapidly rotating cores with $T/|W|\ensuremath{\gtrsim}8%$ at bounce. We construct a numerical template bank from our baseline set of simulations, and carry out additional simulations to generate trial waveforms for injection into simulated Advanced LIGO noise at a fiducial galactic distance of 10 kpc. Using matched filtering, we show that for an optimally oriented source and Gaussian noise, Advanced LIGO could measure the total angular momentum to within $\ifmmode\pm\else\textpm\fi{}20%$, for rapidly rotating cores. For most waveforms, the nearest known degree of precollapse differential rotation is correctly inferred by both our matched filtering analysis and an alternative Bayesian model selection approach. We test our results for robustness against systematic uncertainties by injecting waveforms from simulations utilizing a different EOS and variations in the electron fraction in the inner core. The results of these tests show that these uncertainties significantly reduce the accuracy with which the total angular momentum and its precollapse distribution can be inferred from observations.