Measuring the properties of f-mode oscillations of a protoneutron star by third-generation gravitational-wave detectors

Core-collapse supernovae are among the astrophysical sources of gravitational waves that could be detected by third-generation gravitational-wave detectors. Here, we analyze the gravitational-wave strain signals from two- and three-dimensional simulations of core-collapse supernovae generated using the code fornax. A subset of the two-dimensional simulations has nonzero core rotation at the core bounce. A dominant source of time changing quadrupole moment is the l=2 fundamental mode (f-mode) oscillation of the protoneutron star. From the time-frequency spectrogram of the gravitational-wave strain we see that, starting ∼400 ms after the core bounce, most of the power lies within a narrow track that represents the frequency evolution of the f-mode oscillations. The f-mode frequencies obtained from linear perturbation analysis of the angle-averaged profile of the protoneutron star corroborate what we observe in the spectrograms of the gravitational-wave signal. We explore the measurability of the f-mode frequency evolution of a protoneutron star for a supernova signal observed in the third-generation gravitational-wave detectors. Measurement of the frequency evolution can reveal information about the masses, radii, and densities of the protoneutron stars. We find that if the third-generation detectors observe a supernova within 10 kpc, then we can measure these frequencies to within 5 Hz rms error. We can also measure the energy emitted in the fundamental f-mode using the spectrogram data of the strain signal. We find that the energy in the f-mode can be measured to within 20% error for signals observed by Cosmic Explorer using simulations with successful explosion, assuming source distances within 10 kpc.