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

Core-collapse supernovae are one of the sources of gravitational waves that could be detected by the third-generation gravitational-wave detectors. We analyze the gravitational-wave strain signals from two and three dimensional simulations of core-collapse supernovae. The 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 ∼400ms after the core bounce, most of the power lies within a narrow track that represents the frequency evolution of the f−mode oscillations, as is corroborated by linear perturbation analysis of the angle-averaged profile of the protoneutron star. In this work, we explore the measurability of the frequency evolution and energy of f-mode oscillations 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 and radii of the protoneutron stars. We find that if the third generation detectors observe a supernova within 20 kpc, we can measure these frequencies to within 98% accuracy. We also find that the energy in the f−mode can be measured to within 20% error for simulations with the progenitor mass is higher than 10 solar masses and source distances within 10 kpc.