Measuring the properties of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mtext>−</mml:mtext><mml:mi>mode</mml:mi></mml:mrow></mml:math> oscillations of a protoneutron star by third-generation gravitational-wave detectors
Chaitanya Afle, Suman Kumar Kundu, Jenna Cammerino, Eric R. Coughlin, D. Brown, David Vartanyan, Adam Burrows
Abstract
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 ($f\text{\ensuremath{-}}\mathrm{mode}$) oscillation of the protoneutron star. From the time-frequency spectrogram of the gravitational-wave strain we see that, starting $\ensuremath{\sim}400\text{ }\text{ }\mathrm{ms}$ after the core bounce, most of the power lies within a narrow track that represents the frequency evolution of the $f\text{\ensuremath{-}}\mathrm{mode}$ oscillations. The $f\text{\ensuremath{-}}\mathrm{mode}$ 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 $f\text{\ensuremath{-}}\mathrm{mode}$ 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 $f\text{\ensuremath{-}}\mathrm{mode}$ using the spectrogram data of the strain signal. We find that the energy in the $f\text{\ensuremath{-}}\mathrm{mode}$ can be measured to within 20% error for signals observed by Cosmic Explorer using simulations with successful explosion, assuming source distances within 10 kpc.