Inferring astrophysical parameters of core-collapse supernovae from their gravitational-wave emission

Nearby core-collapse supernovae (CCSNe) are powerful multimessenger sources for gravitational-wave, neutrino, and electromagnetic telescopes as they emit gravitational waves in the ideal frequency band for ground based detectors. Once a CCSN gravitational-wave signal is detected, we will need to determine the parameters of the signal and understand how those parameters relate to the source’s explosion, progenitor, and remnant properties. This is a challenge due to the stochastic nature of CCSN explosions, which is imprinted on their time series gravitational waveforms. In this paper, we perform Bayesian parameter estimation of CCSN signals using an asymmetric chirplet signal model to represent the dominant high-frequency mode observed in spectrograms of CCSN gravitational-wave signals. We use design sensitivity Advanced LIGO noise and CCSN waveforms from four different hydrodynamical supernova simulations with a range of different progenitor stars. We determine how well our model can reconstruct time-frequency images of the emission modes and show how well we can determine parameters of the signal such as the frequency, amplitude, and duration. We show how the parameters of our signal model may allow us to place constraints on the protoneutron star mass and radius, the turbulent kinetic energy onto the protoneutron star, and the time of shock revival.

Figure 1

From top to bottom are models m39, s18, y20, and he3.5. From left to right, the columns show the waveform from simulations, the waveform in Advanced LIGO design sensitivity noise [4], and the reconstructed waveform. The signal has a signal to noise ratio of 25. Our signal model captures the shape of the dominant signal mode but not the stochastic fluctuations in amplitude.

Figure 2

The minimum network SNR needed to detect the m39 model using the noncentral chi-squared likelihood and spectrogram signal model and the standard Gaussian likelihood with the time domain signal model. Performing the analysis in the spectrogram domain significantly decreases the minimum SNR needed for detection.

Figure 3

The reconstructed waveforms for m39 (top) and s18 (bottom) using the Gaussian likelihood function and time domain signal model. The network signal to noise ratio is 25.

Figure 4

The posterior distributions of the peak frequency, duration, and rate of change of frequency at different signal to noise ratios. The left column is for model m39, and the right column is for model s18. The dashed lines show the true values. The model parameters are not constrained at a network SNR of 10. At SNR 12 and 14, only the part of the signal with the highest amplitude is reconstructed. SNR 16 is needed to capture the full length of the signal mode.

Figure 5

Using the frequencies from our reconstructed signal spectrograms, shown in the top row, at a SNR of 25, we estimate the combined protoneutron star mass and radius $M/R^2$ using the ${}^2{g}_2$ universal relation from Torres-Forné et al. [30]. The light blue shows the values estimated using the posterior samples from bilby, and the dark blue line is the true value from our waveform simulations. Left is model y20, and right is model he3.5.

Figure 6

The solid lines show the shock radius from the simulations of models y20, he3.5, and s18. The dashed line shows the time of peak frequency measured by our bilby analysis. Low mass models have their peak frequency around the shock revival time, and higher mass models have their peak frequencies $\sim 100\mathrm{ms}$ after the shock is revived.

Figure 7

The gravitational-wave energy measured by our analysis for model he3.5 (top left), model s18 (top right), model y20 (bottom left), and model m39 (bottom right) at a signal to noise ratio of 25. The black lines are the true values given by the CCSN waveform simulations.