Abstract
We use an asteroseismology method to calculate the frequencies of gravitational waves (GWs) in a long-term core-collapse supernova simulation, with a mass of 9.6 solar mass. The simulation, which includes neutrino radiation transport in general relativity is performed from core-collapse, bounce, explosion and cooling of protoneutron stars (PNSs) up to 20 s after the bounce self-consistently. Based on the hydrodynamics background, we calculate eigenmodes of the PNS oscillation through a perturbation analysis on fluid and metric. We classify the modes by the number of nodes and find that there are several eigenmodes. In the early phase before 1 s, there are low-frequency -modes around 0.5 kHz, midfrequency -modes around 1 kHz, and high-frequency -modes above them. Beyond 1 second, the -modes drop too low in frequency and the -modes become too high to be detected by ground-based interferometers. However, the -mode persists at 1 kHz. We present a novel fitting formula for the ramp-up mode, comprising a mixture of -mode and -mode, using postbounce time as a fitting parameter. Our approach yields improved results for the long-term simulation compared to prior quadratic formulas. We also fit frequencies using combinations of gravitational mass, , and radius, , of the PNS. We test three types of fitting variables: compactness , surface gravity , and average density . We present results of the time evolution of each mode and the fitting for three different ranges, from 0.2 s to 1 s, 4 s, and 20 s for each formula. We then compare the deviation of the formulas from the eigenmodes to determine which fitting formula is the best. In conclusion, any combination of and fits the eigenmodes well to a similar degree. Comparing three variables in detail, the fitting with compactness is slightly the best among them. We also find that the fitting using less than 1 s of simulation data cannot be extrapolated to the long-term frequency prediction.
1 More- Received 2 February 2023
- Accepted 28 February 2023
DOI:https://doi.org/10.1103/PhysRevD.107.083015
© 2023 American Physical Society