Avoided crossing in gravitational wave spectra from protoneutron star

TL;DR

This study links gravitational wave ramp-up signals from supernovae to specific PNS oscillation modes, providing a way to estimate PNS density evolution through observed gravitational waves.

Contribution

The paper identifies mode exchanges via avoided crossing in PNS oscillations and provides fitting formulas to infer PNS density evolution from gravitational wave data.

Findings

Ramp up signals correspond to g1- and f-modes.

Mode exchange occurs via avoided crossing.

Fitting formulas relate modes to PNS density.

Abstract

The ramp up signals of gravitational waves appearing in the numerical simulations could be important signals to estimate parameters of the protoneutron star (PNS) at supernova explosions. To identify the signals with PNS oscillations, we make a linear perturbation analysis and compare the resultant eigenfrequencies with the ramp up signals obtained via the two-dimensional numerical simulations. Then, we find that the ramp up signals correspond well to the $g_1$-mode in the early phase and to the $f$-mode, to which the $g_1$-mode is exchanged via the avoided crossing. We also confirm that the $f$- and $g_1$-modes are almost independent of the selection of the PNS surface density in the later phase after core bounce. In addition, we successfully find that the fitting formula of $g_1$- and $f$-modes, which correspond to the ramp up signals in the numerical simulation, as a function of the PNS average density. That is, via the direct observation of the gravitational waves after supernova explosion, one could extract the time evolution of the PNS average density by using our fitting formula.