Towards asteroseismology of core-collapse supernovae with gravitational-wave observations - I. Cowling approximation

Gravitational waves from core-collapse supernovae are produced by the excitation of different oscillation modes in the protoneutron star (PNS) and its surroundings, including the shock. In this work we study the relationship between the post-bounce oscillation spectrum of the PNS-shock system and the characteristic frequencies observed in gravitational-wave signals from core-collapse simulations. This is a fundamental first step in order to develop a procedure to infer astrophysical parameters of the PNS formed in core-collapse supernovae. Our method combines information from the oscillation spectrum of the PNS, obtained through linear perturbation analysis in general relativity of a background physical system, with information from the gravitational-wave spectrum of the corresponding non-linear, core-collapse simulation. Using results from the simulation of the collapse of a 35 M_⊙ pre-supernova progenitor we show that both types of spectra are indeed related and we are able to identify the modes of oscillation of the PNS, namely g-modes, p-modes, hybrid modes, and standing accretion shock instability (SASI) modes, obtaining a remarkably close correspondence with the time-frequency distribution of the gravitational-wave modes. The analysis presented in this paper provides a proof of concept that asteroseismology is indeed possible in the core-collapse scenario, and it may serve as a basis for future work on PNS parameter inference based on gravitational-wave observations.