Universality in supernova gravitational waves with proto-neutron star properties

Gravitational wave signals from core-collapse supernovae are one of the important observables for extracting the information of dense matter. To extract the properties of proto-neutron stars produced via core-collapse supernovae by asteroseismology, we perform a linear perturbation analysis using data obtained from two-dimensional numerical simulations. We employ 12 and 20 solar-mass progenitors and compare two different treatments of gravity. One is a general relativistic one with a conformal flatness condition and the other is an effective gravitational potential mimicking the Tolman-Oppenheimer-Volkoff solution. We discuss how the frequencies of the proto-neutron star oscillations corresponding to the gravitational wave signals in the simulations depend on the proto-neutron star properties. In our models, we find that the gravitational wave frequencies of the proto-neutron stars determined with the Cowling approximation can be expressed to very good approximation as a function of the proto-neutron star average density almost independently of the progenitor mass, treatment of gravity in the simulations, and the interpolations in the simulations. On the other hand, if one considers the gravitational wave frequencies as a function of the surface gravity of proto-neutron stars, such a relation appears sensitive to the treatment of gravity and other numerical details in the simulations. Thus, the average density of proto-neutron stars seems more suitable for universally expressing the supernova gravitational wave frequencies, instead of the surface gravity.