Universal Relations for Gravitational-Wave Asteroseismology of Protoneutron Stars

State-of-the-art numerical simulations of core-collapse supernovae reveal that the main source of gravitational waves is the excitation of protoneutron star modes during postbounce evolution. In this work we derive universal relations that relate the frequencies of the most common oscillation modes observed, i.e., g modes, p modes, and the f mode, with fundamental properties of the system, such as the surface gravity of the protoneutron star or the mean density in the region enclosed by the shock. These relations are independent of the equation of state, the neutrino treatment, and the progenitor mass and, hence, can be used to build methods to infer protoneutron star properties from gravitational-wave observations alone. We outline how these measurements could be done and the constraints that could be placed on the protoneutron star properties.