Effects of multidimensional treatment of gravity in simulations on supernova gravitational waves

Supernova explosions are expected as one of the promising candidates for gravitational wave sources. In this study, we examine the supernova gravitational waves, focusing on the multidimensional treatment of gravity in the simulation. For this purpose, we newly performed two-dimensional relativistic simulations with a nonmonopole (two-dimensional) potential and compared the resultant gravitational wave signals in the simulations with the frequencies of the proto-neutron stars with and without the Cowling approximation. Then, we find that the proto-neutron star frequencies with the Cowling approximation overestimate the gravitational wave frequencies. On the other hand, the frequencies of the proto-neutron star oscillations with metric perturbations agree well with the gravitational wave signals in the simulations. Employing the new data, we derive a new fitting formula for the supernova gravitational wave frequencies with the two-dimensional gravitational potential, independently of the progenitor mass. Combining this new formula with the previous one derived from the Cowling approximation, we also derive the formula to predict the gravitational wave frequencies with a two-dimensional potential, using those with a monopole potential.