Gravitational radiation from convective instabilities in Type II supernova explosions

We present twoand three-dimensional simulations of convective instabilities during the first second of a Type II supernova explosion. Convective overturn occurs in two distinct, spatially well separated regions: (i) inside the proto-neutron star immediately below the neutrinosphere (r < 50 km) and (ii) in the neutrino-heated “hot-bubble” region interior to the outward propagating revived shock wave (100 km < r < 1000 km). We have calculated the gravitational wave signature of both convective instabilities including the quadrupole waveforms, the energy spectra, and the total amount of the emitted gravitational wave energy. Moreover, we have estimated the amplitude and energy of gravitational waves associated with the anisotropic neutrino emission that is caused by the convective transport of neutrinos and by aspherical perturbations of temperature and density in the neutrinospheric region. For a supernova located at a distance of 10 kpc the maximum dimensionless gravitational wave amplitudes due to convective mass motions range from jhTTj 2 10 22 for the three-dimensional simulation to jhTTj 7 10 21 for the most strongly radiating two-dimensional model. The total emitted energy varies from 10 13 M c2 to 2 10 9 M c2. The convective mass motions inside the proto-neutron star produce a stronger signal than convection in region (ii) with up to a factor of 10 larger amplitudes and 1000 times more gravitational wave energy. Because of smaller convective eddies and structures and slower overturn velocities, the wave amplitudes of threedimensional models are more than a factor of 30 smaller, and the energy emitted in gravitational waves is more than 3 orders of magnitude less than in the corresponding two-dimensional situation. In two dimensions the gravitational wave amplitude associated with the anisotropic emission of neutrinos can be larger (factor 2) than the wave amplitude due to mass motions in the proto-neutron star, although the energy in the neutrino tidal field is 100 times smaller. In three dimensions the neutrino gravitational wave amplitude is reduced by a factor of about 10 and the gravitational wave energy by a factor of roughly 100 relative to the two-dimensional results. Nevertheless, the neutrino tidal field is more than a factor of 10 larger than the Send offprint requests to: E. Müller gravitational wave amplitude from mass motions and the corresponding gravitational wave energies can be of similar size. Most of the gravitational radiation from convection inside the proto-neutron star is emitted in the frequency band 100– 1000 Hz, while convective motions in the hot-bubble region generate waves from several 100 Hz down to a few Hz. Gravitational waves from the anisotropic neutrino emission have most power at frequencies between some 10 Hz and a few 100 Hz and a low-frequency contribution at about 1 Hz to several Hz. Features in the gravitational-wave signal from the neutrinoheated region are well correlated with structures in the neutrino signal, both being associated with sinking and rising lumps of matter and with temporal variations of aspherical accretion flows towards the proto-neutron star. A simultaneous measurement of both signals would impose important contraints on the dynamics of Type II supernovae and theoretical models of the explosion mechanism.