Ray-tracing analysis of anisotropic neutrino radiation for estimating gravitational waves in core-collapse supernovae

We propose a ray-tracing method to estimate gravitational waves (GWs) generated by anisotropic neutrino emission in supernova cores. To calculate the gravitational waveforms, we derive analytic formulae in a useful form, which are applicable also for three-dimensional computations. Pushed by evidence of slow rotation prior to core-collapse, we focus on asphericities in neutrino emission and matter motions outside the protoneutron star. Based on the two-dimensional models, which mimic standing accretion shock instability (SASI)-aided neutrino heating explosions, we compute the neutrino anisotropies via the ray-tracing method in a post-processing manner and calculate the resulting waveforms. For simplicity, neutrino absorption and emission by free nucleons, dominant processes outside the protoneutron stars, are only taken into account, while the neutrino scattering and the velocity-dependent terms in the transport equations are neglected. With these computations, it is found that the waveforms exhibit more variety in contrast to the ones previously estimated by the ray-by-ray analysis. In addition to a positively growing feature, which was predicted to determine the total wave amplitudes predominantly, the waveforms are shown to exhibit large negative growth for some epochs during the growth of SASI. These features are found to stem from the excess of neutrino emission in lateral directions, which can be precisely captured by the ray-tracing calculation. Reflecting the nature of SASI which grows chaotically with time, there is little systematic dependence of the input neutrino luminosities on the maximum wave amplitudes. Due to the negative contributions and the neutrino absorptions appropriately taken into account by the ray-tracing method, the wave amplitudes become more than one order of magnitude smaller than the previous estimation, thus making their detections very hard for a Galactic source. On the other hand, it is pointed out that the GW spectrum from matter motions have its peak near 100 Hz, reflecting the SASI-induced matter overturns of O(10) ms. Such a feature could be characteristic for the SASI-induced supernova explosions. The proposed ray-tracing method will be useful for the GW prediction in the first generation of three-dimensional core-collapse supernova simulations that do not solve the angle-dependent neutrino transport equations as part of the numerical evolution.