Using full Boltzmann neutrino transport, we performed 2D core-collapse supernova simulations in axisymmetry for two progenitor models with 11.2 and 15.0 M ⊙, both rotational and nonrotational. We employed the results obtained in the early post-bounce phase (t 2 20 ms) to assess performance under rapid rotation of some closure relations commonly employed in the truncated moment method. We first made a comparison in 1D under spherical symmetry, though, of the Eddington factor p defined in the fluid rest frame (FR). We confirmed that the maximum entropy closure for the Fermionic distribution (MEFD) performs better than others near the proto-neutron star surface, where p < 1/3 occurs, but does not work well even in 1D when the phase-space occupancy satisfies e < 0.5 together with p < 1/3, the condition known to be not represented by MEFD. For the 2D models with the rapid rotation, we employed the principal-axis analysis of the Eddington tensor. We paid particular attention to the direction of the longest principal axis. We observed in FR that it is aligned neither with the radial direction nor with the neutrino flux in 2D, particularly so in convective and/or rapidly rotating regions, the fact not accommodated in the moment method. We repeated the same analysis in the laboratory frame and found again that the direction of the longest principal axis is not well reproduced by MEFD because the interpolation between the optically thick and thin limits is not very accurate in this frame.
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