Principal-Axis Analysis of the Eddington Tensor for the Early Post-Bounce Phase of Rotational Core-Collapse Supernovae. (arXiv:2109.05846v2 [astro-ph.HE] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Iwakami_W/0/1/0/all/0/1">Wakana Iwakami</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Harada_A/0/1/0/all/0/1">Akira Harada</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Nagakura_H/0/1/0/all/0/1">Hiroki Nagakura</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Akaho_R/0/1/0/all/0/1">Ryuichiro Akaho</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Okawa_H/0/1/0/all/0/1">Hirotada Okawa</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Furusawa_S/0/1/0/all/0/1">Shun Furusawa</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Matsufuru_H/0/1/0/all/0/1">Hideo Matsufuru</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Sumiyoshi_K/0/1/0/all/0/1">Kohsuke Sumiyoshi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Yamada_S/0/1/0/all/0/1">Shoichi Yamada</a>
One- (1D) and two-dimensional (2D) core-collapse supernova simulations using
full Boltzmann neutrino transport for 11.2M and 15.0M progenitor models have
been performed to verify the closure relation for the moment method used in the
approximate radiation transfer. This study finds areas where the results of the
closure relation are inconsistent with those of Boltzmann transport, even for
rotational models. In 1D simulations, the Eddington factors p defined in the
fluid rest frame (FR) are compared to evaluate the maximum entropy closure for
the Fermi-Dirac distribution (MEFD), confirming that MEFD closure performs
better than other closures if p < 1/3 and phase space occupancy e > 0.5. In 2D
simulations for non-rotating progenitor models, similar results are obtained
from the principal-axis analysis of the Eddington tensor kij measured in FR.
However, for rotating progenitor models, the principal axes of kij for
Boltzmann transport tilt toward oblique directions where matter and neutrinos
move relatively fast in azimuthal directions, while the principal axes of kij
for MEFD closure are always parallel or perpendicular to the neutrino flux.
Thus, the assumption of axisymmetric angular distribution to the flux direction
in the closure relation does not hold in the strongly rotating supernova core
in the early post-bounce phase. It is also shown that the deviation of the
principal axes of kij from the flux direction increases when evaluated in a
laboratory frame (LB). The optically thin and thick terms of the pressure
tensor in LB negatively impact results in optically thicker and thinner
regions, respectively.
One- (1D) and two-dimensional (2D) core-collapse supernova simulations using
full Boltzmann neutrino transport for 11.2M and 15.0M progenitor models have
been performed to verify the closure relation for the moment method used in the
approximate radiation transfer. This study finds areas where the results of the
closure relation are inconsistent with those of Boltzmann transport, even for
rotational models. In 1D simulations, the Eddington factors p defined in the
fluid rest frame (FR) are compared to evaluate the maximum entropy closure for
the Fermi-Dirac distribution (MEFD), confirming that MEFD closure performs
better than other closures if p < 1/3 and phase space occupancy e > 0.5. In 2D
simulations for non-rotating progenitor models, similar results are obtained
from the principal-axis analysis of the Eddington tensor kij measured in FR.
However, for rotating progenitor models, the principal axes of kij for
Boltzmann transport tilt toward oblique directions where matter and neutrinos
move relatively fast in azimuthal directions, while the principal axes of kij
for MEFD closure are always parallel or perpendicular to the neutrino flux.
Thus, the assumption of axisymmetric angular distribution to the flux direction
in the closure relation does not hold in the strongly rotating supernova core
in the early post-bounce phase. It is also shown that the deviation of the
principal axes of kij from the flux direction increases when evaluated in a
laboratory frame (LB). The optically thin and thick terms of the pressure
tensor in LB negatively impact results in optically thicker and thinner
regions, respectively.
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