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A&A Supplement series, Vol. 129, April II 1998, 343-351

Received March 26; accepted October 2, 1997

Legendre expansion of the kernel: Influence of high order terms

J.A. Pons - J.A. Miralles - J.M Ibáñez

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  Departament d'Astronomia i Astrofısica, Universitat de Valencia 46100 Burjassot (Valencia), Spain
  Astronomy program, Department of Physics and Astronomy, SUNY at Stony Brook, Stony Brook, New York 11794, U.S.A.

Abstract:

We calculate the Legendre expansion of the rate of the process up to order extending previous results of other authors which only consider the and order terms. Using different closure relations for the moment equations of the radiative transfer equation we discuss the physical implications of taking into account quadratic and cubic terms on the energy deposition outside the neutrinosphere in a simplified model. The main conclusion is that order is necessary in the semi-transparent region and gives good results if an appropriate closure relation is used.

keywords: radiation mechanisms: thermal -- radiative transfer -- stars: neutron -- supernovae: general -- nuclear reactions

• 1. Introduction
• 2. Legendre expansion of emission-absorption TP kernels
• 3. Energy and momentum transfer in two moment neutrino transport
• 4. Discussion
• Appendix A: Expressions of a_ln, c_ln and d_ln coefficients
• Appendix B: Evaluation of the G_n integrals
• References