Legendre expansion of the kernel: Influence of high order terms

¹ Departament d'Astronomia i Astrofísica, Universitat de Valencia 46100 Burjassot (Valencia), Spain
² Astronomy program, Department of Physics and Astronomy, SUNY at Stony Brook, Stony Brook, New York 11794, U.S.A.

Corresponding author: Send offprint request to: J.A. Pons, Jose.A.Pons@uv.es

Received: 26 March 1997
Accepted: 2 October 1997

Abstract

We calculate the Legendre expansion of the rate of the process up to 3^rd order extending previous results of other authors which only consider the ^th and 1^st 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 2^nd order is necessary in the semi-transparent region and gives good results if an appropriate closure relation is used.