## 3. Models## 3.1. Stellar modelsThe time-dependent transport calculations presented here were
performed for background profiles which are representative of
protoneutron star atmospheres during the quasi-static neutrino cooling
phase (Wilson 1988). At this stage, several seconds after core bounce,
the typical evolution timescale of density, temperature, and electron
fraction is much longer than the timescale for neutrinos to reach a
stationary state. Therefore our assumption of a static and
time-independent background is justified. In addition, our interest is
focused on the radial evolution of the Eddington factors and on a test
of the influence of the energy and angle resolution used in the
S Profiles from Wilson's (1988) protoneutron star model were taken
for three different times, 3.32, 5.77, and 7.81 s after core
bounce. With the chosen fundamental variables density
, temperature
## 3.2. Computed transport modelsAll models computed with the Boltzmann code are summarized in Table 2. Models ST are the standard models, in which 105 uniform spatial, 6 angular and 12 energy mesh points were used. The energy mesh is logarithmically uniform and covers 0.9-110 MeV. The numbers of angular grid points and energy grid points were increased in models FA and FE, respectively. In model CS we used the same radial grid as in the Monte Carlo simulations where 15 radial zones were chosen. 105 spatial mesh points were again used in model NI with no interpolations of density, temperature and electron fraction in the radial grid of the Monte Carlo simulations. Model GR took into account the general relativistic effects. We used a non-uniform spatial mesh in model NU. A different interpolation of up-wind differencing and centered differencing was tried for the radial advection term in model DI. We assumed the nucleon scattering to be isotropic in model IS. As is understood from Table 2, most of the comparisons were done for the electron-type antineutrinos, since they are most important from the observational point of view.
© European Southern Observatory (ESO) 1999 Online publication: March 18, 1999 |