## 3. Micro-physical inputsSince comparisons with former results by different authors will
turn out somehow elusive due to our previously untested
evolution/convection/mixing combination, we felt obliged to at least
summarize and shortly describe the micro-physical inputs in ## 3.1. ThermodynamicsThermodynamics tables are given as a function of temperature and
pressure. In First, the tables by Magni & Mazzitelli (MM 1979, recently
updated in full ionization regime) are stored for the five A severe warning is here necessary: contrarily to some more recent
EOS' for non-ideal gas (e.g. Saumon et al. 1995), MM thermodynamics
has been computed not only for As a second step, the tables (covering the
-T plane up to densities where the lattice ion quantum effects begin
to show up) are partially overwritten by the Mihalas et al. (MHD,
1988) equation of state, for the chosen Z and in the range Log
; Log . MHD EOS is in
fact biased (Saumon 1994) at larger densities, where the MM EOS is
instead still quite good. With this second step, correct allowance for
Third and final step: the above tables are partially overwritten by the OPAL EOS tables (Rogers et al. 1996) where available (), for the same five ratios as in MM. In this way, residual anomalies (if any) at high-T in the MM EOS are forgotten, and variable ratios are restored in all the cases of interest. Lastly, one pure-carbon and one pure-oxygen table, computed in full ionization regime with an improved MM-like scheme, are addedd. Bicubic logaritmic interpolation on both P and T are performed on the tables at fixed H-abundances, and linear interpolation on the chemical composition follows, to evaluate the various thermodynamical quantities. ## 3.2. OpacityA procedure similar to the above one is performed also for the
opacities. For each given At lower temperatures ( K), Alexander & Ferguson's (1994) molecular opacities (plus electron conduction when in full ionization) complete the tables, for the same 10 ratios as in OPAL's case. At variance, Kurucz (1993) low temperatures ( K) opacities can be used, but for one ratio only. For mixtures, interpolation on fifteen out
of the 60 OPAL tables (plus conductive opacities) is performed.
Comparisons with the full set of 60 tables show that, with the present
reduced set, interpolation on the chemical composition always gives
agreement better than and, in the vast majority
of cases, better than . Bicubic logaritmic
interpolation on both and ## 3.3. Nuclear networkIt includes the 14 elements: , , , , , , , , , , , , , . We explicitly consider the following 22 reactions: The reactions in parentheses are so fast that they are not
explicitated (in terms of mixing, the half-lifes of the elements are
so short that they are always in Logaritmic nuclear cross sections are in tables with a very thin
spacing in Log ## 3.4. NeutrinosPair, photo, bremsstrahlung and plasma neutrino have been taken
from Itoh et al. (1992). Recombination neutrinos have not been
included, since they are of interest only for more advanced
(pre-supernova) evolutionary phases, which presently lie out of the
domain of Due to the computing time required to evaluate the various neutrino
fluxes with the fitting formulae in the literature, we built up
logaritmic tables of neutrino rates for various elements. Bicubic
logaritmic interpolation on both and ## 3.5. sedimentationAlso gravitational settling and chemical and thermal diffusion of
is optionally included in The following approximations are made, consistently with Muchmore (1984) and Paquette et al. (1986): - radiative force can be neglected
- all particles, including the electrons, have approximately Maxwellian distribution
- mean thermal velocities are much larger than the diffusion velocities
- magnetic fields are absent.
The sedimentation velocities then satisfy (Proffitt & Michaud 1991; Paquette et al. 1986): where are the partial pressure, mass
density, number density, mean charge, and sedimentation velocity for
species In terms of temperature gradient and number density, Eq. (5) may be rewritten as: where is the molecular weight for the species, while is the hydrogen mass. To complete the set of equations we apply the condition for no net mass flow relative to the center of mass and no electrical current. To proceed, we separate out the velocity therm as: where is relative to the gravity components and temperature gradient, while the summatory is relative to the components due to gradients in number densities, that is: where all the symbols have the same meaning as in Iben &
McDonald (1985) but for We then use these expressions in the continuity equation: which can be solved by a conservative, semi-implicit finite
difference method of first-order in time and second-order in the
spatial variable © European Southern Observatory (ESO) 1998 Online publication: June 2, 1998 |