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Astron. Astrophys. 321, 485-491 (1997)

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2. Physical assumptions

As in Paper I we take into account the elements He, C, N, O and Ne, assuming a plane-parallel, one dimensional stratification. The possible effects of mass-loss or convective mixing, which would lead to more complicated momentum equations, are excluded. In contrast to the calculations of Dehner & Kawaler (1995) the background stellar structure is not allowed to evolve: [FORMULA] and [FORMULA] are held fixed during the diffusion calculations. If the diffusion velocities [FORMULA] for each element are small compared to the thermal velocities, the total mass flow is zero and thermal diffusion can be neglected, then the momentum equation for each element can be written according to Burgers (1969):

[EQUATION]

[FORMULA] and [FORMULA] are the particle density and mass, respectively. [FORMULA] is the mean electric charge of the particles of element l, which follows from a solution of the Saha equations as described in Paper I. The mean radiative force [FORMULA] acting on the particles of element l is obtained in the same way as in Paper I. It has been assumed that in photoionization processes the photon momentum is transferred onto the heavy particle alone, so that the selective radiative forces which are due to bound-free transitions are maximized. The [FORMULA] are resistance coefficients which are calculated according to Paquette et al. (1986). The electric field E is obtained from the momentum equation for the electrons (see below). The depth variable z is a length and, in difference to Paper I, increases from the outer boundary towards the stellar interior. As one of these equations is redundant, we replace the momentum equation for helium by the condition of zero mass flow:

[EQUATION]

This set of five linear algebraic equations can be solved for the diffusion velocities of the various elements. In the framework of this theory the particles are assumed as being classical, interacting via Coulomb forces, the possible effects of inelastic and reactive collisions are ignored. Using only one momentum equation for each element, we disregard the fact that the particles in the various ionization states have different diffusion velocities. A consistent treatment of this effect on the chemical statification would require to take into account the momentum exchange between the various ions which is due to photoionization processes and reactive collisions (for a review concerning improvements on diffusion calculations including radiative accelerations see Gonzales et al., 1995 and references therein).

According to Geiss & Bürgi (1986) it is a good approximation to take into account the interaction between free electrons and ions only via the electric field and to neglect the electron collision term. Therefore we assume

[EQUATION]

This equation is solved for the electric field and inserted into the Eqs. (1). The radiative transfer equation is solved by use of the diffusion approximation:

[EQUATION]

where [FORMULA] is the Rosseland mean opacity in [FORMULA], the opacities are computed as described in Paper I.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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