Radiative diffusion in stellar atmospheres: diffusion velocities

Abstract

Aims. The present paper addresses some of the problems in the buildup of element stratification in stellar magnetic atmospheres due to microscopic diffusion, in particular the redistribution of momentum among the various ionisation stages of a given element and the calculation of diffusion velocities in the presence of inclined magnetic fields. Methods. We have considerably modified and extended our CARAT code to provide radiative accelerations, not only from boundbound but also from bound-free transitions. In addition, our code now computes ionisation and recombination rates, both radiative and collisional. These rates are used in calculating the redistribution of momentum among the various ionisation stages of the chemical elements. A careful comparison shows that the two different theoretical approaches to redistribution that are presently available lead to widely discrepant results for some chemical elements, especially in the magnetic case. In the absence of a fully satisfactory theory of redistribution, we propose to use the geometrical mean of the radiative accelerations from both methods. Results. Diffusion velocities have been calculated for 28 chemical elements in a T eff = 12 000 K, log g = 4.00 stellar magnetic atmosphere with solar abundances. Velocities and resulting element fluxes in magnetic fields are discussed; rates of abundance changes are analysed for systematic trends with field strength and field direction. Special consideration is given to the Si case and our results are confronted in detail with well-known results derived more than two decades ago.Key words. diffusion -stars: abundances -stars: chemically peculiar -stars: magnetic fields IntroductionHaving been proposed more than 3 decades ago by Michaud (1970), the diffusion theory still constitutes the only viable scenario for the buildup of abundance inhomogeneities in chemically peculiar (CP) early type main-sequence stars. Early calculations by Michaud et al. (1976) have shown that diffusion in the envelope of main-sequence stars can lead to overabundances of a number of chemical elements by up to 7 dex, which would be sufficient to explain even the largest overabundances found in CP stars.Magnetic fields can be expected to modify diffusion, and indeed Vauclair et al. (1979) outlined a particular mechanism involving upward diffusion of Si i that produces overabundances in magnetic stars at places where the magnetic field is horizontal. Whether vertical or horizontal magnetic fields could lead to the development of spots or rings with enhanced elemental abundances depends on the element in question; silicon appears to concentrate in horizontal field regions (Alecian & Vauclair 1981), whereas gallium is thought to accumulate near vertical field regions (Alecian & Artru 1987).The detailed modelling of 53 Cam by Babel & Michaud (1991b) has shown that a simple diffusion model is not always sufficient and that other processes should be considered, like inhomogeneous mass-loss. Whenever one invokes diffusion of chemical elements as...

Bi-dimensional element stratifications computed for magnetic Ap star atmospheres

“…However, the flux is positive above log τ 5000 = −1.5 for 10 kG when field lines are horizontal as at the magnetic equator of a dipole with 20 kG at the pole. This is a well known effect of horizontal magnetic fields (for a detailed discussion see Alecian & Stift 2006).…”

“…(4) of Alecian & Stift (2006). This led to the so-called zeroth order models in which elements that are strongly pushed up by the radiation field were considered to be good candidates to exhibit overabundances in stellar external layers.…”

“…One can thus in a first approximation consider that, as far as atomic diffusion (which depends mainly on the magnetic field inclination) is concerned, the assumption of axisymmetry about the magnetic axis is well justified. Keeping in mind that the diffusion process essentially acts along the vertical axis (see the discussion about horizontal diffusion in Alecian & Stift 2006), the entire surface of an Ap star can be reasonably approximated as the juxtaposition of independent facets computed along a quadrant of the magnetic meridian, using plane-parallel atmospheres.…”

“…This code calculates the diffusion velocities (with and without magnetic fields) considering the detailed line opacities of stratified elements, taking into account Zeeman splitting, and using an accurate solver of the equation of polarized radiative transfer. The redistribution of momentum, among ions of a given species, is computed following the prescription of Alecian & Stift (2006) and their Eq. (18) for the total radiative acceleration.…”

“…(13) of Alecian & Stift (2006) -of Fe for uniform solar abundance is presented in Fig. 2 for 0 G and 20 kG (vertical field lines), respectively.…”