Time-dependent diffusion in stellar atmospheres

Abstract

The chemical peculiarities of Ap stars are due to abundance stratifications produced by atomic diffusion in their outer layers. Theoretical models can predict such stratifications, but so far only provide equilibrium solutions which correspond to the maximum depth‐dependent abundances for each element that can be supported by the radiation field. However, these stratifications are actually built up through a non‐linear, time‐dependent process which has never been modelled for realistic stellar atmospheres. Here, we present the first numerical simulations of time‐dependent diffusion. We solve the continuity equation after having computed, as accurately as possible, atomic diffusion velocities (with and without a magnetic field) for a simplified fictitious – but still realistic – chemical element: cloudium. The direct comparison with existing observations is not the immediate aim of this work but rather a general understanding of how the stratification build‐up proceeds in time and space. Our results raise serious questions as to the relevance of equilibrium solutions and reinforce the suspicion that certain accumulations of chemical elements might prove unstable.

Discovery of secular variations in the atmospheric abundances of magnetic Ap stars

“…The time variation with height of abundance of a very unabundant element diffusing up through a stellar atmosphere has recently been studied by Alecian et al (2011), who find that a stationary state of constant particle flux with height is generally achieved after a few hundred years, provided that the atoms continue to diffuse out of the top of the atmosphere. The actual value of the flux, and the run of abundance with height, is set by the abundance of the atom supplied at the bottom of the atmosphere from the reservoir below.…”

“…These may well be elements for which the abundance would be closer to that predicted by the assumption of a stationary flow-through state, with atoms fed into the atmosphere from below and lost from the top (cf. Alecian et al 2011). In this case the limiting factor determining the atmospheric abundances is the available number density of Cr or Ti brought up from the envelope by diffusion.…”

“…There are no calculations of the equilibrium abundances of heavy elements such as Nd and Pr near the T eff temperature range of interest to us here, except for the equilibrium stratification calculated for a simplified artificial low-abundance element with T eff = 12 000 K by Alecian et al (2011). This artificial element is expected to behave somewhat like Hg, and the equilibrium abundance computed for it is about −8 dex without a magnetic field, and possibly even smaller high in the atmosphere in the presence of a strong magnetic field.…”

A search for pulsations in the HgMn star HD 45975 with CoRoT photometry and ground-based spectroscopy

“…This is at odds with the predictions of nonmagnetic diffusion models, which indicate that Ti, Cr, Mn, and Hg should all accumulate 7 in the upper atmosphere layers for a HgMn star with a T eff similar to that of HD 45975 (Alecian & Stift 2010; see also LeBlanc et al 2009). We notice, however, that the run of the abundances as a function of depth in the photosphere differs from one element to another, since the buildup of the stratifications, which is non-linear and time-dependent, depends on the atomic properties of each element (as discussed by Alecian et al 2011). In the context of abundance spots, the lack of variability for Hg in HD 45975 might be attributed to geometrical effects (implying that the spot morphology differs from that of the other species) and/or a distribution of mercury at the surface that is more uniform than for Ti, Cr, Mn, and Y.…”

“…Recently, Alecian (2012) has proposed that abundance spots in some HgMn stars could be due to atomic diffusion in a weak (the diffusion velocity was computed for 100 Gauss in Alecian 2013, suggesting a cloud location at log τ = −4) 1 and faintly organised magnetic field in their atmosphere, i.e., multipolar, varying on small spatial scales, and difficult to detect (see also Alecian et al 2009). Besides the possible effect of weak magnetic fields on the formation of high-altitude spots of some elements, the buildup of stratifications in the upper atmosphere is very complex since this process is non-linear, time-dependent, and possibly unstable (see Alecian et al 2011). This could provide an additional mechanism for disrupting a uniform stratification pattern and forming horizontal spot-like discontinuities of accumulations.…”