Diffusion of iron-group elements in the envelopes of HgMn stars

Abstract

The observed abundance anomalies for iron-group elements in atmospheres of HgMn stars are due to diffusive movements which are driven by radiation-pressure forces and which persist in the stellar envelopes, going down to regions with temperatures of about 106 K. Studies of diffusion in the envelopes are required both in order to understand the observed atmospheric abundances and in order to calculate the changes in opacities that result from changes in abundances. Let τ be the Rosseland-mean optical depth. It is shown that one can define an upper boundary, ττu, such that one can obtain solutions for the diffusive movements in the region of τ≥τu without any knowledge of what happens in the higher layers of τ<τu. The paper is concerned with a description of the numerical methods that can be used to obtain such solutions. For Cr and Mn we are able to follow the diffusion for times of order 108 yr with τu=1. For Fe we are also able to obtain some estimates of abundances at τ=1 allowing for diffusion processes. For Mn, Cr and Fe we attempt some comparisons of abundances computed for τu=1 with observed atmospheric abundances and obtain results that are not discouraging. For Fe and Ni, larger values of τu are required as the diffusion proceeds (after 108 yr we require τu≃8 for Fe and τu≃70 for Ni). For the outer regions with τ<τu it will be necessary to obtain solutions allowing for outflows of iron-group elements at the stellar surfaces. In such work it should be possible to match the outer-region solutions to the envelope solutions obtained using the methods described in this paper. The diffusive movements lead to changes in Rosseland-mean opacities by factors of up to 4. For Fe there is a build-up in concentrations in the region of log(T)≃5.1, where the dominant ionization stages are near Ar-like. This leads to the Z-bump in opacities being shifted from its normal position at log(T)≃5.3 to lower values of log(T) and becoming more sharply peaked. There is also a large build-up in Ni concentrations in the outer parts of the envelopes, leading to opacity enhancements. In the present work we allow neither for the normal main-sequence evolution of the stars nor for the modifications in that evolution which will result from changes in opacities. Solution for both envelopes and outer regions will eventually be required.