The results of the previous sections are startling. It has been found that in bands near the equator metals may drift toward the equatorial plane due to the anisotropic radiation field created when the star rotates. However, it is noted that if the mass-loss rate in the equatorial regions is strongly dependent on the metallicity, then the enhanced mass-loss rate will reduce the time that a given layer is bound to the star. Therefore the metallicity enhancement will not be able to build up to such a large level (as estimated below). In this case then a new equilibrium will be approached in which the magnitude of the metallicity enhancement is controlled by the enhanced mass-loss. This aspect of the problem is currently being investigated - the homogenising effect of the outer convection zone in the models has, so far, been neglected. This may homogenise the metallicity fast enough that no effect on the mass-loss rate may be observed.
The drift will slow and eventually stop when the logarithmic concentration gradient becomes comparable with the radiative force (see Eq. 11):
(again note this is an approximation as and are not parallel). As an example, the temperature is set to K corresponding to for both stars. The radii of the stars of (5) and 1.8 (2). From Fig. 2 the radial radiative force is () for the 5 (2) star. If it is assumed that the radiative force around the star is a tenth of this (see Fig. 1) then the right-hand side of Eq. 18 is 1360 and 205 for the 5 and 2 stars respectively. These are clearly large numbers - indicative of a very large abundance build-up in the equatorial plane. However as shown in Sect. 6 it is unlikely that the whole of the meridian will come into equilibrium. It may be surmised, though, that significant abundance inhomogeneities can be generated (without being thwarted by the concentration gradient) through rotation.
In the course of this paper, radial motions due to radiative acceleration or gravitational settling have been neglected. It is likely that a radial component of drift velocity is present as well as the meridional component focussed on here. Therefore, the motion of heavy element ions will not be solely be meridional - if the radial radiative acceleration exceeds gravity, then the drift will be toward the equator and toward the surface.
It is difficult to accurately assess the effects of large latitudinal abundance gradients on the structure of a star. As soon as the abundances change at a given point, then the flux distribution will also change along with the local convective stability criterion. Convection smooths out the abundance overdensity, and provides some feedback to the ionic build up. It is posssible that this feedback will regulate the ionic drift, modifying the structure of parts of the star.
Let us now consider the evolution of the outer envelope of the star during the main sequence. As the very outer layers are lost in a wind, then a given layer becomes slightly more diffuse and the layer moves to lower (which will promote latitudinal ion drift). However, as the layer becomes convectively unstable then it is quickly made homogeneous. The presence of extra radiation-blocking ions in fact make the layer more unstable to convection, and so the equatorial regions of rotating stars can be expected to have a more extensive convective region. Due to this rapid convective homogenisation, it is very unlikely then that this latitudinal drift will be observed in the photosphere of the star during its main sequence lifetime (the possibility of a star having different chemical compositions on the same equipotential has already been considered using radial diffusion and magnetic fields by Michaud, Mégessier & Charland 1981). The possibility of observing a direct manifestation of latitudinal abundance variation in post main-sequence phases of evolution is currently under study. Here the mass-loss rate may be large enough to prevent complete convective chemical homogenisation of regions which have generated abundance gradients during the main sequence.
It is clear that as the timescales over which a significant abundance gradient may be generated in parts of the star are similar to either mass-loss timescales or main-sequence lifetimes. Therefore the evolution of the star needs to be taken into account whilst considering the abundance time dependence - something which is not attempted here. Although difficult due to necessarily 2D nature of the calculation, it appears that time dependence of the abundance distribution needs to be included in models for rotating stars.
© European Southern Observatory (ESO) 1999
Online publication: December 4, 1998