Our analysis was aimed at confirming and quantifying the point made by Brown (1994) that changes in scattering polarisation by redistibution of electrons within an optically thin wind are likely to be small, or even zero, due to cancellation effects, unless the redistribution is on a large scale in angle or radius. Our results show that this is indeed the case. For example Fig. 2 shows that angular AND radial collapse of a conical cap to a point leads to a relative change in polarisation (i.e., ) as large as 0.5 of the maximum possible from the point alone (i.e., in a spherical background wind with no cavity) only over a fairly narrow range of parameters. Over fairly substantial ranges, the relative changes are at only the 0-0.2 level. Figs. 3 and 4 show that for a radial compression event (e.g., produced by a radiatively driven shock), optimised parameters lead to a fractional variation in polarisation of only 0.1 (forward facing shock) to 0.35 (rearward facing shock) of that from a conical plume containing the same material.
What this means is that much care is required in claiming that an inhomogeneous wind model predicts the variable polarisation which is observed. Many inhomogeneities developing within a wind will result in wholly undetectable polarisation changes. On the other hand, the fact that polarisation variations are observed therefore strongly favours models which result in either very large scale redistribution of wind material (with this occuring rapidly enough so that the material remains close enough to the star to scatter significant light), or models where (possibly more localised) dense blobs emerge from the photosphere as genuine local mass loss enhancements. In calculating the polarisation from any model it is very important to consider the entire wind, including any cavities left by redistribution as these often dominate the nett polarisation.
We emphasise that all our discussion is based on single scattering which will not apply to very dense structures. However, multiple scattering will reduce the polarisation contribution most from the densest regions (i.e., from blobs). This can reduce the cancellation effects we have been discussing and so increase the nett polarisation but with the polarisation dominated by the tenuous cavity contribution rather than by the dense blobs as one might have first expected. For intermediate blob optical depths the outcome should really be computed by formal radiative transfer (e.g., using Monte Carlo techniques as in Code & Whitney 1995).
© European Southern Observatory (ESO) 2000
Online publication: April 10, 2000