Evidence for stochastic blob ejection from hot stars into their circumstellar winds has accumulated from a variety of spectropolarimetric studies, with variability appearing at a broad range of timescales. Lupie & Nordsieck (1987) presented low resolution polarisation data of long term (months) variations in a sample of OB supergiants. Taylor et al. (1991) found substantial and random polarimetric fluctuations occurring in P Cygni over a two year span. The data is sparse and irregularly spaced in time, but changes occur on scales of days, weeks, and months. More relevant for the results discussed in this paper, the Montreal group have amassed a large data set for polarimetric variability in Wolf-Rayet stars (e.g., St.-Louis et al. 1987; Drissen et al. 1987, 1992; Robert et al. 1989). Detailed data on the photometric, polarimetric, and spectral line profile variability of WR stars have been presented by Robert (1992) and Moffat & Robert (1992). Moffat & Robert (1992) and Lepine & Moffat (1999) have interpreted these phenomenologically in terms of a distribution of dense blobs in the wind which they suggest may result from hierarchical turbulence, while Brown et al. (1995) have discussed some of the physical properties of the larger blobs which dominate aspects of the data. Brown (1994) and Brown et al. (2000) have shown that blob formation by redistribution of electrons within the wind does not lead to polarimetric or photometric variability unless the redistribution occurs on large spatial scales or leads to very dense blobs. They conclude that blobs arise either by localised mass loss enhancements at the stellar surface or by the action of radiatively driven shocks sweeping up material on large scales. In the present paper we focus on the former case and concentrate on issues of blob velocity law and generation rate, though the ideas are generalisable to the latter situation.
A statistic of special interest found by Robert (1992) is that the broad band polarimetric variation is much smaller than the fractional photometric variability , the mean ratio being about . If the variability in both modes were solely due to electron scattering in a small number of blobs then, for simple geometries at least, one might expect a ratio nearer unity. This discrepancy led Richardson et al. (1996) to investigate the statistical effect of having larger numbers of blobs present. They did so analytically and numerically by distributing blobs (of specified mean number ) randomly in distance and direction around the star. While they found to decrease with , it never became as small as 0.05 no matter how large was. Richardson et al. (1996) concluded that the blobs must be very dense so that their emission is large enough to increase and/or their optical depth is large enough to reduce by multiple scattering. In this paper we revisit and improve on this analysis by carrying out numerical simulations, following blob flow from the star with a velocity law and allowing for the occultation of blobs behind the stellar disk. Note however that we retain the single scattering assumption. In Sect. 2, we define the basic geometry, parameters, and assumptions of the model and explain our algorithm for ejection of blobs randomly in angle and time. In Sect. 3 we present the results of our simulations and in Sect. 4 we relate them to observations and derive wind blob parameters from typical data. In particular we show that the conclusion of Richardson et al. (1996), that high blob density is essential to match variability data, arose from their implicit assumption of constant blob velocity. For large enough velocity index our model allows matching of the data without dense blob multiple scattering or continuum emission being invoked. Valuable constraints on blob velocity law, ejection rate and mass loss rate can be inferred from the observed mean polarisation and the polarimetric and photometric variances, especially when linked to the number of distinct narrow features in emission line profiles.
© European Southern Observatory (ESO) 2000
Online publication: May 3, 2000