The effect of rotational gravity darkening on magnetically torqued Be star discs

In the magnetically torqued disc (MTD) model for hot star discs, as proposed and formulated by Cassinelli et al., stellar wind mass loss was taken to be uniform over the stellar surface. Here account is taken of the fact that as the stellar spin rate S-0 (= rootOmega(0)(2)R(3)/GM) is increased, and the stellar equator is gravity darkened, the equatorial mass flux and terminal speed are reduced, compared with the poles, for a given total M. As a result, the distribution of equatorial disc density, determined by the impact of northbound and southbound flows, is shifted further out from the star. This results, for high S-0(greater than or similar to0.5), in a fall in the disc mass and emission measure, and hence in the observed emission line equivalent width, scattering polarization and infrared emission. Consequently, contrary to expectations, critical rotation S-0 --> 1 is not the optimum for creation of hot star discs which, in terms of emission measure for example, is found to occur in a broad peak around S-0 approximate to 0.5-0.6 depending slightly on the wind velocity law. The relationship of this analytic quasi-steady parametric MTD model to other work on magnetically guided winds is discussed. In particular, the failures of the MTD model for Be-star discs alleged by Owocki and ud-Doula are shown to revolve largely around open observational tests, rather than in the basic MTD physics, and around their use of insufficiently strong fields.