The radiation driven winds of rotating B[e] supergiants

We have formulated the momentum equation for sectorial line driven winds from rotating stars including: (a) the oblateness of the star, (b) gravity darkening (von Zeipel effect), (c) conservation of angular momentum, (d) line driving specified by the force multiplier parameters (k, α, δ), (e) finite disk correction factors for an oblate star with gravity darkening for both the continuum and the line driving. The equations are solved numerically. We calculated the distribution of the mass flux and the wind velocity from the pole to the equator for the winds of B[e]-supergiants. Rotation decreases the terminal velocity in the equatorial region but hardly affects the wind velocity from the poles; it enhances the mass flux from the poles while the mass flux from the equator remains nearly the same. These effects increase with increasing rotation rates. We also calculated models with a bi-stability jump around 25 000 K, using force multipliers recently calculated with a Monte Carlo technique. In this case the mass flux increases drastically from the pole to the equator and the terminal velocity decreases drastically from pole to equator. This produces a density contrast in the wind ρ(equator)/ρ(pole) of about a factor 10 independent of the rotation rate of the star. We suggest that the observed density contrast of a factor ∼ 102 of the disks of B[e] stars may be reached by taking into account the wind compression due to the trajectories of the gas above the critical point towards the equatorial plane.