Ionization structure in the winds of B[e] supergiants

Context.B[e] supergiants are known to have non-spherical winds, and the existence of disks that are neutral in hydrogen close to their stellar surface has been postulated. A suitable mechanism to produce non-spherical winds seems to be rapid rotation, and at least for three B[e] supergiants in the Magellanic Clouds rotation velocities at a substantial fraction of their critical velocity have been found. Aims.We want to find suitable recombination distances in the equatorial plane of rapidly rotating stars that explain the observed huge amounts of neutral material in the vicinity of B[e] supergiants. Methods.We perform ionization structure calculations in the equatorial plane around rapidly rotating luminous supergiants. The restriction to the equatorial plane allows us to treat the ionization balance equations 1-dimensionally, while the stellar radiation field is calculated 2-dimensionally, taking into account the latitudinal variation of the stellar surface parameters. The stellar parameters used correspond to those known for B[e] supergiants. The assumptions made in the computations all have in common that the total number of available ionizing photons at any location within the equatorial plane is overestimated, resulting in upper limits for the recombination distances. Results.We find that despite the drop in equatorial surface density of rapidly rotating stars (neglecting effects like bi-stability and/or wind compression), hydrogen and helium recombine at or close to the stellar surface, for mass loss rates $\dot{M} \ga 5\times 10^{-5}~M_{\odot}$ yr-1 and rotation speeds in excess of $v_{\rm rot, eq}/v_{\rm crit} \simeq 0.8$