Radiatively driven winds and the shaping of bipolar luminous blue variable nebulae

Nebulae around luminous blue variable (LBV) stars are often characterized by a bipolar, prolate form. In the standard interpretation of the generalized interacting stellar winds model, this bipolar form is attributed to an asymmetry in the density structure of the ambient medium. However, there is limited observational evidence to suggest that such an asymmetric medium is present in most LBV nebulae. In this work we use scaling relations derived from the theory of radiatively driven winds to model the outflows from LBV stars, taking account of stellar rotation and the associated latitudinal variation of the stellar flux due to gravity darkening. We show that, for a star rotating close to its critical speed, the decrease in effective gravity near the equator and the associated decrease in the equatorial wind speed results naturally in a bipolar, prolate interaction front, even for a spherically symmetric ambient medium. Moreover, when gravity darkening is included, the resulting density of the outburst is also strongest over the prolate poles. We discuss the implications of these results for the formation of windblown nebulae in general.