The Effect of Rotation on Triggering S Doradus Instabilities in Luminous Blue Variables

Luminous blue variables are an intermediate stage in the evolution of high-mass stars characterized by extreme mass loss and substantial variability. The stars show large irregular episodic variations on timescales of years to decades in these stars' effective temperatures (called "S Dor variations"). Observations show that these variations are triggered when the stars are in a well-defined strip in the HRD that corresponds to the Modified Eddington Limit, where the atmospheric radiation pressure almost balances gravity. In this work we consider the role that rotation plays in the instability that leads to the triggering of S Dor variations in luminous post-main sequence LBVs. We adopt the existing instability criterion that the effective surface gravity is reduced to 10% of the Newtonian gravity due to radiation pressure in the atmosphere of non-rotating stars. We then specifically describe how rotation impacts this instability. By carrying out numerical simulations of model LBVs at both solar and sub-solar metallicities, we confirm that most LBVs should be unstable at both the equator and the poles, and that rotation exacerbates this effect; some models also produce enhanced mass loss at the pole or equator. Our numerical models also predict dense equatorial disks or rings and high-velocity bipolar outflows, in agreement with existing observations of LBV circumstellar nebulae.