Radiative Torque and Partial Spin‐Down of Winds from Rotating Hot Stars

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Abstract
We examine the degree to which the azimuthal component of the line-driving force can remove angular momentum from the equatorial wind of a rapidly rotating hot star, using a straightforward extension of the standard CAK formalism. We illustrate how even in a wind that is azimuthally symmetric, such a net azimuthal line force results from the prograde/retrograde velocity gradient asymmetries that are inherent to a non-rigidly rotating outflow. In particular, we show that the sense of the associated line torque always acts against the rotation whenever (as is generally the case) the azimuthal velocity falls below the linear outward increase (v ~ r) associated with rigid rotation. Through a parameter study based on two-dimensional numerical hydrodynamical simulations, we find that the net loss of wind angular momentum is significant but generally quite moderate, about 30%-40%, for a wide range of conditions. We then present an extensive analytic analysis that further illuminates the physical nature of the wind spin-down and its robust net magnitude. This emphasizes the inherent dynamical feedback between line driving and flow acceleration, which allows the radiative force to effectively amplify the Coriolis force in the rotating frame, and so cause the rotation speed to decrease even more steeply with radius than required to conserve angular momentum. A general conclusion is that, while the moderate net spin-down of the wind is not likely to have a major impact on the overall wind dynamics, it should be observable from emission line diagnostics, and that doing so would provide an independent test of line-driven wind theory.