The effect of magnetic field tilt and divergence on the mass flux and flow speed in a line-driven stellar wind

We carry out an extended analytic study of how the tilt and faster-than-radial expansion from a magnetic field affect the mass flux and flow speed of a line-driven stellar wind. A key motivation is to reconcile results of numerical MHD simulations with previous analyses that had predicted nonspherical expansion would lead to a strong speed enhancement. By including finite-disk correction effects, a dynamically more consistent form for the nonspherical expansion, and a moderate value of the line-driving power index α, we infer more modest speed enhancements that are in good quantitative agreement with MHD simulations and also are more consistent with observational results. Our analysis also explains simulation results that show the latitudinal variation of the surface mass flux scales with the square of the cosine of the local tilt angle between the magnetic field and the radial direction. Finally, we present a perturbation analysis of the effects of a finite gas pressure on the wind mass-loss rate and flow speed in both spherical and magnetic wind models, showing that these scale with the ratio of the sound speed to surface escape speed, a/v_esc, and are typically 10%-20% compared to an idealized, zero-gas-pressure model.