Dynamical Simulations of Magnetically Channeled Line-Driven Stellar Winds: III. Angular Momentum Loss and Rotational Spindown

We examine the angular momentum loss and associated rotational spindown for magnetic hot stars with a line-driven stellar wind and a rotation-aligned dipole magnetic field. Our analysis here is based on our previous 2-D numerical MHD simulation study that examines the interplay among wind, field, and rotation as a function of two dimensionless parameters, one characterizing the wind magnetic confinement (η∗ ≡ B 2 eqR 2 ∗ /Ṁv∞), and the other the ratio (W ≡ Vrot/Vorb) of stellar rotation to critical (orbital) speed. We compare and contrast the 2-D, time variable angular momentum loss of this dipole model of a hot-star wind with the classical 1-D steady-state analysis by Weber and Davis (WD), who used an idealized monopole field to model the angular momentum loss in the solar wind. Despite the differences, we find that the total angular momentum loss J̇ averaged over both solid angle and time follows closely the general WD scaling J̇ = (2/3)ṀΩR A, where Ṁ is the mass loss rate, Ω is the stellar angular velocity, and RA is a characteristic Alfvén radius. However, a key distinction here is that for a dipole field, this Alfvén radius has a strong-field scaling RA/R∗ ≈ η 1/4 ∗ , instead of the scaling RA/R∗ ∼ √ η∗ for a monopole field. This leads to a slower stellar spindown time that in the dipole case scales as τspin = τmass 1.5k/ √ η∗, where τmass ≡ M/Ṁ is the characteristic mass loss time, and k is the dimensionless factor for stellar moment of inertia. The full numerical scaling relation we cite gives typical spindown times of order 1 Myr for several known magnetic massive stars.