Dynamical simulations of magnetically channelled line-driven stellar winds - III. Angular momentum loss and rotational spin-down

We examine the angular momentum loss and associated rotational spin-down 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 two-dimensional numerical magnetohydrodynamics simulation study that examines the interplay among wind, field and rotation as a function of two dimensionless parameters: one characterizing the wind magnetic confinement () and the other the ratio (W ≡ V_rot/V_orb) of stellar rotation to critical (orbital) speed. We compare and contrast the two-dimensional, time-variable angular momentum loss of this dipole model of a hot-star wind with the classical one-dimensional 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 averaged over both solid angle and time closely follows the general WD scaling, where is the mass-loss rate, Ω is the stellar angular velocity and R_A is a characteristic Alfvén radius. However, a key distinction here is that for a dipole field, this Alfvén radius has a strong-field scaling R_A/R_* ≈ η ^1/4_*, instead of the scaling for a monopole field. This leads to a slower stellar spin-down time that in the dipole case scales as, where is the characteristic mass loss time and k is the dimensionless factor for stellar moment of inertia. The full numerical scaling relation that we cite gives typical spin-down times of the order of 1 Myr for several known magnetic massive stars.