Accretion-powered Stellar Winds. II. Numerical Solutions for Stellar Wind Torques

In order to explain the slow rotation observed in a large fraction of accreting pre-main-sequence stars (CTTSs), we explore the role of stellar winds in torquing down the stars. For this mechanism to be effective, the stellar winds need to have relatively high outflow rates, and thus would likely be powered by the accretion process itself. Here, we use numerical magnetohydrodynamical simulations to compute detailed two-dimensional (axisymmetric) stellar wind solutions, in order to determine the spin-down torque on the star. We discuss wind driving mechanisms and then adopt a Parker-like (thermal pressure driven) wind, modified by rotation, magnetic fields, and enhanced mass-loss rate (relative to the Sun). We explore a range of parameters relevant for CTTSs, including variations in the stellar mass, radius, spin rate, surface magnetic field strength, mass-loss rate, and wind acceleration rate. We also consider both dipole and quadrupole magnetic field geometries. Our simulations indicate that the stellar wind torque is of sufficient magnitude to be important for spinning down a “typical” CTTS, for a mass-loss rate of ~10−9 M☉ yr−1. The winds are wide-angle, self-collimated flows, as expected of magnetic rotator winds with moderately fast rotation. The cases with quadrupolar field produce a much weaker torque than for a dipole with the same surface field strength, demonstrating that magnetic geometry plays a fundamental role in determining the torque. Cases with varying wind acceleration rate show much smaller variations in the torque, suggesting that the details of the wind driving are less important. We use our computed results to fit a semianalytic formula for the effective Alfvén radius in the wind, as well as the torque. This allows for considerable predictive power, and is an improvement over existing approximations.