Accretion-Powered Stellar Winds II: Numerical Solutions for Stellar Wind Torques

TL;DR

This paper uses numerical magnetohydrodynamical simulations to quantify how stellar winds can effectively spin down accreting pre-main-sequence stars, considering various magnetic geometries and wind parameters.

Contribution

It provides detailed 2D simulations of stellar wind torques, revealing the impact of magnetic geometry and wind acceleration on star spin-down, and offers a semi-analytic formula for the Alfvén radius and torque.

Findings

Stellar wind torque can significantly slow down CTTSs with high mass loss rates.

Dipolar magnetic fields produce stronger torques than quadrupolar fields.

Wind acceleration rate has a minor effect on the torque magnitude.

Abstract

[Abridged] 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 2-dimensional (axisymmetric) stellar wind solutions, in order to determine the spin down torque on the star. We explore a range of parameters relevant for CTTSs, including variations in the stellar mass, radius, spin rate, surface magnetic field strength, the 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 $\sim 10^{-9} M_\odot$ 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 semi-analytic formula for the effective Alfv\'en radius in the wind, as well as the torque. This allows for considerable predictive power, and is an improvement over existing approximations.