Magnetic Braking of Sun-like and Low-mass Stars: Dependence on Coronal Temperature

Sun-like and low-mass stars possess high-temperature coronae and lose mass in the form of stellar winds, which are driven by thermal pressure and complex magnetohydrodynamic processes. These magnetized outflows probably do not significantly affect the star's structural evolution on the main sequence, but they brake the stellar rotation by removing angular momentum, a mechanism known as magnetic braking. Previous studies have shown how the braking torque depends on the magnetic field strength and geometry, stellar mass and radius, mass-loss rate, and rotation rate of the star, assuming a fixed coronal temperature. For this study, we explore how different coronal temperatures can influence the stellar torque. We employ 2.5D, axisymmetric, magnetohydrodynamic simulations, computed with the PLUTO code, to obtain steady-state wind solutions from rotating stars with dipolar magnetic fields. Our parameter study includes 30 simulations with different coronal temperatures and surface magnetic field strengths. We consider a Parker-like (i.e., thermal-pressure-driven) wind, and therefore coronal temperature is the key parameter determining the velocity and acceleration profile of the flow. Since the mass-loss rates for these types of stars are not well-constrained, we determine how the torque scales for a vast range of stellar mass-loss rates. Hotter winds lead to faster acceleration, and we show that (for a given magnetic field strength and mass-loss rate) a hotter outflow leads to a weaker torque on the star. We derive new predictive torque formulae that quantify this effect over a range of possible wind acceleration profiles.