A Grid of MHD Models for Stellar Mass Loss and Spin-down Rates of Solar Analogs

Abstract: Stellar winds are believed to be the dominant factor in spin down of stars over time. However, stellar winds of solar analogs are poorly constrained due to the challenges in observing them. A great improvement has been made in the last decade in our understanding of the mechanisms responsible for the acceleration of the solar wind and in the development of numerical models for solar and stellar winds. In this paper, we present a grid of Magnetohydrodynamic (MHD) models to study and quantify the values of stellar mass-loss and angular momentum loss rates as a function of the stellar rotation period, magnetic dipole component, and coronal base density. We derive simple scaling laws for the loss rates as a function of these parameters, and constrain the possible mass-loss rate of stars with thermally-driven winds. Despite the success of our scaling law in matching the results of the model, we find a deviation between the "solar dipole" case and a real case based on solar observations that overestimates the actual solar mass-loss rate by a factor of 3. This implies that the model for stellar fields might require a further investigation with higher complexity which might include the use of a filling factor for active regions, as well as the distribution of the strength of the small-scale fields. Mass loss rates in general are largely controlled by the magnetic field strength, with the wind density varying in proportion to the confining magnetic pressure $B^2$. We also find that the mass-loss rates obtained using our grid models drop much faster with the increase in rotation period than scaling laws derived using observed stellar activity. For main-sequence solar-like stars, our scaling law for angular momentum loss vs. poloidal magnetic field strength retrieves the well-known Skumanich decline of angular velocity with time.