Powering Stellar Magnetism: Energy Transfers in Cyclic Dynamos of Sun-like Stars

Abstract

Abstract We use the anelastic spherical harmonic code to model the convective dynamo of solar-type stars. Based on a series of 15 3D MHD simulations spanning four bins in rotation and mass, we show what mechanisms are at work in these stellar dynamos with and without magnetic cycles and how global stellar parameters affect the outcome. We also derive scaling laws for the differential rotation and magnetic field based on these simulations. We find a weaker trend between differential rotation and stellar rotation rate, ( Δ Ω ∝ ( ∣ Ω ∣ / Ω ⊙ ) 0.46 ) in the MHD solutions than in their HD counterpart ∣ Ω ∣ / Ω ⊙ 0.66 ), yielding a better agreement with the observational trends based on power laws. We find that for a fluid Rossby number between 0.15 ≲ Ro f ≲ 0.65, the solutions possess long magnetic cycle, if Ro f ≲ 0.42 a short cycle and if Ro f ≳ 1 (antisolar-like differential rotation), a statistically steady state. We show that short-cycle dynamos follow the classical Parker–Yoshimura rule whereas the long-cycle period ones do not. We also find efficient energy transfer between reservoirs, leading to the conversion of several percent of the star's luminosity into magnetic energy that could provide enough free energy to sustain intense eruptive behavior at the star’s surface. We further demonstrate that the Rossby number dependency of the large-scale surface magnetic field in the simulation ( B L , surf ∼ Ro f − 1.26 ) agrees better with observations ( B V ∼ Ro s − 1.4 ± 0.1 ) and differs from dynamo scaling based on the global magnetic energy ( B bulk ∼ Ro f − 0.5 ).