Saturation of the Large-scale Magnetic Field for Fast Rotating Solar-like Stars Driven by Inefficient Turbulent Angular Momentum Transport

Abstract Magnetic activity in solar-like stars shows a systematic dependence on stellar rotation rate, known as the “activity–rotation relationship.” Recent observations further reveal that large-scale surface magnetic fields in solar-like stars are anticorrelated with the Rossby number (Ro) in the moderate regime (0.1 &lt; Ro &lt; 1), reaching saturation at extremely low Rossby numbers (Ro &lt; 0.1). The cause of this saturation remains one of the open issues in stellar dynamo theory. We performed nonlinear mean-field dynamo simulations with the stellar rotation rate and turbulent diffusivity ( ν 0 ) as free parameters. The dependence of the magnetic field strength ( B ) in the deep convection zone is quantified as ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>B</mml:mi> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">Ro</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.45</mml:mn> </mml:mrow> </mml:msup> <mml:msubsup> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>0.54</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> ). Our analysis of the differential rotation energy shows that this dependence is maintained by a balance between the angular momentum transport by the turbulence and the large-scale magnetic field. Together with the reduction of the convective velocity revealed at extremely low Rossby numbers by recent local three-dimensional simulations, our results suggest that inefficient turbulent angular momentum transport might drive the saturation of the large-scale magnetic field.