Explaining the Observed Relation Between Stellar Activity and Rotation

TL;DR

This paper explains the empirical relationship between stellar activity and rotation by modeling magnetic dynamo processes and magnetic buoyancy, clarifying the transition between different activity regimes based on Rossby number.

Contribution

It introduces a theoretical model that accounts for the observed activity-rotation relation and the transition between regimes in late-type stars, linking dynamo theory with observational scalings.

Findings

The model reproduces the observed power-law dependence of activity on Rossby number for large $Ro$.

It explains the near-constant activity level at low $Ro$ due to shear and differential rotation effects.

The theory connects magnetic helicity buildup with dynamo saturation and magnetic buoyancy.

Abstract

Observations of late-type main-sequence stars have revealed empirical scalings of coronal activity versus rotation period or Rossby number $Ro$ (a ratio of rotation period to convective turnover time) which has hitherto lacked explanation. For $Ro >> 1$, the activity observed as X-ray to bolometric flux varies as $Ro^{-q}$ with $2\le q \le 3$, whilst $|q| < 0.12$ for $Ro << 1$. Here we explain the transition between these two regimes and the power law in the $Ro >> 1$ regime by constructing an expression for the coronal luminosity based on dynamo magnetic field generation and magnetic buoyancy. We explain the $Ro<<1$ behavior from the inference that observed rotation is correlated with internal differential rotation and argue that once the shear time scale is shorter than the convective turnover time, eddies will be shredded on the shear time scale and so the eddy correlation time actually becomes the shear time and the convection time drops out of the equations. We explain the $Ro >> 1$ behavior using a dynamo saturation theory based on magnetic helicity buildup and buoyant loss.