The stellar activity-rotation relationship and the evolution of stellar dynamos

TL;DR

This study analyzes the relationship between stellar rotation and activity across 824 stars, revealing a steeper power law slope than previously thought, and explores the implications for stellar dynamo evolution and magnetic activity regimes.

Contribution

It provides a new estimate of the rotation-activity relationship slope, challenges the canonical value, and investigates the dynamo mechanisms and thresholds for stellar activity saturation.

Findings

The power law slope  .70, steeper than the canonical  .

Differential rotation declines as stars spin down, following  rac{ ext{d}\, ext{ extOmega}}{ ext{ extOmega}} = ext{ extOmega}^{0.7}.

Late F-type stars do not pass through the saturated regime, transitioning directly from super-saturated to unsaturated X-ray emission.

Abstract

We present a sample of 824 solar and late-type stars with X-ray luminosities and rotation periods. This is used to study the relationship between rotation and stellar activity and derive a new estimate of the convective turnover time. From an unbiased subset of this sample the power law slope of the unsaturated regime, L_X / L_bol = Ro^\beta, is fit as \beta = -2.70 +/- 0.13. This is inconsistent with the canonical \beta=-2 slope to a confidence of 5 sigma, and argues for an additional term in the dynamo number equation. From a simple scaling analysis this implies \Delta\Omega / \Omega = \Omega^0.7, i.e. the differential rotation of solar-type stars gradually declines as they spin down. Super-saturation is observed for the fastest rotators in our sample and its parametric dependencies are explored. Significant correlations are found with both the corotation radius and the excess polar updraft, the latter theory providing a stronger dependence and being supported by other observations. We estimate mass-dependent empirical thresholds for saturation and super-saturation and map out three regimes of coronal emission. Late F-type stars are shown never to pass through the saturated regime, passing straight from super-saturated to unsaturated X-ray emission. The theoretical threshold for coronal stripping is shown to be significantly different from the empirical saturation threshold (Ro < 0.13), suggesting it is not responsible. Instead we suggest that a different dynamo configuration is at work in stars with saturated coronal emission. This is supported by a correlation between the empirical saturation threshold and the time when stars transition between convective and interface sequences in rotational spin-down models.