The Stellar Rotation - Activity Relationship and the Evolution of Stellar Dynamos

Wright Nicholas, nwright@cfa.harvard.edu, Harvard-Smithsonian Center for Astrophysics, United States
Drake Jeremy, Harvard-Smithsonian Center for Astrophysics
Mamajek Eric, University of Rochester
Henry Gregory, Tennessee State University

Abstract
We present a unified sample of 824 solar- and late-type stars with X-ray luminosities and rotation periods, more than three times larger than previous compilations. We use this sample to study the relation between these two parameters in the three observed regimes: unsaturated (which acts as a probe of the stellar dynamo), saturated, and super-saturated X-ray emission. From an unbiased subset of this sample we determine the power-law slope of the unsaturated regime, L(X) / L(Bol) = C x Ro^B, and fit B=-2.70+/-0.13. This is inconsistent with the canonical B=-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 = C x 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 supersaturation 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. This explains why previous measurements of the X-ray saturation level of F-type stars found them to be below that of later-type stars. 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 for this observed effect. 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. This is also equivalent to the time when stars finally settle on the main-sequence. Finally I will briefly present results from an X-ray population synthesis model of the galaxy that combines rotational spin-down models with our current understanding of the rotation - activity relation to predict the number counts of stellar X-ray sources in various X-ray observations. I will show how predictions from this model can be compared with star counts from deep extragalactic X-ray observations to test our understanding of the rotation-activity relation.