Angular Momentum Loss from Cool Stars: An Empirical Expression and Connection to Stellar Activity

TL;DR

This paper derives an empirical formula for angular momentum loss in cool stars using open cluster rotation data, revealing dependencies on stellar mass and activity, and linking it to the convective turnover timescale.

Contribution

It provides a new empirical expression for stellar angular momentum loss that incorporates mass-dependent functions and connects stellar rotation to activity via the convective turnover timescale.

Findings

Derived an empirical angular momentum loss rate expression.

Identified dual mass dependencies related to convective turnover timescale.

Connected stellar rotation and activity through a revised theoretical framework.

Abstract

We show here that the rotation period data in open clusters allow the empirical determination of an expression for the rate of loss of angular momentum from cool stars on the main sequence. One significant component of the expression, the dependence on rotation rate, persists from prior work; others do not. The expression has a bifurcation, as before, that corresponds to an observed bifurcation in the rotation periods of coeval open cluster stars. The dual dependencies of this loss rate on stellar mass are captured by two functions, $f(B-V)$ and $T(B-V)$, that can be determined from the rotation period observations. Equivalent masses and other [UBVRIJHK] colors are provided in Table 1. Dimensional considerations, and a comparison with appropriate calculated quantities suggest interpretations for $f$ and $T$, both of which appear to be related closely (but differently) to the calculated convective turnover timescale, $\tau_c$, in cool stars. This identification enables us to write down symmetrical expressions for the angular momentum loss rate and the deceleration of cool stars, and also to revive the convective turnover timescale as a vital connection between stellar rotation and stellar activity physics.