A nonlinear model for rotating cool stars

Abstract

AbstractA simple nonlinear model is introduced here to describe the rotational evolution of main sequence cool (FGKM) stars. It is formulated only in terms of the ratio of a star's rotation period, P, to its convective turnover timescale, τ, and two dimensionless constants which are specified using solar- and open cluster data. The model explains the origin of the two sequences, C/fast and I/slow, of rotating stars observed in open cluster color-period diagrams, and describes their evolution from C-type to I-type through the rotational gap, g, separating them. It explains why intermediate-mass open cluster stars have the longest periods, while higher- and lower-mass cool stars have shorter periods. It provides an exact expression for the age of a rotating cool star in terms of P and τ, thereby generalizing gyrochronology. The possible range of initial periods is shown to contribute upto 128 Myr to the gyro age errors of solar mass field stars. A transformation to color-period space shows how this model explains some detailed features in the color-period diagrams of open clusters, including the shapes and widths of the sequences, and the observed number density of stars across these diagrams.