Relation between Luminosity and Surface Rotation of Spotted Stars

Abstract

This communications explores the existence of a possible relationship between Luminosity and surface rotation for the study of the evolution of spotted stars using the data of Kepler’s and DI spotted stars. For the determination of such a relationship between luminosity and rotation the dependency of rotational shear on effective temperature is to be reviewed first. The strong dependence of rotational shear on the effective temperature in the range of 3000K and 6000K is confirmed by a power law. This dependence in turn introduces rotation as an evolutionary parameter for the study of the evolution of spotted stars. Multivariate Linear regression, Log-Log multivariate and Nonlinear Multivariate (2, 2) Degree models are constructed to determine the Luminosity of Kepler’s and Doppler imaging spotted stars with rotational shear, relative differential rotation and radius as independent variables. In this regard Log-Log model and Nonlinear Multivariate (2, 2) Degree model is best suited as compared to the linear model. In the next stage Log-Log model is applied to the main sequence Kepler’s stars (excluding giants) and also to the stars in the individual spectral classes A, F, G, K, and M. The model appears best for main sequence stars and also for the stars in the individual classes F-M. Applying the model on DI spotted stars the standard errors indicate that the adequacy of the model for DI spotted stars data is weak. A description of stellar motions and description of data and model used is given in the introduction.