Estimation of a star’s radius from its effective temperature and surface gravity taking into account stellar evolution

Abstract

A method for determining the radius of a star based on its effective temperature and surface gravity together with computations of the star’s structure and evolution is proposed. Rotating and nonrotating stellar models are considered, making it possible to take into account uncertainties associated with the lack of data on the rotational velocities of the stars considered. Each point of an evolutionary track is assigned a weight in accordance with the rate of the stellar evolution and the initial mass function. This enables a more correct estimation of the stellar radius. The method is used to calculate the radius corresponding to the effective temperature and surface gravity obtained from theoretical spectra derived from model stellar atmospheres. This makes it possible to calculate not only the color indices, but also the brightness of the star, enabling estimation of the distance to the star based on photometric observations. The method has been tested and its accuracy estimated using more than a hundred binaries and two dozen well-studied bright stars. The derived radius estimates for stars near the main sequence display systematic deviations that do not exceed 0.03%, and standard deviations for the relative errors below 3.87%. Data on well studied bright stars have enabled verification of the applicability of the method for the red giant branch, and hence proved the possibility of applying it in this densely populated area of the Hertzsprung–Russell diagram.