Estimation of the radius of a star based on its effective temperature and surface gravity

Abstract

Amethod for determining the radius of a star using its effective temperature and surface gravity is proposed. The method assumes that the relationship between the radius, effective temperature, and surface gravity can be approximated using models for the internal structure and evolution of the star. The method is illustrated using the Geneva–Toulouse evolutionary computations for two metal abundances—solar and one-tenth of solar. Analysis of the systematic errors shows that the accuracy of the method is better than 10% over most part of the Hertzsprung–Russell diagram, and is about 5% for main-sequence stars. The maximum relative systematic error due to the simplifications underlying the method is about 15%. A test using eclipsing binaries confirms the viability of the proposed method for estimating stellar radii. In the region of the main sequence, systematic deviations do not exceed 2%, and the relative standard deviation is ≤4.7%. It is expected that th maximum relative error over the rest of the Hertzsprung–Russell diagram will likewise be close to the systematic error, about 15–20%. The method is applied to estimate the radii of model stellar atmospheres. Such estimates can be used to synthesize the color index and luminosity of a star. The method can be used whenever accuracies of about 10% in the estimated stellar radius and luminosity are acceptable.