On the Radius of Gyration of Stars.

Abstract

A comparison of the radius of gyration of a star, which is defined by the integral H = ( r4d r)V2 with the apsidal-motion constant for various stellar models shows that, for polytropes and various mainsequence stars, there is a linear relationship between -log (H/R) and -log k, where k is the apsidalmotion constant. Giant models, however, do not fall on this line. The apsidal-motion constant for the Epstein two-source (proton-proton reaction and the carbon cycle) model for the sun is found to be 0.00599, which is equivalent to an effective polytropic index of 3.38. This result is used to draw some conclusions concerning the point along the main sequence where the proton-proton process gives way to the carbon cycle.