Relation between mass and radius of elliptical galaxies

Between the mass M and de Vaucouleurs' effective radius R sub(e) of elliptical galaxies an empirical relation log R sub(e) (in kpc) = (0.64 +- 0.02) x log (M/M sub(solar mass)) - (6.96+-0.02) is found for 21 elliptical galaxies whose masses are computed exclusively from the velocity dispersions recently observed. In elliptical galaxies the radius is to be determined in the course of galaxy formation. A simple model of galaxy formation is considered; a system of a large number of gas clouds contracts due to dissipation in their mutual inelastic collisions. In the course of contraction stars will form in the clouds in a relatively short period. At a certain critical moment the star formation finishes and the contraction ceases. The radius at this moment is shown to satisfy the above relation on a few assumptions. (author)