The Magnitude-Diameter Relation of Galaxies
  We investigate the dependence of the luminosity-diameter relation of galaxies on the environment. This study is based on a comparison between the 80 galaxies in the Shapley-Ames Catalog that are located within a distance of 10 Mpc, and the luminosity-diameter relation for galaxies in great clusters such as Virgo and Coma. A relatively tight linear correlation is observed between the absolute magnitudes and the logarithms of the linear diameters of galaxies located within 10 Mpc. Surprisingly this observed power-law relationship appears to be almost independent of environment and local mass density as defined by Karachentsev & Malakov. However, at a given luminosity, early-type galaxies are (on average) slightly more compact than are objects of a later type. Unexpectedly the present results appear to indicate that the luminosity-diameter relation for the galaxies within 10 Mpc is indistinguishable from what is observed in the much denser Virgo cluster. Galaxies appear to form an almost one-dimensional family in parameter space. It remains a mystery why the luminosity-diameter relation for galaxies is so insensitive to environment. 
Sidney van den Bergh