The parallelism between galaxy clusters and early-type galaxies: III. The mass-radius relationship

Context. This is the third study of a series dedicated to the observed parallelism of properties between galaxy clusters and groups (GCGs) and early-type galaxies (ETGs). Aims. Here we investigate the physical origin of the mass-radius relation (MRR). Methods. Having collected literature data on masses and radii for objects going from globular clusters (GCs) to ETGs and GCGs, we set up the MR plane and compare the observed distribution with the MRR predicted by theoretical models for both the monolithic and hierarchical scenarios. Results. We argue that the distribution of stellar systems in the MR plane is due to complementary mechanisms: (i) on one hand, as shown in Paper II, the relation of the virial equilibrium intersects with a relation that provides the total luminosity as a function of the star formation history; (ii) on the other hand, the locus predicted for the collapse of systems should be convolved with the statistical expectation for the maximum mass of the halos at each cosmic epoch. This second aspect provides a natural boundary limit explaining both the curved distribution observed in the MR plane and the existence of a zone of avoidance. Conclusions. The distribution of stellar systems in the MR plane is the result of two combined evolutions, that of the stellar component and that of the halo component