2023A&A...678A..12C

Contact. This paper is the fourth in a series dedicated to the observed parallelism of properties passing from globular clusters to early-type galaxies. To a lesser extent, it also covers galaxy clusters and groups.
Aims. Here, we investigate the I_e-R_e plane and the 3D-kappa space defined by Bender, Burstein and Faber, as potential diagnostic tools in studies of the past evolution of these stellar systems. In the space of the parameters characterizing a stellar system such as the luminosity, L, stellar mass, M_s, half-light (mass) radius, R_e, central velocity dispersion, σ_c, surface brightness, I_e, and so on, the I_e-R_e plane is one of possible projections that was thoroughly investigated over the years with many important results. The 3D-kappa space relies on three variables that are suitable combinations of the logarithms of the above parameters. Among others, perhaps the most important result from this new space is the discovery of the fundamental plane of early type galaxies. In this paper, we intend to explore in more detail the potential capability of the joined investigation of the I_e-R_e plane and 3D-kappa space.
Methods. Based on the collected literature data on the mass, half-mass (light) radius, velocity dispersion, and surface brightness in different bands for the objects under investigation, we set up the I_e-R_e plane and the 3D-kappa space. We then compared the observed distributions of these objects with those predicted by simple theoretical galaxy models.
Results. We explored the effects of different mass-radius relationships, star formation, infall, and mass assembling histories on the diagnostic planes under examination. We also investigated variations in the 3D-kappa space as a function of the redshift.
Conclusions. We show that the distribution of the stellar systems on the various diagnostic planes can cast light on the mass-radius relation and the history of star formation in stellar systems going from globular clusters to early type galaxies.