In the context of the hierarchical formation of galaxies, we investigated the role played by mergers in shaping the scaling relations of galaxies, that is the projections of their fundamental plane onto the and planes. To this end, based on the scalar virial theorem, we developed a simple theory of multiple dry mergers to read both the large-scale simulations and the companion scaling relations. The aim was to compare the results of this approach with the observational data and with two of the most recent and detailed numerical cosmo-hydro-dynamical simulations: Illustris-TNG and EAGLE (Evolution and Assembly of GaLaxies and their Environments). We derived these scaling relations for the galaxies of the Mapping Nearby Galaxies at APO (MaNGA) and Wide-field Imaging of Nearby Galaxy-Clusters Survey (WINGS) databases and compared them with the observational data, the numerical simulations, and the results of our simple theory of dry mergers. The multiple dry merging mechanism is able to explain all the main characteristics of the observed scaling relations of galaxies, such as slopes, scatters, curvatures, and zones of exclusion. The distribution of galaxies in these planes is continuously changing across time because of the merging activity and other physical processes, such as star formation, quenching, and energy feedback. The simple merger theory presented here yields the correct distribution of galaxies in the main scaling relations at all cosmic epochs. The precision is comparable with that obtained by the modern cosmo-hydro-dynamical simulations, with the advantage of providing a rapid exploratory response on the consequences engendered by different physical effects.
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