A universal relationship between stellar masses and binding energies of galaxies

In this study we demonstrate that stellar masses of galaxies (Mstar) are universally correlated through a double power law function with the product of the dynamical velocities (Ve) and sizes to one-fourth power (Re^0.25) of galaxies, both measured at the effective radii. The product VeRe^0.25 represents the fourth root of the total binding energies within effective radii of galaxies. This stellar mass-binding energy correlation has an observed scatter of 0.14 dex in log(VeRe^0.25) and 0.46 dex in log(Mstar). It holds for a variety of galaxy types over a stellar mass range of nine orders of magnitude, with little evolution over cosmic time. A toy model of self-regulation between binding energies and supernovae feedback is shown to be able to reproduce the observed slopes, but the underlying physical mechanisms are still unclear. The correlation can be a potential distance estimator with an uncertainty of 0.2 dex independent of the galaxy type.