Recovering the fundamental plane of galaxies by f(R) gravity

Abstract

The fundamental plane (FP) of galaxies can be recovered in the framework of f(R) gravity avoiding the issues related to dark matter to fit the observations. In particular, the power-law version f(R)∝Rn, resulting from the existence of Noether symmetries for f(R), is sufficient to implement the approach. In fact, relations between the FP parameters and the corrected Newtonian potential, coming from Rn, can be found and justified from a physical point of view. Specifically, we analyze the velocity distribution of elliptical galaxies and obtain that rc, the scale-length depending on the gravitational system properties, is proportional to re, the galaxy effective radius. This fact points out that the gravitational corrections induced by f(R) can lead photometry and dynamics of the system. Furthermore, the main byproduct of such an approach is that gravity could work in different ways depending on the scales of self-gravitating systems.