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The massive elliptical galaxy NGC 4649 from the perspective of extended gravity

Elliptical galaxies are systems where dark matter is usually less necessary to explain observed dynamics than in the case of spiral galaxies, however there are some instances where Newtonian gravity and the observable mass are insufficient to explain their observed structure and kinematics. Such is the case of NGC 4649, a massive elliptical galaxy in the Virgo cluster for which recent studies report a high fraction of dark matter, 0.78 at $4R_e$. However this galaxy has been studied within the MOND hypothesis, where a good agreement with the observed values of velocity dispersion is found. Using a MONDian gravity force law, here we model this galaxy as a self-consistent gravitational equilibrium dynamical system. This force law reproduces the MOND phenomenology in the $a<a_{0}$ regime, and reduces to the Newtonian case when $a>a_{0}$. Within the MONDian $a<a_{0}$ scales, centrifugal equilibrium or dispersion velocities become independent of radius, and show a direct proportionality to the fourth root of the total baryonic mass, $V^{4}\propto(M G a_{0})$. We find that the recent detailed observations of the surface brightness profile and the velocity dispersion profile for this galaxy are consistent with the phenomenology expected in MONDian theories of modified gravity, without the need of invoking the presence of any hypothetical dark matter.