500 Galaxies Rotations Powered by a Baryonic Dark Matter.

This paper proposes a conceptual framework that predicts the rotational velocity of spiral galaxies as a function of their radial distances from their center of mass and the flattening of these curves at large distances. The model is grounded in an emergent modified gravity paradigm derived from Einstein’s general relativity and relies on an ERFC potential metric, whose constant offset can be assimilated to a baryonic dark matter reservoir. A short recall of the modified gravity model is presented and the equation describing a galaxy velocity profile is established, exploiting a single emergent parameter, the galaxy's proper length σ_Gal. Levenberg-Marquard curve fitting optimizations on the 551 galaxies of Sofue’s (2018) database are reported. The model fits the global velocity behavior all over the radial distances. It predicts very good results (SNR ≧ 20dB) in 78% of the galaxies. The whole description is consistent with the Thully-Fischer relationship that can be derived from it. According to this new paradigm, the constant component of the ERFC potential associated with a given mass provides a huge baryonic energy reservoir playing the role of dark matter in galaxy rotations, fixing for each galaxy, a constant velocity upper limit. In this perspective, taking the other side of the coin, the velocity profile of galaxies, with their tendencies to become constant at large distances, can be interpreted as a direct manifestation of the emergent ERFC potential metrics and its corresponding modified Newton’s law of gravitation.