The modified Newtonian dynamics with an extra anti-dissipation term can yield the MOND model

RESUMO

In this work, we introduced a positive viscosity coefficient into Newtonian dynamics to explore the rotational properties of disk galaxies. Our results show that the rotational behaviors of disk galaxies predicted by this modified Newtonian dynamics share notable similarities with those from the well-known MOND model. Specifically, the modified framework naturally recovers the deep-MOND limit postulated in MOND. Furthermore, we derived an explicit interpolation function relating centripetal acceleration to Newtonian acceleration-a relation that is purely empirical within the MOND model. We also identify key differences from MOND: the critical acceleration a0, regarded as a universal constant in MOND, actually varies with galactic mass and increases for more massive galaxies. Additionally, driven by the anti-dissipation effect of the viscosity coefficient, disk galaxies undergo extremely slow radial expansion over cosmic time, analogous to the expansion of the Universe. But regrettably, the fundamental physical origin of the viscosity coefficient introduced here remains unclear for us. But relevant hints can be found in existing literature, pointing to a promising direction for our future research.