Galaxy rotation curves with lognormal density distribution

The lognormal distribution represents the probability of finding randomly distributed particles in a micro canonical ensemble with high entropy. To a first approximation, a modified form of this distribution with a truncated termination may represent an isolated galactic disc, and this disc density distribution model was therefore run to give the best fit to the observational rotation curves for 37 representative galaxies. The resultant curves closely matched the observational data for a wide range of velocity profiles and galaxy types with rising, flat or descending curves in agreement with Verheijen's classification of 'R', 'F' and 'D' type curves, and the corresponding theoretical total disc masses could be fitted to a baryonic Tully-Fisher relation. Nine of the galaxies were matched to galaxies with previously published masses, suggesting a mean excess dynamic disc mass of dex 0.61 +/- 0.26 over the baryonic masses. Although questionable with regard to other measurements of the shape of disc galaxy gravitational potentials, this model can accommodate a scenario in which the gravitational mass distribution, as measured via the rotation curve, is confined to a thin plane without requiring a dark matter halo or the use of modified Newtonian dynamics.