A Fluid Mechanics Solution for the `Galaxy Rotational Velocity Problem' Using Integral Averaged Euler Equations Without Dark Matter

We argue that the usual non-relativistic Gauss-Newton equations have been incorrectly applied to galaxies. By using integral techniques applied to averaged Euler equations commonly used in fluid mechanics and turbulence, and treating the stars and dust separately, we show that there is no need for `Dark Matter' to explain galactic rotational velocities. We define a momentum thickness which resembles closely the actual galaxy disk thickness. Our computed rotational velocities correspond well to both the shape and magnitude of the M33 Triangulum galaxy velocity measurements of [1] and the Milky Way [2], even at large radius; as well as to recent correlations about most spiral galaxies [3]. The “mean streamlines” computed from the velocity data for the Milky Way [2] are virtually identical to log spirals, consistent with an equilibrium similarity analysis of the same equations.

[1] Corbellietal2014 Corbelli, E., Thiker, D., Zibetti, S., Giovanardi, C and Salucci, P. (2014) ``Dynamical signature of a Λ-CDM-halo and the distributions of baryons in M33., AA, 572, A23, DOI 10:1051/0004-6361/201424033.

[2] Eilers, A. C, Hogg, D.W., Rix, H.W., and Ness, M.K. (2018) ``The circular velocity curve of the Milky Way from 5 to 25 kpc'', arXiv:1810.09466v2 [astro-ph.GA], 4 Dec. 201

[3] McGaugh, S., Lelli, R., and Schombert, J. M. (2016) ``Radial Acceleration in Rotational Supported Galaxies'', PRL 117, 201101.