Generalized Integral Gauss's Law with Non-Spherical Distribution of Gravitational Field Flux to Interpret Tully-Fisher Relation of Disk Galaxies

A 1/r field dependence causing flat rotation curve(RC) of disk galaxies are obtained by a Gaussian surface with cylindrical symmetry where the gravitational flux distribution is converging along the radial direction of the disk plane. The Gaussian disk thickness as a dynamical variable is examined with observational evidences. The monotonically rising RC of low surface brightness galaxies(L-SBGs) can be attributed to a Gaussian disk thinning mechanism. 

A spherical to cylindrical transition of the Gaussian surface symmetry across a critical field (g_c)~10^-10 N/Kg is shown to give the exact M~v⁴ Tully-Fisher relation(TFR). Possible factors causing deviation from the exact TFR of the L-SBGs are discussed. 

The structural-dynamical relation revealed in SPARC(Spitzer Photometry and Accurate Rotation Curves ) data are compared to the field flux distribution picture. The transition from Newtonian behavior above g_c existed near the bulge region of high-SBGs to Non-Newtonian behavior below g_c of both high-SBGs edge and whole bulgeless L-SBGs is mapped to the Gaussian sphere-to-disk transition of the flux distribution within integral Gauss's law of Gravity.
Possible applications of the converging field flux picture to larger scales and  its theoretical implications are discussed.