Gravitational Flux Line Redistribution Across a Critical Field Strength to Interpret the Structural-Dynamical Relations of Galaxies

The structural-dynamical relations of disk galaxies revealed by the radial acceleration relation of SPARC data (Spitzer Photometry and Accurate Rotation Curves) have been interpreted by a "gravitational field flux re-distribution" within a generalized integral Gauss's law of gravity (Reference). In such a non-relativistic picture, the flat rotation curves and the Baryonic Tully Fisher Relation have been shown as due to the re-distribution of the conserved gravitational lines of force from a spherical symmetry to cylindrical one, across a universal critical density. It is discussed in the present report that the "M ∝ v^4" Baryonic Tully-Fisher relation of disk galaxies as well as the Faber-Jackson relation for the central velocity dispersion of elliptical galaxies can be simply realized by a transition off the Newtonian 1/r^2 gravity across a universal field strength, approximately 10^-10 N/Kg, equivalent to the universal acceleration 10^-10 m/s/s. This transition occurred spatially between the core and the outskirts of disk galaxies. Such a spatial re-distribution of gravitational flux may give a geometric mapping between the generalized Gaussian surface of the field flux distribution and the real patterns of objects in various astronomical scales. Furthermore, the close relation of gravitational matter and fields, Newtonian as well as non-Newtonian, may provide an extendable mechanism to explain the observation of close relation between normal matter and dark matter and to bridge the gap between MOND and dark matter modeling. Discussions are to be make in the disk thickness variable in the cylindrical Gaussian surface, extending the flux distribution model to the elliptical galaxies and other structure and scales. Implications of the temporal evolution of the cylindrical to spherical flux line distribution is also discussed.