Conformal theory of central surface density for galactic dark halos

Abstract

Numerous dark matter studies of galactic halo gravitation depend on models with core radius r0 and central density ρ0. Central surface density product ρ0r0 is found to be nearly a universal constant for a large range of galaxies. Standard variational field theory with Weyl conformal symmetry postulated for gravitation and the Higgs scalar field, without dark matter, implies nonclassical centripetal acceleration ∆a, for a = aN +∆a, where Newtonian acceleration aN is due to observable baryonic matter. Neglecting a halo cutoff at very large galactic radius, conformal ∆a is constant over the entire halo and a = aN + ∆a is a universal function, consistent with a recent study of galaxies, with independently measured mass, that constrains acceleration due to dark matter or to alternative theory. An equivalent dark matter source would be a pure cusp distribution with cutoff parameter determined by a halo boundary radius. This is shown to imply universal central surface density for any dark matter core model.