Conformal theory of central surface density for galactic dark halos

Numerous dark matter studies of galactic halo gravitation depend on models with core radius r₀ and central density ρ₀. Central surface density product ρ₀ r₀ 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 Δ a, for a=aN+Δ a, where Newtonian acceleration aN is due to observable baryonic matter. Neglecting a halo cutoff at very large galactic radius, conformal Δ a is constant over the entire halo and a=aN+Δ a is a universal function, consistent with a recent study of galaxies that constrains acceleration due to dark matter or to alternative theory. An equivalent dark matter source is a pure cusp distribution with cutoff parameter determined by a halo boundary radius. This is shown here to imply universal central surface density for any dark matter core model.