Conformal theory of central surface density for galactic dark halos
Numerous dark matter studies of galactic halo gravitation depend on models with core radius $r_0$ and central density $ρ_0$. Central surface density product $ρ_0 r_0$ 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 $Δa$, for $a=a_N+Δa$, where Newtonian acceleration $a_N$ is due to observable baryonic matter. Neglecting a halo cutoff at very large galactic radius, conformal $Δa$ is constant over the entire halo and $a=a_N+Δa$ 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.