1998AJ....116.2177G

A sample of low-density dwarf and spiral galaxies with H I rotation curves available in the literature is used to search for a relation of coupling between the dark mass radial distribution and the visible mass (gas and stars), or between the dark mass and the mass in gas. Relations of the form M_d(r) ~ γM^α(r)r between visible mass M(r) and halo dark mass M_d(r) within radius r are tested. These models combined with Newtonian dynamics provide very good fits to the H I rotation curves, and the average value of α is found to be sharply peaked at α = (1)/(2). In models with α = (1)/(2), γ has the dimension of the square root of a surface density, and the asymptotic velocity of dark halos is in V⁴ ∝ M. In our sample the average surface density, σ_γ ≡ γ²/π has approximately the value of Freeman's central surface density of disk galaxies. An exponential disk galaxy, with a dark halo satisfying the above relation of structure, has a flat rotation curve. If it obeys Freeman's central surface density law, the dark matter and the stellar component have the same central surface density. The above relation is valid for gas dominated galaxies like DDO 154 and UGC 2684; therefore, it seems to apply prior to any process of star formation. In several cases the relation of coupling between dark mass and visible mass (gas and stars) requires unrealistic values of the stellar disk M/L ratio. In such cases the same form of relation of coupling applied to the dark mass and the mass in gas only provides good fits to the rotation curves with reasonable M/L ratios.