Universal Modified Newtonian Dynamics Relation between the Baryonic and "Dynamical" Central Surface Densities of Disc...

I derive a new modified Newtonian dynamics (MOND) relation for pure-disc galaxies: The "dynamical" central surface density, Σ_{D}^{0}, deduced from the measured velocities, is a universal function of only the true, "baryonic'' central surface density, Σ_{B}^{0}: Σ_{D}^{0}=Σ_{M}S(Σ_{B}^{0}/Σ_{M}), where Σ_{M}≡a_{0}/2πG is the MOND surface density constant. This surprising result is shown to hold in both existing, nonrelativistic MOND theories. S(y) is derived: S(y)=∫_{0}^{y}ν(y^{'})dy^{'}, with ν(y) being the interpolating function of the theory. The relation aymptotes to Σ_{D}^{0}=Σ_{B}^{0} for Σ_{B}^{0}≫Σ_{M}, and to Σ_{D}^{0}=(4Σ_{M}Σ_{B}^{0})^{1/2} for Σ_{B}^{0}≪Σ_{M}. This study was prompted by the recent finding of a correlation between related attributes of disc galaxies by Lelli et al.. The MOND central-surface-densities relation agrees very well with these results.