Universal Modified Newtonian Dynamics Relation between the Baryonic and “Dynamical” Central Surface Densities of Disc Galaxies

I derive a new modified Newtonian dynamics (MOND) relation for pure-disc galaxies: The ``dynamical'' central surface density, ΣD⁰, deduced from the measured velocities, is a universal function of only the true, ``baryonic'' central surface density, ΣB⁰: ΣD⁰=ΣMS(ΣB⁰/ΣM), where ΣM≡a₀/2πG 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)=∫₀ʸν(y^')dy^', with ν(y) being the interpolating function of the theory. The relation aymptotes to ΣD⁰=ΣB⁰ for ΣB⁰ΣM, and to ΣD⁰=(4ΣMΣB⁰)1/2 for ΣB⁰ΣM. 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.