Universal MOND relation between the baryonic and `dynamical' central surface densities of disc galaxies

Abstract

I derive a new MOND relation for pure-disc galaxies: The `dynamical' central surface density, ${\Sigma }_D^0$, deduced from the measured velocities, is a universal function of only the true, `baryonic' central surface density, ${\Sigma }_B^0$: ${\Sigma }_D^0={\Sigma }_M\mathcal{S}({\Sigma }_B^0/{\Sigma }_M)$, where ${\Sigma }_M\equiv a_0/2\pi G$ is the MOND surface density constant. This surprising result is shown to hold in both existing, nonrelativistic MOND theories. $\mathcal{S}(y)$ is derived: $\mathcal{S}(y)={\int }_0^y\nu (y^{\prime })d{y}^{\prime }$, with $\nu (y)$ the interpolating function of the theory. The relation aymptotes to ${\Sigma }_D^0={\Sigma }_B^0$ for ${\Sigma }_B^0\gg {\Sigma }_M$, and to ${\Sigma }_D^0=(4{\Sigma }_M{\Sigma }_B^0{)}^{1/2}$ for ${\Sigma }_B^0\ll {\Sigma }_M$. This study was prompted by the recent finding of a correlation between related attributes of disc galaxies by Lelli et al. (2016). The MOND central-surface-densities relation agrees very well with these results.

Physical Review Letters, in press. Added a discussion of generalizations. 5 pages, 1 figure

References in corpus (1)

• The Relation between Stellar and Dynamical Surface Densities in the Central Regions of Disk Galaxies

Cited by in corpus (1)

• The radial acceleration relation and dark baryons in MOND