Central-surface-densities correlation in general MOND theories

Abstract

It is shown that the foundational axioms of MOND alone predict a strong correlation between a bulk measure of the baryonic surface density, ${\Sigma }_B$, and the corresponding dynamical one, ${\Sigma }_D$, of an isolated object, such as a galaxy. The correlation is encapsulated by its high- and low-${\Sigma }_B$ behaviors. For ${\Sigma }_B\gg {\Sigma }_M\equiv a_0/2\pi G$ (${\Sigma }_M$ is the critical MOND surface density) one has ${\Sigma }_D\approx {\Sigma }_B$. Their difference -- which would be interpreted as the contribution of dark matter -- is ${\Sigma }_P={\Sigma }_D-{\Sigma }_B\sim {\Sigma }_M\ll {\Sigma }_B$. In the deep-MOND limit, ${\Sigma }_B\ll {\Sigma }_M$, one has ${\Sigma }_D\sim ({\Sigma }_M{\Sigma }_B{)}^{1/2}$. This is a primary prediction of MOND, shared by all theories that embody its basic tenets. Sharper correlations, even strict algebraic relations, ${\Sigma }_D({\Sigma }_B)$, are predicted in specific MOND theories, for specific classes of mass distribution -- e.g., pure discs, or spherical systems -- and for specific definitions of the surface densities. I proceed to discuss such tighter correlations for the central surface densities of axisymmetric galactic systems, ${\Sigma }_B^0$ and ${\Sigma }_D^0$. Past work has demonstrated such relations for pure discs in the AQUAL and QUMOND theories. Here I consider them in broader classes of MOND theories. For most observed systems, ${\Sigma }_D^0$ can not be determined directly at present, but, in many cases, a good proxy for it is the acceleration integral $\mathcal{G}\equiv {\int }_0^{\infty }{g}_{r}d\ln r$, where $g_r$ is the radial acceleration along a reflection-symmetry plane of a system, such as a disc galaxy. $\mathcal{G}$ can be determined directly from the rotation curve. I discuss the extent to which $\mathcal{G}$ is a good proxy for ${\Sigma }_D^0$, and how the relation between them depends on system geometry, from pure discs, through disc-plus-bulge ones, to quasi-spherical systems.

22 pages, matching the published version

References in corpus (10)

• GHASP : an H alpha kinematic survey of spiral and irregular galaxies. V. Dark matter distribution in 36 nearby spiral galaxies
• The Relation between Stellar and Dynamical Surface Densities in the Central Regions of Disk Galaxies
• Predictions and Outcomes for the Dynamics of Rotating Galaxies
• Rings and shells of "dark matter" as MOND artifacts
• Universal MOND relation between the baryonic and `dynamical' central surface densities of disc galaxies
• Models of modified-inertia formulation of MOND
• The Link Between Light and Mass in Late-type Spiral Galaxy Disks
• Global Deep-MOND Parameter as a Theory Discriminant
• Halo Acceleration Relation
• Deep-MOND polytropes

Cited by in corpus (1)

• Is MOND necessarily nonlinear?