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 (8)

• Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions
• The unexpected diversity of dwarf galaxy rotation curves
• A constant dark matter halo surface density in galaxies
• Quasi-linear formulation of MOND
• The Relation between Stellar and Dynamical Surface Densities in the Central Regions of Disk Galaxies
• MOND laws of galactic dynamics
• The central surface density of "dark halos" predicted by MOND
• Forces in Nonlinear Media

Cited by in corpus (29)

• Small scale problems of the $\Lambda$CDM model: a short review
• MOND vs. dark matter in light of historical parallels
• MOND Prediction for the Velocity Dispersion of the `Feeble Giant' Crater II
• Stellar streams as gravitational experiments I. The case of Sagittarius
• Gas dynamics in dwarf galaxies as testbeds for dark matter and galaxy evolution
• Emergence of the mass discrepancy-acceleration relation from dark matter-baryon interactions
• The radial acceleration relation in galaxy clusters
• The Fifth Force in the Local Cosmic Web
• Fifth force constraints from the separation of galaxy mass components
• Gravitational wave as probe of superfluid dark matter
• Radial acceleration relation of galaxies with joint kinematic and weak-lensing data
• The phantom dark matter halos of the Local Volume in the context of modified Newtonian dynamics
• Constraints on galileons from the positions of supermassive black holes
• Deflection of light by wormholes and its shadow due to dark matter within modified symmetric teleparallel gravity formalism
• Interposing a Varying Gravitational Constant Between Modified Newtonian Dynamics and Weak Weyl Gravity
• The solar system test for the general modified gravity theories
• Origin of the fundamental plane of elliptical galaxies in the Coma Cluster without fine-tuning
• Mass Discrepancy-Acceleration Relation in Einstein Rings
• The radial acceleration relation and dark baryons in MOND
• There is no universal acceleration scale in galaxies
• Deep-MOND polytropes
• Gauss's Law and the Source for Poisson's Equation in Modified Gravity with Varying G
• Towards an explanation of orbits in the extreme trans-Neptunian region: The effect of Milgromian dynamics
• Analytic expressions for the dark matter-baryon relations
• Central-surface-densities correlation in general MOND theories
• Testing CCC+TL Cosmology with Galaxy Rotation Curves
• Gas expulsion in MOND: the possible origin of diffuse globular clusters and ultra-faint dwarf galaxies
• The analytic radial acceleration relation for galaxy clusters
• On the absence of a universal surface density, and a maximum Newtonian acceleration in dark matter haloes: consequences for MOND