Mordehai Milgrom🇮🇱
It is shown that the foundational axioms of MOND alone predict a strong correlation between a bulk measure of the baryonic surface density, ΣB, and the corresponding dynamical one, ΣD, of an isolated object, such as a galaxy. The correlation is encapsulated by its high- and low-ΣB behaviors. For ΣB≫ΣM≡a0/2πG (ΣM is the critical MOND surface density) one has ΣD≈ΣB. Their difference -- which would be interpreted as the contribution of dark matter -- is ΣP=ΣD−ΣB∼ΣM≪ΣB. In the deep-MOND limit, ΣB≪ΣM, one has ΣD∼(ΣMΣB)1/2. This is a primary prediction of MOND, shared by all theories that embody its basic tenets. Sharper correlations, even strict algebraic relations, ΣD(ΣB), 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, ΣB0 and ΣD0. 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, ΣD0 can not be determined directly at present, but, in many cases, a good proxy for it is the acceleration integral G≡∫0∞grdln r, where gr is the radial acceleration along a reflection-symmetry plane of a system, such as a disc galaxy. G can be determined directly from the rotation curve. I discuss the extent to which G is a good proxy for ΣD0, and how the relation between them depends on system geometry, from pure discs, through disc-plus-bulge ones, to quasi-spherical systems.
↳ astro-ph.GAgr-qchep-phPRD(2024)·3 citations