2016/07/31 by Mordehai Milgrom · 66 citations
Physics and Astronomy · #Baryon #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Geometry #Mathematical physics #Particle physics #Physics #Quantum mechanics #Sigma #Surface (topology) #astro-ph.CO #astro-ph.GA #gr-qc #hep-ph
paper · pdf · doi:10.1103/physrevlett.117.141101
published in Physical Review Letters 117(14), 141101 (American Physical Society) · Physical Review Letters, in press. Added a discussion of generalizations. 5 pages, 1 figure
arxiv created 2016/09/04 · openalex publication_date 2016/09/27 · arxiv updated 2016/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
I derive a new modified Newtonian dynamics (MOND) relation for pure-disc galaxies: The ``dynamical'' central surface density, \mathrm\ensuremathΣD0, deduced from the measured velocities, is a universal function of only the true, ``baryonic'' central surface density, \mathrm\ensuremathΣB0: \mathrm\ensuremathΣD0=\mathrm\ensuremathΣMS(\mathrm\ensuremathΣB0/\mathrm\ensuremathΣM), where \mathrm\ensuremathΣM\ensuremath≡a0/2\ensuremathπG 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)=\ensuremath∫0y\ensuremathν(y^\ensuremath')dy^\ensuremath', with \ensuremathν(y) being the interpolating function of the theory. The relation aymptotes to \mathrm\ensuremathΣD0=\mathrm\ensuremathΣB0 for \mathrm\ensuremathΣB0\ensuremath≫\mathrm\ensuremathΣM, and to \mathrm\ensuremathΣD0=(4\mathrm\ensuremathΣM\mathrm\ensuremathΣB0)1/2 for \mathrm\ensuremathΣB0\ensuremath≪\mathrm\ensuremathΣM. 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.