MOND fiducial specific angular momentum of disc galaxies

Abstract

It is pointed out that MOND defines a fiducial specific angular momentum (SAM) for a galaxy of total (baryonic) mass $\mathcal{M}$: $j_M(\mathcal{M})\equiv {\mathcal{M}}^{3/4}(G^3/a_0{)}^{1/4}\approx 383(\mathcal{M}/10^{10}{M}_{\odot }{)}^{3/4}\mathrm{kpc}km/s$. It plays important roles in disc-galaxy dynamics and evolution: It underlies scaling relations in virialized galaxies that involve their angular-momentum. I show that the disc SAM should be $j_D\approx [⟨r⟩/r_M(\mathcal{M})]j_M(\mathcal{M})=[{\Sigma }_M/⟨\Sigma ⟩{]}^{1/2}{j}_M(\mathcal{M})$, with $⟨r⟩$ the mean radius of the disc, $⟨\Sigma ⟩=\mathcal{M}/2\pi ⟨r{⟩}^2$ some mean surface density of the galaxy, $r_M=(\mathcal{M}G/a_0{)}^{1/2}$ is the MOND radius of the galaxy, and ${\Sigma }_M=a_0/2\pi G$ is the (universal) MOND surface density. So, e.g., for a fixed $⟨\Sigma ⟩$, $j_D\propto {\mathcal{M}}^{3/4}$, while for a fixed $⟨r⟩$, $j_D\propto {\mathcal{M}}^{1/4}$. Furthermore, $j_M(\mathcal{M})$ is a reference predictor of the type of galaxy a protogalaxy will settle into, if it evolves in isolation: A protogalaxy of mass $\mathcal{M}$, and SAM $j\gg j_M(\mathcal{M})$ should settle into a low-surface-density disc -- with mean acceleration $⟨a⟩/a_0\approx j_M/j\ll 1$. While a protogalaxy with $j\lesssim j_M(\mathcal{M})$ should end up with a disc of mass ${\mathcal{M}}_D\approx j\mathcal{M}/j_M(\mathcal{M})$, having a SAM $j_D\approx j_M(\mathcal{M})$, which is tantamount to $⟨a⟩\approx a_0$ (i.e., at the `Freeman limit'); it should also develop a low-SAM bulge, taking up the rest of the mass ${\mathcal{M}}_B\approx \mathcal{M}-{\mathcal{M}}_D$.

arXiv comment6 pages, 2 figure. Added a detailed discussion of the recent analysis of j-M correlations in Ref. 25, which lends itself to a much clearer comparison with the predictions of MOND. Version to appear in Phys. Rev. D

References in corpus (20)

• Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions
• SPARC: Mass Models for 175 Disk Galaxies with Spitzer Photometry and Accurate Rotation Curves
• The Formation of Disk Galaxies
• The baryonic Tully-Fisher relation for different velocity definitions and implications for galaxy angular momentum
• Fundamental Mass-Spin-Morphology Relation of Spiral Galaxies
• MOND laws of galactic dynamics
• Galaxy Selection and the Surface Brightness Distribution
• Stability of disk galaxies in the modified dynamics
• The angular momentum-mass relation: a fundamental law from dwarf irregulars to massive spirals
• Andromeda Dwarfs in Light of MOND
• Angular Momentum and Galaxy Formation Revisited: Scaling Relations for Disks and Bulges
• The baryonic specific angular momentum of disc galaxies
• MOND vs. dark matter in light of historical parallels
• A tight angular-momentum plane for disc galaxies
• The formation of exponential disk galaxies in MOND
• A first attempt to differentiate between modified gravity and modified inertia with galaxy rotation curves
• Global Deep-MOND Parameter as a Theory Discriminant
• The specific angular momenta of superthin galaxies: Cue to their origin?
• Low-surface-brightness spheroidal galaxies as Milgromian isothermal spheres
• The $a_0$ -- cosmology connection in MOND

Cited by in corpus (3)

• From galactic bars to the Hubble tension: weighing up the astrophysical evidence for Milgromian gravity
• The galactic acceleration scale is imprinted on globular cluster systems of early-type galaxies of most masses and on red and blue globular cluster subpopulations
• Probing modified gravity with magnetically levitated resonators