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 ${\mathcal{M}}_B\approx \mathcal{M}-{\mathcal{M}}_D$.

6 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

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• Probing modified gravity with magnetically levitated resonators