The angular momentum-mass relation: a fundamental law from dwarf irregulars to massive spirals

In a $\Lambda$CDM Universe, the specific stellar angular momentum ($j_\ast$) and stellar mass ($M_\ast$) of a galaxy are correlated as a consequence of the scaling existing for dark matter haloes ($j_{\rm h}\propto M_{\rm h}^{2/3}$). The shape of this law is crucial to test galaxy formation models, which are currently discrepant especially at the lowest masses, allowing to constrain fundamental parameters, e.g. the retained fraction of angular momentum. In this study, we accurately determine the empirical $j_\ast-M_\ast$ relation (Fall relation) for 92 nearby spiral galaxies (from S0 to Irr) selected from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample in the unprecedented mass range $7 \lesssim \log M_\ast/M_\odot \lesssim 11.5$. We significantly improve all previous estimates of the Fall relation by determining $j_\ast$ profiles homogeneously for all galaxies, using extended HI rotation curves, and selecting only galaxies for which a robust $j_\ast$ could be measured (converged $j_\ast(<R)$ radial profile). We find the relation to be well described by a single, unbroken power-law $j_\ast\propto M_\ast^\alpha$ over the entire mass range, with $\alpha=0.55\pm 0.02$ and orthogonal intrinsic scatter of $0.17\pm 0.01$ dex. We finally discuss some implications for galaxy formation models of this fundamental scaling law and, in particular, the fact that it excludes models in which discs of all masses retain the same fraction of the halo angular momentum.