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.
