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 _ { h } \propto M _ { 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 H i 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 .