The Origin of the Relation Between Stellar Angular Momentum and Stellar Mass in Nearby Disk-dominated galaxies

The IllustrisTNG simulations reproduce the observed scaling relation between stellar specific angular momentum (sAM) $j_{\rm s}$ and mass $M_{\rm s}$ of central galaxies. We show that the local $j_{\rm s}$-$M_{\rm s}$ relation ${\rm log}\ j_{\rm s} = 0.55 \ {\rm log}\ M_{\rm s} + 2.77$ develops at $z\lesssim 1$ in disk-dominated galaxies. We provide a simple model that describes well such a connection between halos and galaxies. The index 0.55 of the $j_{\rm s}$-$M_{\rm s}$ relation comes from the product of the indices of the $j_{\rm tot}\propto M_{\rm tot}^{0.81}$, $M_{\rm tot}\propto M_{\rm s}^{0.67}$, and $j_{\rm s}\propto j_{\rm tot}$ relations, where $j_{\rm tot}$ and $M_{\rm tot}$ are overall sAM and mass of a halo. A non-negligible deviation from the tidal torque theory, which predicts $j_{\rm tot}\propto M_{\rm tot}^{2/3}$, should be included. This model further suggests that the stellar-to-halo mass ratio of disk galaxies increases monotonically following a nearly power-law function that is consistent with the latest dynamical measurements. Biased collapse, in which galaxies form from the inner and lower sAM portion of their parent halos, has a minor effect at low redshifts. The retention factor of angular momentum reaches $\sim 1$ in disk galaxies with strong rotations, and it correlates inversely with the mass fraction of the spheroidal component, which partially explains the morphological dependence of the $j_{\rm s}$-$M_{\rm s}$ relation.