Galaxy spin as a formation probe: the stellar-to-halo specific angular
  momentum relation
  We derive the stellar-to-halo specific angular momentum relation (SHSAMR) of
galaxies at $z=0$ by combining i) the standard $\Lambda$CDM tidal torque theory
ii) the observed relation between stellar mass and specific angular momentum
(Fall relation) and iii) various determinations of the stellar-to-halo mass
relation (SHMR). We find that the ratio $f_j = j_\ast/j_{\rm h}$ of the
specific angular momentum of stars to that of the dark matter i) varies with
mass as a double power-law, ii) it always has a peak in the mass range explored
and iii) it is $3-5$ times larger for spirals than for ellipticals. The results
have some dependence on the adopted SHMR and we provide fitting formulae in
each case. For any choice of the SHMR, the peak of $f_j$ occurs at the same
mass where the stellar-to-halo mass ratio $f_\ast = M_\ast/M_{\rm h}$ has a
maximum. This is mostly driven by the straightness and tightness of the Fall
relation, which requires $f_j$ and $f_\ast$ to be correlated with each other
roughly as $f_j\propto f_\ast^{2/3}$, as expected if the outer and more angular
momentum rich parts of a halo failed to accrete onto the central galaxy and
form stars (biased collapse). We also confirm that the difference in the
angular momentum of spirals and ellipticals at a given mass is too large to be
ascribed only to different spins of the parent dark-matter haloes (spin bias).
