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 Acold dark matter tidal torque theory, (ii) the observed relation between stellar mass and specific angular momentum (the Fall relation), and (iii) various determinations of the stellar-to-halo mass relation (SHMR). We find that the ratio f(j) = j(*)/j(h) of the specific angular momentum of stars to that of the dark matter (i) varies with mass as a double power law, (ii) always has a peak in the mass range explored and iii) is three to five 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(*) = M-*/M-h has a maximum. This is mostly driven by the straightness and tightness of the Fall relation, which requires f(j) and f(*) to be correlated with each other roughly as f(j) proportional to f(*)(2/3), as expected if the outer and more angular momentum rich parts of a halo failed to accrete on to 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).