Is the dark-matter halo spin a predictor of galaxy spin and size?

The similarity between the distributions of spins for galaxies (λ_gal) and for dark-matter haloes (λ_halo), indicated both by simulations and observations, is naively interpreted as a one-to-one correlation between the spins of a galaxy and its host halo. This is used to predict galaxy sizes in semi-analytic models via R_e = f_jλ_haloR_vir, where R_e is the half-mass radius of the galaxy, f_j is the angular momentum retention factor, and R_vir is the halo radius. Using two suites of zoom-in cosmological simulations, we find that λ_gal and the λ_halo of its host halo are in fact barely correlated, especially at z ≥ 1, in line with previous indications. Since the spins of baryons and dark matter are correlated at accretion into R_vir, the null correlation in the end reflects an anticorrelation between f_j and λ_halo, which can arise from mergers and a 'wet compaction' phase that many high-redshift galaxies undergo. It may also reflect that unrepresentative small fractions of baryons are tapped to the galaxies. The galaxy spin is better correlated with the spin of the inner halo, but this largely reflects the effect of the baryons on the halo. While λ_halo is not a useful predictor for R_e, our simulations reproduce a general relation of the form of R_e = AR_vir, in agreement with observational estimates. We find that the relation becomes tighter with A = 0.02(c/10)^−0.7, where c is the halo concentration, which in turn introduces a dependence on mass and redshift.