Is the dark-matter halo spin a predictor of galaxy spin and size?
  The similarity between the distributions of spins for galaxies ($\lambda_{\rm
g}$) and for dark-matter haloes ($\lambda_{\rm h}$), 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 $R_{\rm e}\simeq\lambda_{\rm
h} R_{\rm v}$, with $R_{\rm e}$ the half-mass radius of the galaxy and $R_{\rm
v}$ the halo radius. Utilizing two different suites of zoom-in cosmological
simulations, we find that $\lambda_{\rm g}$ and $\lambda_{\rm h}$ are in fact
only barely correlated, especially at $z\geq 1$. A general smearing of this
correlation is expected based on the different spin histories, where the more
recently accreted baryons through streams gain and then lose significant
angular momentum compared to the gradually accumulated dark matter. Expecting
the spins of baryons and dark matter to be correlated at accretion into $R_{\rm
v}$, the null correlation at the end reflects an anti-correlation between
$\lambda_{\rm g}/\lambda_{\rm h}$ and $\lambda_{\rm h}$, which can partly arise
from mergers and a compact star-forming phase that many galaxies undergo. On
the other hand, the halo and galaxy spin vectors tend to be aligned, with a
median $\cos\theta=0.6$-0.7 between galaxy and halo, consistent with
instreaming within a preferred plane. 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. Following the null spin correlation, $\lambda_{\rm h}$ is not a
useful proxy for $R_{\rm e}$. While our simulations reproduce a general
relation of the sort $R_{\rm e}=AR_{\rm vir}$, in agreement with observational
estimates, 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.
