Angular momentum evolution of stellar disks at high redshifts
  The stellar disk size of a galaxy depends on the ratio of the disk stellar
mass to the halo mass, $m_\star \equiv M_\star/M_{\rm dh}$, and the fraction of
the dark halo angular momentum transferred to the stellar disk, $j_\star \equiv
J_\star/J_{\rm dh}$. Since $m_{\star}$ and $j_{\star}$ are determined by many
star-formation related processes, measuring $j_\star$ and $m_\star$ at various
redshifts is essential to understand the formation history of disk galaxies. We
use the 3D-HST GOODS-S, COSMOS, and AEGIS imaging data and photo-$z$ catalog to
examine $j_\star$ and $m_\star$ for star-forming galaxies at $z \sim$ 2, 3, and
4, when disks are actively forming. We find that the $j_\star/m_\star$ ratio is
$\simeq 0.77\pm 0.06$ for all three redshifts over the entire mass range
examined, $8\times 10^{10} < M_{\rm dh}/h^{-1} M_\odot < 2\times 10^{12}$, with
a possible ($<30\%$) decrease with mass. This high ratio is close to those of
local disk galaxies, descendants of our galaxies in terms of $M_{\rm dh}$
growth, implying a nearly constant $j_\star/m_\star$ over past 12 Gyr. These
results are remarkable because mechanisms controlling angular momentum transfer
to disks such as inflows and feedbacks depend on both cosmic time and halo mass
and indeed theoretical studies tend to predict $j_\star/m_\star$ changing with
redshift and mass. It is found that recent theoretical galaxy formation
simulations predict smaller $j_{\star}/m_{\star}$ than our values. We also find
that a significant fraction of our galaxies appears to be unstable against bar
formation.
