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.