2018ApJ...854...22O

The stellar disk size of a galaxy depends on the ratio of the disk stellar mass to the halo mass, m_* ≡ M_*/M_dh, and the fraction of the dark halo angular momentum transferred to the stellar disk, j_* ≡ J_*/J_dh. Since m_* and j_* are determined by many star formation-related processes, measuring j_* and m_* at various redshifts is essential to understanding 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_* and m_* for star-forming galaxies at z ∼ 2-4, when disks are actively forming. We find that the j_*/m_* ratio is ≃0.77 ± 0.06 for all three redshifts over the entire mass range examined, 8 x 10¹⁰ < M_dh/h^–1 M_☉ < 2 x 10¹², 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_dh growth, implying a nearly constant j_*/m_* over the past 12 Gyr. These results are remarkable because mechanisms controlling angular momentum transfer to disks such as inflows and feedback depend on both cosmic time and halo mass, and, indeed, theoretical studies tend to predict j_*/m_* changing with redshift and mass. It is found that some of the recent theoretical galaxy formation simulations predict a smaller j_*/m_* than our values. We also find that a significant fraction of our galaxies appears to be unstable against bar formation.