Angular momentum of $z\sim 1.5$ galaxies and their local analogues with adaptive optics

We present stellar specific angular momentum $j_*$ measurements of two $z\sim 1.5$ galaxies in the KGES sample and 12 DYNAMO $z\sim 0.1$ analogues of high-redshift galaxies. We combine natural seeing integral field spectroscopic data to trace line emission out to high multiples of effective radius $r_e$, with adaptive optics assisted Keck/OSIRIS observations to trace the rapid rise in rotation curve in the inner regions. Our spaxel-wise integration method gives results that are on average within measurement uncertainty of the traditional rotation curve model method. At $z\sim 0$, combining GMOS and OSIRIS datasets improves the measurement uncertainty in $j_*$ from 13\% (GMOS only) or 16\% (OSIRIS only) to 10\%. At $z\sim 1.5$, systematics allow for at best 20\% uncertainty on $j_*$. DYNAMO analogues of high-$z$ galaxies have low $j_*$ for their stellar mass $M_*$, and low bulge-to-total light ratio $\beta$ for their $j_*/M_*$. The high-$z$ galaxy COSMOS 127977 has $j_*/M_*$ consistent with normal local disk galaxies, while UDS 78317 is consistent with local analogues. However, our high-resolution OSIRIS data reveal that UDS 78317 may be a merging system. We report a relationship between distance to the $\beta-j_*/M_*$ plane and the ratio of velocity dispersion to rotational velocity $\sigma/v_{max}$, where galaxies that deviate more from the plane are more dispersion-dominated due to turbulence. Much of the scatter in $M_*-j_*$ that is not explained by variations in the bulge-to-total ratio or evolution with redshift may be driven by increased turbulence due to star formation, or by treating mergers as rotating disks.