Dynamical Characterization of Galaxies at z ∼ 4-6 via Tilted Ring Fitting to ALMA [C ii] Observations

Until recently, determining the rotational properties of galaxies in the early universe (z > 4, universe age <1.5 Gyr) was impractical, with the exception of a few strongly lensed systems. Combining the high resolution and sensitivity of ALMA at (sub-)millimeter wavelengths with the typically high strength of the [C II] 158 μm emission line from galaxies and long-developed dynamical modeling tools raises the possibility of characterizing the gas dynamics in both extreme starburst galaxies and normal star-forming disk galaxies at z ∼ 4-7. Using a procedure centered around GIPSY's ROTCUR task, we have fit tilted ring models to some of the best available ALMA [C II] data of a small set of galaxies: the MS galaxies HZ9 and HZ10, the damped Lyα absorber host galaxy ALMA J0817+1351, the submm galaxies AzTEC/C159 and COSMOS J1000+0234, and the quasar host galaxy ULAS J1319+0950. This procedure directly derives rotation curves and dynamical masses as functions of radius for each object. In one case, we present evidence for a dark matter halo of O(10¹¹)M_⊙. We present an analysis of the possible velocity dispersions of two sources based on matching simulated observations to the integrated [C II] line profiles. Finally, we test the effects of observation resolution and sensitivity on our results. While the conclusions remain limited at the resolution and signal-to-noise ratios of these observations, the results demonstrate the viability of the modeling tools at high redshift, and the exciting potential for detailed dynamical analysis of the earliest galaxies, as ALMA achieves full observational capabilities.