  Until recently, determining the rotational properties of galaxies in the
early universe (z>4, Universe age <1.5Gyr) 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 [CII] 158um 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 [CII] data of a small set of
galaxies: the MS galaxies HZ9 & HZ10, the Damped Lyman-alpha Absorber (DLA)
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(10^11)
solar masses. We present an analysis of the possible velocity dispersions of
AzTEC/C159 and ULAS J1319+0950 based on matching simulated observations to the
integrated [CII] 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.
