Imaging Molecular Gas at High Redshift
  We perform simulations of the capabilities of the next generation Very Large
Array in the context of imaging low order CO emission from typical high
redshift star forming galaxies at ~ 1 kpc resolution. We adopt as a spatial and
dynamical template the CO 1-0 emission from M 51, scaled accordingly for
redshift, transition, and total gas mass. The molecular gas masses investigated
are factors of 1.4, 3.5, and 12.5 larger that of M 51, at z = 0.5, 2, and 4.2,
respectively. The z = 2 galaxy gas mass is comparable to the lowest mass
galaxies currently being discovered in the deepest ALMA and NOEMA cosmological
CO line surveys, corresponding to galaxies with star formation rates ~ 10 to
100 $M_\odot$ yr$^{-1}$. The ngVLA will perform quality imaging at 1kpc
resolution of the gas distribution and dynamics over this disk. We recover the
overall rotation curve, galaxy orientation properties, and molecular ISM
internal velocity dispersion. The model at z = 4.2 corresponds to a massive
star forming main sequence disk (SFR ~ 130 $M_\odot$ yr$^{-1}$). The ngVLA can
obtain 1kpc resolution images of such a system in a reasonable integration
time, and recover the basic galaxy orientation parameters, and, asymptotically,
the maximum rotation velocity. We compare the ngVLA results with capabilities
of ALMA and the Jansky VLA. ALMA and the VLA can detect the integrated low
order CO emission from these galaxies, but lack the sensitivity to perform the
high resolution imaging to recover the dynamics at 1kpc scales. To do so would
require of order 1000 hrs per galaxy with these current facilities. We
investigate a 'minimal' ngVLA configuration, removing the longest baselines and
much of the very compact core, and find good imaging can still be performed at
1 kpc resolution.
