Resolved Spectroscopy of Gravitationally-Lensed Galaxies: Recovering
  Coherent Velocity Fields in Sub-Luminous z~2-3 Galaxies
  We present spatially-resolved dynamics for six strongly lensed star-forming
galaxies at z=1.7-3.1, each enlarged by a linear magnification factor ~8. Using
the Keck laser guide star AO system and the OSIRIS integral field unit
spectrograph we resolve kinematic and morphological detail in our sample with
an unprecedented fidelity, in some cases achieving spatial resolutions of ~100
pc. With one exception our sources have diameters ranging from 1-7 kpc, star
formation rates of 2-40 Msun/yr (uncorrected for extinction) and dynamical
masses of 10^(9.7-10.3) Msun. With this exquisite resolution we find that four
of the six galaxies display coherent velocity fields consistent with a simple
rotating disk model, which can only be recovered with the considerably improved
spatial resolution and sampling from the combination of adaptive optics and
strong gravitational lensing. Our model fits imply ratios for the systemic to
random motion, V sin(i)/sigma, ranging from 0.5-1.3 and Toomre disk parameters
Q<1. The large fraction of well-ordered velocity fields in our sample is
consistent with data analyzed for larger, more luminous sources at this
redshift. Our high resolution data further reveal that all six galaxies contain
multiple giant star-forming HII regions whose resolved diameters are in the
range 300 pc - 1.0 kpc, consistent with the Jeans length expected in the case
of dispersion support. The density of star formation in these regions is ~100
times higher than observed in local spirals; such high values are only seen in
the most luminous local starbursts. The global dynamics and demographics of
star formation in these HII regions suggest that vigorous star formation is
primarily governed by gravitational instability in primitive rotating disks.
