We present detailed studies of a z = 2.12 submillimeter galaxy,
ALESS67.1, using sub-arcsecond resolution ALMA, adaptive optics-aided
VLT/SINFONI, and Hubble Space Telescope (HST)/CANDELS data to
investigate the kinematics and spatial distributions of dust emission
(870 μm continuum), 12CO(J = 3-2), strong optical
emission lines, and visible stars. Dynamical modeling of the optical
emission lines suggests that ALESS67.1 is not a pure rotating disk but a
merger, consistent with the apparent tidal features revealed in the HST
imaging. Our sub-arcsecond resolution data set allows us to measure
half-light radii for all the tracers, and we find a factor of 4-6
smaller sizes in dust continuum compared to all the other tracers,
including 12CO; also, ultraviolet (UV) and Hα emission
are significantly offset from the dust continuum. The spatial mismatch
between the UV continuum and the cold dust and gas reservoir supports
the explanation that geometrical effects are responsible for the offset
of the dusty galaxy on the IRX-β diagram. Using a dynamical
method we derive an {α }CO}=1.8+/- 1.0, consistent with
other submillimeter galaxies (SMGs) that also have resolved CO and dust
measurements. Assuming a single {α }CO} value we also
derive resolved gas and star formation rate surface densities, and find
that the core region of the galaxy (≲ 5 kpc) follows the trend of
mergers on the Schmidt-Kennicutt relationship, whereas the
outskirts (≳ 5 kpc) lie on the locus of normal star-forming
galaxies, suggesting different star formation efficiencies within one
galaxy. Our results caution against using single size or morphology for
different tracers of the star formation activity and gas content of
galaxies, and therefore argue the need to use spatially resolved,
multi-wavelength observations to interpret the properties of SMGs, and
perhaps even for z> 1 galaxies in general.