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We present detailed studies of a $z=2.12$ submillimeter galaxy, ALESS67.1,using sub-arcsecond resolution ALMA, AO-aided VLT/SINFONI, and HST/CANDELS datato investigate the kinematics and spatial distributions of dust emission (870$\mu$m continuum), $^{12}$CO($J$=3-2), strong optical emission lines, andvisible stars. Dynamical modelling of the optical emission lines suggests thatALESS67.1 is not a pure rotating disk but a merger, consistent with theapparent tidal features revealed in the HST imaging. Our sub-arcsecondresolution dataset allow 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 theother tracers, including $^{12}$CO, and UV and H$\alpha$ emission issignificantly offset from the dust continuum. The spatial mismatch between UVcontinuum and the cold dust and gas reservoir supports the explanation thatgeometrical effects are responsible for the offset of dusty galaxy on theIRX-$\beta$ diagram. Using a dynamical method we derive an $\alpha_{\rmCO}=1.8\pm1.0$, consistent with other SMGs that also have resolved CO and dustmeasurements. Assuming a single $\alpha_{\rm CO}$ value we also derive resolvedgas and star-formation rate surface densities, and find that the core region ofthe galaxy ($\lesssim5$ kpc) follows the trend of mergers on theSchmidt-Kennicutt relationship, whereas the outskirts ($\gtrsim5$ kpc) lie onthe locus of normal star-forming galaxies, suggesting different star-formationefficiencies within one galaxy. Our results caution against using single sizeor morphology for different tracers of the star-formation activity and gascontent of galaxies, and therefore argue the need to use spatially-resolved,multi-wavelength observations to interpret the properties of SMGs, and perhapseven for $z>1$ galaxies in general.

A spatially resolved study of cold dust, molecular gas, HII regions, and stars in the $z=2.12$ submillimeter galaxy ALESS67.1