ALMA resolves the first strongly-lensed Optical/NIR-dark galaxy

We present high-resolution ($\lesssim0.1$arcsec) ALMA observations of the strongly-lensed galaxy HATLASJ113526.2-01460 at redshift $z\sim3.1$ discovered in the Gama 12$^{\rm th}$ field of the Herschel-ATLAS survey. The gravitationally lensed system is remarkably peculiar in that neither the background source nor the foreground lens show a clearly detected optical/NIR emission. We perform accurate lens modeling and source morphology reconstruction in three different (sub-)mm continuum bands, and in the C[II] and CO(8-7) spectral lines. The modeling indicates a foreground lensing (likely elliptical) galaxy with mass $\gtrsim10^{11}\, M_\odot$ at $z\gtrsim1.5$, while the source (sub-)mm continuum and line emissions are amplified by factors $\mu\sim6-13$. We estimate extremely compact sizes $\lesssim0.5$ kpc for the star-forming region and $\lesssim 1$ kpc for the gas component, with no clear evidence of rotation or of ongoing merging events. We perform broadband SED-fitting and retrieve the intrinsic de-magnified physical properties of the source, which is found to feature a very high star-formation rate $\gtrsim10^3\, M_\odot$ yr$^{-1}$, that given the compact sizes is on the verge of the Eddington limit for starbursts; the radio luminosity at 6 cm from available EVLA observations is consistent with the star-formation activity. The galaxy is found to be extremely rich in gas $\sim10^{11}\, M_\odot$ and dust $\gtrsim10^9\, M_\odot$. The stellar content $\lesssim10^{11}\, M_\odot$ places the source well above the main sequence of starforming galaxies, indicating that the starburst is rather young with estimated age $\sim10^8$ yr. Our results indicate that the overall properties of HATLASJ113526.2-01460 are consistently explained by in-situ galaxy formation and evolution scenarios.