The Bright and Dark Sides of High-Redshift starburst galaxies from {it Herschel} and {it Subaru} observations

We present rest-frame optical spectra from the FMOS-COSMOS survey of twelve $z \sim 1.6$ \textit{Herschel} starburst galaxies, with Star Formation Rate (SFR) elevated by $\times$8, on average, above the star-forming Main Sequence (MS). Comparing the H$\alpha$ to IR luminosity ratio and the Balmer Decrement we find that the optically-thin regions of the sources contain on average only $\sim 10$ percent of the total SFR whereas $\sim90$ percent comes from an extremely obscured component which is revealed only by far-IR observations and is optically-thick even in H$\alpha$. We measure the [NII]$_{6583}$/H$\alpha$ ratio, suggesting that the less obscured regions have a metal content similar to that of the MS population at the same stellar masses and redshifts. However, our objects appear to be metal-rich outliers from the metallicity-SFR anticorrelation observed at fixed stellar mass for the MS population. The [SII]$_{6732}$/[SII]$_{6717}$ ratio from the average spectrum indicates an electron density $n_{\rm e} \sim 1,100\ \mathrm{cm}^{-3}$, larger than what estimated for MS galaxies but only at the 1.5$\sigma$ level. Our results provide supporting evidence that high-$z$ MS outliers are the analogous of local ULIRGs, and are consistent with a major merger origin for the starburst event.