Massive molecular gas reservoir in a luminous sub-millimeter galaxy during cosmic noon

We present multi-band observations of an extremely dusty star-forming lensed galaxy (HERS1) at $z=2.553$. High-resolution maps of \textit{HST}/WFC3, SMA, and ALMA show a partial Einstein-ring with a radius of $\sim$3$^{\prime\prime}$. The deeper HST observations also show the presence of a lensing arc feature associated with a second lens source, identified to be at the same redshift as the bright arc based on a detection of the [NII] 205$\mu$m emission line with ALMA. A detailed model of the lensing system is constructed using the high-resolution HST/WFC3 image, which allows us to study the source plane properties and connect rest-frame optical emission with properties of the galaxy as seen in sub-millimeter and millimeter wavelengths. Corrected for lensing magnification, the spectral energy distribution fitting results yield an intrinsic star formation rate of about $1000\pm260$ ${\rm M_{\odot}}$yr$^{-1}$, a stellar mass ${\rm M_*}=4.3^{+2.2}_{-1.0}\times10^{11} {\rm M_{\odot}}$, and a dust temperature ${\rm T}_{\rm d}=35^{+2}_{-1}$ K. The intrinsic CO emission line ($J_{\rm up}=3,4,5,6,7,9$) flux densities and CO spectral line energy distribution are derived based on the velocity-dependent magnification factors. We apply a radiative transfer model using the large velocity gradient method with two excitation components to study the gas properties. The low-excitation component has a gas density $n_{\rm H_2}=10^{3.1\pm0.6}$ cm$^{-3}$ and kinetic temperature ${\rm T}_{\rm k}=19^{+7}_{-5}$ K and a high-excitation component has $n_{\rm H_2}=10^{2.8\pm0.3}$ cm$^{-3}$ and ${\rm T}_{\rm k}=550^{+260}_{-220}$ K. Additionally, HERS1 has a gas fraction of about $0.4\pm0.2$ and is expected to last 250 Myr. These properties offer a detailed view of a typical sub-millimeter galaxy during the peak epoch of star-formation activity.