First Constraints on the ISM Conditions of a Low Mass, Highly Obscured z=4.27 Main Sequence Galaxy

We present the molecular gas content and ISM conditions of MACSJ0717 Az9, a strong gravitationally lensed $z=4.273$, $M_{*} \simeq 2\times10^9M_{\odot}$ star-forming galaxy with an unusually high ($\sim 80\%$) obscured star formation fraction. We detect CO(4-3) in two independent lensed images, as well as [N II]205$\mu$m, with ALMA. We derive a molecular gas mass of log$_{10}[M_{H_{2}} (M_{\odot})] = 9.77$ making it moderately deficient in molecular gas compared to the lower redshift gas fraction scaling relation. Leveraging photodissociation region (PDR) models, we combine our CO(4-3) measurements with existing measurements of the [C II] 158$\mu$m line and total infrared luminosity to model the PDR conditions. We find PDR conditions similar to local star-forming galaxies, with a mean hydrogen density log$_{10}$[$n_H$ $cm^{-3}$] = $4.80\pm0.39$ and a mean radiation field strength log$_{10}$[G$_0$ Habing] = $2.83\pm0.26$. Based on Band 3 continuum data, we derive an upper limit on the intrinsic dust mass of log$_{10}[M_{\rm dust} (M_{\odot})] < 7.73$, consistent with existing estimates. We use the 3D tilted-ring model fitting code 3D-Barolo to determine the kinematic properties of the CO(4-3) emitting gas. We find that it is rotationally dominated, with a $V/\sigma=4.6 \pm 1.7$, consistent with the kinematics of the [C II]. With PDR conditions remarkably similar to normal dusty star-forming galaxies at z ~ 0.2 and a stable molecular disk, our observations of Az9 suggest that the dust-obscured phase for a low-mass galaxy at z$\sim$4 is relatively long. Thus, Az9 may be representative of a more widespread population that has been missed due to insufficiently deep existing millimeter surveys.