Towards Studying Hierarchical Assembly in Real Time: A Milky Way Progenitor Galaxy at z = 2.36 under the Microscope

We use Hubble Space Telescope (HST) imaging and near-infrared spectroscopy from Keck/MOSFIRE to study the sub-structure around the progenitor of a Milky Way-mass galaxy in the Hubble Frontier Fields (HFF). Specifically, we study an $r_e = 40^{+70}_{-30}$pc, $M_{\star} \sim 10^{8.2} M_{\odot}$ rest-frame ultra-violet luminous "clump" at a projected distance of $\sim$100~pc from a $M_{\star} \sim 10^{9.8}$M$_{\odot}$ galaxy at $z = 2.36$ with a magnification $\mu = 5.21$. We measure the star formation history of the clump and galaxy by jointly modeling the broadband spectral energy distribution from HST photometry and H$\alpha$ from MOSFIRE spectroscopy. Given our inferred properties (e.g., mass, metallicity, dust) of the clump and galaxy, we explore scenarios in which the clump formed \emph{in-situ} (e.g., a star forming complex) or \emph{ex-situ} (e.g., a dwarf galaxy being accreted). If it formed \emph{in-situ}, we conclude that the clump is likely a single entity as opposed to a aggregation of smaller star clusters, making it one of the most dense star clusters cataloged. If it formed \emph{ex-situ}, then we are witnessing an accretion event with a 1:40 stellar mass ratio. However, our data alone are not informative enough to distinguish between \emph{in-situ} and \emph{ex-situ} scenarios to a high level of significance. We posit that the addition of high-fidelity metallicity information, such as [OIII]4363A, which can be detected at modest S/N with only a few hours of JWST/NIRSpec time, may be a powerful discriminant. We suggest that studying larger samples of moderately lensed sub-structures across cosmic time can provide unique insight into the hierarchical formation of galaxies like the Milky Way.