An Assessment of the In-Situ Growth of the Intracluster Light in the High Redshift Galaxy Cluster SpARCS1049+56

The formation of the stellar mass within galaxy cluster cores is a poorly understood process. It features the complicated physics of cooling flows, AGN feedback, star formation and more. Here, we study the growth of the stellar mass in the vicinity of the Brightest Cluster Galaxy (BCG) in a z = 1.7 cluster, SpARCS1049+56. We synthesize a reanalysis of existing HST imaging, a previously published measurement of the star formation rate, and the results of new radio molecular gas spectroscopy. These analyses represent the past, present and future star formation respectively within this system. We show that a large amount of stellar mass -- between $(2.2 \pm 0.5) \times 10^{10} \: M_\odot$ and $(6.6 \pm 1.2) \times 10^{10}\: M_\odot$ depending on the data processing -- exists in a long and clumpy tail-like structure that lies roughly 12 kpc off the BCG. Spatially coincident with this stellar mass is a similarly massive reservoir ($(1.0 \pm 0.7) \times 10^{11} \: M_\odot$) of molecular gas that we suggest is the fuel for the immense star formation rate of $860 \pm 130 \: M_\odot$/yr, as measured by infrared observations. Hlavacek-Larrondo et al. 2021 surmised that massive, runaway cooling of the hot intracluster X-ray gas was feeding this star formation, a process that had not been observed before at high-redshift. We conclude, based on the amount of fuel and current stars, that this event may be rare in the lifetime of a cluster, producing roughly 15 to 21% of the Intracluster Light (ICL) mass in one go, though perhaps a common event for all galaxy clusters.