  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.
