Euclid: A blue galaxy population and a brightest cluster galaxy in the making in a $z\sim1.74$ MaDCoWS2 galaxy cluster candidate

Abstract: We present an example cluster follow-up study with Euclid. Our target, a $z\sim 1.74$ candidate cluster nicknamed the `Puddle', was initially discovered by the Massive and Distant Clusters of WISE Survey 2 (MaDCoWS2) as a $z_{phot}\sim 1.65$ candidate cluster. It was also detected independently as a $z_{phot}\sim 1.5$ candidate with both cluster-finding algorithms in Euclid Quick Release 1 (Q1). A Keck MOSFIRE spectrum shows the brightest nucleus is at $z=1.74$ and is AGN-dominated. We focus our analysis on the galaxy population and the Brightest Cluster Galaxy (BCG), using a combination of Euclid and ancillary photometry. Compared to similar fields, we measure an overdensity of $110\pm 14$ galaxies with $H_\mathrm{E}\leq 22.25$ in a 2' radius around the BCG. We estimate that $18\pm 4$% of the completeness-corrected galaxy population is red, which is consistent with some clusters at $z>1.5$ but lower than others. \textit{Euclid} imaging reveals that six or seven galaxies appear to be assembling to form the future BCG. Spectral energy distribution (SED) fitting suggests that the merging BCG has a stellar mass of $5.7\pm 0.3\times 10^{11}\,M_\odot$ and experienced a short burst of star formation about $300\,$Myr ago. Its morphology, stellar mass, and star-formation history suggest that the proto-BCG is a more evolved version of the merging core of SPT2349$-$56. These systems indicate that multiobject mergers might be a common BCG formation process. Assuming a similar density of mergers in the Euclid Wide Survey, we expect that Euclid will discover approximately 400 assembling BCGs by the end of its mission.