Discovery of a Proto-cluster Associated with a Ly-$\alpha$ Blob Pair at z=2.3

Bright Ly-$\alpha$ blobs (LABs) --- extended nebulae with sizes of $\sim$100kpc and Ly-$\alpha$ luminosities of $\sim$10$^{44}$erg s$^{-1}$ --- often reside in overdensities of compact Ly-$\alpha$ emitters (LAEs) that may be galaxy protoclusters. The number density, variance, and internal kinematics of LABs suggest that they themselves trace group-like halos. Here we test this hierarchical picture, presenting deep, wide-field Ly-$\alpha$ narrowband imaging of a 1$^\circ$ $\times$ 0.5$^\circ$ region around a LAB pair at $z$ = 2.3 discovered previously by a blind survey. We find 183 Ly-$\alpha$ emitters, including the original LAB pair and three new LABs with Ly-$\alpha$ luminosities of (0.9--1.3)$\times$10$^{43}$erg s$^{-1}$ and isophotal areas of 16--24 arcsec$^2$. Using the LAEs as tracers and a new kernel density estimation method, we discover a large-scale overdensity (Bo{\"o}tes J1430+3522) with a surface density contrast of $\delta_{\Sigma}$ = 2.7, a volume density contrast of $\delta$ $\sim$ 10.4, and a projected diameter of $\approx$ 20 comoving Mpc. Comparing with cosmological simulations, we conclude that this LAE overdensity will evolve into a present-day Coma-like cluster with $\log{(M/M_\odot)}$ $\sim$ $15.1\pm0.2$. In this and three other wide-field LAE surveys re-analyzed here, the extents and peak amplitudes of the largest LAE overdensities are similar, not increasing with survey size, implying that they were indeed the largest structures then and do evolve into rich clusters today. Intriguingly, LABs favor the outskirts of the densest LAE concentrations, i.e., intermediate LAE overdensities of $\delta_\Sigma = 1 - 2$. We speculate that these LABs mark infalling proto-groups being accreted by the more massive protocluster.