Large-scale structure of Lyman break galaxies around a radio galaxy protocluster at z$\mathsf{\sim 4}$

We present broad-band imaging with the Subaru Telescope of a $25'$$\times$$25'$field surrounding the radio galaxy TN J1338–1942 at redshift $z = 4.1$. The field contains excesses of Lyman-αemitters (LAEs) and Lyman break galaxies (LBGs) identified with a protocluster surrounding the radio galaxy. Our new wide-field images provide information about the boundary of the protocluster and its surroundings. There are 874 candidate LBGs within our field, having redshifts in the range $z = 3.5{-}4.5$. An examination of the brightest of these (with $i' < 25.0$) shows that the most prominent concentration coincides with the previously discovered protocluster. The diameter of this galaxy overdensity corresponds to ~2 Mpc at $z = 4$, consistent with the previous estimation using LAEs. Several other concentrations of LBGs are observed in the field, some of which may well be physically connected with the $z = 4.1$protocluster. The observed structure in the smoothed LBG distribution can be explained as the projection of large-scale structure, within the redshift range $z = 3.5{-}4.5$, comprising compact overdensities and prominent larger voids. If the $5{-}8$observed compact overdensities are associated with protoclusters, the observed protocluster volume density is ~5 $\times$10-6Mpc-3, similar to the volume density of rich clusters in the local Universe.