A Mixture of LBG Overdensities in the Fields of Three $6 < z < 7$ Quasars: Implications for the Robustness of Photometric Selection

The most luminous quasars at $z > 6$ are suspected to be both highly clustered and reside in the most massive dark matter halos in the early Universe, making them prime targets to search for galaxy overdensities and/or protoclusters. We search for Lyman-break dropout-selected galaxies using HST WFC3/ACS broadband imaging in the fields of three $6 < z < 7$ quasars, as well as their simultaneously observed coordinated-parallel fields, and constrain their photometric redshifts using EAZY. One field, J0305-3150, shows a volume density 10$\times$ higher than the blank-field UV luminosity function (UVLF) at M$_{UV} < -20$, with tentative evidence of a 3$\sigma$ overdensity in its parallel field located 15 cMpc away. Another field, J2054-0005, shows an angular overdensity within 500 ckpc from the quasar but still consistent with UVLF predictions within 3$\sigma$, while the last field, J2348-3054, shows no enhancement. We discuss methods for reducing uncertainty in overdensity measurements when using photometric selection and show that we can robustly select LBGs consistent with being physically associated with the quasar, corroborated by existing JWST/NIRCam WFSS data in the J0305 field. Even accounting for incompleteness, the overdensities in J0305 and J2054 are higher for brighter galaxies at short angular separations, suggesting preferential enhancement of more massive galaxies in the immediate vicinity of the quasar. Finally, we compare the LBG population with previously-identified [CII] and mm-continuum companions; the LBG overdensities are not accompanied by an enhanced number of dusty galaxies, suggesting that the overdense quasar fields are not in the bursty star-forming phase sometimes seen in high-redshift protoclusters.