The average SB as a function of the SB variance within a radius of 2 arcsec in the |$-500$| to |$+500\ \mathrm{km\ s^{-1}}$| range for the |$z\sim 6$| sample. Objects with Ly|$\alpha$| halo detection are shown as blue circles, non-detections based on SNR are shown as light blue triangles, and those removed through visual inspection are shown as orange circles. The black line represents the 3|$\sigma$| detection threshold.