Deep $z$-band observations of the coolest Y dwarf

WISE J085510.83-071442.5 (hereafter, WISE 0855-07) is the coolest Y dwarf known to date and is located at a distance of 2.31$\pm 0.08$ pc, giving it the fourth largest parallax of any known star or brown dwarf system. We report deep $z$-band observations of WISE 0855-07 using FORS2 on UT1/VLT. We do not detect any counterpart to WISE 0855-07 in our $z$-band images and estimate a brightness upper limit of AB mag $>$ 24.8 ($F_{\nu}$ $<$ 0.45 $\mu$Jy) at 910 $\pm$ 65 nm with $3\sigma$-confidence. We combine our z-band upper limit with previous near- and mid-infrared photometry to place constraints on the atmospheric properties of WISE 0855-07 via comparison to models which implement water clouds in the atmospheres of $T_{eff} < 300$ K substellar objects. We find that none of the available models that implement water clouds can completely reproduce the observed SED of WISE 0855-07. Every model significantly disagrees with the (3.6 $\mu$m / 4.5 $\mu$m) flux ratio and at least one other bandpass. Since methane is predicted to be the dominant absorber at 3-4 $\mu$m, these mismatches might point to an incorrect or incomplete treatment of methane in current models. We conclude that \mbox{(a) WISE0855-07} has $T_{eff} \sim 200-250$~K, (b) $< 80 \%$ of its surface is covered by clouds, and (c) deeper observations, and improved models of substellar evolution, atmospheres, clouds, and opacities will be necessary to better characterize this object.