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We report on VLT/FORS2 imaging polarimetry observations in the $R_{\rmspecial}$ band of WISE J011601.41-050504.0 (W0116-0505), a heavily obscuredhyper-luminous quasar at $z=3.173$ classified as a Hot, Dust-Obscured Galaxy(Hot DOG) based on its mid-IR colors. Recently, Assef et al. (2020) identifiedW0116-0505 as having excess rest-frame optical/UV emission, and concluded thisexcess emission is most likely scattered light from the heavily obscured AGN.We find that the broad-band rest-frame UV flux is strongly linearly polarized(10.8$\pm$1.9\%, with a polarization angle of 74$\pm$9~deg), confirming thisconclusion. We analyze these observations in the context of a simple modelbased on scattering either by free electrons or by optically thin dust,assuming a classical dust torus with polar openings. Both can replicate thedegree of polarization and the luminosity of the scattered component for arange of geometries and column densities, but we argue that optically thin dustin the ISM is the more likely scenario. We also explore the possibility thatthe scattering medium corresponds to an outflow recently identified forW0116-0505. This is a feasible option if the outflow component is bi-conicalwith most of the scattering occurring at the base of the receding outflow. Inthis scenario the quasar would still be obscured even if viewed face on, butmight appear as a reddened type 1 quasar once the outflow has expanded. Wediscuss a possible connection between blue-excess Hot DOGs, extremely redquasars (ERQs), reddened type 1 quasars, and unreddened quasars that depends ona combination of evolution and viewing geometry.

Imaging Polarization of the Blue-Excess Hot Dust-Obscured Galaxy WISE J011601.41-050504.0