Ly$alpha$ nebulae are giant ($sim$100 kpc), glowing gas clouds in the distant universe. The origin of their extended Ly$alpha$ emission remains a mystery. Some models posit that Ly$alpha$ emission is produced when the cloud is photoionized by UV emission from embedded or nearby sources, while others suggest that the Ly$alpha$ photons originate from an embedded galaxy or AGN and are then resonantly scattered by the cloud. At least in the latter scenario, the observed Ly$alpha$ emission will be polarized. To test these possibilities, we are conducting imaging polarimetric observations of seven Ly$alpha$ nebulae. Here we present our results for LABd05, a cloud at $z$ = 2.656 with an obscured, embedded AGN to the northeast of the peak of Ly$alpha$ emission. We detect significant polarization. The highest polarization fractions $P$ are $sim$10-20% at $sim$20-40 kpc southeast of the Ly$alpha$ peak, away from the AGN. The lowest $P$, including upper-limits, are $sim$5% and lie between the Ly$alpha$ peak and AGN. In other words, the polarization map is lopsided, with $P$ increasing from the Ly$alpha$ peak to the southeast. The measured polarization angles $theta$ are oriented northeast, roughly perpendicular to the $P$ gradient. This unique polarization pattern suggests that 1) the spatially-offset AGN is photoionizing nearby gas and 2) escaping Ly$alpha$ photons are scattered by the nebula at larger radii and into our sightline, producing tangentially-oriented, radially-increasing polarization away from the photoionized region. Finally we conclude that the interplay between the gas density and ionization profiles produces the observed central peak in the Ly$alpha$ emission. This also implies that the structure of LABd05 is more complex than assumed by current theoretical spherical or cylindrical models.
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