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We present a morphological study of the 17 lensed Lyman-$\alpha$ emitter(LAE) galaxies of the Baryon Oscillation Spectroscopic Survey Emission-LineLens Survey (BELLS) for the GALaxy-Ly$\alpha$ EmitteR sYstems (BELLS GALLERY)sample. This analysis combines the magnification effect of strong galaxy-galaxylensing with the high resolution of the Hubble Space Telescope ($HST$) toachieve a physical resolution of $\sim$80 pc for this $2<z<3$ LAE sample,allowing a detailed characterization of the LAE rest-frame ultravioletcontinuum surface brightness profiles and substructure. We use lens-modelreconstructions of the LAEs to identify and model individual clumps, which wesubsequently use to constrain the parameters of a generative statistical modelof the LAE population. Since the BELLS GALLERY sample is selected primarily onthe basis of Lyman-$\alpha$ emission, the LAEs that we study here are likely tobe directly comparable to those selected in wide-field narrow-band LAE surveys,in contrast with the lensed LAEs identified in cluster lensing fields. We findan LAE clumpiness fraction of approximately 88%, significantly higher thanfound in previous (non-lensing) studies. We find a well-resolved characteristicclump half-light radii of $\sim$350 pc, a scale comparable to the largest H IIregions seen in the local universe. This statistical characterization of LAEsurface-brightness profiles will be incorporated into future lensing analysesusing the BELLS GALLERY sample to constrain the incidence of dark-mattersubstructure in the foreground lensing galaxies.

The BOSS Emission-Line Lens Survey V. Morphology and Substructure of Lensed Lyman-$\alpha$ Emitters at redshift $z\approx2.5$ in the BELLS GALLERY