The BOSS Emission-Line Lens Survey V. Morphology and Substructure of
  Lensed Lyman-$\alpha$ Emitters at redshift $z\approx2.5$ in the BELLS GALLERY
  We present a morphological study of the 17 lensed Lyman-$\alpha$ emitter
(LAE) galaxies of the Baryon Oscillation Spectroscopic Survey Emission-Line
Lens Survey (BELLS) for the GALaxy-Ly$\alpha$ EmitteR sYstems (BELLS GALLERY)
sample. This analysis combines the magnification effect of strong galaxy-galaxy
lensing with the high resolution of the Hubble Space Telescope ($HST$) to
achieve a physical resolution of $\sim$80 pc for this $2<z<3$ LAE sample,
allowing a detailed characterization of the LAE rest-frame ultraviolet
continuum surface brightness profiles and substructure. We use lens-model
reconstructions of the LAEs to identify and model individual clumps, which we
subsequently use to constrain the parameters of a generative statistical model
of the LAE population. Since the BELLS GALLERY sample is selected primarily on
the basis of Lyman-$\alpha$ emission, the LAEs that we study here are likely to
be directly comparable to those selected in wide-field narrow-band LAE surveys,
in contrast with the lensed LAEs identified in cluster lensing fields. We find
an LAE clumpiness fraction of approximately 88%, significantly higher than
found in previous (non-lensing) studies. We find a well-resolved characteristic
clump half-light radii of $\sim$350 pc, a scale comparable to the largest H II
regions seen in the local universe. This statistical characterization of LAE
surface-brightness profiles will be incorporated into future lensing analyses
using the BELLS GALLERY sample to constrain the incidence of dark-matter
substructure in the foreground lensing galaxies.
