  We present deep Hubble Space Telescope (HST) photometry of ten targets from
Treasury Program GO-14734, including six confirmed ultra-faint dwarf galaxies
(UFDs), three UFD candidates, and one likely globular cluster. Six of these
targets are satellites of, or have interacted with, the Large Magellanic Cloud
(LMC). We determine their structural parameters using a maximum-likelihood
technique. Using our newly derived half-light radius ($r_h$) and $V$-band
magnitude ($M_V$) values in addition to literature values for other UFDs, we
find that UFDs associated with the LMC do not show any systematic differences
from Milky Way UFDs in the magnitude-size plane. Additionally, we convert
simulated UFD properties from the literature into the $M_V-r_h$ observational
space to examine the abilities of current dark matter (DM) and baryonic
simulations to reproduce observed UFDs. Some of these simulations adopt
alternative DM models, thus allowing us to also explore whether the $M_V-r_h$
plane could be used to constrain the nature of DM. We find no differences in
the magnitude-size plane between UFDs simulated with cold, warm, and
self-interacting dark matter, but note that the sample of UFDs simulated with
alternative DM models is quite limited at present. As more deep, wide-field
survey data become available, we will have further opportunities to discover
and characterize these ultra-faint stellar systems and the greater low
surface-brightness universe.
