The Elusive Distance Gradient in the Ultra-Faint Dwarf Galaxy Hercules:
  A Combined Hubble Space Telescope and Gaia View
  The ultra-faint dwarf galaxy Hercules has an extremely elongated morphology
with both photometric overdensities and kinematic members at large radii,
suggesting that it may be tidally disrupting due to a previous close encounter
with the Milky Way. To explain its observational peculiarities, we present a
deep Hubble Space Telescope (HST) imaging study of Hercules and its surrounding
regions and investigate its tidal history through a careful search for a
distance gradient along its stretched body. Our off-center HST data clearly
resolve a main sequence, showing that the stellar extension seen along the
major-axis of Hercules is genuine, not a clump of background galaxies.
Utilizing Gaia DR2 data, we clean the region around Hercules of field
contamination, and find four new plausible member stars, all of which are
located at the outskirts of the dwarf galaxy. We update the distance to
Hercules, and find $130.6\pm1.2$ kpc ($m-M=20.58\pm0.02$) for the main body,
which is consistent with earlier estimates in the literature. While we find no
conclusive evidence for a distance gradient, our work demonstrates that
constraining a distance gradient in such a faint system is not trivial, and the
possible thickness of the dwarf along the line of sight and field contamination
make it harder to make decisive conclusions even with these high-precision
data. Future studies coupled with tailored theoretical models are needed to
understand the true nature of Hercules and of tidal distortion observables in
ultra-faint galaxies in general.
