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The ultra-faint dwarf galaxy Hercules has an extremely elongated morphologywith both photometric overdensities and kinematic members at large radii,suggesting that it may be tidally disrupting due to a previous close encounterwith the Milky Way. To explain its observational peculiarities, we present adeep Hubble Space Telescope (HST) imaging study of Hercules and its surroundingregions and investigate its tidal history through a careful search for adistance gradient along its stretched body. Our off-center HST data clearlyresolve a main sequence, showing that the stellar extension seen along themajor-axis of Hercules is genuine, not a clump of background galaxies.Utilizing Gaia DR2 data, we clean the region around Hercules of fieldcontamination, and find four new plausible member stars, all of which arelocated at the outskirts of the dwarf galaxy. We update the distance toHercules, 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 noconclusive evidence for a distance gradient, our work demonstrates thatconstraining a distance gradient in such a faint system is not trivial, and thepossible thickness of the dwarf along the line of sight and field contaminationmake it harder to make decisive conclusions even with these high-precisiondata. Future studies coupled with tailored theoretical models are needed tounderstand the true nature of Hercules and of tidal distortion observables inultra-faint galaxies in general.

The Elusive Distance Gradient in the Ultra-Faint Dwarf Galaxy Hercules: A Combined Hubble Space Telescope and Gaia View