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We present deep Hubble Space Telescope (HST) photometry of the ultra-faintdwarf galaxy Eridanus II (Eri II). Eri II, which has an absolute magnitude ofM_V = -7.1, is located at a distance of 339 kpc, just beyond the virial radiusof the Milky Way. We determine the star formation history of Eri II and measurethe structure of the galaxy and its star cluster. We find that a star formationhistory consisting of two bursts, constrained to match the spectroscopicmetallicity distribution of the galaxy, accurately describes the Eri II stellarpopulation. The best-fit model implies a rapid truncation of star formation atearly times, with >80% of the stellar mass in place before z~6. A smallfraction of the stars could be as young as 8 Gyr, but this population is notstatistically significant; Monte Carlo simulations recover a component youngerthan 9 Gyr only 15% of the time, where they represent an average of 7 +/- 4% ofthe population. These results are consistent with theoretical expectations forquenching by reionization. The HST depth and angular resolution enable us toshow that Eri II's cluster is offset from the center of the galaxy by aprojected distance of 23 +/- 3 pc. This offset could be an indication of asmall (~50-75 pc) dark matter core in Eri II. Moreover, we demonstrate that thecluster has a high ellipticity of 0.31 +0.05/-0.06 and is aligned with theorientation of Eri II within 3 +/- 6 degrees, likely due to tides. The stellarpopulation of the cluster is indistinguishable from that of Eri II itself.

Eridanus II: A Fossil from Reionization with an Off-Center Star Cluster