The Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST) enabled the search for the first galaxies observed at z ~ 8 - 11 (500 - 700 Myr after the Big Bang). To continue quantifying the number density of the most luminous galaxies (M_AB ~ -22.0) at the earliest epoch observable with HST, we search for z ~ 10 galaxies (F125W-dropouts) in archival data from the Brightest of Reionizing Galaxies (BoRG[z8]) survey, originally designed for detection of z ~ 8 galaxies (F098M-dropouts). By focusing on the deepest 293 arcmin^2 of the data along 62 independent lines of sight, we identify six z ~ 10 candidates satisfying the color selection criteria, detected at S/N > 8 in F160W with M_AB = -22.8 to -21.1 if at z = 10. Three of the six sources, including the two brightest, are in a single WFC3 pointing (~ 4 arcmin^2), suggestive of significant clustering, which is expected from bright galaxies at z ~ 10. However, the two brightest galaxies are too extended to be likely at z ~ 10, and one additional source is unresolved and possibly a brown dwarf. The remaining three candidates have m_AB ~ 26, and given the area and completeness of our search, our best estimate is a number density of sources that is marginally higher but consistent at 2{sigma} with searches in legacy fields. Our study highlights that z ~ 10 searches can yield a small number of candidates, making tailored follow-ups of HST pure-parallel observations viable and effective.
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