Small galaxies consisting entirely of population III (pop III) stars may form at high redshifts, and could constitute one of the best probes of such stars. Here, we explore the prospects of detecting gravitationally lensed pop III galaxies behind the galaxy cluster J0717.5+3745 (J0717) with both the Hubble Space Telescope (HST) and the upcoming James Webb Space Telescope (JWST). By projecting simulated catalogs of pop III galaxies at z~7-15 through the J0717 magnification maps, we estimate the lensed number counts as a function of flux detection threshold. We find that the ongoing HST survey CLASH, targeting a total of 25 galaxy clusters including J0717, potentially could detect a small number of pop III galaxies if ~1% of the baryons in these systems have been converted into pop III stars. Using JWST exposures of J0717, this limit can be pushed to ~0.1% of the baryons. Ultra-deep JWST observations of unlensed fields are predicted to do somewhat worse, but will be able to probe pop III galaxies with luminosities intermediate between those detectable in HST/CLASH and in JWST observations of J0717. We also explain how current measurements of the galaxy luminosity function at z=7-10 can be used to constrain pop III galaxy models with very high star formation efficiencies (~10% of the baryons converted into pop III stars).
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