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We study the small population of z>2.7 quasars detected by GALEX, whosefar-UV emission is not extinguished by intervening HI Lyman limit systems.These quasars are of particular importance to detect intergalactic HeIIabsorption along their sightlines. We correlate verified z>2.7 quasars to theGALEX GR4 source catalog, yielding 304 S/N>3 sources. However, ~50% of theseare only detected in the GALEX NUV band, signaling the truncation of the FUVflux by low-redshift Lyman limit systems. We exploit the GALEX UV color to cullthe most promising targets for follow-up studies, with blue (red) GALEX colorsindicating transparent (opaque) sightlines. Monte Carlo simulations indicate aHeII detection rate of ~60% for quasars with FUV-NUV<1 at z<3.5, a ~50%increase over GALEX searches that do not include color information. We regard52 quasars detected at S/N>3 to be most promising for HST follow-up, with anadditional 114 quasars if we consider S/N>2 detections in the FUV. SDSSprovides just half of the NUV-bright quasars that should have been detected bySDSS & GALEX. We revise the SDSS quasar selection function, finding that SDSSsystematically misses quasars with blue u-g<2 colors at 3<z<3.5 due to overlapwith the stellar locus in color space. Our color-dependent SDSS selectionfunction naturally explains the inhomogeneous u-g color distribution of SDSSquasars with redshift and the color difference between color-selected andradio-selected SDSS quasars. Moreover, it yields excellent agreement betweenthe observed and the predicted number of UV-bright SDSS quasars. We confirm ourprevious claims that SDSS preferentially selects 3<z<3.5 quasars withintervening HI Lyman limit systems. Our results imply that broadband opticalcolor surveys for 3<z<3.5 quasars have likely underestimated their spacedensity by selecting IGM sightlines with an excess of strong HI absorbers.

GALEX far-UV color selection of UV-bright high-redshift quasars