We quantify the fraction of galaxies at moderate redshifts (0.1<z<0.5) that appear red-and-dead in the optical, but in fact contain obscured star formation detectable in the infrared (IR), with the PRIsm MUlti-object Survey (PRIMUS). PRIMUS has measured ~120,000 robust redshifts with a precision of sigma_z/(1+z)~0.5% over 9.1 square degrees of the sky to the depth of i~23 (AB), up to redshift z~1. We specifically targeted 6.7 square degree fields with existing deep IR imaging from the Spitzer Space Telescope from the SWIRE and S-COSMOS surveys. We select in these fields an i band flux-limited sample (i<20 mag in the SWIRE fields and i<21 mag in the S-COSMOS field) of 3310 red-sequence galaxies at 0.1<z<0.5 for which we can reliably classify obscured star-forming and quiescent galaxies using IR color. Our sample constitutes the largest galaxy sample at intermediate redshift to study obscured star formation on the red sequence, and we present the first quantitative analysis of the fraction of obscured star-forming galaxies as a function of luminosity. We find that on average, at L ~ L*, about 15% of red-sequence galaxies have IR colors consistent with star-forming galaxies. The percentage of obscured star-forming galaxies increases by ~8% per mag with decreasing luminosity from the highest luminosities to L~0.2L*. Our results suggest that a significant fraction of red-sequence galaxies have ongoing star formation and that galaxy evolution studies based on optical color therefore need to account for this complication.
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