We present far-infrared (FIR) analysis of 68 Brightest Cluster Galaxies (BCGs) at 0.08 < z < 1.0. Deriving total infrared luminosities directly from Spitzer and Herschel photometry spanning the peak of the dust component (24-500um), we calculate the obscured star formation rate (SFR). 22(+6.2,-5.3)% of the BCGs are detected in the far-infrared, with SFR= 1-150 M_sun/yr. The infrared luminosity is highly correlated with cluster X-ray gas cooling times for cool-core clusters (gas cooling time <1 Gyr), strongly suggesting that the star formation in these BCGs is influenced by the cluster-scale cooling process. The occurrence of the molecular gas tracing Ha emission is also correlated with obscured star formation. For all but the most luminous BCGs (L_TIR > 2x10^11 L_sun), only a small (<0.4 mag) reddening correction is required for SFR(Ha) to agree with SFR_FIR. The relatively low Ha extinction (dust obscuration), compared to values reported for the general star-forming population, lends further weight to an alternate (external) origin for the cold gas. Finally, we use a stacking analysis of non-cool-core clusters to show that the majority of the fuel for star formation in the FIR-bright BCGs is unlikely to originate form normal stellar mass loss.
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