Long-duration gamma-ray bursts (GRBs) accompany the deaths of some massive stars and hence, because massive stars are short-lived, are a tracer of star formation activity. Given that GRBs are bright enough to be seen to very high redshifts and detected even in dusty environments, they should therefore provide a powerful probe of the global star formation history of the Universe. The potential of this approach can be investigated via submillimetre (submm) photometry of GRB host galaxies. Submm luminosity also correlates with star formation rate, so the distribution of host-galaxy submm fluxes should allow us to test the two methods for consistency. Here, we report new JCMT/SCUBA 850-μm measurements for 15 GRB hosts. Combining these data with results from previous studies, we construct a sample of 21 hosts with <1.4 mJy errors. We show that the distribution of apparent 850-μm flux densities of this sample is reasonably consistent with model predictions, but there is tentative evidence of a dearth of submm-bright (>4 mJy) galaxies. Furthermore, the optical/infrared properties of the submm-brightest GRB hosts are not typical of the galaxy population selected in submm surveys, although the sample size is still small. Possible selection effects and physical mechanisms which may explain these discrepancies are discussed
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