David Coward, Eric Howell, Marica Branchesi, Giulia Strata, Dafne Guetta, Bruce Gendre, Damien Macpherson
We constrain the dominant optical selection effects biasing the Gamma-Ray Burst (GRB) redshift distribution using Swift triggered redshifts acquired from the optical afterglow (OA). Models for the Malmquist, redshift desert, and dust extinction biases are used to show how the "true" GRB redshift distribution is distorted to its presently observed biased distribution. We find that that the statistically optimal model shows that GRB host galaxy dust extinction could account for up to 17% of missing redshifts, but the bias is negligible at very high-$z$. The redshift desert, and optically faint bursts missed because they are at high-$z$, reduce the overall fraction of redshifts by only 4% and \sim2% respectively. Significant sources of bias for the very high-$z$ sample include the limiting sensitivity of the telescopes, the time to acquire spectroscopic/photometric redshifts, and Lyman-$\alpha$ dropout. The statistically optimal model requires an increasing mean optical afterglow luminosity with redshift. This could be explained by a decrease in dust obscuration in GRB hosts at high-$z$. Alternatively, the optimal model can also be obtained without optical afterglow brightness evolution, but requires a source rate evolution four times higher than the star formation rate at $z=10$ compared to z=0. We find it is not necessary to invoke high-energy GRB luminosity evolution with redshift to account for the observed GRB rate excess at high-$z$.
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http://arxiv.org/abs/1210.2488
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