Tests for Selection Effects in GRB High-Energy Correlations

Several correlations among observables derived from modelling the high-energy properties of GRBs have been reported in the literature. We show that well-known examples of these have common features indicative of an origin in selection effects. In particular, we focus here on the possible origin of the $E_{\rm pk}$-$E_{\rm iso}$ correlation in Swift data due to detector threshold truncation. The existence of faint Swift events calls into question inferences based on pre-Swift surveys which must be subject to complicated incompleteness effects. We review methods for treating data truncation effects in correlation analyses and apply these methods to Swift and pre-Swift data. Also, we show that the $E_{\rm pk}$-$E_{\gamma}$ ("Ghirlanda") correlation is effectively independent of the GRB redshifts, which suggests it contains little intrinsic physics. We recommend verifying that a correlation has significantly reduced scatter in the rest frame relative to the observer frame and also establishing that GRB redshifts contribute meaningfully.