A time–luminosity correlation for γ-ray bursts in the X-rays

Abstract γ-ray bursts (GRBs) have recently attracted much attention as a possible way to extend the Hubble diagram to a very high redshift. However, the large scatter in their intrinsic properties prevents directly using them as a distance indicator so that the hunt is open for a relation involving an observable property to standardize GRBs in the same way as the Phillips law makes it possible to use Type Ia supernovae as standardizable candles. We use here the data on the X-ray decay curve and spectral index of a sample of GRBs observed with the Swift satellite. These data are used as input to a Bayesian statistical analysis looking for a correlation between the X-ray luminosity LX(Ta) and the time constant Ta of the afterglow curve. We find a linear relation between log [LX(Ta)] and log [Ta/(1 +z)] with an intrinsic scatter σint= 0.33 comparable to previously reported relations. Remarkably, both the slope and the intrinsic scatter are almost independent on the matter density ΩM and the constant equation of state w of the dark energy component thus suggesting that the circularity problem is alleviated for the LX–Ta relation.