A time - luminosity correlation for Gamma Ray Bursts in the X - rays

TL;DR

This paper identifies a new correlation between X-ray luminosity and afterglow time in gamma-ray bursts, which could standardize them as cosmological distance indicators, reducing previous uncertainties.

Contribution

It introduces a novel L_X-T_a relation for GRBs that is less dependent on cosmological parameters, aiding their use in high-redshift cosmology.

Findings

Found a linear log-log relation between L_X(T_a) and T_a/(1+z).

Intrinsic scatter comparable to previous GRB relations.

Relation is nearly independent of cosmological parameters.

Abstract

Gamma ray bursts (GRBs) have recently attracted much attention as a possible way to extend the Hubble diagram to very high redshift. However, the large scatter in their intrinsic properties prevents directly using them as 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 (SNeIa) 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 L_X(T_a) and the time constant T_a of the afterglow curve. We find a linear relation between \log{[L_X(T_a)]} and \log{[T_a/(1+z)]} with an intrinsic scatter sigma_{int} = 0.33 comparable to previously reported relations. Remarkably, both the slope and the intrinsic scatter are almost independent on the matter density Omega_M and the constant equation of state w of the dark energy component thus suggesting that the circularity problem is alleviated for the $L_X - T_a$ relation.