2008MNRAS.391..411B

Several interesting correlations among gamma-ray burst (GRB) observables with available redshifts have been recently identified. Proper evaluation and calibration of these correlations may facilitate the use of GRBs as standard candles constraining the expansion history of the universe up to redshifts of z > 6. Here we use the 69 GRB data set recently compiled by Schaefer and we test the calibration of five of the above correlations [(1) E_peak-E_γ, (2) E_peak-L, (3) τ_lag-L, (4) V- L, (5) τ_RT-L] with respect to two potential sources of systematics: evolution with redshift and cosmological model used in the calibration. In examining the model dependence we assume flat ΛCDM and vary Ω_m. Our approach avoids the circularity problem of previous studies since we do not fix Ω_m to find the correlation parameters. Instead we simultaneously minimize χ² with respect to both the log-linear correlation parameters a, b and the cosmological parameter Ω_m. We find no statistically significant evidence for redshift dependence of a and b in any of the correlation relations tested [the slopes of a(z) and b(z) are consistent with 0 at the 2σ level]. We also find that one of the five correlation relations tested (E_peak-E_γ) has a significantly lower intrinsic dispersion compared to the other correlations. For this correlation relation, the maximum likelihood method (χ² minimization) leads to b₁= 50.58±0.04, a₁ = 1.56±0.11, Ω_m= 0.30^+1.60_–0.25, respectively. The other four correlation relations minimize χ² for a flat matter dominated universe Ω_m≃ 1. Finally, a cross-correlation analysis between the GRBs and type Ia supernova data for various values of Ω_m has shown that the E_peak-E_γ relation traces well the SnIa regime (within 0.17 ≤ z ≤ 1.755). In particular, for Ω_m≃ 0.15 and Ω_m ≃ 0.30 we get the highest correlation signal between the two populations. However, due to the large error bars in the cross-correlation analysis (small number statistics) even the tightest correlation relation (E_peak-E_γ) provides much weaker constraints on Ω_m than current SnIa data.