A new redshift indicator of gamma-ray bursts to measure the cosmos

Using 64 ms count data of long gamma-ray bursts (LBs, T > 2.6 s), we analyze the quantity named relative spectral lag (RSL), τ/FWHM = τ, 31. We investigate in detail the properties of the RSL for a sample of nine LBs, using the general cross-correlation technique that includes the lag between two different energy bands. We find that the distribution of RSLs is normal and has a mean value of 0.1. Our important discovery is that redshift (z) and peak luminosity (L ) are strongly correlated with the RSL, which can be measured easily and directly, making the RSL a good redshift and peak luminosity indicator. In addition, we find that the redshift and luminosity estimator can also hold for short gamma-ray bursts (SBs, T < 2.6 s). With it, we estimate the median of redshift and peak luminosity of SBs to be about z≤P.06 and L∼1.68×10 erg/s, which are in excellent agreement with the results suggested by some previous authors. We thus argue that the sources including SBs and LBs with positive spectral lags might be one united category with the same physical process.