A possible Cepheid-like luminosity estimator for the long gamma-ray bursts

We present a possible Cepheid-like luminosity estimator for the long gamma- ray bursts based on the variability of their light curves. To construct the luminosity estimator, we use CGRO/BATSE data for 13 bursts, Wind/Konus dat a for fie bursts, Ulysses/GRB data for one burst, and NEAR/XGRS data for on e burst. Spectroscopic redshifts, peak fluxes, and high-resolution light cu rves are available for 11 of these bursts; partial information is available for the remaining nine bursts. We find that the isotropic equivalent peak luminosities L of these bursts positively correlate with a rigorously const ructed measure V of the variability of their light curves. We fit to these data a model that accommodates both intrinsic scatter (statistical variance ) and extrinsic scatter (sample variance). We find that L similar to V--0.9 (3.3 +/-)+1.1. If one excludes GRB 980425 from the fit, on the grounds that its association with SN 1998bw at a redshift of z = 0.0085 is not secure, the luminosity estimator spans approximate to2.5 orders of magnitude in L, and the slope of the correlation between L and V is positive with a probabi lity of 1 - (1.4 x 10(-4)) (3.8 sigma). Although GRB 980425 is excluded fro m this fit, its L and V values are consistent with the fitted model, which suggests that GRB 980425 may well be associated with SN 1998bw and that GRB 980425 and the cosmological bursts may share a common physical origin. If one includes GRB 980425 in the fit, the luminosity estimator spans approxim ate to6.3 orders of magnitude in L, and the slope of the correlation is pos itive with a probability of 1--(9.3 x 10(-7)) (4.9 sigma). In either case, the luminosity estimator yields best-estimate luminosities that are accurat e to a factor of approximate to4, or best-estimate luminosity distances tha t are accurate to a factor of approximate to2. Regardless of whether GRB 98 0425 should be included in the fit, its light curve is unique in that it is much less variable than the other approximate to 17 light curves of bursts in our sample for which the signal-to-noise ratio is reasonably good.