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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 data for five bursts, Ulysses/GRB data for one burst, and NEAR/XGRS data for one burst. Spectroscopic redshifts, peak fluxes, and high-resolution light curves 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 constructed 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 ~ V. 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 ≈2.5 orders of magnitude in L, and the slope of the correlation between L and V is positive with a probability of 1 - (1.4 × 10-4) (3.8 σ). Although GRB 980425 is excluded from 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 ≈6.3 orders of magnitude in L, and the slope of the correlation is positive with a probability of 1 - (9.3 × 10-7) (4.9 σ). In either case, the luminosity estimator yields best-estimate luminosities that are accurate to a factor of ≈4, or best-estimate luminosity distances that are accurate to a factor of ≈2. Regardless of whether GRB 980425 should be included in the fit, its light curve is unique in that it is much less variable than the other ≈17 light curves of bursts in our sample for which the signal-to-noise ratio is reasonably good.