A Possible Cepheid‐like Luminosity Estimator for the Long Gamma‐Ray Bursts

Abstract

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 Ðve bursts, Ulysses/GRB data for one burst, and NEAR/XGRS data for one burst. Spectroscopic redshifts, peak Ñuxes, and high-resolution light curves are available for 11 of these bursts; partial information is available for the remaining nine bursts. We Ðnd 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 Ðt to these data a model that accommodates both intrinsic scatter (statistical variance) and extrinsic scatter (sample variance). We Ðnd that L DV 3.3~ `0 1..9 1. If one excludes GRB 980425 from the Ðt, on the grounds that its association with SN 1998bw at a redshift of z\0.0085 is not secure, the luminosity estimator spans B2.5 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 p). Although GRB 980425 is excluded from this Ðt, its L and V values are consistent with the Ðtted 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 Ðt, the luminosity esti- mator spans B6.3 orders of magnitude in L , and the slope of the correlation is positive with a probabil- ity of 1[(9.3]10~7) (4.9 p). In either case, the luminosity estimator yields best-estimate luminosities that are accurate to a factor of B4, or best-estimate luminosity distances that are accurate to a factor of B2. Regardless of whether GRB 980425 should be included in the Ðt, its light curve is unique in that it is much less variable than the other B17 light curves of bursts in our sample for which the signal-to- noise ratio is reasonably good.