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 5 bursts , Ulysses /GRB data for 1 burst , and NEAR/XGRS data for 1 burst .
Spectroscopic redshifts , peak fluxes , and high resolution light curves are available for 11 of these bursts ; partial information is available for the remaining 9 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 a model to these data that accommodates both intrinsic scatter ( statistical variance ) and extrinsic scatter ( sample variance ) .
We find that L \sim V ^ { 3.3 ^ { +1.1 } _ { -0.9 } } .
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 \approx 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 \times 10 ^ { -4 } ( 3.8 \sigma ) .
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 \approx 6.3 orders of magnitude in L , and the slope of the correlation is positive with a probability of 1 - 9.3 \times 10 ^ { -7 } ( 4.9 \sigma ) .
In either case , the luminosity estimator yields best-estimate luminosities that are accurate to a factor of \approx 4 , or best-estimate luminosity distances that are accurate to a factor of \approx 2 .
Independently of whether or not GRB 980425 should be included in the fit , its light curve is unique in that it is much less variable than the other \approx 17 light curves of bursts in our sample for which the signal-to-noise is reasonably good .