The variable activity of a gamma-ray burst (GRB) source is thought to be correlated with its absolute peak luminosity—a relation that, if confirmed, can be used to derive an independent estimate of the redshift of a GRB. We find that bursts with highly variable light curves have greater νFν spectral peak energies when we transform these energies to the cosmological rest frame using the redshift estimates derived either from optical spectral features or from the luminosity-variability distance indicator itself. This positive correlation between peak energy and variability spans ≈2 orders of magnitude and appears to accommodate GRB 980425, lending credibility to the association of this burst with SN 1998bw. The existence of such a correlation not only provides an interesting clue to the nature of this luminosity indicator but potentially reinforces the validity of the redshift estimates derived from this method. It also implies that the rest-frame GRB peak energy is correlated with the intrinsic luminosity of the burst, as has been suggested in the past as an explanation of the observed hardness-intensity correlation in GRBs.
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