New three-parameter correlation for gamma-ray bursts with a plateau phase in the afterglow

Aims. Gamma ray bursts (GRBs) offer strong advantages because of their huge burst energies, luminosities, and high redshifts in probing the Universe. A few interesting luminosity correlations of GRBs have been used to test cosmology models. Especially, for a subsample of long GRBs with known redshifts and a plateau phase in the afterglow, a correlation between the end time of the plateau phase (in the GRB rest frame) and the corresponding X-ray luminosity has been found. Here, we add the isotropic γ-ray energy release as a third parameter to get a tighter three-parameter correlation. Methods. We reanalyzed the subsample and found that a significantly tighter correlation exists when we add the isotropic γ-ray energy release into the consideration. We used the Markov-chain Monte Carlo techniques to get the best-fit coefficients. Results. A new three-parameter correlation is found for the GRBs with an obvious plateau phase in the afterglow. The best fit correlation is found to be LX ∝ Ta-0.87 Eγ, iso0.88. Additionally, both long and intermediate duration GRBs are consistent with the same three-parameter correlation equation. Conclusions. We argue that the new three-parameter correlation is consistent with the hypothesis that the subsample of GRBs with a plateau phase in the afterglow is associated with the birth of rapidly rotating magnetars and that the plateau is due to the continuous energy-injection from the magnetar. It is suggested that the newly born millisecond magnetars associated with GRBs might provide a good standard candle in the Universe