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

¹ Department of Astronomy, Nanjing University, 210093 Nanjing, PR China
e-mail: hyf@nju.edu.cn
² Department of Physics, Yunnan University, 650091 Kunming, PR China
³ Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, PR China

Received: 22 July 2011
Accepted: 25 November 2011

Abstract

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 L_X ∝ T_a^-0.87 E_{γ, iso}^0.88. 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.