Discovery of a tight correlation among the prompt emission properties of long Gamma Ray Bursts

We report the discovery of a correlation among three prompt emission properties of GRBs. These are the isotropic peak luminosity L_iso, the peak energy of the time-integrated prompt emission spectrum E_pk, and the ``high signal" timescale T_0.45, previously used to characterize the variability behavior of bursts. In the rest frame of the source the found correlation reads L_iso\propto E_pk^1.62 T_0.45^-0.49. We find other strong correlations, but at the cost of increasing the number of variables, involving the variability and the isotropic energy of the prompt emission. With respect to the previous tight correlations found in GRBs the newly found correlation does not require any information from the afterglow phase of the bursts, nor any model-dependent assumption. In the popular scenario in which we are receiving beamed radiation originating in a fireball pointing at us, the found correlation preserves its form in the comoving frame. This helps to explain the small scatter of the correlation, and underlines the role of the local brightness (i.e. the brightness of the visible fraction of the fireball surface). This correlation has been found for 19 objects, and it is hard to establish if any selection bias affects it. Its connection with the prompt local brightness is promising, but a solid physical understanding is still to be found. Despite all that, we find that some properties of the correlation, which we discuss, support its true existence, and this has important implications for the GRB physics. Furthermore, it is possible to use such correlation as an accurate redshift estimator, and its tightness will allow us to use it as a tool to constrain the cosmological parameters (abridged)