A universal scaling for short and long gamma-ray bursts: E_x,iso - e_γ,iso - e_pk

The comprehensive statistical analysis of Swift X-ray light curves, collecting data from six years of operation, revealed the existence of a universal scaling among the isotropic energy emitted in the rest-frame 1 - 10⁴keV energy band during the prompt emission (Eγ, iso ), the peak of the prompt emission energy spectrum (E_pk) and the X-ray energy emitted in the 0.3-10keV observed energy band (E_{X, iso}). In this paper, we show that this three-parameter correlation is robust and does not depend on our definition of E_{X, iso}. It is shared by long, short and low-energetic gamma-ray bursts (GRBs), and thus reflects the existence of some properties which are shared by the GRB class as a whole. A more intuitive way to express the three-parameter correlation is in the form of a two-parameter correlation between the GRB efficiency and E_pk. We speculate that the physical origin of such a relation is connected with the outflow Lorentz factor.