Timescales and Characteristic Energy as Observable Signature of GRBs

There are other GRB observable quantities often employed in the literature, e.g., to construct GRB correlations (see Section 6.1). They span from characteristic energies to timescales measured in several wavelengths. More specifically, a selection of them is summarized below:


$$L\_{\mathcal{X}/0} = 4\pi d\_{\mathcal{L}}^2 \mathcal{F}\_{\mathcal{X}/0} \frac{\int\_{0.3/(1+z)}^{10/(1+z)} E N\_{\mathcal{E}}^{\mathcal{X}/0}(E) dE}{\int\_{0.3}^{10} E N\_{\mathcal{E}}^{\mathcal{X}/0}(E) dE} = 4\pi d\_{\mathcal{L}}^2 \mathcal{F}\_{\mathcal{X}/0} (1+z)^{\gamma - 2} \tag{11}$$

where we used the fact that X-ray data are observed by the *Swift*-XRT in the 0.3–10 keV energy band and the SED is in general a power-law spectrum with *N* X/0 E (*E*) ∝ *E* −*γ* and power-law index *γ* > 0.

• *V*, the variability of the GRB light curve. It is computed by taking the difference between the observed light curve and its smoothed version, squaring this difference, summing these squared differences over time intervals, and appropriately normalizing the resulting sum.
