Quasi-universal Gaussian jets: a unified picture for gamma-ray bursts and X-ray flashes

An observed correlation Ep \propto (E_{iso})^{1/2} extending from Gamma-ray Bursts (GRBs) to X-ray flashes (XRFs) poses problems both for a power-law universal jet model where the energy per solid angle decreases as the inverse square of the angle respect to the jet axis, and for a conical jet model with a uniform energy density within the jet beam and a sharp energy cut-off at the jet edge. Here we show that the current GRB-XRF prompt emission/afterglow data can be understood in terms of a picture in which the GRB-XRF jets are quasi-universal and structured, with a Gaussian-like or similar structure, i.e., one where the jet has a characteristic angle, with a mild variation of energy inside and a rapid (e.g. exponential) decrease of energy outside of it. A Monte Carlo simulation shows that the current data is compatible with such a quasi-universal Gaussian jet with a typical opening angle of 5.7(+3.4)(-2.1) degrees, and with a standard jet energy of about log (E_j/1 erg)= 51.1+-0.3. According to this model, the true-to-observed number ratio of the whole GRB-XRF population is about 14 with the current instrumental sensitivity.