Quasi-universal Gaussian Jets: A Unified Picture for Gamma-Ray Bursts and X-Ray Flashes

An observed correlation E_p~(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, in which the energy per solid angle decreases as the inverse square of the angle with respect to the jet axis, and for a conical jet model with a uniform energy density within the jet beam and a sharp energy cutoff 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 deg 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.