Structure of gamma-ray burst jets: Intrinsic Versus apparent properties

With this paper we introduce the concept of apparent structure of a gamma-ray burst (GRB) jet, as opposed to its intrinsic structure. The latter is customarily defined specifying the functions ε{lunate}(θ) (the energy emitted per jet unit solid angle) and Γ(θ) (the Lorentz factor of the emitting material); the apparent structure is instead defined by us as the isotropic equivalent energy E<inf>iso</inf>(θ<inf>v</inf>) as a function of the viewing angle θ<inf>v</inf>.We show how to predict the apparent structure of a jet given its intrinsic structure. We find that a Gaussian intrinsic structure yields a power-law apparent structure: this opens a new viewpoint on the Gaussian (which can be understood as a proxy for a realistic narrow, well-collimated jet structure) as a possible candidate for a quasi-universal GRB jet structure. We show that such a model (a) is consistent with recent constraints on the observed luminosity function of GRBs; (b) implies fewer orphan afterglows with respect to the standard uniform model; (c) can break out the progenitor star (in the collapsar scenario) without wasting an unreasonable amount of energy; (d) is compatible with the explanation of the Amati correlation as a viewing angle effect; (e) can be very standard in energy content, and still yield a very wide range of observed isotropic equivalent energies.