Gamma-ray burst beaming: A universal configuration with a standard energy reservoir?

We consider a gamma-ray burst (GRB) model based on an anisotropic fireball with an axisymmetric energy distribution of the form ε(θ) ∝ θ^-k and allow for the observer's viewing direction being at an arbitrary angle θ_ν with respect to the jet axis. This model can reproduce the key features expected from the conventional on-axis uniform jet models, with the novelty being that the achromatic break time in the broadband afterglow light curves corresponds to the epoch during which the relativistic beaming angle is equal to the viewing angle, θ _ν, rather than to the jet half-opening angle, θ _j. If all the GRB fireballs have such a similar energy distribution form with 1.5 < k ≲ 2, then GRBs may be modeled by a quasi-universal beaming configuration and an approximately standard energy reservoir. This conclusion also holds for some other forms of angular energy distributions, such as the Gaussian function.