A “Boosted Fireball” Model for Structured Relativistic Jets

We present a model for relativistic jets which generates a particular angular distribution of Lorentz factor and energy per solid angle. We consider a fireball with specific internal energy E / M launched with bulk Lorentz factor γ B . In its center-of-momentum frame the fireball expands isotropically, converting its internal energy into radially expanding flow with asymptotic Lorentz factor η 0 ∼ E / M . In the lab frame the flow is beamed, expanding with Lorentz factor Γ = 2η 0 γ B in the direction of its initial bulk motion and with characteristic opening angle θ 0 ∼ 1/γ B . The flow is jet-like with Γθ 0 ∼ 2η 0 such that jets with Γ > 1/θ 0 are naturally produced. The choice η 0 ∼ γ B ∼ 10 yields a jet with Γ ∼ 200 on-axis and angular structure characterized by opening angle θ 0 ∼ 0.1 of relevance for cosmological gamma-ray bursts (GRBs), while γ B ≳ 1 may be relevant for low-luminosity GRBs. The model produces a family of outflows, of relevance for different relativistic phenomena with structures completely determined by η 0 and γ B . We calculate the energy per unit solid angle for the model and use it to compute light curves for comparison with the widely used top-hat model. The jet break in the boosted fireball light curve is greatly subdued when compared to the top-hat model because the edge of the jet is smoother than for a top-hat. This may explain missing jet breaks in afterglow light curves.