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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. This "boosted fireball" model is motivated by the phenomenology of collapsar jets, but is applicable to a wide variety of relativistic flows. 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= 2 η_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 ~ 2 η_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 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.