A "Boosted Fireball" Model for Structured Relativistic Jets

TL;DR

This paper introduces the 'boosted fireball' model for structured relativistic jets, explaining their angular energy distribution and Lorentz factor, with implications for gamma-ray burst observations and jet break features.

Contribution

The paper presents a new analytical model for relativistic jets that naturally produces structured jets with specific angular and Lorentz factor profiles, extending previous simplified models.

Findings

The model generates jets with Lorentz factors around 200 and opening angles of 0.1 radians.

Jet edges are smoother than in top-hat models, reducing observable jet breaks.

The model explains the absence of jet breaks in some afterglow light curves.

Abstract

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 \gamma_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 \eta_0 ~ E/M. In the lab frame the flow is beamed, expanding with Lorentz factor \Gamma = 2 \eta_0 \gamma_B in the direction of its initial bulk motion and with characteristic opening angle \theta_0 ~ 1/\gamma_B. The flow is jet-like with \Gamma \theta_0 ~ 2 \eta_0 such that jets with \Gamma > 1/\theta_0 are naturally produced. The choice \eta_0 ~ \gamma_B ~ 10 yields a jet with \Gamma ~ 200 on-axis and angular structure characterized by opening angle \theta_0 ~ 0.1 of relevance for cosmological GRBs, while \gamma_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 \eta_0 and \gamma_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.