Opening Angles of Collapsar Jets

TL;DR

This paper models the propagation and opening angles of collapsar jets in gamma-ray bursts, revealing how jet dynamics influence observed properties and spectral relations through simulations and analytical approaches.

Contribution

It introduces a new analytical model linking jet opening angles to initial Lorentz factors and explains GRB duration and spectral relations with jet-cocoon interactions.

Findings

Jet opening angle is approximately one-fifth of the initial Lorentz factor.

Jet Lorentz factor remains low inside the star due to collimation shocks.

GRB duration is set by the cocoon's sound crossing time, affecting luminosity and opening angle.

Abstract

We investigate the jet propagation and breakout from the stellar progenitor for gamma-ray burst (GRB) collapsars by performing two-dimensional relativistic hydrodynamic simulations and analytical modeling. We find that the jet opening angle is given by $\theta_j \sim 1/5 \Gamma_{0}$, and infer the initial Lorentz factor of the jet at the central engine, $\Gamma_0$, is a few for existing observations of $\theta_j$. The jet keeps the Lorentz factor low inside the star by converging cylindrically via collimation shocks under the cocoon pressure, and accelerates at jet breakout before the free expansion to a hollow-cone structure. In this new picture the GRB duration is determined by the sound crossing time of the cocoon, after which the opening angle widens, reducing the apparent luminosity. Some bursts violating the maximum opening angle $\theta_{j,\max}\sim 1/5 \sim 12^{\circ}$ imply the existence of a baryon-rich sheath or a long-acting jet. We can explain the slopes in both Amati and Yonetoku spectral relations using an off-centered photosphere model, if we make only one assumption that the total jet luminosity is proportional to the initial Lorentz factor of the jet. We also numerically calibrate the pre-breakout model (Bromberg et al.) for later use.