Systematic Study of Forward and Reverse Shock Afterglow Emission from Two-Component Jets

Abstract

Two-component jets are frequently invoked to explain complex features in gamma-ray burst (GRB) afterglows, such as late-time rebrightening and chromatic breaks. While many studies fit these models to individual events, a systematic exploration mapping the broader parameter space, particularly the reverse shock contribution, is currently lacking. To address this, we present a comprehensive systematic analysis of two-component jet signatures using numerical modeling with the VegasAfterglow code. Our modeling shows that observable rebrightenings in the forward shock require the wing to carry substantially more energy, while for the reverse shock the energies can be comparable. Because the two components can occupy different spectral regimes, spectral breaks may arise when the wing emission overtakes the core. When the wing's initial velocity is high, relativistic beaming can render its emission invisible to the on-axis observer. As the flow decelerates, the resulting debeaming produces a steeper rise in the observed emission, reaching temporal slopes as steep as about $4.5$ and peaking shortly after the core jet break. In this case, the wing masks the core's break, leaving only a single late-time break. Slower wings that are not initially beamed away do not obscure the core, allowing the observer to see two distinct jet breaks. At late times, the decaying post-jet-break slopes are unaffected and limited to temporal slopes of about $-p$. Additionally, the forward shock dominates the emission across most of the parameter space, while the reverse shock contributes noticeably only under conditions of high magnetization and long engine durations.

Figures (14)

• Figure 1: Schematic illustration of a two-component jet structure and the associated forward–reverse shock pairs formed in both the jet core and the wing. The top panel depicts the case of a fast wing, in which the emission is relativistically beamed away from an on-axis observer. The bottom panel shows the case of a slower wing, where the wing emission lies within the observer’s beaming cone and is therefore detectable. The wavy arrows indicate the radiation originating from the forward- and reverse-shocked regions.
• Figure 2: Evolution of Lorentz factor of the forward-shocked region for different engine durations. The initial Lorentz factor is set at $\Gamma_0=150$ and $\Gamma_0=50$ for the ISM and wind mediums, respectively. Shell thickness is determined by parameter $\xi$ with $\xi>1$ corresponding to 'thin shell' and vice versa. The colored vertical lines on both panels depict $T_{\rm eng}$. The colored horizontal dotted lines on the right panel show the critical Lorentz factor $\Gamma_\mathrm{c}$ for thick-shell cases.
• Figure 3: Multi-band light curves of forward shock for different values of the varied parameters for the ISM. Each row corresponds to a distinct parameter, while columns correspond to different frequency bands: radio (5 GHz), R-band (650 nm), and X-ray (5 keV). The solid vertical lines in the last row depict max$(t_{\rm dec}, T_{\rm eng})$.
• Figure 4: Multi-band light curves of reverse shock for different values of the varied parameters for the ISM. Each row corresponds to a distinct parameter, while columns correspond to different frequency bands: radio (5 GHz), R-band (650 nm), and X-ray (5 keV). The solid vertical lines in the last row depict max$(t_{\rm dec}, T_{\rm eng})$.
• Figure 5: Multi-band light curves of forward shock for different values of the varied parameters in the wind medium. Each row corresponds to a distinct parameter, while columns correspond to different frequency bands: radio (5 GHz), R-band (650 nm), and X-ray (5 keV). The solid vertical lines in the last row depict max$(t_{\rm dec}, T_{\rm eng})$. The core deceleration time is outside the range, $t_{\rm dec, n}\approx6~\rm{s}$.