TeV Afterglows of Gamma-Ray Bursts: Theoretical Analysis and Prospects for Future Observations

TL;DR

This work uses an optimized relativistic fireball model with a finite maximum particle energy $γ_{\text{max}}$ (and possible time-evolving microphysical parameters) to analyze the afterglows of five TeV-detected GRBs: GRB 180720B, GRB 190114C, GRB 190829A, GRB 201216C, and GRB 221009A. By fitting multiwavelength data (optical, X-ray, GeV, and TeV) and incorporating SSC, KN effects, and EBL absorption, the authors show that late-time TeV light curves provide diagnostics of $E_{\text{max}}= γ_{\text{max}} m_e c^2$, with GRB 221009A and GRB 180720B requiring $γ_{\text{max}}$ on the order of $10^6$–$10^7$ to account for observed steepening. The results demonstrate that TeV afterglows can discriminate between emission scenarios and highlight the importance of extended TeV monitoring (days) alongside MeV–GeV data to constrain particle acceleration physics; future facilities like CTAO, with improved sensitivity, will greatly enhance these studies. Key contributions include (i) quantifying how finite $γ_{\text{max}}$ shapes late-time TeV emission, (ii) identifying diverse afterglow behaviors across TeV-detected GRBs, and (iii) outlining observational strategies for early and late TeV coverage to diagnose acceleration mechanisms.

Abstract

Recent detections of gamma-ray bursts (GRBs) at TeV energies opened new prospects for investigating radiative environments and particle acceleration mechanisms under extreme conditions. In this paper, we study the afterglows of these GRBs - namely GRB 180720B, GRB 190114C, GRB 190829A, GRB 201216C, and GRB 221009A - modeling their synchrotron and inverse Compton emission within the framework of an optimized relativistic fireball model. We constrain the model parameters and their temporal evolution by applying our theoretical model to the high-energy emission in the X-ray and GeV-TeV energy bands observed at intermediate and late times. Our results reveal interesting differences among the TeV-detected GRBs, potentially reflecting a variety of underlying physical processes that lead to different maximum energies $E_{\text{max}}= \, γ_{\text{max}}\, m_e \, c^2$ of the accelerated particles responsible for the GRB high-energy emission. We indeed obtain different behaviors of the late TeV afterglows that ultimately depend on $γ_{\text{max}}$. We discuss how late afterglow observations - on timescales of hours and days - of X-ray and GeV-TeV emissions are crucial for providing diagnostics of the physical processes behind GRBs, and we emphasize the theoretical expectations for future TeV observations.

Figures (9)

• Figure 1: (Left panel) Observed and calculated flux temporal evolution of GRB 180720B within the global modeling described in Section \ref{['sec:modeling']}. For all plots, we have adopted the following color code: violet for optical data, orange for X-ray data, red for gamma-ray data, and green for TeV data. The X-ray data are well matched by our model throughout the whole evolution of the GRB afterglow; optical and HE gamma-ray data are also well reproduced. The shaded areas indicate early times during which prompt-like dynamical activity influences the emission. This phase is not intended to be described by the model; however, we notice that our model evolution at early times matches well with that data. A late-time steepening in the X-ray and gamma-ray bands is due to the crossing of the critical cooling frequency $\nu_c$ and the role of the maximum electron energy, $\gamma_{\text{max}}$, which is crucial for matching the late-time TeV gamma-ray data. (Right panel) The calculated broad-band spectrum at the time of the TeV detection within $\Delta t = 36300-43560$ s after trigger. We show the H.E.S.S. spectral data and optical data.
• Figure 2: Similarly to Figure \ref{['fig:lightcurve_and_sed_GRB180720B']}, for GRB 190114C. (Left panel) Observed and calculated light curves: our model accurately matches the X-ray and TeV gamma-ray bands throughout the GRB's evolution, while HE gamma-ray data are well reproduced after the prompts phase. (Right panel) The calculated broad-band spectrum at the onset of the TeV detection in the time interval $\Delta t = 68 - 110$ s after trigger. In the spectrum, we use the dataset reported in MAGIC_GRB190114C, and include data of Swift-XRT and BAT, and Fermi-LAT.
• Figure 3: Similarly to Figure \ref{['fig:lightcurve_and_sed_GRB180720B']}, for GRB 190829A. (Left panel) Light curves: the X-ray and TeV gamma-ray bands are well matched by our model along the whole time evolution of the GRB. The former are not expected to be reproduced during the very early phase of the prompt activity. The HE gamma-ray upper limits are consistent with our modeling. (Right panel) The calculated broad-band spectrum at the time of the TeV detection in the time interval $\Delta t = 15480 - 28440$ s after trigger. In the spectrum, we use the dataset reported in 2021Sci...372.1081H, and include data of Swift-XRT and BAT, and Fermi-LAT.
• Figure 4: Similarly to Figure \ref{['fig:lightcurve_and_sed_GRB180720B']}, for GRB 201216C. (Left panel) Light curves: The X-ray and TeV gamma-ray bands are well matched by our model as whole time evolution of the GRB, together with the HE gamma-ray upper limit. Our model reproduces well the optical flux at early times, and underestimates it at later times. (Right panel) Calculated broad-band spectrum during the time of the TeV detection within $\Delta t = 56 - 1224$ s after trigger. We show the EBL-deabsorbed intrinsic MAGIC data, and the average optical spectral point.
• Figure 5: Similarly to Figure \ref{['fig:lightcurve_and_sed_GRB180720B']}, for GRB 221009A. (Left panel) Light curves: our model reproduces well the time evolution of the flux light curves in different energy bands for the afterglow phase starting near $T' = 100$ s. Introducing a finite $\gamma_{\text{max}}$ is crucial to reproduce the TeV gamma-ray (and the X-ray) steepening at late times. (Right panel) Calculated broad-band spectrum at the time of the early GeV and TeV detections within $\Delta T' = 22 - 100$ s after trigger, for $T' = T_0 + 226$ s. The calculated spectrum shows the SED reported in foffano2024_GRB221009A with simultaneous data of AGILE-GRID and LHAASO LHAASO_2023.