Variation of Microphysical Parameters in Reverse-shock Scenario

TL;DR

We address how time variation of microphysical parameters in relativistic reverse shocks affects SSC emission in GRB afterglows. We derive SSC light curves and closure relations for the RS in both homogeneous and wind-like media, allowing $\varepsilon_{\rm e,r} \propto t^{-a}$ and $\varepsilon_{\rm B,r} \propto t^{-b}$, for two electron populations with $1<p<2$ and $2<p$, in thick- and thin-shell regimes. Using these CRs and LAT/2FLGC observations, we perform MCMC fits to obtain best-fit $(a,b)$ and find that evolving microphysics is required for many bursts, with a preference for thin-shell wind configurations in several cases; plateaus, soft-to-hard transitions, and steep decays are naturally reproduced, and SSC RS is necessary to explain a substantial fraction of high-energy photons beyond standard synchrotron expectations. The results constrain circumburst environments and magnetic-field evolution, highlighting the role of RS SSC in shaping LAT/TeV emission and providing a diagnostic for afterglow microphysics and progenitor environments.

Abstract

Gamma-ray bursts (GRBs), among the most compelling astrophysical phenomena, are potential candidates for exploring the evolution of energy distribution among magnetic fields and particles through multiwavelength observations. The fraction of energy transferred between particles and the magnetic field is governed by microphysical parameters, typically assumed to be constant during relativistic shocks but may in fact vary with time. In this work, we derive the light curves and closure relations (CRs) of the synchrotron-self Compton (SSC) process from the external reverse shock (RS) with variations of microphysical parameters in a homogeneous and stellar-wind medium. We consider the evolution of the RS in the thick- and thin-shell regimes. We demonstrate that, depending on the microphysical parameters, this process can mimic plateau phases and produce temporal decay indices steeper than those predicted by high-latitude emission alone. The current model is employed to examine the evolution of the spectral and temporal indices of GRBs reported in the Second Fermi-LAT Gamma-ray Burst Catalog (2FLGC) and bursts detected at very high energies, using Markov Chain Monte Carlo (MCMC) simulations.

Figures (14)

• Figure 1: Corner plots resulting for the MCMC process to maximize the CRs reported in Table \ref{['table:cr_ssc']}. The first column corresponds to $\nu < \nu^{\rm ssc}_{\rm m, r}$, the second to $\nu^{\rm ssc}_{\rm m, r} < \nu < \nu^{\rm ssc}_{\rm cut, r}$, and the third to $\nu^{\rm ssc}_{\rm cut,r} < \nu$. We consider the SSC RS evolving thick-shell regime for a constant interstellar medium (upper), and a wind-like medium (lower).
• Figure 2: The same as \ref{['fig:MCMC_ISM']}, but for the thin-shell regime.
• Figure 3: These panels show the CRs of SSC RS emission evolving in a thick-shell regime for ISM (above) and stellar wind (below). From left to right panels correspond to the cooling condition $\nu < \nu^{\rm ssc}_{\rm m,r}$, $\nu^{\rm ssc}_{\rm m,r} < \nu < \nu^{\rm ssc}_{\rm cut,r}$ and $\nu^{\rm ssc}_{\rm cut,r} < \nu$. The purple ellipses are displayed when the confidence regions are within 1$\sigma$ error margins. The red lines and dots represent the estimated CRs.
• Figure 4: The same as Figure \ref{['fig1:CRsthick']}, but for the RS evolving in the thin-shell regime.
• Figure 5: Range of microphysical parameters ($a$ and $b$) for which the CRs of bursts reported in 2FLGC are satisfied when the SSC model lies in the cooling condition ${\rm \nu_m^{ssc} < \nu_{\rm LAT} < \nu_{\rm cut}^{ssc} }$. Panels from left to right correspond to the evolution of the RS in the thick-shell regime for ISM and stellar wind, and in the thin-shell regime for ISM and stellar wind, respectively. Panels from top to bottom are for GRBs 080916C, 081009, 090323, 090328, 090626, 091003, 091031, 100414A, 100728A and 110428A.