Double-Peaked Optical Afterglow in GRB 110213A Inferring a Magnetized Thick Shell Ejecta

TL;DR

The paper addresses the origin of double-peaked optical afterglows and X-ray shallow decay in GRBs by introducing a semi-analytic magnetized bullet (thick-shell) ejecta model for forward and reverse shocks in a stratified circumstellar medium. It fits multiwavelength data from GRB 110213A using multimodal nested sampling, and introduces Magglow, an open-source Julia tool for simulating multi-messenger afterglows. The analysis finds that a highly magnetized, thick ejecta with $E_0\sim10^{55}$ erg, $\Gamma_0\sim40$, and $\sigma_0\sim10$, along with a large shell width $\Delta_0/c\sim10^3$ s, can reproduce the two optical peaks (RS-driven first peak and FS-driven second peak) and the extended X-ray shallow decay during the transition phase, while implying a low radiative efficiency in the prompt phase. This work provides a unified framework for interpreting early afterglows and enables predictive multi-messenger emission modeling with Magglow.

Abstract

Gamma-ray bursts early afterglows are important tracers for determining the radial structure and magnetization of the ejecta. In this paper, we focus on GRB 110213A that shows double-peaked optical afterglow lightcurves and the shallow decay feature of the X-ray afterglow. We adopt a semi-analytic model for the dynamics of forward and reverse shocks generated through an interaction between an arbitrary magnetized ejecta with a finite thickness and a stratified circumstellar medium. Multiwavelength radiation from forward and reverse shocks seen from an arbitrary viewing angle is calculated under a thin-shell approximation. Our analysis with multimodal nested sampling methods for GRB 110213A suggests that the thick shell ejecta naturally explains the shallow decay feature of the X-ray afterglow. The combination of the reverse shock emission in the strongly magnetized jet and forward shock emission in the weakly magnetized circumstellar medium makes the double peak feature of the optical afterglows. The estimated low radiative efficiency in the prompt phase may be a consequence of the high magnetization of the jet in this case. A multi-messenger emission simulator based on the magnetic bullet afterglow model is publicly available as the open source Julia package "Magglow".

Figures (5)

• Figure 1: The afterglow lightcurves of GRB 110213A in $I$-band (787 nm, blue), $V$-band (520 nm, purple), $z$-band (904 nm, green), $r$-band (624 nm, red), $u$-band (347 nm, yellow), and X-ray (10 keV, black). The data points represent extinction-corrected observations. The solid line shows the total theoretical flux, which is the sum of the emission from the forward shock (dashed line) and the reverse shock (dotted line) emission, calculated using the computational tool for the magnetic bullet afterglow Magglow with the best-fit parameters corresponding to the maximum posterior probability :$E_0 = 9.5\times10^{54}~{\rm erg}$, $\Gamma_0 = 39.4$, $\sigma_0 = 16.6$, $\Delta_0/c = 1.1\times10^3$ s, $n_0 = 0.15~{\rm cm^{-3}}$, $k=0.001$, $\epsilon_{e, {\rm FS}} = 0.49$, $\epsilon_{B, {\rm FS}} = 9.9\times10^{-5}$, $p_{\rm FS}=2.32$, $f_{e, {\rm FS}}=0.71$, $\epsilon_{e, {\rm RS}} = 0.075$, $p_{\rm RS}=2.82$, $f_{r, {\rm RS}}=0.047$, and $\theta_{\rm j} = 9.7\times10^{-3}~{\rm rad}$. The model assumes $\theta_{\rm obs} = 0~{\rm rad}$.
• Figure 2: The evolution of the Lorentz factor of the forward and reverse shocks as a function of the radius. The initial magnetic acceleration lasts until $\sim10^{16}$ cm, then the transition phase starts immediately. The deceleration phase begins after $\sim10^{18}$ cm. The reverse shock exists in $10^{16}\sim10^{18}$ cm.
• Figure 3: The synthetic spectrum of synchrotron and SSC components for the forward and reverse shocks at $t_{\rm obs}=10^2$ s. The bump at the VHE components in the synchrotron spectrum is due to the spectral hardening of the accelerated particle distribution due to the Klein-Nishina effect.
• Figure 4: The predicted lightcurves of the radio and GeV afterglow. The solid line shows the total theoretical flux, which is the sum of the emission from the forward shock (dashed line) and the reverse shock (dotted line) emission, calculated using the magnetic bullet afterglow model Magglow with the best-fit parameters corresponding to the maximum posterior probability.
• Figure 5: Corner plot showing the posterior probability distributions of the model parameters for the GRB 110213A afterglow, obtained using the magnetic bullet afterglow model. Two-dimensional projections of the parameter samples are shown to highlight correlations and covariances between parameters. The uncertainties correspond to the 16th and 84th percentiles of the marginalized posterior distributions, representing the 1$\sigma$ credible intervals, and are indicated by black dashed lines. Flat priors were adopted for all parameters in the multimodal nested sampling analysis.