Late-afterglow Emission from a Quasi-spherical Outflow in a stratified environment
Nissim Fraija, Boris Betancourt-Kamenetskaia, Antonio Galván, Alvaro Montalvo, A. C. Caligula Do E. S. Pedreira, Peter Veres, Rosa Leticia Becerra, Maria G. Dainotti, Simone Dichiara, Hermes León Vargas
TL;DR
The paper develops an analytical synchrotron afterglow model for a quasi-spherical cocoon-like outflow decelerating in a stratified circumburst medium with density $n(r)\propto r^{-k}$, encompassing the coasting phase, self-absorption, and fractional electron acceleration. It unifies relativistic and sub-relativistic regimes and applies the model to a set of llGRBs (eg, GRB 980425, 031203, 060218, 100316D, 130603B, 150101B, 171205A) and Swift-detected short bursts at nearby distances, using MCMC to constrain $\tilde{E}$, $A_{st}$, $\Gamma_0$, $\varepsilon_B$, $\varepsilon_e$, $p$, $\alpha_s$, and $\theta_c$ across wind and ISM-like environments. The analysis finds a preference for constant-density media in llGRBs, moderate magnetization, and large half-opening angles, with radio and optical bands particularly sensitive to density and stratification, and X-ray excesses that the model can accommodate in several cases. The work extends previous shock-breakout/cocoon interpretations by providing closed-form light curves, closure relations, and a consistent parameter-space framework that links late-time radio/X-ray behavior to ejecta velocity structure and ambient density, offering a tool to interpret nearby GW-associated transients. Overall, the framework strengthens the connection between cocoon/shock-breakout physics and multiwavelength afterglows, enabling predictive modeling of late-time emission in llGRBs and potential GW counterparts.
Abstract
Gamma-ray bursts (GRBs) are cosmic events occurring at large distances beyond our galaxy. They provide a unique opportunity to study electromagnetic patterns not seen elsewhere. When the collimated GRB outflow interacts with the outer layers of a star or the wind generated by a binary neutron star merger, it releases energy, forming a quasi-spherical outflow around it. This broad outflow begins to radiate once it has transferred enough energy to the surrounding medium. We have developed a new analytical model that describes the synchrotron afterglow scenario of the quasi-spherical outflow, including factors such as stratified density, self-absorption regime, and the fraction of electrons accelerated by the shock front. We also successfully describe the multiwavelength observations of a sample of llGRB afterglows (GRB 980425, 031203, 060218, 100316D, 130603B, 150101B and 171205A) that exhibited a late component, analyzed in both stellar wind and constant-density environments. Our analysis shows that a constant-density environment is favored. Additionally, we consider the multiwavelength upper limits of the short bursts reported in the Swift-BAT database.