Modeling the Multi-Wavelength Afterglow of Short Gamma-Ray Bursts with a Plateau Phase

TL;DR

Short GRB plateaus likely trace magnetar spin-down, but X-ray-only analyses suffer strong degeneracies in $B_p$ and $P_0$. The authors perform broadband afterglow modeling of seven plateauing short GRBs within a magnetar energy-injection framework, using MCMC to fit X-ray, optical, and radio data and assuming an ISM environment. They find that broadband constraints yield systematically lower $B_p$ and shorter $P_0$ (hence higher $L_0$) than X-ray-only inferences, with $E_{inj}$ often comparable to or exceeding $E_{K,iso}$ and $\,\,\,\Gamma_0>100$ for most bursts; GRB 090510 shows negligible injection. The multi-wavelength approach reduces degeneracies between magnetar parameters and radiative efficiency and reveals a distinct $\,\\Gamma_0-\\!E_{\\gamma,iso}$ distribution for short GRBs relative to long GRBs, highlighting the value of coordinated broadband follow-up for probing GRB central engines.

Abstract

Short gamma-ray bursts (GRBs) exhibiting a plateau phase provide valuable insights into the post-merger activity of their central engines. Although the physical origin of the plateau remains uncertain, the magnetar energy injection model offers a compelling explanation that reproduces the observed temporal and luminosity features. However, previous studies relying solely on X-ray data have suffered from strong parameter degeneracies when constraining the magnetar parameters. Here we perform broadband afterglow modeling on seven short GRBs with plateau features by combining X-ray, optical, and radio observations within the framework of the magnetar energy injection model. Key model parameters are derived by using the Markov Chain Monte Carlo method. It is found that the energy injection substantially modifies the afterglow dynamics in most events. Compared with X-ray--only analyses, our broadband modeling yields systematically a lower magnetic field strength and a shorter spin period for the central magnetar, corresponding to a higher injection luminosity. The study clearly shows that incorporating multi-wavelength data effectively alleviates the degeneracy between the magnetar parameters and X-ray radiative efficiency. In addition, the distribution of our short GRBs differs markedly from long GRBs when they are plotted on the initial Lorentz factor versus gamma-ray energy plane. This offset, consistent with the observed harder spectrum of short GRBs, may serve as a useful diagnostic for investigating the progenitor as larger samples are available.

Figures (1)

• Figure 1: Correlation between the rest-frame spectral peak energy $E_{\mathrm{p,i}}$ and the isotropic-equivalent energy $E_{\gamma,\mathrm{iso}}$ (the Amati relation). Our sample is compared with long GRBs (cyan points) and short GRBs (pink points), of which the data are taken from Minaev:2020MNRAS.492.1919M. The solid and dashed lines represent the best-fit relations and their $2\sigma$ regions.