Gamma-ray Burst Empirical Correlation between Peak Luminosity and Peak Energy in The ICMART Model

TL;DR

This work tests whether the Internal-Collision-induced MAgnetic Reconnection and Turbulence (ICMART) model can reproduce the GRB prompt-emission empirical relations Yonetoku and Liang. The authors perform extensive Monte Carlo simulations of reconnection-driven mini-jets, modeling energy dissipation, Doppler boosting, and synchrotron emission to generate GRB-like spectra and light curves, and then assess whether the resulting $L_{p,iso}$–$E_{p,z}$–$\,\Gamma_f$ relations align with observations. A key result is that matching the observed relations requires a derived parameter constraint, $(k/f_e^4)^{\alpha} = F_K (f_p\sigma_0+2)^{3-2\alpha-2\beta} M^{1-\alpha} / \sigma_0^{4-2\beta}$, with $(\alpha,\beta)=(0.8,0)$ for Yonetoku and $(\alpha,\beta)\approx(\tfrac{2}{3},\tfrac{2}{3})$ for Liang; about 45–52% of simulated events satisfy the relations, and many of those also satisfy the parameter relation. The physical interpretation is that the magnetic field in the emission region must scale as $B_e^{2\alpha} \propto M/\sigma_0^{4-2\beta}$, implying more violent local dissipation with stronger fields and a weaker residual field. Significance lies in linking microphysical magnetic reconnection dynamics to observed GRB correlations, thereby constraining jet magnetization and energy-dissipation physics within the ICMART framework.

Abstract

Internal-Collision-induced Magnetic Reconnection and Turbulence (ICMART) model is a widely accepted model for explaining how high-magnetization jets produce gamma-ray burst (GRB) prompt emissions. In previous works, we show that this model can produce: 1) light curves with a superposition of fast and slow components; 2) a Band-shaped spectrum whose parameters could follow the typical distribution of GRB observations; 3) both ``hard to soft" and ``intensity tracking" patterns of spectral evolution. In this work, through simulations of a large sample with methods established in previous work, we show that the ICMART model can also explain the observed empirical relationships (here we focus on the Yonetoku and Liang relations), as long as the magnetic field strength in the magnetic reconnection radiation region is proportional to the mass of the bulk shell, and inversely proportional to the initial magnetization factor of the bulk shell. Our results suggest that during extreme relativistic magnetic reconnection events, an increase in magnetic field strength leads to more intense dissipation, ultimately resulting in a weaker residual magnetic field.

Figures (5)

• Figure 1: A schematic illustration about the spatial geometric relation between jet and mini-jets. The yellow circle is the central engine and the blue sector is the jet ejected from the engine. Each purple dot represent a mini-jet launched by the magnetic reconnection.
• Figure 2: Each blue dot represents a simulated GRB. The black lines represent: (a) the Yonetoku relation; (b) the Liang relation, with the red and blue lines delineating their $\pm 3\sigma$ error.
• Figure 3: Distributions of initial setup parameters. The purple lines are for the total 157 events. The red and blue lines are for samples that satisfy the Yonetoku relation and the Liang relation separately.
• Figure 4: This figure shows the correspondence between the correlation relationship among the ICMART model parameters given by \ref{['eq:k-fe relation']} and the observed empirical relationship. Dots with different colors represent different kinds of events: (1) green: satisfy both the empirical relations and \ref{['eq:k-fe relation']}; (2) blue: do not satisfy the empirical relations but satisfy \ref{['eq:k-fe relation']}; (3) orange: satisfy the empirical relations but do not satisfy \ref{['eq:k-fe relation']}. In the top panel, the black lines represent the two empirical relations and the red and blue lines mark their $\pm3\sigma$ error range. In the bottom panel, the pink and the purple lines delineate the upper and lower limits of \ref{['eq:k-fe relation']}.
• Figure 5: Each purple dot in this figure represents an ICMART event whose parameters satisfy \ref{['eq:k-fe relation']}. The red lines are the best fit results for these simulated events, with the shades delineating their $\pm2\sigma$ region. The blue lines show the the statistical relationship obtained from the observational data, with the shades delineating their $\pm2\sigma$ region.