Comprehensive Measurement of Spectral Evolution in a GRB Flare: High Time-Resolution Insights into the "Double-Tracking" Phenomenon

Abstract

The spectral evolution characteristics of the prompt emission in gamma-ray bursts (GRBs) have been extensively studied, but detailed investigations of spectral evolution in a GRB flare remain lacking. In this work, we present the first analysis of spectral parameter evolution in a GRB flare through high time-resolved spectral fitting of the Brightest Flare in GRB 221009A. We find that the $α$-Flux, $E_p$-Flux, and $E_p$-$α$ relationships during both the overall phase and the rise phase of flare can be well described by simple power-law model, showing positive correlations. Therefore, we conclude that Brightest Flare exhibits "Double-tracking" behavior. Since values of $α$ do not exceed the synchrotron "death line" (-2/3), we explain this phenomenon using a magnetic dissipation synchrotron radiation model. In the decay phase of flare, the $E_p$-Flux and $E_p$-$α$ correlations become notably flatter, with their power-law indices decreasing significantly compared to those in the rise phase. This may be due to the fact that the next flare begins to erupt before the Brightest Flare has completely ended, resulting in the combined effects of both two flares. Our study of spectral parameter relations of the Brightest Flare provides new insights into the radiation mechanisms of both GRB prompt emission and flares.

Figures (4)

• Figure 1: Panel (a): Light curves of BFL in different energy bands from keV to MeV. The vertical red dashed lines indicate the time-bin boundaries adopted from the S-2 scheme proposed by 09A_flare. A distinct high-energy pulse is observed between $T_0$+511 s and $T_0$+512 s. After $T_0$+512 s, the light curve gradually transitions into a smooth decay. Panel (b): Evolution of the spectral parameters of the BFL. The three subplots, arranged from top to bottom, correspond to the evolution of flux, $E_{\text{p}}$, and $\alpha$. The $E_{\text{p}}$, and $\alpha$ calculated from different models are marked with distinct colors. Panel (C): Flux light curve of the GRB 221009A. The fitting parameters for the flare and afterglow are adopted from 09A_flare. The dark red vertical line marks the boundary within the decay phase, separating it into the pulse phase and the post-pulse phase. The dark blue and light blue dashed curves represent the fitting curves for the BFL and the flare following the BFL, respectively. Enlarged views of the boundary and the two fitted flares are shown on the left side of the figure.
• Figure 5: Three energy spectrum fitting result with the CPL model and their corner plots. The energy spectrum fitting result graphs include the $\nu F_{\nu}$ plot and the residual maps. Corner plot showing the results of the spectral fitting. The contours represent the 1$\sigma$, 2$\sigma$, and 3$\sigma$ confidence levels.
• Figure 12: The figure shows the relation between spectral parameters. Panel (a)–(c): The relation between $\alpha$ and $F$ during the overall phase, rise phase, and decay phase are presented. Panel (d)–(f): They show the relation between $E_{\text{p}}$ and $F$ across the three phases. Panel (g)–(i): They display the relation between $E_{\text{p}}$ and $\alpha$ for the three phases.
• Figure 22: Panel (a)-(b):Evolution of the $E_{\text{p}} - F$ . Panel (a): The dark blue curve represents the fitting of the $E_{\text{p}} - F$ relation for the decay phase using the BPL model, while the light blue dashed line represents the fitting using the powerlaw model. The green triangular data points and the green circular data points respectively represent the scatter plots of the $E_{\text{p}} - F$ for the pulse phase and the post-pulse phase. Panel (b): Blue and orange fitting curves with data points represent the $E_{\text{p}} - F$ fits for the pulse phase and post-pulse phase, respectively. Panel (c)-(d): Evolution of the $E_{\text{p}} - \alpha$ relation. Legends are similar to those in panel (a) and panel (b).