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 $\alpha$-Flux, $E_p$-Flux, and $E_p$-$\alpha$ 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 $\alpha$ 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 $E_p$-$\alpha$ 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.