Ze-Lian Du, Zhao-Yang Peng, Jia-Ming Chen, Yue Yin, Ting Li

The origins of the main burst and second burst of gamma-ray bursts (GRBs) and the composition of their jets remain uncertain. To explore this complex subject more thoroughly, we conduct a spectral analysis on 18 GRBs with a main and a second burst observed by Fermi/GBM. First, we employ Bayesian time-resolved spectral analysis to compare the spectral components of the main and the second burst, finding that $83.3\%$ of the main and second bursts contain a thermal component. $67\%$ of the GRBs, the thermal component gradually decreased from the main to the second burst and the number of spectra exceeding the "Synchrotron line-of-death" is significantly higher in the main burst than in the second burst. Subsequently, we ascertain that for both the main and second bursts, $71.4\%$ of the low-energy spectral index $\alpha$ and $77.8\%$ of the peak energy $E_{p}$ evolve in a similar fashion. There are $50.0\%$ and $72.2\%$ of the GRBs exhibit comparable correlations for the $Flux-\alpha$ and $\alpha-E_{p}$, respectively. For $Flux-E_{p}$ both the main and second burst show a positive correlation. Moreover, from the perspective of the temporal evolution of characteristic radii, the transition from the main to the second burst appeared to be seamless. Finally, we find that both the main and the second burst follow the same Amati relation and Yonetoku relation. Our analysis strongly indicates that the second burst is a continuation of the main burst and is highly likely to share a common physical origin.