"Double-tracking" Characteristic of the Spectral Evolution of GRB 131231A: Synchrotron Origin?

The characteristics of the spectral evolution of the prompt emission of gamma-ray bursts (GRBs), which are closely related to the radiation mechanism (synchrotron or photosphere), are still an unsolved subject. Here, by performing the detailed time-resolved spectral fitting of GRB 131231A, which has a very bright and well-defined single pulse, some interesting spectral evolution features have been found. (i) Both the low-energy spectral index $\alpha$ and the peak energy $E_{\rm p}$ exhibit the "flux-tracking" pattern ("double-tracking" characteristics). (ii) The parameter relations, i.e., $F$ (the energy flux)-$\alpha$, $F$-$E_{\rm p}$, and $E_{\rm p}$-$\alpha$, along with the analogous Yonetoku $E_{\rm p}$-$L_{\gamma,\rm iso}$ relation for the different time-resolved spectra, show strong monotonous (positive) correlations, both in the rising and the decaying phases. (iii) The values of $\alpha$ do not exceed the synchrotron limit ($\alpha$= -2/3) in all slices across the pulse, favoring the synchrotron origin. We argue that the one-zone synchrotron emission model with the emitter streaming away at a large distance from the central engine can explain all of these special spectral evolution characteristics.