Shear Particle Acceleration in Structured Gamma-Ray Burst Jets: IV. Thermal {\em vs.} Non-thermal Emission of the Jet Cocoon

Abstract: A distinct thermal or quasi-thermal spectral component is occasionally observed in gamma-ray burst (GRB) prompt emission spectra. Taking GRB 090902B as a case study, we investigate its origin within a structured jet framework, in which the outflow consists of an ultra-relativistic uniform core surrounded by a structured cocoon. In the weak-scattering regime with inefficient shear acceleration, electrons pre-energized in the thin jet-cocoon interaction layer are further heated in the mixed jet-cocoon (MJC) region, forming a quasi-thermal electron distribution. Parameterizing the radial temperature profile of electrons as a power law with index $q_T$, we demonstrate that both the peak flux and spectral width of the thermal component are sensitive to maximum temperature $T_{\max}$ and $q_T$. Combined with the synchrotron emission of shock-accelerated electrons in the jet core, our model reproduces both the quasi-thermal component in the keV-MeV range and the broadband non-thermal emission observed in the time-integrated and time-resolved spectra of GRB 090902B. A comparative analysis of GRB 240825A within a shear-acceleration dominated (strong-scattering) scenario shows that shear-accelerated electrons produce broader spectra than thermalized electrons in the weak-scattering regime. These results indicate that GRB spectral diversity likely arises from the additional emission component originating in the MJC region under different physical conditions.