Two-component $\gamma$-Ray Structure from the CR Sources Within Dense Clouds

Recent observations have revealed that several cosmic ray (CR) sources themselves exhibit pronounced double power-law features in their radiation spectra. Combined with the phenomenon of two-component structure in the observed CR energy spectrum supported by multi-messenger data, this raises a fundamental question: can the two-component structure of the cosmic ray energy spectrum and the double power-law feature of the gamma-ray radiation energy spectrum from supernova remnants be understood within a unified picture? In this study, we propose a two-component model that incorporates the re-acceleration of background ``sea" CR particles by astrophysical sources to systematically explain the formation of double power-law spectra within those sources. Our model successfully reproduces the gamma-ray observations of multiple CR sources. The results support that double power-law structures may be a generic feature of Galactic CR sources within crushed clouds. This work offers a new theoretical perspective on the origin and propagation of cosmic rays, and its predictions may be further tested with future observations of a larger sample of CR sources.