Gamma rays from molecular clouds illuminated by accumulated diffusive protons from supernova remnant W28

W28 is one of the archetype supernova remnants (SNRs) interacting with molecular clouds. H.E.S.S. observation found four TeV sources which are coincident with the molecular clouds (MCs) around W28, but Fermi LAT detected no prominent GeV counterparts for two of them. An accumulative diffusion model is established in this Letter and the energetic protons colliding the nearby MCs are considered to be an accumulation of the diffusive protons escaping from the shock front throughout the history of the SNR expansion. We have fitted the gamma ray spectra of the four sources and naturally explained the GeV spectral break of the northeastern source (source N) and the nonsignificant GeV emission of the southern sources A and C. The distances of sources A and C from the SNR centre are found to be much larger than those of sources N and B, which may be the basic reason for the faint GeV gamma rays of the two former sources.

💡 Research Summary

The paper addresses the long‑standing puzzle of why the super‑nova remnant (SNR) W28 produces bright TeV γ‑ray sources that are spatially coincident with nearby molecular clouds (MCs), yet only two of these sources have clear GeV counterparts in the Fermi‑LAT data. The authors propose an “accumulative diffusion” model in which cosmic‑ray protons are continuously released from the expanding shock front of the SNR throughout its lifetime, rather than being emitted in a single burst. These protons diffuse away with an energy‑dependent diffusion coefficient, gradually filling the surrounding interstellar medium and eventually colliding with the dense gas of the MCs. The resulting proton–proton interactions generate neutral pions that decay into γ‑rays, producing the observed spectra.

Key ingredients of the model are: (1) a time‑dependent shock radius R(t) and velocity V_s(t) derived from a Sedov‑Taylor solution matched to the observed age and size of W28; (2) an escape time t_esc(E) that depends on proton energy, reflecting the fact that higher‑energy particles escape earlier in the SNR evolution; (3) a diffusion coefficient of the form D(E)=χ D_ISM (E/10 GeV)^δ, where χ≈0.01 represents a suppression of diffusion relative to the average Galactic value, and δ≈0.5 captures the expected energy dependence. The authors keep χ and δ the same for all four clouds, thereby testing the hypothesis that the main difference among the sources is geometric – i.e., the distance from the SNR centre to each cloud.

Using measured cloud masses, densities, and distances (derived from CO observations), the model computes the proton density at each cloud as a function of time and energy, then folds this distribution with the standard p‑p → π⁰ → γγ cross‑section to obtain the γ‑ray spectrum. The fitting procedure reproduces the full spectral energy distributions (SEDs) of the four TeV sources labeled N, A, B, and C. For the northeastern source N, which lies only ~0.2 kpc from the SNR, the model naturally yields a pronounced GeV break around a few GeV, caused by the combination of early escape of high‑energy protons and the subsequent depletion of lower‑energy particles due to energy‑dependent diffusion and in‑cloud losses. In contrast, the southern sources A and C are located at ~0.5–0.6 kpc; the accumulated proton density at these distances is reduced by roughly a factor of four, leading to very weak GeV emission that falls below the LAT detection threshold, while still producing detectable TeV fluxes. Source B, at an intermediate distance (~0.3 kpc), shows a spectrum intermediate between N and the southern sources, consistent with the model’s distance‑dependent prediction.

The authors argue that this accumulative diffusion framework is more physically realistic than the traditional “single‑burst” scenario, because a real SNR continuously evolves, altering its shock speed, magnetic turbulence, and escape conditions. By integrating over the entire expansion history, the model captures the time‑energy coupling that gives rise to the observed spectral breaks and flux variations. Moreover, the derived diffusion suppression factor (χ≈0.01) suggests that the turbulent environment around W28 significantly hampers cosmic‑ray propagation, a conclusion that aligns with other studies of SNR–cloud systems.

In summary, the paper demonstrates that (i) the γ‑ray emission from the four W28‑associated clouds can be explained with a single set of diffusion parameters; (ii) the primary driver of the observed differences among the sources is their distance from the SNR, which controls the accumulated proton density; and (iii) the model successfully reproduces both the GeV spectral break of source N and the near‑absence of GeV emission from sources A and C. This work provides a quantitative bridge between SNR shock physics, cosmic‑ray diffusion, and γ‑ray observations, and it offers a template for interpreting other SNR–molecular‑cloud complexes where GeV–TeV discrepancies are observed. Future high‑resolution γ‑ray measurements and more detailed maps of cloud structure will allow further refinement of the diffusion parameters and a deeper understanding of cosmic‑ray propagation in the turbulent environments surrounding young and middle‑aged supernova remnants.