Scaling of cosmic-ray escape and acceleration parameters

Characterize how the cosmic-ray escape efficiency, diffusion coefficient, and maximum proton energy scale with supernova-remnant age and environment in middle-aged supernova remnants.

Background

The paper develops a time-dependent model of cosmic-ray acceleration, confinement, and escape and applies it to four middle-aged supernova remnants. The authors emphasize that observations spanning the GeV-to-PeV range could constrain these processes, but that a systematic understanding across remnants is not yet available. The unresolved issue concerns whether and how the escape efficiency, surrounding-medium diffusion coefficient, and maximum proton energy vary as functions of remnant age and environmental conditions.

References

Despite the wealth of data, a systematic comparison of acceleration and escape parameters across different middle-aged SNRs is still lacking. In particular, it remains unclear how the escape efficiency, diffusion coefficient, and maximum proton energy scale with SNR age and environment.

— Constraining Cosmic-Ray Acceleration and Escape in Middle-Aged Supernova Remnants with GeV-TeV Gamma-Ray Observations  (2608.18954 - Chen et al., 19 Aug 2026) in Section 2, subsection “Cosmic ray acceleration and escape from SNRs”

While this suggests a possible explanation for the morphology and spectrum of the gamma-ray emission, the scenario we discussed is based on simple considerations and requires the poorly constrained age of the system to lie within a narrow fraction of the currently allowed range. Therefore, more in-depth observational and theoretical work is needed to test its viability.

— Extended gamma-ray emission in the vicinity of the Westerlund 1 massive star cluster and Kes 41 supernova remnant seen by the Fermi Large Area Telescope  (2609.10176 - Tibaldo et al., 9 Sep 2026) in Section 5.1, Source B

Especially, the actual spectrum of accelerated protons in the radiative phase is yet not clear.

— The Potential Contribution of Radiative Supernova Remnants to the Local Cosmic Ray Spectrum  (2610.08474 - Cristofari et al., 6 Oct 2026) in Section 5, Conclusions

A single crossing shows the boundary at one moment and cannot tell how fast it moves to higher energy. The speed of the boundary decides the highest energy the shock confines in its lifetime. As the shock expands and its field and scattering environment change, the boundary need not rise monotonically, and the limits set by age and size move as well. Those two limits are the standard estimates of the highest energy a shock can reach, from coronal shocks to supernova remnants. Does any traveling shock ever confine the energies that its age and its size allow, or does the growth of its own waves set the limit at every age?

— Does Diffusive Shock Acceleration Reach Steady State? Insights from a Near-Sun Shock Observed by Parker Solar Probe  (2610.08034 - Jebaraj et al., 6 Oct 2026) in Section 6, Discussion and conclusions, final paragraph