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Table 1

Constraints on BμG and n0 based on standard DSA predictions (assuming Bohm diffusion) and the ULs on the maximum particle energy derived from the Fermi-LAT and H.E.S.S. measurements.

Scenario Constraints

Radiative losses τrad (τacc>τrad)
τ p−p B μG < 1.1 × 10-4n0Emax
τ br B μG < 1.8 × 10-4n0Emax
τ syn B μG >

Age-limited: τacc(Emax) > age B μG < 1.4 Emax

Size-limited: B μG <

Notes. BμG, n0, and the maximum particle energy Emax are in units of μG, cm-3 and TeV, respectively. The shock velocity vsh = 700 km s-1 is used as it leads to conservative constraints on BμG. The ratio between the diffusion length of particles at E = Emax and the shock radius χ defines the upstream diffusion region size, where (e.g. Zirakashvili & Ptuskin 2008). τp−p, τbr, and τsyn are the radiative loss timescales for p-p collision, Br, and syn processes, τacc and τrad are the acceleration and radiative timescales, respectively, and D(Emax) the diffusion coefficient at the maximum energy.

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