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Table 3

Constraints on the maximum magnetic-field strength, cut-off energy of the electron spectrum, photon spectral index of the filament, and the difference between the photon indices of the spectra of filament and plateau at three different photon energies, Eν, for four young SNRs.

Weak damping
SNR l d B max E cut Γf Γf−Γp
[pc] [μG] [TeV] Eν = 0.1   keV Eν = 1   keV Eν = 10   keV Eν = 0.1   keV Eν = 1   keV Eν = 10   keV
SN 1006 0.03 65 50 1.78 2.12 2.64 0.04 0.08 0.07
(0.03) (57) (32) (1.93) (2.35) (2.95) (0.05) (0.09) (0.08)
Cas A 0.015 260 27 1.71 1.98 2.51 0.04 0.02 0.01
Tycho 0.02 150 34 1.71 2.00 2.57 0.06 0.04 0.02
Kepler 0.03 135 36 1.71 2.01 2.59 0.05 0.04 0.02
(0.03) (115) (52) (1.67) (1.93) (2.43) (0.04) (0.05) (0.02)
Strong damping
SNR l d B max E cut Γf Γf−Γp
[pc] [μG] [TeV] Eν = 0.1   keV Eν = 1   keV Eν = 10   keV Eν = 0.1   keV Eν = 1   keV Eν = 10   keV
SN 1006a 0.02 64 51 1.81 2.16 2.66 0.04 0.10 0.13
(0.02) (56) (32) (1.97) (2.39) (2.96) (0.04) (0.11) (0.13)
Cas A 0.004 115 40 1.81 2.12 2.58 0.07 0.16 0.19
Tycho 0.008 85 45 1.82 2.14 2.61 0.05 0.13 0.17
Keplerb 0.01 80 47 1.81 2.14 2.62 0.04 0.11 0.14
(0.012) (80) (62) (1.74) (2.03) (2.48) (0.03) (0.09) (0.12)

Notes. These values are calculated using the magnetic-field damping model and the parameters given in Table 1.

(a)

The values in brackets were calculated using the shock velocity vs = 2900   km s-1 as measured in the northwestern limb.

(b)

The values in brackets were calculated using the upper limit of 6.4 kpc to the distance.

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