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Table 3

Photon-photon optical depth as a function of energy and redshift.

Energy τ(z,Eγ) τ(z,Eγ) τ(z,Eγ) τ(z,Eγ) τ(z,Eγ) τ(z,Eγ) τ(z,Eγ) τ(z,Eγ) τ(z,Eγ)
[TeV] z = 0.01 z = 0.03 z = 0.1 z = 0.3 z = 0.5 z = 1.0 z = 1.5 z = 2.0 z = 3.0

0.0200 2.91E-19 8.692E-19 2.758E-18 4.659E-07 1.167E-03 0.0545 0.2543 0.5830 1.206
0.0240 2.91E-19 8.692E-19 2.758E-18 8.606E-05 3.773E-03 0.0946 0.3564 0.7786 1.528
0.0289 2.91E-19 8.692E-19 2.758E-18 6.880E-04 9.205E-03 0.1390 0.4979 1.037 1.928
0.0347 2.91E-19 8.692E-19 4.388E-06 2.531E-03 1.899E-02 0.2100 0.6946 1.374 2.420
0.0417 2.11E-07 2.832E-06 1.523E-04 6.572E-03 3.506E-02 0.3138 0.9642 1.806 3.016
0.0502 2.12E-05 9.445E-05 8.587E-04 1.402E-02 6.016E-02 0.4659 1.325 2.352 3.730
0.0603 1.13E-04 4.241E-04 2.546E-03 2.635E-02 9.868E-02 0.6841 1.797 3.028 4.574
0.0726 3.14E-04 1.103E-03 5.605E-03 4.571E-02 0.1577 0.9877 2.400 3.847 5.556
0.0873 6.64E-04 2.258E-03 1.058E-02 7.572E-02 0.2476 1.396 3.151 4.817 6.681
0.104 1.22E-03 4.097E-03 1.849E-02 0.1221 0.3814 1.929 4.060 5.935 7.960
0.126 2.12E-03 7.039E-03 3.104E-02 0.1928 0.5738 2.602 5.129 7.194 9.406
0.151 3.55E-03 1.167E-02 5.045E-02 0.2971 0.8389 3.425 6.342 8.576 11.06
0.182 5.74E-03 1.872E-02 7.953E-02 0.4447 1.188 4.394 7.672 10.07 12.97
0.219 8.96E-03 2.907E-02 0.1216 0.6441 1.629 5.490 9.091 11.71 15.24
0.263 1.36E-02 4.378E-02 0.1800 0.9006 2.163 6.681 10.57 13.55 17.99
0.316 1.98E-02 6.367E-02 0.2573 1.214 2.781 7.928 12.13 15.70 21.35
0.381 2.80E-02 8.935E-02 0.3540 1.580 3.465 9.193 13.85 18.29 25.55
0.458 3.79E-02 0.1205 0.4683 1.988 4.187 10.46 15.83 21.47 31.00
0.550 4.95E-02 0.1563 0.5963 2.420 4.918 11.75 18.20 25.40 38.11
0.662 6.22E-02 0.1953 0.7337 2.858 5.630 13.14 21.10 30.39 47.92
0.796 7.56E-02 0.2364 0.8742 3.282 6.306 14.74 24.72 36.89 61.48
0.957 8.89E-02 0.2768 1.010 3.678 6.942 16.65 29.37 45.61 81.33
1.15 0.101 0.3152 1.137 4.039 7.564 19.03 35.50 57.71 110.4
1.38 0.113 0.3501 1.251 4.368 8.223 22.05 43.75 75.25 153.5
1.66 0.123 0.3810 1.352 4.685 8.990 26.01 55.34 101.6 216.5
2.000 0.132 0.4076 1.442 5.029 9.957 31.34 72.36 142.1 305.3
2.40 0.140 0.4318 1.528 5.452 11.21 38.75 98.22 204.1 428.1
2.89 0.147 0.4560 1.627 6.017 12.88 49.44 138.5 296.5 589.3
3.47 0.157 0.4863 1.756 6.783 15.16 65.46 201.3 428.0 793.1
4.17 0.170 0.5284 1.938 7.825 18.32 90.25 296.0 606.7 1040.
5.02 0.188 0.5887 2.195 9.254 22.88 129.3 431.7 836.3 1328.
6.03 0.215 0.6732 2.539 11.24 29.62 190.3 615.8 1115. 1649.
7.26 0.250 0.7847 3.011 14.14 39.94 281.8 851.4 1439. 1998.
8.73 0.301 0.9447 3.680 18.50 56.15 411.0 1134. 1796. 2361.
10.5 0.373 1.171 4.662 25.23 81.67 582.1 1458. 2172. 2727.
12.6 0.479 1.513 6.175 35.83 121.1 795.1 1806. 2546. 3080.
15.2 0.646 2.048 8.516 52.53 179.6 1043. 2163. 2905. 3406.
18.2 0.901 2.871 12.18 78.21 260.5 1315. 2505. 3235. 3699.
21.9 1.30 4.162 17.95 115.9 365.0 1596. 2821. 3516. 3941.
26.4 1.92 6.177 26.78 167.9 491.0 1869. 3090. 3742. 4129.
31.7 2.86 9.181 39.64 234.1 633.0 2119. 3306. 3910. 4258.
38.1 4.22 13.47 57.24 312.4 781.9 2330. 3462. 4016. 4325.
45.8 6.05 19.14 79.29 398.3 927.3 2494. 3555. 4055. 4331.
55.1 8.29 26.00 104.6 485.1 1059. 2604. 3585. 4034. 4278.
66.2 10.8 33.59 131.5 566.2 1168. 2658. 3555. 3958. 4168.
79.6 13.4 41.42 158.0 635.6 1248. 2659. 3470. 3829. 4013.
95.7 15.9 48.81 181.3 688.3 1294. 2609. 3340. 3657. 3816.
115. 18.1 54.98 199.9 721.9 1307. 2518. 3171. 3451. 3587.
138. 19.9 59.82 213.4 735.3 1290. 2393. 2974. 3220. 3338.
166. 21.0 63.03 220.5 729.6 1247. 2244. 2759. 2975. 3076.

Notes. The absorption multiplicative factor is eτ(z,Eγ).

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