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Table 4

Correlations between Liso, Eiso, and Ep with Γ0.

s = 0

r P m q r P m q

LisoΓ0 (points) 0.86 2 × 10-20 3.02 ± 0.24 –0.59 ± 0.10 0.92 1.42 × 10-27 2.78 ± 0.17 –0.40 ± 0.05
(points+LL) 0.62 1.2 × 10-17 2.60 ± 0.16 –0.67 ± 0.06 0.80 1.9 × 10-36 2.87 ± 0.05 –0.25 ± 0.02
EisoΓ0 (points) 0.81 3.0 × 10-16 2.85 ± 0.22 –0.20 ± 0.10 0.93 1.0 × 10-29 2.66 ± 0.13 –1.13 ± 0.04
(points+LL) 0.46 2.8 × 10-9 2.19 ± 0.10 –0.02 ± 0.16 0.73 1.2 × 10-26 2.66 ± 0.05 –0.83 ± 0.02
EpΓ0 (points) 0.73 5 × 10-12 1.47 ± 0.13 –0.24 ± 0.06 0.80 3.3 × 10-16 1.41 ± 0.11 0.25 ± 0.04
(points+LL) 0.42 8 × 10-8 1.28 ± 0.03 –0.40 ± 0.03 0.61 1 × 10-16 1.43 ± 0.03 0.07 ± 0.01

Notes. Spearman’s rank correlation coefficient r and associated chance probability P, correlation slope m and normalisation q for a model Y = mX + q (normalised according to Eqs. (17) and (18)) are reported for the homogeneous (s = 0) and wind (s = 2) case. For each correlation the results considering only GRBs with estimated Γ0 and including lower limits are given.

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