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Table 1

Common hyper-parameters for both the BNS- and BHNS-originated GRB population model.

Hyper-parameter Description Default value
Rn Normalisation factor of the cosmic merger rate of BNS merger 50 Gpc−3 yr−1
τ the averaged time-delay between the binary star formation and BNS merger 10 Gyr
Δθmean Mean jet opening angle 15°
Δθstd Standard deviation of the jet opening angle
log r0,mean Mean log GRB radius 13 log cm
log r0,std Standard deviation of log GRB radius 0.1 log cm
log EGRB,mean Mean of total GRB energy 49.3 log ergs
log EGRB,std Standard deviation of total GRB energy 0.5 log ergs
the mean value of the reference frequency in the jet co-moving frame 0.001 MeV
Standard deviation of the reference frequency in the jet co-moving frame 0.00075 MeV
γmean Mean of the bulk Lorentz factor 250
γstd Standard deviation of the bulk Lorentz factor 75
td,std Standard deviation of the time delay td 0.4 s

Notes. Their default values are listed in the third column, with which the historical observation can be optimally reconstructed.

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