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Table 1.

Summary of the properties and calculated quantities used to describe the LGRBs in our population model.

Properties describing an LGRB:
Property Units Type Distribution Description

z Adjusted The redshift of the LGRB source
L erg s−1 Pk Adjusted The isotropic-equivalent bolometric peak luminosity
Ep keV Pk Adjusted The peak energy of the LE/E photon spectrum in the source frame

α Pk Fixed The low-energy slope of the photon spectrum LE/E in the source frame
β Pk Fixed The high-energy slope of the photon spectrum LE/E in the source frame

T90 s Ti Computed The duration over which 5–95% of photons are emitted in the source frame
Cvar Ti Computed The variability coefficient defined as the mean luminosity divided by the peak luminosity

Calculated quantities:

Quantity Units Type Description

Ep obs keV Pk The peak energy of the E2NEobs spectrum in the observer frame, Ep obs = Ep/(1 + z).
Npk ph s−1 cm−2 Pk The peak photon flux, calculated from z, L, Ep, α, β for any [Emin, obs;Emax, obs] (see Eq. (1))
Fpk erg s−1 cm−2 Pk The peak energy flux, calculated from z, L, Ep, α, β for any [Emin, obs;Emax, obs] (see Eq. (3))

T90 obs s Ti The duration over which 5–95% of photons are received in the observer frame, T90 obs = T90 (1 + z)
𝒩 ph cm−2 Ti The photon fluence, calculated from z, L, Ep, α, β, T90 and Cvar for any [Emin, obs;Emax, obs] (see Eq. (15))
erg cm−2 Ti The energy fluence, calculated from z, L, Ep, α, β, T90 and Cvar for any [Emin, obs;Emax, obs] (see Eq. (16))
Eiso erg Ti The isotropic-equivalent bolometric energy, Eiso = CvarT90L

Notes. In each table, the Pk type refers to quantities defined at peak brightness of the LGRB while the Ti indicates the quantity is time-integrated (i.e., it depends on the light curve of the LGRB). The first table lists the properties describing a single LGRB, always defined in the source frame. The top three properties’ distributions are adjusted by comparing the population to the observational constraints described in Sect. 3. They are completed by the next two properties, with fixed distribution (see Sect. 2.4) to entirely describe the emission at the peak brightness. The last two properties are only used for the additional crosschecks described in Sect. 3.5. Their distributions are computed (see Sect. 2.5). The second table lists the main quantities that are calculated from the physical properties in the first table, usually in the observer frame. They are used to build the mock samples as described in Sect. 2.6.

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