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 E2 NEobs 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)) | |
ℱ | 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 = Cvar T90 L |
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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