Open Access
Table 1.
Full set of population parameters and the associated priors.
| Parameter | Prior | Description |
|---|---|---|
| Empirical luminosity function model | ||
| αBPL | Uniform, αBPL ∈ [ − 1, 5] | |
| βBPL | Uniform, βBPL ∈ [0, 5] | Slopes of the luminosity PDF in the dP/dlnL representation |
| γBPL | Uniform, γBPL ∈ [ − 5, 5] | |
| L0 | Uniform-in-log, L0 ∈ [1044, 1047] erg s−1 | Minimum luminosity |
| L** | Uniform-in-log, L** ∈ [L0, 1051 erg s−1] | Low-luminosity break |
| L* | Uniform-in-log, L* ∈ [1051, 1056] erg s−1 | High-luminosity break |
| Ep★ | Uniform-in-log, Ep★ ∈ [102, 105] keV | Central Ep at L = L* in L − Ep correlation |
| Quasi-universal structured jet model | ||
| θc | Isotropic, θc ∈ [0.01, π/2] rad | Core half-opening angle |
| θw | Isotropic, θw ∈ [θc, π/2 rad] | Structure ‘break’ angle |
| αL | Uniform, αL ∈ [0, 6] | Slope of ℓ at intermediate viewing angles θc ≤ θv < θw |
| βL | Uniform, βL ∈ [ − 3, 6] | Slope of ℓ at large viewing angles θv ≥ θw |
| Lc★ | Uniform-in-log, Lc★ ∈ [3 × 1051, 1055] erg s−1 | Typical luminosity for on-axis observers (θv = 0) |
| A | Uniform, A ∈ [1.5, 5] | Slope of Lc distribution |
| Ep, c★ | Uniform-in-log, Ep, c★ ∈ [102, 105] keV | Typical Ep for on-axis observers (θv = 0) |
| αEp | Uniform, αEp ∈ [0, 6] | Slope of η at intermediate viewing angles θc ≤ θv < θw |
| βEp | Uniform, βEp ∈ [ − 3, 6] | Slope of η at large viewing angles θv ≥ θw |
| Common parameters | ||
| y | Uniform, y ∈ [ − 3, 3] | L − Ep correlation slope |
| σc | Uniform-in-log, σc ∈ [0.3, 3] | Ep dispersion in L − Ep correlation |
| τdmin | Uniform-in-log, τdmin ∈ [0.005, 3] Gyr | Minimum delay between progenitor formation and SGRB |
| ατ | Uniform, αt ∈ [0, 5] | Slope of power-law DTD |
| μτ | Uniform-in-log, μt ∈ [0.01, 5] Gyr | Median of the log-normal DTD |
| στ | Uniform-in-log, σt ∈ [0.01, 5] | Standard deviation for the log-normal DTD |
| R0 | Uniform-in-log, R0 ∈ [1, 104] Gpc−3 yr−1 | Short GRB local rate density |
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