Table 1
Parameters of all the GRB pulse models discussed in the paper.
| Case | Dynamics | Microphysics | Spec. @ max. | Spectro-temporal properties | Figures | |||||||||
| Ejection | E kin,iso | Γ(t) |
|
ζ | ϵ B | p | E p,obs | α | τ r / τ d | a(W(E)) | δ (HIC) | κ (HIC) | ||
| [erg] | [keV] | |||||||||||||
|
|
||||||||||||||
| A | Ė = cst | 1.00 × 1054 | smooth | 340 | 3.00 × 10-3 | 1 / 3 | 2.5 | 731 | -1.5 | 0.38 | 0.29 | 2.28 | 2.16 | 1, 2, 3, 4, 18, 16, 17 |
| 3.40 × 10-3 | 2.7 | 731 | −1.5 | 0.39 | 0.30 | 2.15 | 1.97 | 15, 17 | ||||||
| varying | 744 | −1.4 | 0.31 | 0.28 | 2.23 | 1.55 | 10, 18, 16, 17 | |||||||
| varying | 2.7 | 744 | −1.4 | 0.30 | 0.29 | 2.12 | 1.48 | 15, 17 | ||||||
|
|
||||||||||||||
| 4.00 × 10-4 | 2.1 | 912 | −1.2 | 0.41 | 0.14 | / | / | 5, 6, 7 | ||||||
| 8.80 × 10-4 | 2.3 | 666 | −1.1 | 0.46 | 0.18 | / | / | 5, 6, 7 | ||||||
| B | Ė = cst | 1.00 × 1054 | smooth | 340 | 1.00 × 10-3 | 10 -3 | 2.5 | 642 | -1.1 | 0.43 | 0.23 | / | / | 1, 2, 3, 4, 5, 6, 7, 12, 18, 16, 17 |
| 1.10 × 10-3 | 2.7 | 619 | −1.1 | 0.54 | 0.24 | 0.97 | 0.89 | 5, 6, 7, 15, 17 | ||||||
| 1.15 × 10-3 | 2.9 | 630 | −1.1 | 0.54 | 0.27 | 1.23 | 1.05 | 5, 6, 7 | ||||||
| 1.20 × 10-3 | 3.1 | 619 | −1.1 | 0.54 | 0.27 | 1.31 | 1.07 | |||||||
| 1.23 × 10-3 | 3.3 | 619 | −1.1 | 0.54 | 0.28 | 1.32 | 1.06 | |||||||
| varying | 679 | −1.1 | 0.33 | 0.24 | 0.96 | 0.80 | 8, 10, 11, 9, 18, 16, 17 | |||||||
| varying | 2.7 | 679 | −1.1 | 0.32 | 0.27 | 1.27 | 0.97 | 15, 17 | ||||||
| 1.50 × 1054 | 360 | varying | 691 | −1.1 | 0.37 | 0.24 | / | / | 8, 10, 11, 9, 18, 16, 17 | |||||
| 1.50 × 1054 | 360 | varying | 2.7 | 679 | −1.1 | 0.36 | 0.26 | 0.92 | 0.78 | 15, 17 | ||||
| 5.85 × 1053 | sharp | 2.00 × 10-3 | 744 | −1.2 | 0.68 | 0.18 | / | / | 13, 12, 18, 16 | |||||
| 5.85 × 1053 | sharp | varying | 772 | −1.1 | 0.04 | 0.25 | / | / | 13, 18, 16 | |||||
| Ṁ = cst | 1.85 × 1054 | 6.00 × 10-4 | 679 | −1.1 | 0.75 | 0.16 | 0.13 | 0.17 | 14, 12, 18, 16 | |||||
| Ṁ = cst | 1.85 × 1054 | varying | 630 | −1.1 | 0.60 | 0.16 | / | / | 14, 18, 16 | |||||
|
|
||||||||||||||
| C | Ė = cst | 1.00 × 1053 | smooth | 1020 | 1.00 × 10-3 | 10 -1 | 2.5 | 164 | -0.7 | 0.55 | 0.11 | / | / | 1, 2, 3, 4 |
Notes. The three reference cases defined in Sect. 3 are listed in bold face. For other models discussed in Sects. 4 and 5, we list only the input parameters that are modified compared to the reference case. The first columns list the parameters for the dynamics and the microphysics (see text). In all cases, ϵe = 1/3. The last columns list a few properties of the corresponding simulated GRB pulse: spectral properties at the maximum of the GBM light curve (peak energy and low-energy photon index), and four indicators of the spectral and temporal properties: ratio of the rise time over the decay time of the pulse (BATSE 2+3 channel), index a for the evolution of the pulse width W(E) with energy (W(E) ∝ E− a), slopes of the hardness-intensity correlation (δ is the slope when using the photon flux and κ the energy flux), see text. Cases where it is not possible to define the slopes of the HIC are indicated with “/”. For reference, typical observed values are τr/τd ≃ 0.3−0.5 (Norris et al. 1996), a ≃ 0.3−0.4 (Norris et al. 1996; Bissaldi et al. 2011), δ ≃ 0.4−1.1 (Ryde & Svensson 2002), and κ ≃ 0.3−1.2 (Lu et al. 2012); see Sect. 2. The last column lists figures in the paper where some properties of each case are shown.
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