Synchrotron cooling in energetic gamma-ray bursts observed by the Fermi Gamma-Ray Burst Monitor

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Table 2

Electron distribution index p for different cases.

Case^a	α	p = f(Δs)	f(1.2)–f(1.6)^b	f(1.0) ^c	p = g(β)	g(−2.0)–g(−2.4)^b	g(−1.7) ^c
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)

Fast, high	− 3/2	2Δs + 1	3.4–4.2	3.0	− 2(β + 1)	2.0–2.8	1.4
Slow, low	− 2/3	2(Δs + 1/6)	2.73–3.53	2.33	− 2β − 1	3.0–3.8	2.4
Both	− 2/3	2(Δs − − 1/3)	1.73–2.53	1.33	− 2(β + 1)	2.0–2.8	1.4

Notes.

^(a)

Preece et al. (2002), Eqs. (9), (10), and (12).

^(b)

Calculated from the ranges of peak and average values of Δs and β distributions for all eight bursts, given that 1.2 < (Δs)_peak< 1.4, 1.4 < (Δs)_average< 1.6, −2.2 <β_peak< −2.0, and −2.4 <β_average< −2.2.

^(c)

Calculated from the average values of Δs and β distributions for GRB 100724B alone.

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