Microphysics and dynamics of the gamma-ray burst 121024A

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Table 4

Closure relations^*. β = 0.86 ± 0.02 was use in the analysis.

		Instantaneous injection			Energy injection			Section^**
		α(β)			q(β,α)

		Spherical outflow

ν _c/m < ν ^a	ISM		=	0.95 ± 0.01		=	1.07 ± 0.05	4.1
ν _c/m < ν ^a	Wind		=	0.96 ± 0.01		=	1.07 ± 0.05	4.1

ν _m < ν < ν _c ^b	ISM		=	1.29 ± 0.03		=	0.69 ± 0.04	4.2
ν _m < ν < ν _c ^b	Wind		=	1.79 ± 0.03		=	−0.01 ± 0.05	4.2

		Uniform non-spreading jet

ν _c/m < ν ^a	ISM		=	1.70 ± 0.01		=	0.95 ± 0.05	4.1
ν _c/m < ν ^a	Wind		=	1.47 ± 0.01		=	1.13 ± 0.04	4.1

ν _m < ν < ν _c ^b	ISM		=	1.64 ± 0.01		=	0.65 ± 0.03	4.3
ν _m < ν < ν _c ^b	Wind		=	1.84 ± 0.01		=	0.43 ± 0.04	4.3

		Uniform spreading jet

ν _c/m < ν ^a	ISM/Wind		=	1.93 ± 0.01		=	0.79 ± 0.05	4.3

ν _m < ν < ν _c ^b	ISM/Wind	2β + 1	=	2.72 ± 0.04		=	0.35 ± 0.03	4.3

Notes. When determining the energy-injection parameter q, we use the measured α_pre = 0.86 ± 0.05 and α_post = 1.47 ± 0.03. The equations used for q are for the case when p > 2, for both spectral regimes. More details in Racusin et al. (2009).

^(*)

When ν_c < ν <ν_mβ = 0.5 and it does not depend on p or α. We did not include this scenario as it is not compatible with our data at any time.

^(**)

Details on the results and implications of the closure relations are discussed in the outlined section.

^(a)

For ν_c > ν, p = 2β. When β = 0.86 ± 0.02 we have p = 1.73 ± 0.03 (1 < p < 2).

^(b)

For ν_m < ν <ν_c. When β = 0.86 ± 0.02 we have p = 2.73 ± 0.03 (p > 2).

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