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Table 5:

$\nu _{\rm c}$ estimated for possible cases on $\nu _{\rm m}^\prime $ and $\nu _{\rm c}^\prime $ in the two-component external shock model.

Case 		Condition $\nu _{\rm c}$ (Hz)
    Formula GRB 071112C GRB 080506

S1 		$\nu_{\rm m}^\prime < \nu_{\rm O} < \nu_{\rm c}^\prime < \nu_{\rm X}$ $\left( \frac{a}{A}\right)^2 10^{3(p-p^\prime)} \nu_{\rm c}^\prime$ < $ 1\times 10^{14}$ < $1 \times 10^{10}$

S2

 $\nu_{\rm m}^\prime < \nu_{\rm O} < \nu_{\rm X} < \nu_{\rm c}^\prime$ $\left( \frac{a}{A}\right)^2 10^{3(p-p^\prime)+18} $ < $ 6 \times 10^{14}$ $\surd$ $< 5 \times 10^{11}$

S3

 $\nu_{\rm O} < \nu_{\rm m}^\prime < \nu_{\rm c}^\prime < \nu_{\rm X}$ $\left( \frac{a}{A}\right)^2 10^{3p-18p^\prime+5} \nu_{\rm m}^{\prime p^\prime -1} \nu_{\rm c}^{\prime 5/3}$ see Fig. 5 $\surd$ see Fig. 5

S4

 $\nu_{\rm O} < \nu_{\rm m}^\prime < \nu_{\rm X}< \nu_{\rm c}^\prime $ $\left( \frac{a}{A}\right)^2 10^{3p-18p^\prime+23} \nu_{\rm c}^\prime$ < $ 3 \times 10^{17}$ $\surd$ < $3 \times 10^{15}$ $\surd$

S5

 $\nu_{\rm m}^\prime < \nu_{\rm c}^\prime < \nu_{\rm O} < \nu_{\rm X}$ $\left( \frac{a}{A}\right)^2 10^{33(p-p^\prime) +15}$ < $3 \times 10^{-8}$ <2

F1

 $\nu_{\rm c}^\prime < \nu_{\rm O} < \nu_{\rm m}^\prime < \nu_{\rm X}$ $\left(\frac{a}{A}\right)^2 10^{3p-9p^\prime+30}\nu_{\rm c}^{\prime (p^\prime -1)}$ < $ 1\times 10^{22}$ $\surd$ < $5 \times 10^{36}$ $\surd$

F2

 $\nu_{\rm c}^\prime < \nu_{\rm O} < \nu_{\rm X} < \nu_{\rm m}^\prime$ $\left( \frac{a}{A}\right)^2 10^{3p+12}$ < $2 \times 10^{13}$ < $ 1 \times 10^{15}$ $\surd$

F3

 $\nu_{\rm O} < \nu_{\rm c}^\prime < \nu_{\rm m}^\prime < \nu_{\rm X}$ $\left( \frac{a}{A}\right)^2 10^{3p-18p^\prime+5} \nu_{\rm m}^{\prime p^\prime -1/3} \nu_{\rm c}^\prime$ see Fig. 5 $\surd$ see Fig. 5

F4

 $\nu_{\rm O} < \nu_{\rm c}^\prime < \nu_{\rm X}< \nu_{\rm m}^\prime $ $\left(\frac{a}{A}\right)^2 10^{3p-18p^\prime+5}\nu_{\rm c}^{\prime p^\prime +2/3}$ < $ 5 \times 10^{16}$ $\surd$ < $ 6 \times 10^{13}$

F5

 $\nu_{\rm c}^\prime < \nu_{\rm m}^\prime < \nu_{\rm O} < \nu_{\rm X}$ $\left( \frac{a}{A}\right)^2 10^{33(p-p^\prime) +15} \nu_{\rm m}^\prime$ < $3 \times 10^{-8}$ < $4 \times 10^{13}$

Notes. The checks ($\surd$) show the cases that the present model can reproduce the observed SED variations.


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