It is possible to derive a critical ratio of the total energy injected over the density
(see
Sari & Piran 1995):
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(2) |
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(3) |
The total energy being fixed, if the density is smaller than the critical value, the reverse shock does not contribute in gamma-rays and only produces a delayed X-ray emission with an intensity which increases with n. If the density reaches or exceeds the critical value, the X-ray and the gamma-ray profiles become very affected.
We have represented in Fig. 2 the profiles for a ratio (
). The gamma-ray profile is unchanged and the X-ray
profiles are improved. The corresponding E-W(E) diagram in Fig. 2
shows a well reproduced power-law over the complete energy range with an index -0.45
in agreement with the observations of GRB 960720. In the spectrum the contribution of
the reverse shock to the late emission appears like a X-ray plateau, which is observed
(and is even more extended) in GRB 960720.
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