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General kinematic considerations impose constraints on the temporal structure produced when the energy of a relativistic shell is converted to radiation. The enormous variability of the temporal profiles of GRBs from one burst to another in contrast to the relatively regular spectral characteristics, was probably the reason that until recently this aspect of GRBs was largely ignored. However, it turns out that the observed temporal structure sets a strong constraint on the energy conversion models [20, 230]. GRBs are highly variable (see section 2.2) and some configurations cannot produce such temporal profiles.

7.1. Time-scales

Special relativistic effects determine the observed duration of the burst from a relativistic shell (see Fig. 14).

Figure 14

Figure 14. Different time scales in terms of the arrival time of four photons: tA,tB, tC, and tD. Tradial = tC - tA; Tangular = tD - tA, Delta / c = tB - tA.

In addition there are two other time scales that are determined by the flow of the relativistic particles. These are:

Clearly Delta and delta must satisfy:

Equation 31 (31)

Finally we have to consider the cooling time scale.

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