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8.5. Radiative Efficiency

The efficiency of a burst depends on three factors: First only the electrons' energy is available. This yields a factor epsilone. Second, if epsilonB < epsilone there is an additional factor of min[1, (epsilonB / epsilone)1/2] if the IC radiation is not observed. Third, there is a specific Lorentz factor, hat{gamma}e, of an electron which emits synchrotron (or IC) radiation in the 100 keV energy band. Therefore, only the energy radiated by electrons with gammae geq hat{gamma}e is observed as soft gamma-rays. Assuming a power law electron distribution with an index p = 2.5 (see [103]) this gives a factor of (gammae,min / hat{gamma}e)1/2 (which is valid of course provided that gammae,min < hat{gamma}e). The total efficiency is the multiplication of those three factors and it is given by:

Equation 72 (72)

The efficiency depends first of all on the electrons' energy density and to a lesser extend on the magnetic energy density. Both should be close to equipartition in order that the efficiency will be large. Additionally, in order that there will be photons in the 100 keV range gammae,min should be smaller than hat{gamma}. However efficient production of soft gamma-rays requires that gammae,min will not be too small compared with hat{gamma}. This estimate is, of course, different if the observed gamma-rays are produced by inverse Compton scattering.