8.5. Radiative Efficiency
The efficiency of a burst depends on three factors: First only the electrons' energy is available. This yields a factor e. Second, if B < e there is an additional factor of min[1, (B / e)1/2] if the IC radiation is not observed. Third, there is a specific Lorentz factor, e, of an electron which emits synchrotron (or IC) radiation in the 100 keV energy band. Therefore, only the energy radiated by electrons with e e is observed as soft -rays. Assuming a power law electron distribution with an index p = 2.5 (see ) this gives a factor of (e,min / e)1/2 (which is valid of course provided that e,min < e). The total efficiency is the multiplication of those three factors and it is given by:
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 e,min should be smaller than . However efficient production of soft -rays requires that e,min will not be too small compared with . This estimate is, of course, different if the observed -rays are produced by inverse Compton scattering.