The burst continuum from 10 keV to 100 MeV has a very simple shape: it is curved at low energies and becomes a power law at high energy. Indeed, the spectrum over these four decades can be characterized by a four-parameter function (Band et al. 1993)
where A' is chosen so that N(E) is continuous and differentiable at E = (alpha - beta)E0. All four parameters vary within and between bursts, but typically alpha~-1 and beta~ -2. The energy Ep at which E2 N(E) (which is proportional to vFv, the energy flux per energy decade) peaks characterizes whether a spectrum is hard or soft. If beta < -2 then Ep=(2+alpha)E0, otherwise Ep is above the energy where the high energy power law rolls over (such a rollover is not included in the above expression). Usually Ep is calculated from the low energy component, regardless of the value of beta. The observed Ep distribution is between 50 keV and 1 MeV, with a maximum at ~150 keV. The true Ep distribution may be broader because the energy band over which a detector triggers introduces a selection effect; in particular, there may be a large number of bursts with a high Ep (Piran and Narayan 1996). The Ep distribution is important since the relativistic fireball models link Ep to the fireball's Lorentz factor.
Deviations from this simple functional form are seen at high and low energies. Approximately 10% of a sample of bright BATSE bursts have low energy excesses; unfortunately this excess was discovered using a single broad low energy channel, and spectral information on this excess is unavailable (Preece et al. 1996). One of the 22 bursts observed by Ginga also has a low energy excess; otherwise the four parameter function describes the Ginga spectra between 2 and 400 keV (Strohmayer et al. 1998). The EGRET instrument on CGRO detects individual high energy photons with energies above 30 MeV with a spark chamber. Usually too few high energy photons are recorded to provide detailed spectral information. Nonetheless, there is a tendency for the emission at a ~GeV to linger after the lower energy burst (Dingus et al. 1994). In GRB 940217, a particularly bright burst, the high energy emission continued for ~90 minutes after the 160 second burst, with an 18 GeV photon, the highest energy burst emission yet observed, detected towards the end of this 90 minute period (Hurley et al. 1994).