Spectral properties

With no realistic information on the emission mechanism the interpretation of the energy spectra of the recorded events must start with an empirical approach. This was done by several authors who have tried to classify the GRBs on the basis of their spectral properties. An interesting result is that there is a general correlation between the hardness (that is, the ratio between a high energy channel and a low energy one) and the duration of the GRB: shorter bursts tend to be harder ([Kouveliotou et al. 1993]).

Another general spectral property of the GRBs is the characteristic hard-to-soft evolution during a single peak ([Norris et al. 1986,Ford et al. 1995,Piro et al. 1998a]). This is observed basically in every GRB for which time-resolved spectra, or at least hardness ratios, are available. Possibly connected with this (in case a synchrotron emission mechanism is responsible for the observed radiation) is also the observed property that the duration of single-peaks increases with the square root of decreasing energy ([Fenimore et al 1995]).

A very recent analysis on the global spectral properties of GRBs has been performed by Pendleton et al. ([Pendleton et al. 1997]) with the very intriguing result of a classification of GRB pulses in HE (High Energy) and NHE (No High Energy) types, on the basis of existence of emission at energies above 300 keV. These two classes seem rather well separated and the NHE type shows an effective homogeneous intensity distribution, unlike the NHE one.

Finally, for what concerns the time-averaged GRB spectra, Band et al. ([Band et al. 1993]) found a good analytical description over the energy range covered by the BATSE experiment, that is 30 keV to 2 MeV. This law is basically consisting of two power laws smoothly connected through an exponential:

$N(E) = A\cdot\left(\frac{E}{100keV}\right)^{\alpha}\cdot\exp{\left({-E/E_{0}}\right)}$, $({\alpha} - {\beta})\cdot E_{0}\hbox{ }\ge\hbox{ } E$

$N(E) = A\cdot\left[\frac{({\alpha} - {\beta})\cdot E_{0}}{100keV}\right]^{\alpha - \beta}\cdot \exp{(\beta - \alpha)}\cdot \left(\frac{E}{100keV}\right)^{\beta}$, $({\alpha} - {\beta})\cdot E_{0}\hbox{ }\le\hbox{ } E$

The physical parameters of this functional are the two photon indices and the break energy. They are almost free to vary, but for the fact that the high energy power law index $\beta$ must always be larger than the low energy one $\alpha$. Band et al. find, on a sample of 54 GRBs detected by the BATSE experiment from 1991 to 1992, that the parameters vary in a rather limited range. In particular $-1.5<\alpha<+1.0$, $-5.0<\beta<-1.5$ and E₀ ranges from below 100 keV to above 1 MeV, but with a distribution peaked around 200 keV.

It is very interesting that the Band law is able to account for the GRB energy spectra on the basis of only 3 parameters. The values of these can be actually biased by the restricted energy range of the BATSE experiment. Unfortunately the available sample of energy spectra of GRBs in energy ranges other than the BATSE one is pretty limited. In the past a good sample of GRBs (about 122) were detected by the X and Gamma detectors aboard the Japanese-US satellite Ginga. An analysis of about one third of them by Strohmayer et al. ([Strohmayer et al. 1998]) in the energy range from 2 to 400 keV suggests the possible existence of a further energy break at low energies. A drastic change has been inferred by BeppoSAX satellite that has so far detected 15 GRBs in the energy range from 2 to 700 keV and will detect more in the next two years. The analysis of these events (see chapter 6) reveals a substantial agreement with the Band law.