2 Spectral-hardness intensity correlation

We study the spectral hardness- intensity correlation with a direct approach. We plot 1191 events of the catalog on the intensity and spectral hardness plane (Fig. 1).

  

Figure 1: Peak counting rate of 1191 GRBs of the BATSE catalog against hardness-ratio, for the 1024 s temporal bin reported in the catalog. The events signed in grey color are those of the Pendleton et al. class, without photons with energy higher then 300 keV

The spectral hardness HR is given by the hardness-ratio, the ratio of the fluences in the energy ranges 100-300 and 50-100 keV; and the intensity ${P_{\rm C}}$ ($\rm s^{-1}~cm^{-2}$) by the peak counting rate of the GRB light curve, evaluated in the energy range 50-300 keV. Three values of this last parameter relative to three different bins of the accumulation time, 64, 256, 1024 ms respectively, are available in the catalog. Figure 1 shows the plot for 1024 ms accululation time. We observe that for each value of HR there are many possible values of the peak counting rate ${P_{\rm C}}$. One reason for this is the unknown distance at which the events occur. Another reason could be the presence of subsets with different luminosity functions for different light curve shapes and/or different spectral behaviors. As an example we recall the subset of GRBs without fluence over 300 keV (Pendleton et al. 1997), see the grey plot in Fig. 1. We consider for the analysis only the maximum and minimum value of the count rate for each HR.

  

Figure 2: Plots of peak photon flux ($\rm cm^{-2}\,s^{-1}$) and hardness-ratio of the BATSE GRBs, for the 1024 s temporal bins of Class I; the error bars are reported in the catalog

Observing the plot in Fig. 1, we can see that the intensity of GRBs (the maximum peak counting rate) can be represented as an increasing function of the spectral hardness HR below a given value of this parameter; for higher values it becomes a decreasing function. The best fit with a power law of the increasing part is: ${P_{\rm C}} = 2.95 \; {\rm HR}^{2.3}$, and of the decreasing part is: ${P_{\rm C}} = 2500 \; {\rm HR}^{-2.3}$, the best fits resulting the same for the three temporal bins. In a previous paper we devided GRBs in two Classes I and II in the plane D-HR, duration hardness-ratio. The two classes are at the right and at the left of the straight line ${\rm HR} = 2 \; {\rm D}^{0.5}$ respectively. Class I is essentially composed of the longest events and Class II of the shortest ones but not only. The two classes are characterized by two parameters, duration and hardness-ratio (Belli 1995). The reported effect is evident in Class II, and not in Class I (Fig. 2 and Fig. 3).