Derivation of flux and spectral evolution from 1 s ratemeters

The ratio between counts in the GRBM and AC bands depends on source direction and spectrum. Because, as we have discussed in chapter 3, these data are equivalent to 2-channels spectra, we must assume simple model spectra, like a single power-law (PL) or an optically thin thermal bremsstrahlung (OTTB). Given the response in the two ratemeters bands (chapter 3), i.e. the efficiency as a function of photon energy at the given source direction, the GRBM/AC counts ratio is a function of the photon index (in case of PL) or temperature (in case of OTTB). Off course, these functions do not depend on the incident spectrum normalization. Thus, to derive these relationship we have convolved spectra having different photon indexes or temperature values with the detector response in the two ratemeters bands. In Fig. 4.7 we show the relationship between spectral index and counts ratio for LS1 and for on-axis source. Given the measured ratio, the spectral index or temperature is then derived by means of a cubic spline interpolation.

  

Figure 4.7: LS1 - Relationship between the ratio of GRBM and AC counts and spectral index for on-axis source assuming an high energy break in the photon spectrum at 700 keV

The normalization parameter of the spectrum can then be calculated by convolving an input spectrum of the extrapolated spectral index or temperature with the the responses of the GRBM detector in the entire energy band and comparing the measured counts to expected counts.

Background subtraction, for both the ratemeters , is generally a safe procedure, due to stable background. Exceptions have occurred, as for GRB970228 (Frontera et al., 1998) which occurred during the above mentioned 'pre-SAGA' anomaly and required specific efforts to extrapolate the background during the event. Generally, we interpolate the background in the GRBM and AC ratemeters during the event with a polynomial fit to the data before and after the event (about 150 s time intervals). After background subtraction, ratemeters data are analyzed through software which applies the methods described above to infer spectral index or temperature evolution together with photon flux evolution. Data are usually grouped to obtain more statistics quality for weak GRBs or to obtain average values in correspondence of the rise or fall of the pulses. It is important to note that with the actual thresholds values the energy bounds are 40-700 keV for the GRBM band and > 100 for the AC band. Because of the low efficiency of the detectors above 700 keV and the general shape of GRB spectra, we make the assumption that, except for the very first instants of some events, the source contribution to the counts above 700 keV is negligible. Thus, the difference between the counts in the GRBM and AC bands can be assumed to be almostly due to photons leaving in the detector an energy between 40 and 100 keV. Moreover, the 2 bands are overlapped in the region 100-700 keV, where the data are completely co-variant. This is taken into account when estimating the variance of the GRBM - AC (40-100 keV band) computed counts. In this computation we introduce the variance of the background above 700 keV, which is estimated by comparison of the AC average counts with the 240 channel spectra counts, from which it is possible to estimate the average 100-700 keV background contribution.
A typical result of GRBM spectral evolution analysis of a GRB obtained by applying the above methods is shown in Fig. 4.8 for GRB970111 ([Amati, L. et al. 1999]), One of the brightest events detected by the GRBM. The source were close to the LS3 axis ($\theta$=12.4$\rm ^{\circ}$,$\phi$=7.7$\rm ^{\circ}$); the GRB position was derived with high accuracy from WFC data.

  

Figure 4.8: Upper panel: GRB970111 1s light curves in the GRBM and AC (dashed) bands; lower panel: GRB970111 1s spectral index evolution inferred from the ratio between GRBM and AC counts assuming a power-law spectrum