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Astron. Astrophys. 326, 51-58 (1997)

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2. The average source

Here we have summed all EGRET data taken between May 1991 and October 1994 to obtain [FORMULA] -ray allsky maps of counts and exposure. A quality cut has been imposed by restricting the field-of-view in the individual viewing periods to 30 [FORMULA] off-axis angles before summing. At energies above 100 MeV we have performed a standard search for point sources using a maximum-likelihood technique (Mattox et al., 1996). The data in the energy range between 30 MeV and 100 MeV are usually neglected in this task since they add little to the statistics and source positioning, but require the energy-dependent point-spread function be averaged over an even larger energy range with corresponding systematic uncertainties. In total we found 148 excesses with a likelihood test statistic [FORMULA] of least 9, of which 44 are positionally coincident with AGN known to emit [FORMULA] -rays in the EGRET range. Table 1 lists these sources which can be further divided into BL Lacs on one side (11 objects) and FSRQs on the other side (33 objects). All sources except one (2155-304) have been observed with likelihood test statistic higher than 25 in individual viewing periods or specific combinations thereof (Thompson et al. 1995, 1996). The source 2155-304 is observed with likelihood test statistic of 33 in a later viewing period (VP 404) during Phase 4 of the CGRO observing program (Vestrand et al. 1996). We do not intend to find new AGN in our sample, but select the already identified ones for further analysis. Our threshold criterion of [FORMULA] thus corresponds to a detection significance of at least 3 [FORMULA] in the time-averaged data. Some AGN which have been found with high significance in individual viewing periods fail to show up in Table 1 since they have been absent in other viewing periods so that their average signal is below threshold.


Table 1. A list of radio sources which can be identified with point sources in the summed EGRET data of the time period 5/91 to 10/94 at energies above 100 MeV. The sources are categorized to belong either to the BL Lac class or to the class of FSRQ. The second column indicates the EGRET reference with acronyms for the second EGRET catalogue (2EG, Thompson et al. 1995), its supplement (2EGS, Thompson et al. 1996), and the papers by Mukherjee et al. (1997) (M) and Vestrand et al. (1996) (V). If there is at least a moderate level of variability, the third column gives the viewing period number for the peak flux in standard EGRET notation. No entry in this column indicates no evidence for variability. Note the following constraints for the selection of the viewing period of peak flux: the total statistical significance is required to be [FORMULA] and preference is given to data taken with smaller aspect angle in case of viewing periods of comparable duration and comparable source flux.

For all 44 AGN we have performed a spectral analysis. The positions of the [FORMULA] -ray sources have been set to those of the corresponding radio sources before doing a likelihood analysis of all 148 excesses in ten energy bands. Since the best model for the data consists of diffuse emission and 148 sources, we have to fit all these quasisimultaneously although we are interested only in the results for the 44 AGN. Observations of [FORMULA] -ray pulsars have shown that the calibrated effective area in the two low energy bins (30-50 MeV and 50-70 MeV) is overestimated. In the standard analysis the observed source flux is multiplied by a correction factor which accounts for the miscalibration. The accuracy of this correction factor can be estimated to be better than 30% at 30 MeV to 50 MeV and better than 10% at 50 MeV to 70 MeV (Fierro 1995, [FORMULA] 3.4).

We have summed the observed intensity in the ten energy bands to derive the spectrum of the average AGN. This spectrum is what we would get as contribution to the diffuse extragalactic background if the AGN were unresolved. This 'average' AGN spectrum can not be directly compared to other studies in which power-law fits of the spectra of individual AGN are averaged (e.g. Mukherjee et al. 1997). However for the purpose of comparison with the diffuse extragalactic background co-adding of the observed intensity spectra without any normalization or fitting procedure is the appropriate method. Since the radio catalogues are incomplete near the galactic plane we do not expect - and in fact we do not get - identifications for sources located at [FORMULA]. Thus effectively there are only [FORMULA] 10.4 steradian sky area which we have searched for point sources and which is to be used to derive the corresponding average [FORMULA] -ray intensity. The results is shown in Fig.1 separately for FSRQs and BL Lacs.

[FIGURE] Fig. 1. The summed intensity spectrum of the 33 identified FSRQ and 11 identified BL Lacs in the total EGRET allsky data above 100 MeV. The error bars are derived by Gaussian error propagation of the individual uncertainty measures. The spectrum of FSRQ is significantly softer than that of the diffuse background, while that of BL Lacs is consistent with it.

The sum of the [FORMULA] -ray intensity contribution of all 44 AGN is about 7% of the total diffuse background intensity. It is interesting to see that the [FORMULA] -ray spectrum of the average BL Lac seems to be harder than that of the average FSRQ. The difference in spectral index is [FORMULA] and is thus not very significant which is mainly due to the large uncertainties in the average BL Lac spectrum. This does not imply that in single viewing periods BL Lacs have always harder spectra than FSRQ. In fact we see a remarkable spread of spectral indices for both classes of objects when individual viewing periods are considered (Mukherjee et al., 1997). We also know that individual sources can change their spectrum: there is a trend that the spectrum hardens with increasing flux level (Mücke et al. 1996). But this concerns individual sources. The spectrum of the average in both object classes appears to be different, and therefore they would contribute with different spectral characteristic to the diffuse [FORMULA] -ray background.

The spectrum of the average AGN is dominated by that of the FSRQs and it differs significantly from that of the observed diffuse extragalactic background (Kniffen et al. 1996; Sreekumar et al., 1997) as we show in Fig.2. When fitting the ratio of both spectra with a power-law we find the background spectrum harder than that of the average AGN by [FORMULA] when all energy bins are considered and by [FORMULA] when only the data with very good statistics between 70 MeV and 4 GeV are considered. The goodness-of-fit for a constant is [FORMULA] and [FORMULA], respectively, which corresponds to about 2.7 [FORMULA] significance. A Fischer-Snedecor-test indicates that with 3.5 [FORMULA] significance a linear relation is a better fit to the intensity ratio than a constant. Especially between 70 MeV and 4 GeV the uncertainty of the background intensity is so small that the assumption of Gaussian statistics for the uncertainty of the intensity ratio can be regarded as a reasonable approximation. Since we see some objects only at flare state when they tend to have harder spectra, the true average spectrum of AGN may be even softer and thus further away from agreement with the observed spectrum of the [FORMULA] -ray background.

[FIGURE] Fig. 2. The ratio of the average intensity of all observed AGN to that of the extragalactic diffuse [FORMULA] -ray background. This ratio is not compatible with a constant and thus the observed AGN would, if they were unresolved, give a softer diffuse emission than we observe in the background. This implies that the background can not be the superposition of unresolved AGN with the same characteristics as the observed objects.

There is no cut-off visible in the [FORMULA] -ray spectra with the possible exception of a weak deficiency below 100 MeV for the FSRQs which may be the outer extension of the usual roll-over at a few MeV (Schönfelder et al. 1996). However, the expected spectral form of the average intensity is not necessarily power-law. Here we have summed over many sources with different spectra. Also some of the individual sources have changed their [FORMULA] -ray spectrum over the last years. A summation over different power-law like spectra results in a positive curvature of the average spectrum (Brecher and Burbidge 1972). Given the spread in spectral indices for the 44 sources we can estimate that the averaging should change the spectral index by around 0.1 between 100 MeV and 10 GeV.

We have also searched for systematic deviations from power-law behaviour in the [FORMULA] -ray spectra of the 44 AGN. For each individual AGN we have fitted a power-law spectrum to the data. The difference between this fit and the measured intensity in the ten energy bands weighted by the observational uncertainty, i.e. [FORMULA], has been summed for all N FSRQ and BL Lacs, respectively, to obtain the net deviation


where the applicability of Gaussian statistics has been assumed for the renormalization [FORMULA].

We have verified with Monte-Carlo simulations that there are no significant deviations from a Gaussian distribution of the number [FORMULA]. The results are shown in Fig.3. No significant deviations from power-law behaviour in the AGN spectra are observed, either for FSRQ or for BL Lacs. The BL Lac fit statistic is noisy.

[FIGURE] Fig. 3. The summed power-law fit statistic of the 33 identified FSRQ and 11 BL Lacs in the total EGRET allsky data according to Eq.1. There is no significant deviation from power-law behaviour in the average FSRQ and BL Lac spectrum. The two extreme values with opposite sign between 100 MeV and 300 MeV in the BL Lac result are unlikely to be real.
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Online publication: April 20, 1998