In the last few years detailed spectral data of AGNs have been obtained by GINGA in the energy range 2-30 keV. These high quality data have changed substantially our views on the spectral characteristics of AGNs. As shown convincingly by Pounds et al. (1990) and Nandra (1991), the typical spectrum of Seyfert 1 galaxies shows a flattening at ~ 10 keV, with respect to the observed power law slope in the range 2-10 keV. Such a flattening has been interpreted either as a partial coverage of an underlying X-ray power law continuum or as reprocessed emission (reflection) from thick relatively cold matter, possibly in an accretion disk. These observations showed that the average spectrum for these objects is very similar to the shape of the spectrum hypothesized by Schwartz and Tucker (1988). In their illuminating paper they had shown that such a spectrum, integrated through redshift with reasonable assumptions on the cosmological evolution, could provide an adequate fit to the shape of the observed XRB above 3 keV.
The Ginga data have immediately led a number of groups to construct models for fitting the XRB spectrum with various combinations of AGN spectra (see, for example, Morisawa et al. (1990), Fabian et al. (1990), Terasawa (1991), Rogers and Field (1991)). Although qualitatively in agreement with the overall shape of the XRB in the energy range 3-100 keV, these first models have been shown not to be able to fit satisfactorily the position and the width of the peak of the XRB spectrum (Zdziarski et al. 1993a). In the same paper Zdziarski et al. discuss two models which produce improved fits to the XRB. In the first model the major contribution to the XRB is due to an as yet unobserved AGN population at high redshift, while in the second model most of the XRB emission comes from foreground AGNs. Neither model is, however, fully compatible with the observed XRB spectrum and/or with the available AGN spectral data; in particular, the average spectra of the required foreground AGNs are different from the observed ones.
Figure 4 shows the results of a fit to the XRB spectrum obtained by Comastri et al. (1993). This model takes into account the observed spectral properties of different classes of AGNs over a broad energy range and is based on the X-ray properties of AGN unified schemes (Setti and Woltjer 1989). The main ingredients of the model are the following:
Given these assumptions, all of them consistent with the available observational data, the fit shown in Figure 4 has been obtained assuming an evolving volume emissivity (nL)z = (nL)0 x (1 + z), with = 2.75 (Boyle et al. 1993) for z zmax = 3.0. The number ratio between absorbed and unabsorbed Seyfert galaxies which is more consistent with the data is ~ 2.5, in good agreement with results from optical surveys (Huchra and Burg 1992). As shown in the Figure, the fit is really good over the energy range 3-100 keV; above 100 keV the computed model starts to departure significantly from the XRB data. It may be interesting to note, however, that while the data points in the energy range 20-100 keV derive essentially from the low energy experiment on HEAO-1 A4, most of the data between 100 and a few hundred keV are from the medium and high energy experiments on HEAO-1 A4: a difference in relative calibration of about (20-25)% between the low and high energy data would be enough to allow an acceptable fit at least up to ~ 300 keV. At even higher energies additional ingredients to the model are required in order to reproduce the observed data.
Figure 4. The XRB spectrum: comparison between model (continuous line) and data. The soft (0.5-2.0 keV) XRB spectrum is from ROSAT (solid lines from Hasinger et al. 1993; dashed lines from Wang and McCray 1993), while the data above 3 keV are taken from a compilation of the best experimental results by Gruber (1992).
Given the good fit to the XRB spectrum shown in Figure 4, can we conclude that the problem of the production of the XRB is definitely solved? Unfortunately, the answer is still "no." In fact, equally good fits to the XRB spectrum in the energy range 3-100 keV have recently been obtained with significantly different assumptions on the dominating AGN population by Zdziarski et al. (1993b) and Madau et al. (1993). While one of Zdziarski et al. models does not include any contribution from self-absorbed AGNs and identifies the primary sources of the XRB with AGNs detectable by soft X-ray imaging, Madau et al. model is instead dominated by type 2 objects at all energies > 3 keV.
The somewhat paradoxical conclusion from these results is that using the most recent AGN spectral data it has become too easy to obtain good fits to the XRB spectrum: very different models give equally good fits! As a consequence, a model that produces an acceptable fit to the XRB spectrum may not be the correct model. Before accepting it, one has to compare its predictions with other observational constraints, such as the soft (ROSAT) and hard (GINGA) log N - log S, the redshift distributions and the average spectra of soft and hard X-ray selected AGNs as a function of flux (see, for example, Franceschini et al. 1993). Finally, also the optical classification of X-ray selected AGNs (i.e. type 1 versus type 2) as a function of the X-ray band and flux would provide additional constraints and would help in reducing the wide parameter space still acceptable.