4. Contribution to the soft X-ray background
In this section, we discuss the contribution of AGNs to the soft X-ray background using the various models of the SXLF. As the absolute intensity level of the extragalactic 0.5-2 keV CXRB intensity, we use the results of an ASCA-ROSAT simultaneous analysis on the ASCA LSS field (Miyaji et al. in preparation), which covers a much larger field than Miyaji et al. (1998) and thus is subject to less uncertainties due to source fluctuations. There still are uncertainties in separation of the Galactic hard thermal and extragalactic components. Especially, it is still not clear whether the extragalactic component has also a soft excess at [keV] over the extrapolation from higher energies or whether the observed excess is dominated by the Galactic hard thermal component. Some authors prefer a model where the extragalactic component also contributes to the [keV] excess because fit with a single power-law plus a thermal plasma would require an unusally low metal abundance of the thermal component for a Galactic plasma (Gendreau et al. 1995) and/or because many AGNs show soft excesses (e.g. Parmar et al. 1999). On the other hand, a self-consistent population synthesis model, including the AGN soft-excess below 1.3 keV, still predicts that the low-energy excess is not prominent in the 0.5-2 keV range (Miyaji et al. 1999b), mainly because the break energy shifts to the observed photon enrgy of [keV] for AGNs at , where the largest contribution to the CXRB is expected. The 0.25 keV extragalactic component measured using a shadowing of a few nearby galaxies (Warwick & Roberts 1998) is consistent with both the single power-law extrapolation case and a slight soft excess ( for [keV]).
In our comparison, we use as a probable range of the extragalactic 0.5-2 keV intensity, where the smaller value corresponds to the single power-law form of the extragalactic component and the larger value corresponds to the case where the extragalactic component steepens to a photon index of at [keV]. This range can be compared with the integrated intensity expected from the models.
In Fig. 10, we plot the cumulative soft X-ray (0.5-2 [keV]) intensities of the model AGN populations as functions of redshift, . As a reference, we have also plotted the cumulative contribution of the resolved AGNs in the sample, estimated by , where is the flux of the object i and is the available survey area at this flux (Fig. 1). The portion of the model curves above this line represents extrapolations to fainter fluxes than the limit of the deepest survey.
It is apparent from Fig. 10 that the PDE model produces almost 100% of the upper-estimate of the CXRB intensity, giving no room for, e.g. 10% contribution from clusters of galaxies (M99b), in the universe. In the low density universe with , the PDE model certainly overproduces the CXRB intensity. The PLE model produces about of the lower estimate of the CXRB in both cosmologies. The LDDE1 model, which best describes the data in the observed regime, explains about of the lower estimate of the CXRB intensity. The estimates are highly dependent on how one extrapolates the SXLF to fluxes fainter than the survey limit. In view of this, we explore an alternative LDDE model, which has been adjusted to make of the lower estimate of the extragalactic CXRB intensity, allowing contribution from clusters of galaxies. This version of the LDDE model (designated as LDDE2) has a fixed minimum evolution index in the LDDE formula. Then the first case of Eq. (10) is replaced by:
We do not intend to represent a particular physical picture behind this formula. We rather intend to search for a formally simple expression which makes 90% of the CXRB and is still consistent with our sample in the regime it covers. We have searched for models accepted by the KS tests by adjusting parameters , and by hand and fitting by the maximum-likelihood method with respect to other variable parameters, requiring that the models give an integrated intensity of . The parameter values of such LDDE2 models are listed in Table 4.
Table 4. Best-Fit LDDE2 Parameters.
By considering LDDE2, we have shown that there still is a resonable extrapolation of the AGN SXLF which makes up most of the soft CXRB. Of course this is not a unique solution. One may consider LDDE1 and LDDE2 as two possible extreme cases of how the SXLF can be extrapolated. Further implications are discussed in Sect. 6.
© European Southern Observatory (ESO) 2000
Online publication: December 8, 1999