The whole X-ray sky has been well-surveyed in the energy band 2-10 keV to flux levels of > 3 x 10-11 erg cm-2 s-1 (Piccinotti et al 1982). The X-ray source counts have been extended down to a flux level of > 7 x 10-12 erg cm-2 s-1 in the 4-12 keV band over a small area of sky by Kondo (1990) using Ginga. The major classes of extragalactic X-ray sources found at the high flux levels are clusters of galaxies and AGN (mostly Seyfert galaxies, but also quasars and BL Lacs).
We can be certain that clusters are not a major contributor to the XRB since their luminosity functions are well-determined and their evolution with redshift known. The evolution of the X-ray luminosity of clusters is negative in the sense that the most luminous clusters are most numerous at the present epoch (Edge et al 1990, Gioia et al 1990a). An integration of their contribution to the XRB in the 4-12 keV band gives a result of about 3%. This fractional contribution increases in the soft X-ray band to about 10-12% and could be higher if most clusters had cooling flows that were stronger in the past.
Estimating the contribution of AGN is more difficult. Splitting them into the two major classes of Seyfert galaxies and quasars, we can make fair estimates of each class separately. The Seyfert luminosity function (which is dominated by Seyfert 1 galaxies) breaks at a luminosity, Lx ~ 1043 erg s-1, which dominates the resulting contribution of 10-20%. Their evolution is uncertain (see Danese et al 1986 for estimates and Section 4.2). The contribution of Seyfert 2 galaxies, which show strong intrinsic absorption, is poorly known but could be important. Using a recent compilation of Ginga X-ray data on Seyfert 2 galaxies, Awaki (1991) has shown that they could produce all the hard XRB if their number density exceeds three times that of Seyfert 1 galaxies and their spectra steepen above about 50 keV. Some optical studies suggest that the number density of Seyfert 2 galaxies is high.
The quasar contribution (and perhaps Seyferts evolve from quasars) is more difficult to assess since there is no reliable hard X-ray luminosity function. The well-measured soft X-ray luminosity function is discussed in the next section. Only a few quasars have been detected at energies above 3 keV. Most estimates of their contribution use some parametrization of the soft X-ray to optical luminosity ratio of quasars and their optical source counts, together with some assumption about the X-ray spectral shape of quasars. The results vary between a few 10s to 100%. More recently a number of isotropy results, to be discussed later, require that the quasar contribution be 70% or less.
A major problem with AGN as the source of the XRB is their spectra. Most of them are fitted by a power law of spectral index > 0.5 (Mushotzky 1982, Turner & Pounds 1989, Williams et al 1991), in the 2-10 keV band at least, whereas the XRB spectral index in that band is ~ 0.4. As will be discussed in the next section, radio-quiet quasars, the most numerous class, have soft X-ray spectra with > 1 (Wilkes & Elvis 1987, Canizares & White 1989). If this power law continues to higher energies then quasars are only a minor contributor to the XRB above 3 keV (Fabian et al 1989). However, it is possible that the spectra of AGN are complex, perhaps with 0.7 at lower energies, flattening to an index of 0.4 above 10 keV and then steepening to 1.5 or greater above about 100 keV (Schwartz & Tucker 1988).
Others have suggested that the intrinsic spectra of many AGN are steep, but are flattened at energies below 20 keV or so by intrinsic photoelectric absorption (Setti & Woltjer 1989, Morisawa et al 1990, Grindlay & Luke 1989). Seyfert 2 galaxies may be the dominant contributor. Although some reasonable fits have been made, to the spectrum of the XRB, this model provides no simple explanation for the 40 keV break in the XRB spectrum.
Strong limits on the total contribution of local sources have been obtained by Jahoda et al (1991) from their cross-correlation of the HEAO-1 A2 X-ray sky with bright galaxy counts. The weak positive signal that they obtain means that unevolved populations of X-ray sources correlated with present epoch galaxies can contribute only 13 ± 5% of the 2-10 keV XRB. This limit must include all classes of Seyfert galaxy, as well as groups and clusters, and, from the previous discussion, therefore provides a limit on the space density of Seyfert 2 galaxies (although some corrections from their different spectra are needed before a quantitative limit can be made).