Annu. Rev. Astron. Astrophys. 1992. 30: 429-456
Copyright © 1992 by Annual Reviews Inc. All rights reserved

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The lack of obvious anisotropies (except for the dipole) in the high-Galactic latitude XRB strongly suggests that it can provide strong constraints on the lumpiness of the X-ray Universe Given that its origin is presumably due to redshifts of 0.5-3, it is striking that the enormous observed inhomogeneities in the local Universe (voids, walls, superclusters) are not strongly mapped as anisotropies in the XRB, diluted of course by the presence of many such structures along the line of sight. As seen in Figure 2, some nearby structures do show through at the low level of a few percent or less [as indicated by the strength of W(theta)], but there are no signs of the effect of more distant structures, nor do the isotropy measures allow for much variation or inhomogeneities in the distribution of the sources that contribute most of the XRB. The smoothness of the XRB argues that the Universe is smooth on scales greater than about a hundred Mpc.

Upper limits to the correlation function on several angular scales are especially relevant here. Taking z = 1 as a reference redshift. 1 Mpc corresponds to angular separations of 4 arcmin, implying that the ACF of the XRB on those scales will be dominated by the extension of the clustering of clusters of galaxies, galaxies, and QSOs. Recent analyses of ROSAT deep images, where about 30% of the XRB has been identified as arising in (subsequently removed) sources, still have very stringent limits on the autocorrelation function of the residual background (W ltapprox 10-3). This constrains any correlation length of these sources to less than 4 or 5 Mpc (Carrera et al 1992) and may provide strong evidence for the evolution of clustering in the Universe.

On degree scales, the general upper limit to the ACF is about 10-4 with a possible detection at the level of 3 x 10-5 at 10° (Mushotzky 1992). This leads to similar conclusions about the correlation length. On the other hand, Carrera et al (1991a) found weak evidence for a negative autocorrelation function on a scale of ~ 2°. Subsequent analysis of some Ginga scans seems to show a similar tendency although on slightly larger scales and at a similar significance level (less than 2sigma; Carrera et al 1992). This is expected if a few per cent of the XRB arises in sources following a void- and-wall distribution as is currently seen in optical redshift surveys (de Lapparent et al 1986).

Upper limits to any excess fluctuations in the P(D) noise (see again Figure 5) can be directly related to density fluctuations in the Universe (delta rho/rho) assuming that X-rays trace mass. Specific conclusions require a redshift distribution to be assumed for the X-ray sources contributing to the background. In Figure 9 we show upper limits to the density fluctuations on several comoving scales assuming. for simplicity, that the XRB comes from a redshift range Deltaz approx 1 around z = 2 and that the source correlation function has a Gaussian shape. Current upper limits on (DeltaI/I)excess constitute the best direct evidence of large-scale homogeneity of the Universe at these intermediate redshifts. If ROSAT or future ~ 1 arcmin resolution telescopes can constrain (DeltaI/I)excess ltapprox 0.1, relevant upper limits to the lumpiness of the Universe on scales ltapprox 10 Mpc will be found.

Figure 9

Figure 9. Upper limits to the density fluctuations in the Universe as a function of comoving scale (see text for details) derived from upper limits on excess fluctuations. The dotted curve illustrates the constraints obtained if an upper limit of 10% is obtained from an instrument with an ~ arcmin beam. The solid point represents a present mass overdensity of 1.4 on a scale of 37h-1 Mpc, as inferred for the Shapley Supercluster by Fabian (1991). Astro-D should enable limits to be placed which are about ten times lower (in delta rho/rho) than the ROSAT ones shown here.

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