The autocorrelation function and fluctuations of the soft X-ray sky on scales from 1 arcmin to 5°

We investigate the spatial anisotropy and inhomogeneity of the soft X-ray sky, using one field of deep exposure and six collinear fields of medium exposure observed with the ROSAT Position Sensitive Proportional Counter. We first remove time-variable contaminations and excise bright sources from the data, followed by simultaneous spectral fitting to determine the diffuse extragalactic X-ray background count rate; we then reconstruct the strip composed of the six medium fields which span 2° (RA) x 7° (Dec.) of the sky. Using the deep field and the merged strip, we calculate the weighted angular autocorrelation function and the rms fluctuation of the surface intensity of the X-ray sky in the energy band-0.4-2.4 keV from 1 arcmin to 5°. The 2σ upper limit to excess fluctuation on scales down to a few arcmin is found to be lower than 20 per cent. As a result of using the low extragalactic background count rate determined from spectral fitting, the 2 a upper limits on the autocorrelation function are similar to previous values, some of which cover a higher energy band and some of which use a higher estimate of the extragalactic X-ray background (due to various contaminations or to the presence of brighter discrete sources). The weighted fitting of the observed autocorrelation function to a theoretical power-law model scaling as θ^-0.8 reduces the uncertainty and yields a 2σ upper limit = 3.86 x 10^-3θ^-0.8 over the scale of θ = 2-300 arcmin. It implies that the sources contributing the residual soft X-ray background must have a correlation length r₀ < 2 h^-1 Mpc if they lie at redshifts < 1, otherwise in general r₀ < 4 h^-1 Mpc.