Boltzmann approach to the large-angle cosmic X-ray background fluctuations

Large-angle fluctuations in the cosmic X-ray background are investigated by a new formalism with a simple model of the X-ray sources. Our method is formulated from the Boltzmann equation and a simple extension of the work by Lahav et al. to be applicable to a hyperbolic (open) universe. The low multipole fluctuations due to the source clustering are analysed in various cosmological models in both numerical and analytic ways. The fluctuations strongly depend on the X-ray source evolution model, as pointed out previously. It turns out that the nearby (z less than or similar to 0.1) sources are the dominant contributors to the large-angle fluctuations. If these nearby sources are removed in an observed X-ray map, the dipole (low multipole) moment of the fluctuation drastically decreases. In this case the Compton-Getting effect of an observer's motion can be a dominant contribution to the dipole fluctuation. This feature of fluctuation, relating to the matter power spectrum, is discussed.