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 ≲ 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.
The chiral magnetic effect emerges from a miroscopic level, and its interesting consequences have been discussed in the dynamics of the early universe, neutron stars and quark-gluon plasma. An instability is caused by anomalous electric current along magnetic field. We investigate effects of plasma motion on the instability in terms of linearized perturbation theory. A magnetic field can inhibit magnetohydrodynamic waves to a remarkable degree and thereby affects the instability mode. We also found that the unstable mode is consisted of coupling between Alfvén and one of magneto-acoustic waves. Therefore, the propagation of a mixed Alfvén wave driven by magnetic tension is very important. The direction of unperturbed magnetic field favors the wave propagation of the instability mode, when Alfvén speed exceeds sound speed.
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