Scaling Laws in High-Energy Inverse Compton Scattering. II. Effect of Bulk Motions

We study the inverse Compton scattering of the CMB photons off high-energy nonthermal electrons. We extend the formalism obtained by the previous paper to the case where the electrons have non-zero bulk motions with respect to the CMB frame. Assuming the power-law electron distribution, we find the same scaling law for the probability distribution function P_{1,K}(s) as P_{1}(s) which corresponds to the zero bulk motions, where the peak height and peak position depend only on the power-index parameter. We solved the rate equation analytically. It is found that the spectral intensity function also has the same scaling law. The effect of the bulk motions to the spectral intensity function is found to be small. The present study will be applicable to the analysis of the X-ray and gamma-ray emission models from various astrophysical objects with non-zero bulk motions such as radio galaxies and astrophysical jets.

Scaling Laws in High-Energy Inverse Compton Scattering

Based upon the rate equations for the photon distribution function obtained in the previous paper, we study the inverse Compton scattering process for high-energy nonthermal electrons. Assuming the power-law electron distribution, we find a scaling law in the probability distribution function P_1(s), where the peak height and peak position depend only on the power index parameter. We solved the rate equation analytically. It is found that the spectral intensity function also has the scaling law, where the peak height and peak position depend only on the power index parameter. The present study will be particularly important to the analysis of the X-ray and gamma-ray emission models from various astrophysical objects such as radio galaxies and supernova remnants.

The Second Born Corrections to the Electrical and Thermal Conductivities of Dense Matter in the Liquid Metal Phase

The second Born corrections to the electrical and thermal conductivities are calculated for the dense matter in the liquid metal phase for various elemental compositions of astrophysical importance. Inclusion up to the second Born corrections is sufficiently accurate for the Coulomb scattering of the electrons by the atomic nuclei with Z < 26. Our approach is semi-analytical, and is in contrast to that of the previous authors who have used fully numerical values of the cross section for the Coulomb scattering of the electron by the atomic nucleus. The merit of the present semi-analytical approach is that this approach affords us to obtain the results with reliable Z-dependence and rho-dependence. The previous fully numerical approach has made use of the numerical values of the cross section for the scattering of the electron off the atomic nucleus for a limited number of Z-values, Z=6, 13, 29, 50, 82, and 92, and for a limited number of electron energies, 0.05MeV, 0.1MeV, 0.2MeV, 0.4MeV, 0.7MeV, 1MeV, 2MeV, 4MeV, and 10MeV. Our study, however, has confirmed that the previous results are sufficiently accurate. They are recovered, if the terms higher than the second Born terms are taken into account. We make a detailed comparison of the present results with those of the previous authors. The numerical results are parameterized in a form of analytic formulae that would facilitate practical uses of the results. We also extend our calculations to the case of mixtures of nuclear species. The corresponding subroutine can be retrieved from http://www.ph.sophia.ac.jp/~itoh-ken/subroutine/subroutine.htm