各向异性电子的康普顿散射理论
Theory of Compton scattering by anisotropic electrons
摘要：
康普顿散射在吸积黑洞、中子星、中子星、相对论喷流、星系团以及早期宇宙等天体物理中起着重要的作用。在大多数计算中，假定电子在某一坐标系中具有各向同性角分布。然而，存在由于体运动、或由同步辐射进行的各向异性冷却、或种子软光子的各向异性源而导致各向异性可能显著的情况。本文发展了一种各向异性分布的电子康普顿散射的解析理论，大大简化了计算。假设电子的角分布可以表示为一个二阶多项式的余弦的一些角度（偶极和四极各向异性），我们整合的角度上的确切的克莱因-Nishina截面。本文导出了描述任意角分布光子与各向异性电子康普顿散射的再分布函数的精确解析和近似公式。导出了相应的光子散射截面、散射光子的平均能量、色散和辐射压力的解析表达式。我们应用发达的形式主义的精确计算的热和运动的Sunyaev-Zeldovich效应的任意电子分布。
英文摘要：
Compton scattering plays an important role in various astrophysical objects such as accreting black holes and neutron stars, pulsars, and relativistic jets, clusters of galaxies as well as the early Universe. In most of the calculations it is assumed that the electrons have isotropic angular distribution in some frame. However, there are situations where the anisotropy may be significant due to the bulk motions, or anisotropic cooling by synchrotron radiation, or anisotropic source of seed soft photons. We develop here an analytical theory of Compton scattering by anisotropic distribution of electrons that can simplify significantly the calculations. Assuming that the electron angular distribution can be represented by a second order polynomial over cosine of some angle (dipole and quadrupole anisotropy), we integrate the exact Klein-Nishina cross-section over the angles. Exact analytical and approximate formulae valid for any photon and electron energies are derived for the redistribution functions describing Compton scattering of photons with arbitrary angular distribution by anisotropic electrons. The analytical expressions for the corresponding photon scattering cross-section on such electrons as well as the mean energy of scattered photons, its dispersion and radiation pressure force are also derived. We applied the developed formalism to the accurate calculations of the thermal and kinematic Sunyaev-Zeldovich effects for arbitrary electron distributions.
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