X射线脉冲星的谱形成及与Laguerre多项式有关的恒等式
Spectral Formation in X-Ray Pulsars and Associated Identities Involving the Laguerre Polynomials
摘要：
通过求解激波等离子体吸积到X射线脉冲星上时辐射谱形成的偏微分方程，得到了描述在恒星上方固定高度处注入等离子体的单色辐射散射的格林函数。光子和下落的电子之间的碰撞导致等离子体能量的有序和随机分量都被转移到辐射中，辐射通过扩散穿过吸积柱的壁而逃逸。格林函数的解析解提供了重要的物理洞察的形成，在X射线天体观测光谱。有趣的数学方面的问题，包括建立一个新的求和公式，涉及拉盖尔多项式的基础上计算的光子数密度通过整合的格林函数。
英文摘要：
The partial differential equation governing the formation of the radiation spectrum in the shocked plasma accreting onto an x-ray pulsar is solved to obtain the associated Green's function describing the scattering of monochromatic radiation injected into the plasma at a fixed altitude above the star. Collisions between the photons and the infalling electrons cause both the ordered and random components of the plasma energy to be transferred to the radiation, which escapes by diffusing through the walls of the accretion column. The analytical solution for the Green's function provides important physical insight into the formation of the observed spectra in x-ray pulsars. Interesting mathematical aspects of the problem include the establishment of a new summation formula involving the Laguerre polynomials, based on the calculation of the photon number density via integration of the Green's function.
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