arXiv 0802.44522008-02astro-phastro-ph.COastro-ph.HE

超高能cosmic ray核能谱的解析计算I. CMB辐射的情况

Analytic calculations of the spectra of ultra-high energy cosmic ray nuclei. I. The case of CMB radiation

R. Aloisio, V. Berezinsky, S. Grigorieva

备注：: The paper is the first part of a two papers series, it is composed by 41 pages, 4 appendixes and 27 eps figures, version accepted for publication in Astroparticle Physics
发表信息：: Astropart.Phys. 41 (2013) 73-93
DOI：: 10.1016/j.astropartphys.2012.07.010

摘要：

本文系统地研究了超高能核扩散谱的各种解析计算方法。在星系际空间中传播的核，由于与宇宙微波背景和河外背景光的相互作用，会发生光致衰变，降低其洛伦兹因子。我们计算了原子质量数$A$和洛伦兹因子$Γ$随红移$z$的后向时间演化轨迹。比较了三种光谱计算方法：{ \it（i）}轨迹法、{ \it（ii）}动力学方程结合轨迹法和{ \it（iii）}耦合动力学方程法。我们相信，这三种方法至少穷尽了问题的任何解析解的主要可能性。在最直接的方法{ \it（i）}中，仅使用轨迹计算来将观测到的核通量与初级（加速）核$A_0$的产生率联系起来。在第二种方法{ \it（ii）}中，借助于动力学方程计算了初级核、次级核和质子的通量（空间密度），而轨道仅用于确定这些核的产生率。第三种方法{ \it（iii）}包括求解完整的耦合动力学方程组，从初级核$A_0$开始，然后对于$A_0-1$等，直到感兴趣的$A$。前一个方程的解给出了下一个方程的生成率。所有方法的计算的一个重要元素是系统地使用洛伦兹因子而不是能量。这里考虑原子核只与宇宙微波背景相互作用的情况，这种情况特别适合于理解物理结果。

英文摘要：

We present a systematic study of different methods for the analytic calculation of ultra-high energy nuclei diffuse spectra. Nuclei propagating in the intergalactic space are photo-disintegrated and decrease their Lorentz factor due to the interaction with cosmic microwave background and extragalactic background light. We calculate the evolution trajectories in the backward time, that describe how atomic mass number $A$ and Lorentz factor $Γ$ change with redshift $z$. Three methods of spectra calculations are investigated and compared: {\it (i)} trajectory method, {\it(ii)} kinetic equation combined with trajectory calculations and {\it (iii)} coupled kinetic equations. We believe that these three methods exhaust at least the principal possibilities for any analytic solution of the problem. In the most straightforward method {\it(i)} only trajectory calculations are used to connect the observed nuclei flux with the production rate of primary (accelerated) nuclei $A_0$. In the second method {\it (ii)} the flux (space density) of primary nuclei, and secondary nuclei and protons are calculated with the help of kinetic equation and trajectories are used only to determine the generation rates of these nuclei. The third method {\it (iii)} consists in solving the complete set of coupled kinetic equations, written starting with primary nuclei $A_0$, then for $A_0-1$ etc down to the $A$ of interest. The solution of the preceding equation gives the generation rate for the one which follows. An important element of the calculations for all methods is the systematic use of Lorentz factor instead of energy. We consider here the interaction of nuclei only with the cosmic microwave background, this case is particularly suitable for understanding the physical results.

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