Analytical fits to the synchrotron functions

作     者：Mourad Fouka Saad Ouichaoui 

作者机构：Research Center in Astronomy Astrophysics and GeophysicsB. P. 63 Algiers ObservatoryBouzaréah Algiers Algeria Université des Sciences et de la Technologie Houari Boumediène (USTHB) Faculté dePhysique Laboratoire SNIRMB.P. 32 El-Alia 16111 Bab Ezzouar Algiers Algeria 

出 版 物：《Research in Astronomy and Astrophysics》 (天文和天体物理学研究（英文版）)

年 卷 期：2013年第13卷第6期

页      面：680-686页

核心收录：

学科分类：07[理学] 070401[理学-天体物理] 0704[理学-天文学] 

基　　金：supported by the National Administration of Scientific Research NASR-DZ  of Algeria  in the framework of National Projects of Research (NPR) 

主　　题：radiation processes: non thermal    methods: analytical 

摘      要：Accurate fitting formulae to the synchrotron function, F（x）, and its com- plementary function, G（x）, are performed and presented. The corresponding relative errors are less than 0.26% and 0.035% for F（x） and G（x）, respectively. To this end we have, first, fitted the modified Bessel functions, Ks/3（x） and K2/3（x）. For all the fitted functions, the general fit expression is the same, and is based on the well known asymptotic forms for low and large values of z for each function. It consists of multi- plying each asymptotic form by a function that tends to unity or zero for low and large values of z. Simple formulae are suggested in this paper, depending on adjustable parameters. The latter have been determined by adopting the Levenberg-Marquardt algorithm. The proposed formulae should be of great utility and simplicity for com- puting spectral powers and the degree of polarization for synchrotron radiation, both for laboratory and astrophysical applications.