Aboueisha Mohamed S, Nouh Mohamed I, Abdel-Salam Emad A-B, Kamel Tarek M, Beheary M M, Gadallah Kamel A K
Astronomy Department, National Research Institute of Astronomy and Geophysics, Helwan, 11421, Cairo, Egypt.
Department of Mathematics, Faculty of Science, New Valley University, El-Kharja, 72511, Egypt.
Sci Rep. 2023 Aug 31;13(1):14304. doi: 10.1038/s41598-023-41392-y.
Many stellar configurations, including white dwarfs, neutron stars, black holes, supermassive stars, and star clusters, rely on relativistic effects. The Tolman-Oppenheimer-Volkoff (TOV) equation of the polytropic gas sphere is ultimately a hydrostatic equilibrium equation developed from the general relativity framework. In the modified Riemann Liouville (mRL) frame, we formulate the fractional TOV (FTOV) equations and introduce an analytical solution. Using power series expansions in solving FTOV equations yields a limited physical range to the convergent power series solution. Therefore, combining the two techniques of Euler-Abel transformation and Padé approximation has been applied to improve the convergence of the obtained series solutions. For all possible values of the relativistic parameters ([Formula: see text]), we calculated twenty fractional gas models for the polytropic indexes n = 0, 0.5, 1, 1.5, 2. Investigating the impacts of fractional and relativistic parameters on the models revealed fascinating phenomena; the two effects for n = 0.5 are that the sphere's volume and mass decrease with increasing [Formula: see text] and the fractional parameter ([Formula: see text]). For n = 1, the volume decreases when [Formula: see text] = 0.1 and then increases when [Formula: see text] = 0.2 and 0.3. The volume of the sphere reduces as both [Formula: see text] and [Formula: see text] increase for n = 1.5 and n = 2. We calculated the maximum mass and the corresponding minimum radius of the white dwarfs modeled with polytropic index n = 3 and several fractional and relativistic parameter values. We obtained a mass limit for the white dwarfs somewhat near the Chandrasekhar limit for the integer models with small relativistic parameters ([Formula: see text], [Formula: see text]). The situation is altered by lowering the fractional parameter; the mass limit increases to M = 1.63348 M at [Formula: see text] and [Formula: see text].
许多恒星结构，包括白矮星、中子星、黑洞、超大质量恒星和星团，都依赖于相对论效应。多方气体球的托尔曼 - 奥本海默 - 沃尔科夫（TOV）方程最终是一个从广义相对论框架发展而来的流体静力学平衡方程。在修正的黎曼 - 刘维尔（mRL）框架中，我们构建了分数阶TOV（FTOV）方程并引入了一个解析解。在求解FTOV方程时使用幂级数展开会使收敛的幂级数解的物理范围有限。因此，已应用欧拉 - 阿贝尔变换和帕德逼近这两种技术来提高所得到的级数解的收敛性。对于相对论参数（[公式：见原文]）的所有可能值，我们针对多方指数n = 0、0.5、1、1.5、2计算了二十个分数气体模型。研究分数阶参数和相对论参数对模型的影响揭示了一些有趣的现象；对于n = 0.5的两种效应是，球体的体积和质量随着[公式：见原文]和分数阶参数（[公式：见原文]）的增加而减小。对于n = 1，当[公式：见原文] = 0.1时体积减小，然后当[公式：见原文] = 0.2和0.3时体积增加。对于n = 1.5和n = 2，球体的体积随着[公式：见原文]和[公式：见原文]的增加而减小。我们计算了用多方指数n = 3以及几个分数阶和相对论参数值建模的白矮星 的最大质量和相应的最小半径。对于具有小相对论参数（[公式：见原文]，[公式：见原文]）的整数模型，我们得到的白矮星质量极限有点接近钱德拉塞卡极限。通过降低分数阶参数情况会发生变化；在[公式：见原文]和[公式：见原文]时，质量极限增加到M = 1.63348 M。
