Ourabah Kamel
Theoretical Physics Laboratory, Faculty of Physics, University of Bab-Ezzouar, USTHB, Boite Postale 32, El Alia, Algiers 16111, Algeria.
Phys Rev E. 2022 Jun;105(6-1):064108. doi: 10.1103/PhysRevE.105.064108.
The observed distributions of stellar parameters, in particular, rotational and radial velocities, often depart from the Maxwellian (Gaussian) distribution. In the absence of a consistent statistical framework, these distributions are, in general, accounted for phenomenologically by employing power-law distributions, such as Tsallis or Kaniadakis distributions. Here we argue that the observed distributions correspond to locally Gaussian distributions, whose characteristic width is regarded as a statistical variable, in accordance with common knowledge that this parameter is mass dependent. The distributions arising within this picture correspond to superstatistics-a formalism emerging naturally in the context of self-gravitating media. We discuss in detail the distributions arising within this formalism and confront them with observational data of open clusters. We compute their moments and show that the Chandrasekhar-Münch relation remains invariant in this scenario. We also address the effect of these distributions on the thermalization of a massive body, e.g., a supermassive black hole, immersed in a stellar gas. We further discuss how the superstatistical picture clarifies certain ambiguities while offering a whole family of distributions (of which asymptotic power laws represent a special case), opening possibilities for fitting observational data.
观测到的恒星参数分布，特别是自转速度和径向速度，常常偏离麦克斯韦（高斯）分布。在缺乏一致的统计框架的情况下，一般通过采用幂律分布，如Tsallis分布或Kaniadakis分布，从现象学角度来解释这些分布。在此我们认为，观测到的分布对应于局部高斯分布，其特征宽度被视为一个统计变量，这与该参数依赖于质量这一常识相符。在此图景中产生的分布对应于超统计——一种在自引力介质背景下自然出现的形式体系。我们详细讨论了在此形式体系中产生的分布，并将它们与疏散星团的观测数据进行对比。我们计算了它们的矩，并表明在这种情况下钱德拉塞卡-明奇关系保持不变。我们还探讨了这些分布对沉浸在恒星气体中的大质量天体（如超大质量黑洞）热化的影响。我们进一步讨论了超统计图景如何在提供一整个分布族（其中渐近幂律是一个特殊情况）的同时澄清某些模糊之处，为拟合观测数据开辟了可能性。
