球状星团中致密双星群体的演化：Boltzmann研究II。引入随机性
Evolution of Compact-Binary Populations in Globular Clusters: A Boltzmann Study II. Introducing Stochasticity
摘要：
我们继续探索Banerjee和Ghosh（2007，以下简称论文I）提出的研究球状星团致密双星种群演化的Boltzmann方案，在本文中介绍了我们处理球状星团中双星形成、破坏和硬化动力学过程中固有随机性的方法。我们描述这些随机过程为“维纳过程”，于是玻尔兹曼方程成为一个随机偏微分方程，其解决方案需要使用“伊藤演算”（这是第一次使用，据我们所知，在这个主题），除了普通的微积分。我们着重研究了球状星团中X射线双星$N_{XB}$的数量和轨道周期分布的演化。我们表明，虽然在上述数量的波动的细节不同，从一个“实现”到另一个随机过程，一般的趋势遵循那些发现在连续极限研究的论文我，和平均结果在许多这样的实现是接近连续极限的结果。我们研究了通过这些计算得到的$N_{XB}$对两个基本的球状星团参数的依赖性，这两个参数是恒星-恒星和恒星-双星的加速率参数$Γ$和$γ$，我们在论文I中为它们取了Verbunt参数的名字。我们比较了我们的计算结果与银河系球状星团的CHANNEL观测结果，表明预期的$N_{XB}$与Verbunt参数的标度与观测结果吻合得很好。我们指出什么额外的功能可以纳入该计划在未来，以及如何更复杂的问题可以解决。
英文摘要：
We continue exploration of the Boltzmann scheme started in Banerjee and Ghosh (2007, henceforth Paper I) for studying the evolution of compact-binary populations of globular clusters, introducing in this paper our method of handling the stochasticity inherent in dynamical processes of binary formation, destruction and hardening in globular clusters. We describe these stochastic processes as "Wiener processes", whereupon the Boltzmann equation becomes a stochastic partial differential equation, the solution of which requires the use of "Ito calculus" (this use being the first, to our knowledge, in this subject), in addition to ordinary calculus. We focus on the evolution of (a) the number of X-ray binaries $N_{XB}$ in globular clusters, and (b) the orbital-period distribution of these binaries. We show that, although the details of the fluctuations in the above quantities differ from one "realization" to another of the stochastic processes, the general trends follow those found in the continuous-limit study of Paper I, and the average result over many such realizations is close to the continuous-limit result. We investigate the dependence of $N_{XB}$ found by these calculations on two essential globular-cluster parameters, namely, the star-star and star-binary encounter-rate parameters $Γ$ and $γ$, for which we had coined the name Verbunt parameters in Paper I. We compare our computed results with those from CHANDRA observations of Galactic globular clusters, showing that the expected scalings of $N_{XB}$ with the Verbunt parameters are in good agreement with the observed ones. We indicate what additional features can be incorporated into the scheme in future, and how more elaborate problems can be tackled.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
