标题： 寻找热椭圆度分布 显示英文标题

标题： In Search of the Thermal Eccentricity Distribution

摘要： 大约一个世纪以前， Jeans（1919）发现，如果双星达到接近能量均分的状态，例如通过多次交换能量的动力学相互作用，它们的偏心率分布可以由以下公式描述：dN/de = 2e。 这被称为热化偏心率分布，并且已被广泛用于双星理论研究中的初始条件。 然而，观测表明，大多数观测到的双星的偏心率分布，尤其是那些质量小于 5 倍太阳质量的双星，比热化分布更平坦，并且更接近于均匀分布。 尽管如此，通常认为星团中的动力学相互作用会快速使双星热化，这可以证明在所有双星诞生时施加热化偏心率分布是合理的。 本文探讨了这一假设的有效性。 我们开发了自己的快速半解析模型来模拟星团中双星的演化，并与其他详细的 N体和蒙特卡洛星团模型进行了比较。 我们展示了，在几乎所有双星的情况下，动力学相互作用未能在星团的生命周期内将最初的均匀偏心率分布转换为热化分布。 因此，如果观察到热化偏心率分布，很可能是形成时就已印刻，而不是通过随后的长期动力学过程形成的。 那些初始化所有双星为热化分布的理论研究可能会对双星群体的演化做出错误预测。 这类模型可能会过高估计中等轨道分离双星的合并率，高估约两倍。 显示英文摘要

摘要： About a century ago, Jeans (1919) discovered that if binary stars reach a state approximating energy equipartition, for example through many dynamical encounters that exchange energy, their eccentricity distribution can be described by : dN/de = 2e. This is referred to as the thermal eccentricity distribution, and has been widely used for initial conditions in theoretical investigations of binary stars. However, observations suggest that the eccentricity distributions of most observed binaries, and particularly those with masses < 5 Msun, are flatter than thermal and follow more closely to a uniform distribution. Nonetheless, it is often argued that dynamical interactions in a star cluster would quickly thermalize the binaries, which could justify imposing a thermal eccentricity distribution at birth for all binaries. In this paper we investigate the validity of this assumption. We develop our own rapid semi-analytic model for binary evolution in star clusters, and also compare with detailed N-body and Monte Carlo star cluster models. We show that, for nearly all binaries, dynamical encounters fail to convert an initially uniform eccentricity distribution to thermal within a star cluster's lifetime. Thus, if a thermal eccentricity distribution is observed, it is likely imprinted upon formation rather than through subsequent long-term dynamical processing. Theoretical investigations that initialize all binaries with a thermal distribution will make incorrect predictions for the evolution of the binary population. Such models may overpredict the merger rate for binaries with modest orbital separations by a factor of about two.