论文标题
宽二进制的偏心分布
The Eccentricity Distribution of Wide Binaries
论文作者
论文摘要
未来的Gaia和Legacy对时空数据发布的调查以及广泛的光谱调查将提供具有相位空间坐标的已解决的二进制恒星样本，尽管具有低效果。给定一个偏心法$ f（ε）$，我们得出（i）（i）速度分布$ v/\ sqrt {g m/r} $由圆形轨道归一化的速度分布$ v/\ sqrt {g m/r} $在测量的分离$ r $; （ii）天文加速度分布$ a/\ left（g m/r^2 \右）$再次正常于圆形轨道值。如果数据采样的时间尺度可与二进制时期相媲美，则我们的公式对某些常用的偏心率定律的完整统计分布产生了分析预测。特别是，线性偏心定律的速度分布非常简单。通过贝叶斯分析，我们建议一种基于测得的速度分布来推断偏心率分布的方法。
Future Gaia and Legacy Survey of Space and Time data releases, together with wide area spectroscopic surveys, will deliver large samples of resolved binary stars with phase space coordinates, albeit with low-cadence. Given an eccentricity law $f(ε)$, we derive properties of (i) the velocity distribution $v/\sqrt{G M/r}$ normalised by the value for a circular orbit at the measured separation $r$; (ii) the astrometric acceleration distributions $a/\left(G M/r^2\right)$ again normalised to the circular orbit value. Our formulation yields analytic predictions for the full statistical distribution for some commonly used eccentricity laws, if the timescale of data-sampling is comparable to or exceeds the binary period. In particular, the velocity distribution for the linear eccentricity law is surprisingly simple. With Bayesian analysis, we suggest a method to infer the eccentricity distribution based on the measured velocity distribution.
