Black hole-main sequence star (BH-MS) binaries are one of the targets of the future data releases of the astrometric satellite {\it Gaia}. They are supposed to be formed in two main sites: a galactic field and star clusters. However, previous work has never predicted the number of BH-MS binaries originating in the latter site. In this paper, we estimate the number of BH-MS binaries formed in open clusters and detectable with {\it Gaia} based on the results of {\it N}-body simulations. By considering interstellar extinction in the Milky Way (MW) and observational constraints, we predict $\sim 10$ BH-MS binaries are observable. We also find that chemical abundance patterns of companion MSs will help us to identify the origin of the binaries as star clusters. Such MSs are not polluted by outflows of the BH progenitors, such as stellar winds and supernova ejecta. Chemical anomalies might be a good test to confirm the origin of binaries with relatively less massive MSs ($\lesssim 5M_{\odot}$), orbital periods ($\sim 1.5\;$year) and higher eccentricities ($e \gtrsim 0.1$).

中文翻译：

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盖亚对疏散星团中形成的黑洞-主序星双星的可探测性

黑洞-主序星 (BH-MS) 双星是天体测量卫星 {\it Gaia} 未来数据发布的目标之一。它们应该在两个主要地点形成：银河场和星团。然而，以前的工作从未预测源自后一个站点的 BH-MS 二进制文件的数量。在本文中，我们基于 {\it N}-body 模拟的结果估计了在疏散星团中形成的 BH-MS 双星的数量，并且可以用 {\it Gaia} 检测。通过考虑银河系中的星际灭绝 (MW) 和观测限制，我们预测 $\sim 10$ BH-MS 双星是可观测的。我们还发现伴随 MS 的化学丰度模式将帮助我们确定双星作为星团的起源。这样的 MS 不会被 BH 祖细胞的外流污染，例如恒星风和超新星喷射物。化学异常可能是确认具有相对较小质量 MS（$\lesssim 5M_{\odot}$）、轨道周期（$\sim 1.5\;$year）和较高离心率（$e \gtrsim 0.1 美元）。