标题： 超亮X射线源的综合星族：光学-X射线相关性 显示英文标题

标题： A Synthetic Population of Ultra-Luminous X-ray Sources: Optical-X-ray Correlation

摘要： 本文分析了超亮X射线源（ULXs）中预测的光学至X射线谱指数（$\alpha_{\rm ox}$），这些ULXs与恒星质量黑洞和中子星相关联。我们使用种群合成代码COSMIC来模拟双星系统的演化，并研究ULX阶段紫外和X射线发射之间的关系，即$\alpha_{\rm ox}$关系。本研究调查了金属丰度对$\alpha_{\rm ox}$值的影响。值得注意的是，它预测了$\alpha_{\rm ox}$与紫外亮度（$L_{\rm UV}$）之间存在显著的反相关性，这与观测结果一致，且对于黑洞ULXs来说，这种关系的斜率会随着金属丰度的变化而变化。中子星ULX种群在不同金属丰度下显示出相对一致的$-0.33$斜率，变化较小。ULX的数量随着金属丰度的增加而减少，这与观测数据一致，X射线亮度函数在不同金属丰度下的斜率略有变化，在较低金属丰度下显示出高亮度ULX的相对过剩。在分析中加入束状效应显示对X射线亮度函数（XLF）和$\alpha_{\rm ox}$有显著影响，尤其是在高吸积率的情况下，此时辐射集中在更窄的锥体内。 此外，研究发现，ULX中的紫外发射主要由盘主导，这可能是 $\alpha_{\rm ox}$ 关系的起源，随着金属丰度的增加，盘主导的ULX百分比也随之增加。 显示英文摘要

摘要： This paper presents an analysis of the predicted optical-to-X-ray spectral index ($\alpha_{\rm ox}$) within the context of ultra-luminous X-ray sources (ULXs) associated with stellar mass black holes and neutron stars. We use the population synthesis code COSMIC to simulate the evolution of binary systems and investigate the relationship between UV and X-ray emission during the ULX phase, namely the $\alpha_{\rm ox}$ relation. The study investigates the impact of metallicity on $\alpha_{\rm ox}$ values. Notably, it predicts a significant anti-correlation between $\alpha_{\rm ox}$ and UV luminosity ($L_{\rm UV}$), consistent with observations, with the slope of this relationship varying with metallicity for BH-ULXs. The NS-ULX population shows a relatively consistent slope around $-0.33$ across metallicities, with minor variations. The number of ULXs decreases with increasing metallicity, consistent with observational data, and the X-ray luminosity function shows a slight variation in its slope with metallicity, exhibiting a relative excess of high-luminosity ULXs at lower metallicities. Inclusion of beaming effect in the analysis shows a significant impact on the XLF and $\alpha_{\rm ox}$, particularly at high accretion rates, where the emission is focused into narrower cones. Furthermore, the study finds that UV emission in ULXs is predominantly disk-dominated, which is the likely origin of the $\alpha_{\rm ox}$ relation, with the percentage of disk-dominated ULXs increasing as metallicity rises.