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

Abstract

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.