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

TL;DR

This study uses population synthesis to predict optical-X-ray spectral indices of ULXs, revealing metallicity-dependent correlations and effects of beaming, with implications for understanding ULX emission mechanisms.

Contribution

It introduces a comprehensive simulation of ULX populations analyzing the $ m extit{α}_{ox}$ relation and metallicity effects, including beaming impacts, which is novel in ULX spectral studies.

Findings

Anti-correlation between $ m extit{α}_{ox}$ and UV luminosity consistent with observations.

Number of ULXs decreases with increasing metallicity.

Beaming significantly affects X-ray luminosity functions and spectral indices.

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.