A synthetic population of ultra-luminous X-ray sources

Optical–X-ray correlation

¹ Centre for Astro-Particle Physics (CAPP) and Department of Physics, University of Johannesburg, PO Box 524 Auckland Park 2006, South Africa
² Department of Physics, The George Washington University, Washington, DC 20052, USA
³ National Institute for Theoretical and Computational Sciences (NITheCS), Private Bag X1, Matieland, South Africa
⁴ U.S. Naval Research Laboratory, Code 7653, 4555 Overlook Ave. SW, Washington, DC 20375-5352, USA

^⋆ Corresponding authors; lnyadzani@uj.ac.za, srazzaque@uj.ac.za, justin.d.finke.civ@us.navy.mil

Received: 11 January 2024
Accepted: 21 January 2025

Abstract

This paper presents an analysis of the predicted optical-to-X-ray spectral index (α_ox) within the context of ultra-luminous X-ray sources (ULXs) associated with stellar-mass black holes (BHs) and neutron stars (NSs). We used the population synthesis code COSMIC to simulate the evolution of binary systems and investigate the relationship between ultraviolet (UV) and X-ray emission during the ULX phase, namely the α_ox relation. Furthermore, we investigated the impact of metallicity on α_ox values. Notably, it predicts a significant anti-correlation between α_ox and UV luminosity (L_UV), consistent with observations. The slope of this relationship varies with metallicity for black hole ULXs (BH-ULXs). The neutron star ULX (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. The X-ray luminosity function (XLF) shows a slight variation in its slope with metallicity, exhibiting a relative excess of high-luminosity ULXs at lower metallicities. The inclusion of the beaming effect in the analysis shows a significant impact on the XLF and α_ox, particularly at high accretion rates, where the emission is focused into narrower cones. We found that UV emission in ULXs is predominantly disc-dominated, which is the likely origin of the α_ox relation, with the percentage of disc-dominated ULXs increasing as metallicity rises.