Context. Ultra-luminous X-ray sources (ULXs) are sources observed to have extreme X-ray luminosities exceeding the Eddington limit of a stellar-mass black hole (BH). A fraction of ULXs show X-ray pulsations, which are evidence for accreting neutron stars (NSs). Theoretical studies have suggested that NSs, rather than BHs, dominate the compact objects of intrinsic ULX populations, even though the majority of the observed sample is non-pulsating, implying that X-ray pulses from many NS ULXs are unobservable.
Aims. We simulate populations of X-ray binaries covering a range of starburst ages spanning from 5 to 1000 Myr with the aim of comparing the properties of observed ULXs at the different ages. Additionally, we compare two models describing different assumptions for the physical processes governing binary evolution.
Methods. We used the new population synthesis code POSYDON to generate multiple populations of ULXs spanning multiple burst ages. We employed a model for geometrically beamed emission from a super-Eddington accretion disk in order to estimate the luminosities of ULXs. Following theoretical predictions for the alignment of the spin axis of an NS with the accretion disk due to mass transfer, we estimated the required mass to be accreted by the NSs in the ULX populations so that the alignment suppresses observable X-ray pulses.
Results. While we find that the properties of ULX populations are sensitive to model assumptions, there are certain trends that the populations follow. Generally, young and old stellar populations are dominated by BH and NS accretors, respectively. The donor stars go from being massive H-rich main-sequence stars in young populations (< 100 Myr) to low-mass post-main sequence H-rich stars in older populations (> 100 Myr), with stripped He-rich giant donors dominating the populations at around 100 Myr. In addition, we find that NS ULXs exhibit stronger geometrical beaming than BH ULXs, leading to an underrepresentation of NS accretors in observed populations. Coupled with our finding that X-ray pulses are suppressed in at least 60% of the NS ULXs, we suggest that the observed fraction of ULXs with detectable X-ray pulses is very small, in agreement with observations.
Conclusions. We show that geometrical beaming and the mass-accretion phase are critical aspects of understanding ULX observations. Our results suggest that even though most ULXs have accreting NSs, those with observable X-ray pulses would be very few.
