  Ultra-luminous X-ray sources (ULXs) are sources observed to exceed the
Eddington limit of a stellar-mass black hole (BH). A fraction of ULX sources
show X-ray pulses which are evidence for accreting neutron stars (NSs).
Theoretical studies have suggested that NSs dominate the compact objects of
intrinsic ULXs, even though the majority of observed sample is non-pulsating,
implying that X-ray pulses from many NS ULXs are unobservable. We use POSYDON
to generate and study X-ray binary populations spanning starburst ages 5 to
1000Myr. Following theoretical predictions for the alignment of the NS spin
axis with the accretion disc, we estimate the required accreted mass in ULXs so
that the alignment suppresses observable X-ray pulses. While the properties of
ULXs are sensitive to model assumptions, there are certain trends that the
populations follow. Young and old stellar populations are dominated by BH and
NS accretors, respectively. The donors go from massive H-rich main-sequence
(MS) stars in young populations (<100Myr) to low-mass post-MS H-rich stars in
older populations (>100Myr), with stripped He-rich giant stars dominating the
populations at around 100Myr. In addition, we find that NS ULXs exhibit
stronger geometrical beaming than BH ULXs, leading to an under-representation
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. This study investigates the effects of age on ULXs
as well as the effects of different model assumptions on ULX demographics. 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.
