Abstract
The evolutionary history of double compact objects (DCOs) detected by gravitational
wave (GW) detectors is an active field of research. Two main formation channels are generally
considered: isolated binary evolution and dynamical interactions in dense stellar environments.
This study focuses on the isolated binary evolution channel. We investigate the
connection between ultraluminous X-ray sources (ULXs) and the formation of merging double
compact objects (mDCOs) using binary population synthesis simulations performed with
the COSMIC code.
To model emission during the X-ray binary phase, we adopt the supercritical accretion
disc (SCAD) model of Vinokurov et al. (2013). The X-rays originate from the accretion disc,
and UV emission is a combination of disc-heated wind and the donor star’s surface emission.
The two key parameters fout, the fraction of thermalised flux, and the funnel opening angle
θf , strongly shape the UV and X-ray emissions. Higher fout increases the UV output, while
smaller θf collimates X-rays. In this study, fout is treated as a free parameter and fixed at
fout = 0.03. Our ULX study is split into two parts: the unbeamed population and the beamed
population. First (unbeamed population), we keep θf = 45◦ as a constant and in the second
part (beamed population), we use the beaming model from King et al. (2001) to compute θf
from the accretion rate.
We find that the number of ULXs declines with increasing metallicity, with BH-ULXs decreasing
at a higher rate than NS-ULXs. The combined ULX population follows a metallicitydependent
power law with slope α = 0.16 ± 0.01, consistent with observations. ULX lifetimes
are short (an average lifetime < 1 Myr), with NS-ULXs generally shorter-lived than
BH-ULXs. The temporal distribution shows two peaks, with the first peak at ∼ 10 Myr dominated
by BH-ULXs, and a secondary one at ∼ 100 Myr dominated by NS-ULXs. X-ray
and UV luminosities vary over time, and we find cases where systems transition from NSULX
to BH-ULX during the ULX phase. In unbeamed cases, NS-ULX X-ray luminosities
scale with accretion rate, while for BH-ULXs they scale with black hole mass. With beaming
(b ∝ 1/m˙ 2), the X-ray luminosity correlates with the accretion rate in both NS- and
BH-ULXs.
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Our simulations reproduce the observed anti-correlation between αox and UV luminosity
at 2500 Å. The slope of the αox−Lν,UV relation for BH-ULXs varies with metallicity, whereas
for NS-ULXs, it remains relatively constant. Including beaming flattens the αox–UV relation
and shifts αox to higher values, overpredicting those seen in current ULX samples.
The ULX luminosity function (XLF) shows metallicity dependence: flatter slopes and
more high-luminosity sources in low-metallicity environments. Beaming further flattens the
XLF, in agreement with observational values from Walton et al. (2011) and Salvaggio et al.
(2023). Higher wind velocities reduce UV emission while leaving X-rays unchanged, leading
to more positive αox values. NS-ULXs, due to their strong beaming, which results in
narrow emission cones, are intrinsically harder to detect. Overall, our results support the interpretation
that super-Eddington accretion onto stellar-mass BHs and NSs can reproduce the
observed ULX population without invoking intermediate-mass black holes (IMBHs).
We use our unbeamed ULX population to trace the formation of mDCOs from the ULX
population. Population properties of the mDCO that went through the ULX phase: mass,
delay times, mass ratio, and chirp mass distributions are compared with previous studies and
observational constraints. Our results confirm that low-metallicity environments favour both
the formation and merging of DCOs, particularly those involving BHs. We also estimate
the SGRB rate arising from DNS and BHNS mergers, applying a simplified jet-launching
criterion based on remnant mass and binary mass ratio.
Although only ∼10% of all DCOs originate from ULX systems, we find that 70–97%
of mDCOs pass through a ULX phase at some point in their evolution. These mDCOs are
typically near-equal mass binaries, and our simulations reproduce a distinct mass gap between
neutron stars and black holes, consistent with the adopted “rapid” supernova engine.
We predict local merger rate densities of 26.91, 56.13, and 169.94 Gpc−3 yr−1 for DBH,
DNS, and BHNS systems, respectively. These rates are within LIGO/Virgo O3a constraints
for DBH and DNS populations, but slightly overestimate the BHNS contribution. The intrinsic
volumetric SGRB rate is estimated at 3.49 Gpc−3 yr−1, with nearly equal contributions
from DNS and BHNS channels, lower than most observationally inferred SGRB rates. Finally,
the metallicity dependence of our simulated SGRB rate shows qualitative agreement
with the observed metallicity distribution of SGRB host galaxies.