  X-ray binaries (XRBs) are thought to regulate cosmic thermal and ionization
histories during the Epoch of Reionization and Cosmic Dawn ($z\sim
5-30$).Theoretical predictions of the X-ray emission from XRBs are important
for modelling such early cosmic evolution. Nevertheless, the contribution from
Be-XRBs, powered by accretion of compact objects from decretion disks around
rapidly rotating O/B stars, has not been investigated systematically. Be-XRBs
are the largest class of high-mass XRBs (HMXBs) identified in local
observations and are expected to play even more important roles in metal-poor
environments at high redshifts. In light of this, we build a physically
motivated model for Be-XRBs based on recent hydrodynamic simulations and
observations of decretion disks. Our model is able to reproduce the observed
population of Be-XRBs in the Small Magellanic Cloud with appropriate initial
conditions and binary stellar evolution parameters. We derive the X-ray output
from Be-XRBs as a function of metallicity in the (absolute) metallicity range
$Z\in [10^{-4},0.03]$ with a large suite of binary population synthesis (BPS)
simulations. The simulated Be-XRBs can explain a non-negligible fraction
($\gtrsim 30\%$) of the total X-ray output from HMXBs observed in nearby
galaxies for $Z\sim 0.0003-0.02$. The X-ray luminosity per unit star formation
rate from Be-XRBs in our fiducial model increases by a factor of $\sim 8$ from
$Z=0.02$ to $Z=0.0003$, which is similar to the trend seen in observations of
all types of HMXBs. We conclude that Be-XRBs are potentially important X-ray
sources that deserve greater attention in BPS of XRBs.
