Formation, disruption and energy output of Population III X-ray binaries
  The first astrophysical objects shaped the cosmic environment by reionizing
and heating the intergalactic medium (IGM). In particular, X-rays are very
efficient at heating the IGM before it became completely ionized, an effect
that can be measured through the 21 cm line of neutral hydrogen. High-mass
X-ray binaries (HMXBs), known to be prolific X-ray sources in star-forming
galaxies at lower redshifts, are prime candidates for driving the thermal
evolution of the IGM at redshifts $z > 20$. Despite their importance, the
formation efficiency of HMXBs from the first stellar populations is not well
understood---as such, their collective X-ray emission and the subsequent
imprint on the 21 cm signature are usually evaluated using free parameters.
Using $N$-body simulations, we estimate the rate of HMXB formation via mutual
gravitational interactions of nascent, small groups of the first stars (Pop III
stars). We run two sets of calculations: one in which stars form in small
groups of five in nearly Keplerian initial orbits, and another in which two
such groups collide (expected from mergers of host protogalaxies). We find that
HMXBs form at a rate of one per $~10^{4}~{\rm M}_{\odot}$ in newly born stars,
and that they emit with a power of $\sim 10^{41} ~{\rm erg}~{\rm s} ^{-1}$ in
the $2-10$ keV band per solar mass per year of star formation. This value is a
factor $\sim 10^{2}$ larger than what is observed in star forming galaxies at
lower redshifts; the X-ray production from early HMXBs would have been even
more copious, if they also formed $in$ $situ$ or via migration in protostellar
disks. Combining our results with earlier studies suggests that early HMXBs
were highly effective at heating the IGM and leaving a strong 21 cm signature.
We discuss broader implications of our results, such as the rate of long GRBs
from PopIII stars and the direct collapse black hole formation.
