The near-infrared radiation background, gravitational wave background
  and star formation rate of Pop III and Pop II during cosmic reionization
  In this paper, we obtain the NIRB and SBGWs from the early stars, which are
constrained by the observation of reionization and star formation rate. We
study the transition from Pop III to Pop II stars via the star formation model
of different population, which takes into account the reionization and the
metal enrichment evolution. We calculate the two main metal pollution channels
arising from the supernova-driven protogalactic outflows and "genetic channel".
We obtain the SFRs of Pop III and Pop II and their NIRB and SBGWs radiation. We
predict that the upper limit of metallicity in metal-enriched IGM (the galaxies
whose polluted via "genetic channel") reaches $Z_{\rm crit}=10^{-3.5}Z_{\odot}$
at $z\sim13$ ($z\sim11$), which is consistent with our star formation model. We
constrain on the SFR of Pop III stars from the observation of reionization. The
peak intensity of NIRB is about $0.03-0.2~nW m^{-2}{sr}^{-1}$ at $\sim 1 \mu m$
for $z>6$. The prediction of NIRB signal is consistent with the metallicity
evolution. We also obtain the gravitational wave background from the black
holes formed by these early stars. The predicted gravitational wave background
has a peak amplitude of $\Omega_{GW}\simeq8\times10^{-9}$ at $\nu=158$ Hz for
Pop II star remnants. However, the background generated by Pop III.2 stars is
much less than Pop II stars, with a peak amplitude of
$\Omega_{GW}\simeq1.2\times10^{-11}$ at $\nu=28~Hz$. The background of Pop
III.1 shifts to lower frequencies, and the amplitude of $\Omega _{GW}$ for Pop
III.1 stars shows a minimum value at $\nu\simeq 10$ Hz, due to the lack of
gravitational wave signals from the stars with
$140~M_{\odot}<M_\ast<260~M_{\odot}$.
