Upper Bound on the First Star Formation History
  Our understanding of the nature of the extragalactic background light (EBL)
has improved with the recent development of gamma-ray observation techniques.
An open subject in the context of the EBL is the reionization epoch, which is
an important probe of the formation history of first stars, the so-called
Population III (Pop III) stars. Although the mechanisms for the formation of
Pop III stars are rather well understood on theoretical grounds, their
formation history is still veiled in mystery because of their faintness. To
shed light into this matter, we study jointly the gamma-ray opacity of distant
objects and the reionization constraints from studies of intergalactic gas. By
combining these studies, we obtain a sensitive upper bound on the Pop III star
formation rate density as $\dot\rho_{*}(z)<0.01[(1+z)/{(1+7.0)}]^{3.4}({f_{\rm
esc}}/{0.2})^{-1}({C}/{3.0})\ {\rm M}_{\odot} {\rm yr}^{-1}\ {\rm Mpc}^{-3}$ at
$z\ge7$, where $f_{\rm esc}$ and $C$ are the escape fraction of ionizing
photons from galaxies and the clumping factor of the intergalactic hydrogen
gas. This limit is a $\sim10$ times tighter constraint compared with previous
studies that take into account gamma-ray opacity constraints only. Even if we
do not include the current gamma-ray constraints, the results do not change.
This is because the detected gamma-ray sources are still at $z\le4.35$ where
the reionization has already finished.
