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 _ { esc } } / { 0.2 } ) ^ { -1 } ( { C } / { 3 % .0 } ) { M } _ { \odot } { yr } ^ { -1 } { Mpc } ^ { -3 } at z \geq 7 , where f _ { 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 \sim 10 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 \leq 4.35 where the reionization has already finished .