Implications of the cosmic infrared background excess for the cosmic star formation

By phenomenologically describing the high-redshift star formation history, i.e., $\dot{\rho}_{*}(z)\propto[(1+z)/4.5]^{-\alpha}$, and semi-analytically calculating the fractions of high-redshift Pop I/II and Pop III stars, we investigate the contributions from both high-redshfit Pop I/II and Pop III stars to the observed near-infrared ($3 \mu\rm m<\lambda<5 \mu m$) excess in the cosmic infrared background emission. In order to account for the observational level of the near-infrared excess, the power-law index $\alpha$ of the assumed star formation history is constrained to within the range of $0\lesssim\alpha\lesssim1$. Such a constraint is obtained under the condition that the virial temperature of dark matter halos belongs to the range of $500 {\rm K}\leq T_{\rm vir}\leq10^4$ K.