Constraining the near-infrared background light from Population III stars using high-redshift gamma-ray sources

The Fermi satellite has detected GeV emission from a number of gamma-ray bursts and active galactic nuclei at high redshift, z≳ 1.5. We examine the constraints that the detections of gamma-rays from several of these sources place on the contribution of Population III stars to the extragalactic background light. Emission from these primordial stars, particularly redshifted Lyman α emission, can interact with gamma-rays to produce electron-positron pairs and create an optical depth to the propagation of gamma-ray emission, and the detection of emission at >10 GeV can therefore constrain the production of this background. We consider two initial mass functions for the early stars and use derived spectral energy distributions for each to put upper limits on the star formation rate density of massive early stars from redshifts 6 to 10. Our limits are complementary to those set on a high near-infrared background flux by ground-based TeV-scale observations and show that current data can limit star formation in the late stages of re-ionization to less than 0.5 M⊙ yr−1 Mpc−3. Our results also show that the total background flux from Population III stars must be considerably less than that from resolved galaxies at wavelengths below 1.5 μm.