2014ApJ...795...91S

The very high-energy (VHE) gamma-ray spectral index of high-energy peaked blazars correlates strongly with its corresponding redshift, whereas no such correlation is observed in the X-ray or GeV bands. We attribute this correlation to photon-photon absorption of TeV photons with the extragalactic background light (EBL), and utilizing this we compute the allowed flux range for the EBL, which is independent of previous estimates. The observed VHE spectrum of the sources in our sample can be well approximated by a power law, and if the de-absorbed spectrum is also assumed to be a power law, then we show that the spectral shape of EBL will be εn(ε) ∼ klog (ε/ε_p). We estimate the range of values for the parameters defining the EBL spectrum, k and ε_p, such that the correlation of the intrinsic VHE spectrum with redshift is nullified. The estimated EBL depends only on the observed correlation and the assumption of a power-law source spectrum. Specifically, it does not depend on the spectral modeling or radiative mechanism of the sources or on any theoretical shape of the EBL spectrum obtained through cosmological calculations. The estimated EBL spectrum is consistent with the upper and lower limits imposed by different observations. Moreover, it also agrees closely with the theoretical estimates obtained through cosmological evolution models.