Redshifts of Distant Blazars Limited by Fermi and VHE γ-Ray Observations

Abstract

Abstract Our goal is to limit the redshifts of three blazars, PG 1553$+$113, 3C 66A, and PKS 1424$+$240, through an investigation of their Fermi and VHE (very high energy) $\gamma$-ray observations. We assume that the intrinsic spectra of PG 1553$+$113, 3C 66A, and PKS 1424$+$240 have no cutoff across the Fermi and VHE $\gamma$-ray energy ranges. The intrinsic spectra of VHE $\gamma$-rays are obtained through extrapolation of the Fermi spectra. Comparing the measured and intrinsic VHE spectra due to extragalactic background light (EBL) absorption, we give the redshift upper limits of three blazars, while assuming a specific EBL model. The redshift upper limits of PG 1553$+$113, 3C 66A, and PKS 1424$+$240 are 0.78, 0.58, and 1.19, respectively. Near to the TeV energy the optical depth of VHE $\gamma$ photons might be overestimated by the Franceschini EBL model (Franceschini et al. 2008, A&A, 487, 837), or the second emission component might be present in the VHE spectra and lead the intrinsic photon index to be harder than the Fermi ones.