Constraining blazar distances with combined Fermi and TeV data: an empirical approach

We discuss a method to constrain the distance of blazars with unknown redshift using combined observations in the GeV and TeV regimes. We assume that the Very High Energies (VHE) spectrum corrected for the absorption through the interaction with the extragalactic background light cannot be harder than the spectrum in the Fermi/Large Area Telescope (LAT) band. Starting from the observed VHE spectral data we derive the EBL-corrected spectra as a function of the redshift z and fit them with power laws to be compared with power-law fits to the LAT data. We apply the method to all TeV blazars detected by LAT with known distance and derive an empirical law describing the relation between the upper limits and the true redshifts that can be used to estimate the distance of unknown redshift blazars. Using different EBL models leads to systematic changes in the derived upper limits. Finally, we use this relation to infer the distance of the unknown redshift blazar PKS 1424+240.