Fermi -LAT Stacking Analysis Technique: An Application to Extreme Blazars and Prospects for their CTA Detection

We present a likelihood profile stacking technique based on the Fermi-Large Area Telescope (LAT) data to explore the γ-ray characteristics of Fermi-LAT undetected astrophysical populations. The pipeline is applied to a sample of γ-ray unresolved extreme blazars, i.e., sources with the highest synchrotron peak frequencies (${\nu }_{\mathrm{Syn}}^{\mathrm{peak}}\geqslant {10}^{17}\,\mathrm{Hz}$), and we report a cumulative γ-ray detection with more than 32σ confidence for 2 degrees of freedom. Comparing the generated stacked γ-ray spectrum with the sensitivity limits of the upcoming Cherenkov Telescope Array (CTA), we find that the Fermi-LAT undetected population of such extreme blazars, on average, may remain well below the CTA detection threshold due to their faintness and extragalactic background light (EBL) absorption. However, γ-ray detected blazars belonging to the same class are promising candidates for CTA observations. The EBL-corrected stacked spectra of these sources do not show any softening up to 1 TeV. This finding suggests the inverse Compton peak of extreme blazars lies above 1 TeV, thus indicating a hard intrinsic TeV spectrum. Our analysis also predicts that at 100 GeV, at least ∼10% of the diffuse extragalactic γ-ray background originates from the γ-ray undetected extreme blazars. These results highlight the effectiveness of the developed stacking technique to explore the uncharted territory of γ-ray undetected astrophysical objects.