High-energy and Very High-energy Constraints from Log-parabolic Spectral Models in Narrow-line Seyfert 1 Galaxies

Narrow-line Seyfert 1 galaxies (NLSy1s) are a well-established class of $gamma$-ray sources, showing the presence of a jet like the more common flat-spectrum radio quasars. The evidence of $gamma$-ray emission poses the issue of the location of the $gamma$-ray emitting zone and of the contribution of the $gamma$-$gamma$ absorption within the broad-line region (BLR), since such objects have been detected by Fermi-LAT in the MeV-GeV energy range but not by imaging atmospheric Cherenkov telescopes beyond 100 GeV. We discuss how the spectral properties of three NLSy1s (SBS 0846+513, PMN J0948+0022, and PKS 1502+036) derived from the Fermi Large Area Telescope Fourth Source Catalog (4FGL) compare with theoretical models based on the observed properties of the BLR. In particular, we focus on the question on how simple power-law spectral models and log-parabolic ones could be disentangled in $gamma$-ray narrow-line Seyfert 1 galaxies by means of current Fermi-LAT or future imaging atmospheric Cherenkov telescopes data. We find that the only possibility for a log-parabolic model to mimic a power-law model in the energy band above $E sim 100$ GeV is to have a very small value of the curvature parameter $ beta sim 0.05$.