A study of Intrinsic $\gamma$-ray Emission for {\it Fermi}/LAT-detected BL Lacs

BL Lacs are one subclass of blazars with highly energetic $\gamma$-ray emission, which is strongly boosted by a relativistic beaming effect. The latest catalogue of the 10 years of {\it Fermi}/LAT data Abdollahi et al. (2020) and the $\gamma$-ray Doppler factors in Pei et al. (2020) provide us with a large BL Lac sample to study their jet emission morphologies and intrinsic properties. In this paper, we collected a sample of 294 {\it Fermi} BL Lacs and probed the correlations between the $\gamma$-ray emissions and luminosity distances. Our analyses give following conclusions: (1) the observed $\gamma$-ray emissions are really boosted by the $\gamma$-ray Doppler factor, and the intrinsic $\gamma$-ray emissions are closely correlated with luminosity distances. (2) the morphology of jet emissions for HBLs may be continuous, while that for IBLs may be the case of a moving sphere in the $\gamma$-ray bands.