Can the one-zone hadronuclear model explain the hard-TeV spectrum of BL Lac objects?

Context. The intrinsic TeV emission of some BL Lacs is characterized by a hard spectrum (the hard-TeV spectrum) after correcting for the extragalactic background light. The hard-TeV spectra pose a challenge to conventional one-zone models, including the leptonic model, the photohadronic model, the proton synchrotron model, and others. Aims. In this work, we aim to investigate whether or not the one-zone hadronuclear ( pp ) model can be used to interpret the hard-TeV spectra of BL Lacs without introducing extreme parameters. Methods. We provide analytical calculations that can be used to study whether or not there is a parameter space, and whether or not the charge neutrality condition of the jet can be satisfied when interpreting the hard-TeV spectra of BL Lacs without introducing a super-Eddington jet power. Results. We find that in a sample of hard-TeV BL Lacs previously collected, only the hard-TeV spectrum of 1ES 0229+200 can be explained by γ -rays from π 0 decay produced in the pp interactions, but at the cost of setting a small radius of the radiation region than the Schwarzschild radius of the central black hole. Combining our findings with those of previous studies of other one-zone models, we suggest that the hard-TeV spectra of BL Lacs cannot be explained by a one-zone model without introducing extreme parameters, and should originate from the multiple radiation regions.