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

Context. The intrinsic TeV emission of some BL Lacs are 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, etc. Aims. In this work, we study if the one-zone hadronuclear (pp) model can be used to interpret the hard-TeV spectra of BL Lacs without introducing extreme parameters. Methods. We give analytical calculations to study if there is a parameter space and the charge neutrality condition of 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 collected by Xue et al. (2019a), only the hard-TeV spectrum of 1ES 0229+200 could be explained by gamma-ray from pi-0 decay produced in the pp interactions, but at the cost of setting a small radius of the radiation region that comparable to the Schwarzschild radius of the central black hole. Combining with previous studies of other one-zone models, we suggest that the hard-TeV spectra of BL Lacs cannot be explained by any one-zone models without introducing extreme parameters, and should originate from the multiple radiation regions.