Hadronic Processes in Advection-Dominated Accretion Flow as the Origin of TeV Excesses in BL Lac Objects

The spectral energy distributions (SEDs) of certain BL Lac objects (BL Lacs) exhibit an additional hard $\gamma$-ray component in the TeV energy range that surpasses the predictions of the one-zone leptonic jet model. The origin of this excess emission remains unclear. In this study, we selected five BL Lacs whose SEDs display a very hard intrinsic spectrum in the TeV band and successfully reproduced their broadband SEDs using a two-zone lepto-hadronic model. Within this framework, the emission observed in the optical, X-ray, GeV $\gamma$-ray, and sub-TeV $\gamma$-ray bands is modeled using the synchrotron and synchrotron self-Compton radiation processes of the relativistic electrons in the jets. Meanwhile, the TeV excess is attributed to $\gamma$-ray emission resulting from the photomeson ($p\gamma$) process via $\pi^0$ decay occurring within advection-dominated accretion flows (ADAFs). This scenario requires a hard proton spectrum with a spectral index of $p \sim 1.6-1.7$ and a cutoff energy ranging from 30 to 90 TeV, as well as a relatively large ADAF radius. Such hard proton spectra suggest that the dominant acceleration mechanisms are likely magnetic reconnection and/or stochastic acceleration processes within ADAFs. Additionally, the emission from the cascaded electrons results in a bump in the keV--MeV band; however, it is overwhelmed by the jet emission. Although the hadronuclear ($pp$) process cannot be entirely ruled out, it would necessitate an even harder proton spectrum and a higher cutoff energy compared to the $p\gamma$ process, making it a less favorable explanation for the observed TeV excess.