tokens: is , these IC emissions are detectable with CTA, provided that the distance is within a few tens of Mpc and that the dimensionless accretion rate is in the range . If , they are detectable with CTA, provided that the distance is within a few Mpc and that . 6.1. Improvement from H16 In the present work, there are two major improvements from H16 , which formulated the BH gap model and applied it to various BH masses in . First, the distribution functions of electrons and positrons are solved as a function of the Lorentz factor, γ , in the present work, whereas a monoenergetic approximation was adopted in H16 . It is found that the Lorentz factors broadly distribute below the saturated value that was estimated in the monoenergetic approximation. This fact causes an important impact on the gap electrodynamics. Since only the highest-energy IC photons contribute in the gap closure (Section 4.2.5 ), the monoenergetic approximation has overestimated the pair creation in the gap, thereby underestimating the gap width and luminosity (cf. Figure 10 of the present paper and Figure 23 of H16 ). Moreover, the reduced Lorentz factors significantly suppress the curvature process, whose power is proportional to . Also, the primary IC spectrum is softened to peak between 1 and 10 TeV in the present work, whereas it peaked between 10 and 100 TeV in H16 . Since CTA increases its sensitivity with decreasing photon energy around 10 TeV, this result encourages us to observe nearby low-luminosity AGNs in VHE. Second, in the present work, we take into account an anisotropic and inhomogeneous RIAF specific intensity in computing the IC and pair creation. In particular, it is found that the polar region is less efficiently illuminated by the RIAF photon field compared to the middle latitudes . It leads to a harder and stronger VHE emission along the rotation axis than that into the middle latitudes. On the contrary, in H16 it was simply assumed that the RIAF photon field was constant for θ . Thus, although the VHE flux decreased with θ owing to the reduced near the equatorial boundary, it decreased more slowly than the present analysis. 6.2. Comparison with Pulsar Emission Models Let us compare the present BH gap model with the pulsar outer gap model. In both gap models, the gap appears around the null-charge surface where the GJ charge density vanishes, as the stationary solution of the Maxwell–Boltzmann equations. There are, however, differences as described below. In pulsar magnetospheres, the neutron star (NS) emits X-ray photons from its surface, losing its thermal energy. The luminosity of these soft photons decreases as the NS ages. The decreased soft-photon density in the outer magnetosphere results in an extended gap along the magnetic field line. For middle-aged pulsars, w becomes comparable to the radius of the outer light surface, within which the special relativistic GJ charge density changes substantially owing to the convex geometry of the magnetic field
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