Variable TeV emission as a manifestation of jet formation in M87?

It is proposed that the variable TeV emission observed in M87 may be produced in a starved magnetospheric region, above which the outflow associated with the VLBA jet is established. It is shown that annihilation of MeV photons emitted by the radiative inefficient flow in the vicinity of the black hole, can lead to injection of seed charges on open magnetic field lines, with a density that depends sensitively on accretion rate, $n_\pm\propto\dot{m}^{4}$. For an accretion rate that corresponds to the inferred jet power, and to a fit of the observed SED by an ADAF model, the density of injected pairs is found to be smaller than the Goldreich-Julian density by a factor of a few. It is also shown that inverse Compton scattering of ambient photons by electrons (positrons) accelerating in the gap can lead to a large multiplicity, $\sim 10^3$, while still allowing photons at energies of up to a few TeV to freely escape the system. The estimated gap width is not smaller than $0.01 r_s$ if the density of seed charges is below the Goldreich-Julian value. The VHE power radiated by the gap can easily account for the luminosity of the TeV source detected by H.E.S.S. The strong dependence of injected pair density on accretion rate should render the gap emission highly intermittent. We also discuss briefly the application of this mechanism to Sgr A$^\star$.