Multi-epoch study of the gamma-ray emission within the M87 magnetosphere model

M87 is a nearby radio galaxy that has been detected at energies ranging from radio to very high energy (VHE) gamma-rays. Its proximity and its jet, misaligned from the line of sight allow detailed morphological studies. The imaging atmospheric Cherenkov technique (from 100 GeV to 10 TeV) provides insufficient angular resolution (few arc-minutes) to resolve the M87 emission region. However, the short time scale variability observed by MAGIC, HESS and VERITAS suggests the TeV emission is coming from a very small region, most likely close to the core. We propose that the variable TeV emission may be produced in a pair-starved region of the central black hole (BH) magnetosphere, i.e. a region where the density of the electron-positron plasma is not sufficient to completely screen the accelerating electric field. The funnel, a low density and magnetically dominated region around the poles, appears as a favourable site of low-density where a Blandford-Znajek process may explain the main properties of the TeV γ-ray emission from M87. We produce a broadband spectral energy distribution (SED) of the resulting radiation and compare the model with the observed fluxes from the nucleus of M87, for both low and high γ-ray activities. We finish with a brief discussion on the connection between the accretion rate and the intermittence in the formation of gaps in the magnetosphere