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$^\star$.
Combined VLBA and TeV observations of M87 reveal a rapidly varying TeV emission that appears to be associated with the m.a.s VLBA jet (Acciari et al. 2009). The rapid flaring activity of the TeV source, with timescales t = 1t day day as low as 1-2 days, implies a source size of d ∼ 4r s t day for a black hole mass M BH = 4 × 10 9 solar masses. 1This, and the fact that the TeV emission appears to be correlated with the VLBA jet but not with emission from larger scales (and in particular HST-1), motivates the consideration that the observed TeV photons originate from the black hole magnetosphere (Neronov & Aharonian 2007;Rieger & Aharonian 2008). A plausible magnetospheric process discussed in the literature is curvature and/or IC emission by particles, either hadrons or leptons, accelerating in a vacuum gap of a starved magnetosphere. An alternative explanation for the observed fast TeV variability is emission from small regions located at larger radii, r ∼ 100r g , as, e.g., in the misaligned minijets model of Giannios et al. (2010), or perhaps interaction of the jet with red giant stars closer to its base (Barkov et al. 2010).
The presence of the VLBA jet implies that a force-free (or ideal MHD) flow is established on scales < 100r g (Walker et al. 2008, Acciari et al. 2009), so that the magnetosphere is anticipated to be screened in the sense that the invariant E • B nearly vanishes everywhere. However, as in pulsar theory, there must be a plasma source that replenishes charges which escape the system (both, to infinity and across the horizon) along the open magnetic field lines in the polar region. The nature of this plasma source is poorly understood at present.
The injection of charges into the magnetosphere may be associated with the accretion process. Direct feeding seems unlikely, as charged particles would have to cross magnetic field lines on timescale shorter than the accretion time in order to reach the polar outflow. Free neutrons that may be produced in a radiative inefficient accretion flow (RIAF) can cross field lines, however, they will decay over a distance ∼ 0.03r s for a 10 9 M ⊙ black hole, and even if existent at sufficient quantity, will not reach the inner regions. On the other hand, MeV photons that are emitted by the hot gas near the horizon can annihilate in the polar region to produce charged leptons. Below, it is shown that the density of the charges thereby injected depends sensitively on the accretion rate and the conditions in the RIAF. Naive estimates suggest that in case of M87 this process cannot provide complete screening at accretion rates that corresponds to the inferred jet power, and to a fit of the observed SED by an ADAF model. Those estimates are, however, highly uncertain, as explained below.
Another plausible plasma source is cascade formation in starved magnetospheric regions. The size of the gap then depends on the conditions in the magnetosphere and the pair production opacity. As shown elsewhere (Levinson 2000), vacuum breakdown by backreaction is unlikely, as it requires magnetic field strength in excess of a few times 10 5 G, higher than the equipartition value for Eddington accretion. Pair production via absorption of TeV photons by the ambient radiation field is more likely. However, the spectrum of the VHE photons observed by H.E.S.S. extends up to ∼ 10 TeV (e.g., Aharonian et al. 2006), and the assumption that these photons originate from the magnetosphere (or even the VLBA jet) implies that the pair production opacity at these energies must not exceed unity. This raises the question whether pair cascades in the magnetosphere can at all account for the multiplicity required to establish a force-free flow.
In what follows it is shown that inverse Compton scattering (IC) of ambient photons by electrons (positrons) accelerating in the gap can lead to a large multiplicity, ∼ 10 3 , while still allowing photons at energies of up to a few TeV to freely escape the system. The electromagnetic cascade is initiated by IC photons having much higher energies, up to ∼ 10 4 TeV, for which the γγ-optical depth is much larger. The seed charges are provided by annihilation of MeV photons from the RIAF. It is found that the gap width is not smaller than 0.01r s if the density of seed charges is below the Goldreich-Julian (GJ) value. The luminosity of the VHE photons produced in the gap can account for the TeV luminosity observed by H.E.S.S. Any intermittencies of the cascade formation process would naturally lead to variability of both, the magnetospheric TeV emission and the resultant force-free flow, as observed. A schematic illustration of the model is presented in figure 1.
The strength of the magnetic field in a black hole magnetosphere is limited by the rate at which matter is accreted into the black hole. At sufficiently low accretion rates the flow becomes radiative inefficient (RIAF) and the electron temperature in the inner region of the RIAF may exceed m
This content is AI-processed based on open access ArXiv data.
