Magnetization degree at the jet base of M87 derived from the event horizon telescope data: Testing magnetically driven jet paradigm

We explore the degree of magnetization at the jet base of M87 by using the observational data of the event horizon telescope (EHT) at 230~GHz obtained by Doeleman et al. By utilizing the method in Kino et al., we derive the energy densities of magnetic fields ($U_{B}$) and electrons and positrons ($U_{\pm}$) in the compact region detected by EHT (EHT-region) with its full-width-half-maximum size $40~{\rm \mu as}$. First, we assume that an optically-thick region for synchrotron self absorption (SSA) exists in the EHT-region. Then, we find that the SSA-thick region should not be too large not to overproduce the Poynting power at the EHT-region. The allowed ranges of the angular size and the magnetic field strength of the SSA-thick region are $21~{\rm \mu as} \le \theta_{\rm thick}\le 26.3~{\rm \mu as}$ and $50~{\rm G}\le B_{\rm tot}\le 124~{\rm G}$, respectively. Correspondingly $U_{B}\gg U_{\pm}$ is realized in this case. We further examine the composition of plasma and energy density of protons by utilizing the Faraday rotation measurement ($RM$) at 230~GHz obtained by Kuo et al. Then, we find that $U_{B}\gg U_{\pm}+U_{p}$ still holds in the SSA-thick region. Second, we examine the case when EHT-region is fully SSA-thin. Then we find that $U_{B}\gg U_{\pm}$ still holds unless protons are relativistic. Thus, we conclude that magnetically driven jet scenario in M87 is viable in terms of energetics close to ISCO scale unless the EHT-region is fully SSA-thin and relativistic protons dominated.