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Relativistic electrons and magnetic field of the M87 jet on ~ten Schwarzschild radii scale

We explore energy densities of magnetic field and relativistic electrons in the M87 jet. Since the radio core at the jet base is identical to the optically thick surface against synchrotron self absorption (SSA), the observing frequency is identical to the SSA turnover frequency. As a first step, we assume the radio core as a simple uniform sphere geometry. Using the observed angular size of the radio core measured by the Very Long Baseline Array at 43 GHz, we estimate the energy densities of magnetic field ($U_{B}$) and relativistic electrons ($U_{e}$) based on the standard SSA formula. Imposing the condition that the Poynting power and relativistic electron one should be smaller than the total power of the jet, we find that (i) the allowed range of the magnetic field strength ($B_{tot}$) is from 1 G to 15 G, and that (ii) $1 times 10^{-5} < U_{e}/U_{B} < 6 times 10^{2}$ holds. The uncertainty of $U_{e}/U_{B}$ comes from the strong dependence on the angular size of the radio core and the minimum Lorentz factor of non-thermal electrons ($gamma_{e,min}$) in the core. It is still open that the resultant energetics is consistent with either the magnetohydrodynamic jet or with kinetic power dominated jet even on ~10 Schwarzschild radii scale.