We show existence of strong negative correlation between the temporal variations of magnetic field toroidal component of the solar tachocline (the bottom of convective zone) and the Earth magnetic field (Y-component). The possibility that hypothetical solar axions, which can transform into photons in external electric or magnetic fields (the inverse Primakoff effect), can be the instrument by which the magnetic field of convective zone of the Sun modulates the magnetic field of the Earth is considered. We propose the axion mechanism of Sun luminosity and "solar dynamo geo-dynamo" connection, where an energy of solar axions emitted in M1 transition in ⁵⁷Fe nuclei is modulated at first by the magnetic field of the solar tachocline zone (due to the inverse coherent Primakoff effect) and after that is resonance absorbed in the core of the Earth, thereby playing the role of an energy source and a modulator of the Earth magnetic field. Within the framework of this mechanism estimations of the strength of an axion coupling to a photon (g_{a gamma} ~ 1,64х10^-9 GeV^-1), the axion-nucleon coupling (g_aN^eff ~ 10^-5) and the axion mass (m_a ~ 30 eV) have been obtained.

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