  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 - geodynamo" 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 (ga_gamma about 1.64*10^-9 GeV^-1),
the axion-nucleon coupling (ga_gamma_eff about 10^-5) and the axion mass (ma
about 30 eV) have been obtained.
