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We show the existence of the strong inverse correlation between the temporalvariations of the toroidal component of the magnetic field in the solartachocline (the bottom of the convective zone) and the Earth magnetic field(the Y-component). The possibility that the hypothetical solar axions, whichcan transform into photons in external electric or magnetic fields (the inversePrimakoff effect), can be the instrument by which the magnetic field of the Sunconvective zone modulates the magnetic field of the Earth is considered.  We propose the axion mechanism of Sun luminosity and "solar dynamo --geodynamo" connection, where the energy of one of the solar axion fluxcomponents emitted in M1 transition in 57Fe nuclei is modulated at first by themagnetic field of the solar tachocline zone (due to the inverse coherentPrimakoff effect) and after that is resonantly absorbed in the core of theEarth, thereby playing the role of the energy modulator of the Earth magneticfield. Within the framework of this mechanism estimations of the strength ofthe axion coupling to a photon (g_{a \gamma} = 7.07e-11 1/GeV), theaxion-nucleon coupling (g_{an} = 3.20e-7), the axion-electron coupling (g_{ae}= 5.28e-11) and the axion mass (m_a = 17eV) have been obtained. It is alsoshown that the claimed axion parameters do not contradict to any knownexperimental and theoretical model-independent limitations.  We consider the effect of dark matter in the form of 17eV axions on theextragalactic back-ground light (EBL) and find that the theoretical spectralintensity of the EBL from decaying axions as a function of the observedwavelength is in good agreement with the known experimental data for the nearultraviolet, optical and near infrared bands (1500-20000 angstrom).

Axion mechanism of Sun luminosity, dark matter and extragalactic background light