This paper deals with the estimation of hidden periodicities in a non-linear regression model with stationary noise displaying cyclical dependence. Consistency and asymptotic normality are established for the least-squares estimates.
In a very conservative approach, supposing that total heat flow of the Earth is exclusively due to resonant capture inside the Earth of axions, emitted by 57-Fe nuclei on Sun, we obtain limit on mass of hadronic axion: m_a<1.8 keV. Taking into account release of heat from decays of 40-K, 232-Th, 238-U inside the Earth, this estimation could be improved to the value: m_a<1.6 keV. Both the values are less restrictive than limits set in devoted experiments to search for 57-Fe axions (m_a<216-745 eV), but are much better than limits obtained in experiments with 83-Kr (m_a<5.5 keV) and 7-Li (m_a<13.9-32 keV).
