Data analysis of sunspot oscillation based on 6-hr SDO run of observation showed that low frequency (0.2 < ! < 1 mHz) oscillations are local similar to three and five minute oscillations. The oscillations in the sunspot are concentrated in cells of a few arcsec, each of which has its own oscillation spectrum. The analysis of two scenario for sunspot oscillations leads to conclusion that local sunspot oscillations occur due to subphotospheric resonator for slow mhd waves. Empirical models of sunspot atmosphere and the theory of slow waves in thin magnetic flux tubes is applied to the modeling of subphotospheric resonator. Spectrum of local oscillations consists of a great number of lines. This kind of spectrum can occur only if the subphospheric resonator is a magnetic tube with a rather weak magnetic field.Magnetic tubes of this sort are umbral dots that appear due to the convective tongues in the monolithic sunspots. The interrelation of local oscillations with umbral dots and wave fronts of traveling waves in sunspots is discussed.
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