  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.
