We present results of investigations into chromospheric velocity oscillations in sunspots, carried out at the Sayan Solar Observatory. It is shown that the "chevron" structures in the spacetime diagrams demonstrate wavetrain properties. Such structures are indicators of a propagating wave process and they are typical of many sunspots. In the authors' opinion, three-minute umbral oscillations are not the source of running penumbral waves (RPW). It is very likely that umbral oscillations and RPW initially propagate along different magnetic field lines. We explain the decrease in RPW propagation velocity and frequency in the outer penumbra, as compared with the inner, by the combined action of different frequency modes. To better reveal the properties of these modes, frequency filtering was used. Our measurements of the RPW (five-minute mode) wavelength and RPW propagation velocity in different sunspots vary from 12 to 30 and from 28 to 60 -70 km s −1 correspondingly.

Abstract. We investigate the line-of-sight velocity oscillations in the sunspot NOAA 0051 during its disk transit. The data obtained in this study provide evidence for the existence of running umbral waves in the chromosphere. These waves have a period of 2.8 min and propagate from the sunspot center outward with the phase velocity of 45-60 km s −1 with the line-of-sight velocity amplitude of about 2 km s −1 . In most cases the waves terminate rather abruptly on the umbra boundary and show no direct linkage with running penumbral waves. The spatial coherence of the waves at the umbra center is no more than 2 . At the photospheric level there are clearly pronounced periodic motions (T ∼ 5 min) propagating from the inner penumbral boundary and from the superpenumbra to the lines of maximum Evershed velocity.

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Authors have investigated the line-of-sight velocity difference in the radial direction of sunspot penumbrae simultaneously at two height levels, Nil 4857 and H,a by the differential method. Power spectra of time series exhibit in the range under consideration three groups of periods: 30-40, 12-15, and 8-10 minutes. Particular emphasis has been placed on the low-frequency portion of the spectrum (0.5-2 mHz). In addition to the 12-minute oscillations as detected by Rimmele the line-ofsight velocity component that is caused by Evershed motion is responsible for oscillations with periods of 15-35 minutes, which occur concurrently at the two height levels.