tokens: an oscillatory process, in which two pulses with different directions are superimposed. In the first case, a random velocity with normal distribution is simulated, see upper panel of Figure 8 . In order to apply exactly the same method used with the real data, we filtered the simulated velocity signal employing the EMD (middle panel of Figure 8 ). The polarization of this filtered signal is then visualized through a compass diagram just like what was done in the case of the observed data. Besides, we simulated a simple oscillatory signal of the form:where A is the amplitude of the velocity signal, T 1 is period, and T 2 is long-term modulation to simulate a wave train (see lower panel of Figure 8 ). Figure 8. Top panel: simulated random velocity signal with normal distribution. Middle panel: same velocity signal filtered using the EMD. Bottom panel: simulated velocity signal made with two superimposed pulses in the x and y direction respectively. The two pulses are exactly the same, but slightly shifted and with different amplitudes. The compass diagrams of the two simulated velocity signals are shown in Figure 9 . In comparison with the oscillatory signal, the random process does not display polarization (top panel). This confirms the validity of our findings. In contrast, the same kind of polarization of the compass diagram is indeed obtained with a superposition of two pulses in different directions (bottom panel). Figure 9. Compass diagram of the simulated random velocity signal with normal distribution (top), and the one obtained from a superposition of two velocity pulses in two perpendicular directions (bottom). 4. Discussion and Conclusion The results presented above show low-frequency (5–6 mHz) kink-like horizontal oscillations of SSMEs in chromosphere with an elliptic polarization of the velocity vector (see Figure 1 for a schematic representation) observed in all of the 35 SSMEs analyzed in the quiet chromosphere. This frequency range is inconsistent with residual seeing aberrations. In this regard, it is worth noting that the orientation of the velocity vector in time is not random, but reflects a long-term coherency (several minutes). This timescale is by far longer than the typical timescale of atmospheric turbulence (a few ms). Indeed, Stangalini et al. ( 2016 ) have deeply analyzed the decorrelation timescales of adaptive optic residual aberrations using on-sky data, and found them to be of the order of 10–20 ms at visible wavelengths (∼630 nm). This is consistent with independent works in the literature (see, for example, Davis Tango 1996 ). Since the turbulence timescales at the Ca ii H wavelengths is even shorter (Roddier 1999 ), we expect a large reduction of the turbulence coherence time, resulting in a turbulence timescale that is even more inconsistent with that of the process observed here. In addition, since the seeing residual aberrations are a random process, one cannot expect any coherent helical motion of the
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