Cross-Correlation of Oscillations in A Fragmented Sunspot

Oscillations in a sunspot are easily detected through the Doppler velocity observation. Although the sunspot oscillations look erratic, the wavelet analysis show that they consist of successive wave packets which have strong power near three or five minutes. Previous studies found that 3-min oscillation at the chromosphere is a visual pattern of upward propagating acoustic waves along the magnetic field lines. Resent multi-height observations help this like vertical study, however, we also focus on horizontal facet to extend three dimensional understand of sunspot waves. So, we investigate a fragmented sunspot expected to have complex wave profiles according to the positions in the sunspot observed by the Fast Imaging Solar Spectrograph. We choose 4 points at different umbral cores as sampling positions to determine coherence of oscillations. The sets of cross-correlation with three and five minutes bandpass filters during a single wave packet reveal interesting results. Na I line show weak correlations with some lags, but Fe I and Ni I have strong correlations with no phase difference over the sunspots. It is more remarkable at Ni I line with 3-min bandpass that all sets of cross-correlation look like the autocorrelation. We can interpret this as sunspot oscillations occur spontaneously over a sunspot at photosphere but not at chromosphere. It implies a larger or deeper origin of 3-min sunspot oscillation.