Evidence for coherent spicule oscillations from correcting Hinode/SOT Ca ii H in the south-east limb of the Sun

Wave theories of heating the chromosphere, corona, and solar wind due to photospheric fluctuations are strengthened by the existence of observed wave coherency up to the transition region (TR). The coherency of solar spicules' intensity oscillations was explored using the Solar Optical Telescope (SOT) on the Hinode spacecraft with a height increase above the solar limb in active region (AR). We used time sequences near the southeast region from the Hinode/SOT in Ca II H line obtained on April 3, 2015 and applied the de-convolution procedure to the spicule in order to illustrate how effectively our restoration method works on fine structures such as spicules. Moreover, the intensity oscillations at different heights above the solar limb were analysed through wavelet transforms. Afterwards, the phase difference was measured among oscillations at two certain heights in search of evidence for coherent oscillations. The results of wavelet transformations revealed dominant period peaks in 2, 4, 5.5, and 6.5 min at four separate heights. The dominant frequencies for coherency level higher than 75 percent was found to be around 5.5 and 8.5 mHz. Mean phase speeds of 155-360 km s-1 were measured. We found that the mean phase speeds increased with height. The results suggest that the energy flux carried by coherent waves into the corona and heliosphere may be several times larger than previous estimates that were based solely on constant velocities. We provide compelling evidence for the existence of upwardly propagating coherent waves.