We investigate the role of active-region spicules in the mass balance of the solar wind and energy supply in heating the solar atmosphere. We use high-cadence observations from the Solar Optical Telescope (SOT) onboard the Hinode satellite in the Ca ii H-line filter obtained on 26 January 2007. The observational technique provides the high spatio-temporal resolution required to detect fine structures such as spicules. We apply a Fourier power spectrum and wavelet analysis to Hinode/SOT time series of an active-region data set to explore the existence of coherent intensity oscillations. Coherent waves could be evidence of energy transport that serves to heat the solar atmosphere. Using time series, we measure the phase difference between two intensity profiles obtained at two different heights, which gives information about the phase difference between oscillations at those heights as a function of frequency. The results of a fast Fourier transform (FFT) show peaks in the power spectrum at frequencies in the range from 2 to 8 mHz at four different heights (above the limb), while the wavelet analysis indicates dominant frequencies similar to those of the Fourier power spectrum results. A coherency study indicates coherent oscillations at about 5.5 mHz (3 min). We measure mean phase speeds in the range 250–425kms−1\documentclass[12pt]{minimal}
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\begin{document}$250\,\mbox{--}\,425~\mbox{km}\,\mbox{s}^{-1}$\end{document} increasing with height. The energy flux of these waves is estimated to be F=1.8×106–11.2×106ergcm−2s−1\documentclass[12pt]{minimal}
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\begin{document}$F = 1.8 \times 10^{6}\,\mbox{--}\,11.2 \times 10^{6}~\mbox{erg}\,\mbox{cm}^{ - 2}\,\mbox{s}^{ - 1}$\end{document} or 1.8–11.2kWm−2\documentclass[12pt]{minimal}
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\begin{document}$1.8\,\mbox{--}\,11.2~\mbox{kW}\,\mbox{m}^{ - 2}$\end{document}, which indicates that they are sufficiently energetic to accelerate the solar wind and heat the corona to temperatures of several million degrees. We compute the the mass flux carried by spicules of 3×10−10–2×10−9gcm−2s−1\documentclass[12pt]{minimal}
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\begin{document}$3 \times 10^{ - 10}\,\mbox{--}\,2 \times 10^{ - 9}~\mbox{g}\,\mbox{cm}^{ - 2}\,\mbox{s}^{ - 1}$\end{document}, which is 10 – 60 times higher than the mass that is carried away from the corona because of the solar wind (about 3×10−11gcm−2s−1\documentclass[12pt]{minimal}
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\begin{document}$3 \times 10^{ - 11}~\mbox{g}\,\mbox{cm}^{ - 2}\,\mbox{s}^{ - 1}$\end{document}). Therefore, our results indicate that about 0.02 – 0.1 of the spicule mass is ejected from the corona, while the remainder reverts to the chromosphere. In other words, spicules can supply the mass lost due to the slow solar wind.
