Abstract
We report the observations of the magneto-hydrodynamic waves propagating along magnetic flux tubes in the solar photosphere. We identified 20 isolated strong peaks (8 peaks for pores and 12 peaks for inter-granular magnetic structure) in the power spectra of the l.o.s. (line-of-sight) magnetic flux, the l.o.s. velocity, and the intensity for 14 different magnetic concentrations. The observation is performed with the spectro-polarimeter of the Solar Optical Telescope aboard the \emph{Hinode} satellite. The observed phase relation between the magnetic and the photometric intensity fluctuation would not be consistent with that caused by the opacity effect, if the magnetic field strength decreases with height along the oblique line of sight. We suggest that the observed fluctuations are due to longitudinal (sausage mode) and/or transverse (kink mode) MHD waves. The observed phase relation between the fluctuations in the magnetic flux and the velocity is consistent with the superposition of the ascending wave and the descending wave reflected at chromosphere/corona boundary (standing wave). Even with such reflected waves, the residual upward Poynting flux is estimated to be $2.7 \times 10^{6}$ erg cm$^{-2}$ s$^{-1}$ for a case of the kink wave. Seismology of the magnetic flux tubes is possible to obtain various physical parameters from the observed period and amplitude of the oscillations.
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