Acoustic and Slow Sausage Oscillations in the Stratified Solar Photosphere: Hinode Observations and Phase Relationships

Based on the linearized magnetohydrodynamic (MHD) equations within the framework of the thin flux tube approximation, the phase relationships between the disturbed quantities of evanescent acoustic and slow sausage MHD modes excited in the adiabatically stratified solar atmosphere are considered. It has been shown that the sign of the phase differences (equal to +/-pi/2) between the velocity and other disturbed quantities such as pressure, density, magnetic field, and temperature, depends on the wave frequency omega. The obtained phase relationships agree well with SOT/Hinode observations obtained by Fujimura and Tsuneta (Astrophys. J. 702, 1443, 2009) when omega approximate to omega(c), where omega(c) is the cutoff frequency. The role of various modes excited in the solar atmosphere in the light of the chromospheric and coronal heating problems are discussed.