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Energy loss of solar p modes due to the excitation of magnetic sausage tube waves: importance of coupling the upper atmosphereWe consider damping and absorption of solar p modes due to their energy loss to magnetic tube waves that can freely carry energy out of the acoustic cavity. The coupling of p modes and sausage tube waves is studied in a model atmosphere composed of a polytropic interior above which lies an isothermal upper atmosphere. The sausage tube waves, excited by p modes, propagate along a magnetic fibril which is assumed to be a vertically aligned, stratified, thin magnetic flux tube. The deficit of p-mode energy is quantified through the damping rate, Γ, and absorption coefficient, α. The variation of Γ and α as a function of frequency and the tube's plasma properties is studied in detail. Previous similar studies have considered only a subphotospheric layer, modeled as a polytrope that has been truncated at the photosphere. Such studies have found that the resulting energy loss by the p modes is very sensitive to the upper boundary condition, which, due to the lack of an upper atmosphere, have been imposed in a somewhat ad hoc manner. The model presented here avoids such problems by using an isothermal layer to model the overlying atmosphere (chromosphere, and, consequently, allows us to analyze the propagation of p-mode-driven sausage waves above the photosphere. In this paper, we restrict our attention to frequencies below the acoustic cut off frequency. We demonstrate the importance of coupling all waves (acoustic, magnetic) in the subsurface solar atmosphere with the overlying atmosphere in order to accurately model the interaction of solar f and p modes with sausage tube waves. In calculating the absorption and damping of p modes, we find that for low frequencies, below ≈3.5 mHz, the isothermal atmosphere, for the two-region model, behaves like a stress-free boundary condition applied at the interface (z = –z 0).
Five-minute oscillation power within magnetic elements in the solar atmosphereIt has long been known that magnetic plage and sunspots are regions in which the power of acoustic waves is reduced within the photospheric layers. Recent observations now suggest that this suppression of power extends into the low chromosphere and is also present in small magnetic elements far from active regions. In this paper we investigate the observed power suppression in plage and magnetic elements, by modeling each as a collection of vertically aligned magnetic fibrils and presuming that the velocity within each fibril is the response to buffeting by incident p modes in the surrounding field-free atmosphere. We restrict our attention to modeling observations made near the solar disk center, where the line-of-sight velocity is nearly vertical and hence, only the longitudinal component of the motion within the fibril contributes. Therefore, we only consider the excitation of axisymmetric sausage waves and ignore kink oscillations as their motions are primarily horizontal. We compare the vertical motion within the fibril with the vertical motion of the incident p mode by constructing the ratio of their powers. In agreement with observational measurements we find that the total power is suppressed within strong magnetic elements for frequencies below the acoustic cut-off frequency. However, further physical effects need to be examined for understanding the observed power ratios for stronger magnetic field strengths and higher frequencies. We also find that the magnitude of the power deficit increases with the height above the photosphere at which the measurement is made. Furthermore, we argue that the area of the solar disk over which the power suppression extends increases as a function of height.