Importance of Solar Atmospheric Coupling on P-Mode Power within Magnetic Elements

It has long been known that the power of p-mode oscillations is reducedwithin magnetic plages and sunspots at photospheric level. Recent observations now suggest that this suppression of power extends into the low chromosphere and isalso present in small magnetic elements far from active regions. Weconstruct a model to investigate a possible mechanism of this powerloss whereby p modes buffet small magnetic elements and excite MHDsausage tube waves. These magnetic tube waves propagate along the manymagnetic fibrils which are embedded in the convection zone and expandinto the chromosphere due to the fall in density with height of thesurrounding plasma. We treat the magnetic fibrils as verticallyaligned, thin flux tubes embedded in a two region polytropic-isothermalatmosphere to study the coupling of p-mode driven sausage waves,which are excited in the convection zone and propagate into theoverlying chromosphere. The excited tube waves carry energy away fromthe p-mode cavity resulting in a deficit of p-mode energy which wequantify by computing the associated damping rate and absorptioncoefficient of the driving p modes. We also compare the verticalmotion within the fibril with the vertical motion of the incident p modeby constructing the ratio of their powers using HMI data and theory.In agreement with observational measurements we find that the totalpower is suppressed within strong magnetic elements for frequenciesbelow the acoustic cut-off frequency. We also find that the magnitudeof the power deficit increases with the height above the photosphereat which the measurement is made. Further, we argue that the area ofthe solar disk over which the power suppression extends increases as afunction of height.