A new method to calculate the resonant response of a sunspot model atmosphere to magneto-atmospheric waves

In order to understand the observed oscillations in sunspots we present a new method for calculating the resonant response of a realistic semi-empirical model of the sunspot umbral atmosphere and subphotosphere to magneto-atmospheric waves in a vertical magnetic field. The depth dependence of both the adiabatic coefficient and the turbulent pressure is taken into account. This requires an extension of the wave equations by Ferraro & Plumpton (1958). We compare the coefficients of wave transmission, re flection, and conversion between fast mode and slow mode waves for different assumptions, compare the results with those from earlier modelling efforts, and point out possible sources of mistakes. The depth dependence of the adiabatic coefficient strongly influences the resulting spectrum of resonance frequencies. The condition of a conservation of wave flux is violated if the depth dependence of the turbulent pressure is not properly considered.     

Acceleration Effects in MDI Magnetogram Data

Acceleration effects are found in the Michelson Doppler Imager (MDI) magnetogram data because changes in the line profiles during the 30-s measurement are introduced by underlying p-mode velocity variations. This imparts an oscillatory component to the magnetic flux signal. Simulated profiles using Maltby M and Harvard Smithsonian Reference Atmospheres (HSRA) are shifted in accordance with a given velocity amplitude and period and the MDI algorithm for data measurement is applied. The simulated oscillatory component to the magnetic flux density always has a phase difference with respect to the underlying velocity of –90°. The maximum introduced RMS amplitude is a function of velocity amplitude and field strength, but realistic errors are on the order of 5/2000 G, or 0.25% of field strength. Comparison of simulations with observations shows RMS amplitudes of MDI flux density are much greater than predicted by this effect. A 2-component HSRA model, tested to determine if stronger fields with smaller fill factors could fit the data, still can not reproduce the observations. It is concluded that oscillatory amplitudes of magnetic flux density measured with MDI are not due to acceleration effects, although the effect could contribute up to 25% of the measured amplitude. Attempts to remove acceleration effects from the magnetic flux signal are not successful. Also, we confirm that velocities measured in linearly polarized light in the vicinity of a strong magnetic field contain larger errors than velocities measured in circularly polarized light (Yang and Norton, 2001).     

Waves in Sunspots: Resonant Transmission and the Adiabatic Coefficient

We investigate linear acoustic-gravity waves in three different semi-empirical model atmospheres of large sunspot umbrae. The sunspot filter theory is applied, that is, the resonant transmission of vertically propagating waves is modelled. The results are compared with observed linear sunspot oscillations. For three umbral models we present the transmission coefficients and the energy density of the oscillations with the maxima of transmission. The height dependence of the adiabatic coefficient (the ratio of specific heats) strongly influences the calculated resonance frequencies. The variable can explain the observed closely spaced resonance period peaks. The first resonance in the 3 min range is interpreted as a resonance of the upper chromosphere only, while the higher order peaks are resonances of the whole chromosphere.