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 n ew method for calculating the resonant response of a realistic semi-empiric al model of the sunspot umbral atmosphere and subphotosphere to magneto-atm ospheric waves in a vertical magnetic field. The depth dependence of both t he adiabatic coefficient and the turbulent pressure is taken into account. This requires an extension of the wave equations by Ferraro & Plumpton (195 8). We compare the coefficients of wave transmission, reflection, and conve rsion between fast mode and slow mode waves for different assumptions, comp are the results with those from earlier modelling efforts, and point out po ssible sources of mistakes. The depth dependence of the adiabatic coefficie nt strongly influences the resulting spectrum of resonance frequencies. The condition of a conservation of wave flux is violated if the depth dependen ce of the turbulent pressure is not properly considered.