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.