Waves in sunspots: Resonant transmission and the adiabatic coefficient

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