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Sunspot umbrae show a change in the dominant period of their oscillationsfrom five minutes in the photosphere to three minutes in the chromosphere. Inthis paper, we explore the two most popular models proposed to explain thethree-minute oscillations: the chromospheric acoustic resonator and thepropagation of waves with frequency above the cutoff value directly from lowerlayers. We employ numerical simulations of wave propagation from the solarinterior to the corona. Waves are driven by a piston at the bottom boundary. Wehave performed a parametric study of the measured chromospheric power spectrain a large number of numerical simulations with differences in the drivingmethod, the height of the transition region (or absence of transition region),the strength of the vertical magnetic field, and the value of the radiativecooling time. We find that both mechanisms require the presence of waves withperiod in the three-minute band at the photosphere. These waves propagateupward and their amplitude increases due to the drop of the density. Theiramplification is stronger than that of evanescent low-frequency waves. Thiseffect is enough to explain the dominant period observed in chromosphericspectral lines. However, waves are partially trapped between the photosphereand the transition region, forming an acoustic resonator. This chromosphericresonant cavity strongly enhances the power in the three-minute band. Thechromospheric acoustic resonator model and the propagation of waves in thethree-minute band directly from the photosphere can explain the observedchromospheric three-minute oscillations. They are both important in differentscenarios. Resonances are produced by waves trapped between the temperatureminimum and the transition region. Strong magnetic fields and radiative lossesremove energy from the waves inside the cavity, resulting in weaker amplituderesonances.

Origin of the chromospheric three-minute oscillations in sunspot umbrae