Why Do Chromospheric Oscillations in Sunspot Umbrae Appear to Propagate Downward?

Umbral oscillations constitute the most noticeable chromospheric feature of sunspot umbrae—large-amplitude oscillations of intensity (umbral flashes, if very strong) and line-of-sight velocity, with periods of about 3 minutes. These umbral oscillations are usually interpreted as acoustic waves propagating upward under the effect of gravity. However, there have been observational reports that intensity peaks tend to occur in downflowing phases of umbral oscillations, and this appears to be more compatible with downward propagation. We investigate whether this intensity–velocity correlation occurs persistently or not, by determining the vertical flux of the wave energy, based on Hα line measurements of the temperature and velocity. As a result, we find that the wave flux is persistently negative in sunspot umbrae, confirming the discrepancy specified above. We attribute this discrepancy to the nonzero fluctuation of net radiative heating. We find that when this effect is taken into account in the energy equation, the pressure is peaked during upflowing phases, being compatible with the notion of upward propagation. We conclude that temperature (and intensity) peaks occur during downflowing phases, not because of downward propagation, but because of radiative heat transport.