A Statistical Analysis of Spiral-shaped Wave Patterns in Sunspot Umbrae

Spiral-shaped wave patterns (SWPs) observed in sunspot umbrae represent the superposition of axisymmetric patterns and nonaxisymmetric patterns of umbral oscillations. These patterns give us physical information about the source of oscillations below the surface. Here we present the statistics of their observational properties determined from the 304 Å line-intensity data obtained with the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory. From the 2013 to 2018 data set, we examined each of the 496 sunspots near the disk center for 2 hr. As a result, we identified 241 SWPs from 140 sunspots, which corresponds to the detection rate of 0.24 per hour in each sunspot. Most of the SWPs had one spiral arm, 48 SWPs had two arms, and only one had three. The oscillation period was estimated at 151 ± 27 s and the lifetime, at 770 ± 250 s, being comparable to those of conventional umbral oscillations. The rotation period of the SWPs was estimated at 190 ± 69 s for the one-armed SWPs and 299 ± 115 s for the two-armed SWPs. We found that the properties of the SWPs have no dependence on hemisphere, latitude, and sunspot size. From the apparent radial speeds of the SWPs and a simple model of wave propagation, we infer that the SWPs may be generated between 2 and 11 Mm below the photosphere with a mean value of about 6 Mm.