1.Astronomy Program, Department of Physics and Astronomy, Seoul National University
It is widely accepted that the three minute oscillations inside sunspots are an observable feature of upward-propagating slow MHD waves. As slow MHD waves mainly propagate along magnetic field lines, it is expected that they only propagate vertically in sunspot umbrae. It is often found, however, horizontally propagating oscillation patterns inside sunspot umbrae.
Figure 1| (a) Path of wave propagation inside sunspot umbrae when waves were generated at 2000 km depth. The orange solid lines indicate an isochrone every 30 s. (b) Wave speed as a function of height. The red and blue solid lines indicate the sound speed and Alfvén speed, respectively. The formation height of Fe I 5435 Å line and the plasma β ~ 1 layer are drawn in gray and green solid lines, respectively.
These unexpected phenomena can be explained with a wave excitation source which is located below the photosphere (See figure 1). It is expected that the plasma β > 1 even though the location is inside the sunspot below the photosphere. In this environment, we assume that some events related to magnetoconvection may generate fast MHD waves that propagate quasi-isotropically. These waves would eventually reach a layer near the photosphere where the plasma β ~ 1 and some of the waves convert into slow MHD waves . Since paths of fast MHD waves are different (Figure 1a), the arrival time at the plasma β ~ 1 layer is delayed with distance from the oscillation source. Thus, upward propagating slow MHD waves show horizontal apparent motions that are observed in the higher atmosphere.
Figure 2| Time-distance plot for horizontally propagating oscillation patterns. The dashed lines represent apparent wave propagations from the calculations with 100, 500, 1000, 2000, and 5000 km source depths. The cross symbols and the solid lines are the ripple positions from the FISS observations and their fitting results, respectively. Colors indicate different ripples.
According to this scenario, the horizontally propagating patterns carry information about the source depth. Faster (slower) horizontal propagation enables us to anticipate a deeper (shallow) source. We develop a sunspot model and calculate the distance of the horizontal propagation as a function of time and source depth (dashed curves in Figure 2). We then compare the time-distance relation with those derived from observational data. The velocity oscillations near the temperature minimum region are obtained using Fe I 5435 Å line observations taken with the Fast Imaging Solar Spectrograph (FISS ). After filtering out the 3-minute signals, we identify 5 well-defined horizontally propagating ripples and estimate their propagation distances as a function of time (cross symbol in Figure 2). The model fitting clearly shows that the sources are located between 1000 and 2000 km below the photosphere. Our results are in agreement with previous studies using various methods (Figure 3).
Figure 3| Positions of wave sources in a 3D map (small sphere). Colored circles are the projected positions on the xz plane. The TiO image, which represents the photospheric features, is shown on the xy plane. Vertical solid lines are the auxiliary lines that show positions in the xy plane. Same colors as in Figure 2 are used to indicate the results from the different ripples. Previous studies are presented on the right. Note that the x, y, and z axes are drawn with the same physical scale.
Our study provides insight into the convective motion in a sunspot. Our earlier study  found that the umbral oscillations were spatially and temporally associated with umbral dots. Considering that umbral dots are manifestations of convection inside the umbra, we speculate vertically elongated convection cells: From Figure 3 one can find that the size of umbral dots (~100 km) is much smaller than the source depth (~ 1000 km). This is reasonable because horizontal motions are suppressed by vertically strong magnetic fields inside the umbra . Further studies are needed to investigate internal structures of sunspots.
For more information, please refer to Cho et al.
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