Junwei Zhao1, Ruizhu Chen2,1, Thomas Hartlep3, & Alexander G. Kosovichev4
1 W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA, USA
2 Department of Physics, Stanford University, Stanford, CA, USA
3 BAER Institute, NASA Ames Research Center, Moffet Field, CA, USA
4 Department of Physics, New Jersey Institute of Technology, Newark, NJ, USA
In this nugget, we report the detection of a fast-moving wave propagating from sunspot umbra through penumbra to about 15 Mm beyond the sunspot boundary. This wave is thought to be the wavefront of a magnetoacoustic wave, excited at about 5 Mm beneath the sunspot’s surface, sweeping across the sunspot photosphere and beyond.
The sunspot we analyzed was located in NOAA active region 11312, and the data are SDO/HMI Doppler observations taken from 2011 October 8 to October 12, a total of 5 days. We calculated cross-correlation functions between various locations to reconstruct how waves propagate away from one location to its surrounding areas. A similar analysis technique was developed by Cameron et al.1, and the analysis procedure used in this work is same as described in Ref.  except that here the wave sources were selected inside the sunspot.
Figure 1 | Selected snapshots of the reconstructed waves propagating away from the sunspot penumbra, shown as foreground color images. The background black-and-white image shows continuum intensity of the studied region. The snapshots taken at 3.75, 5.25, 6.75, and 9.00 min show the fast-moving wave along the sunspot’s radial direction, and the snapshots taken at 14.25 and 23.25 min mainly show the typical helioseismic waves expanding in all directions.
Figure 1 displays a few selected snapshots of the waveform obtained for a virtual source located inside the penumbra. For the time lags from 3.75 min to 14.25 min, a fast-moving wave is seen propagating along the sunspot’s radial direction from the penumbra to the outside of the sunspot. The wave signal terminates at approximately 30 Mm away from the sunspot center, or about 15 Mm beyond the sunspot boundary. This fast-moving wave is clearly distinguishable from the usual helioseismic waves, which can be seen in the snapshots at 14.25 min and 23.25 min. Actually, in our analysis, the helioseismic wave is first identified only at 12.00 min.
Figure 2 | (a) Time–distance diagram obtained along the sunspot’s radially outward direction. (b) Same as (a), but with two white boxes delimiting the areas of the fast-moving wave (lower box) and helioseismic waves (upper box). The green line shows a linear fitting of the fast-moving wave, corresponding to a speed of 45.3 km s-1. (c) Time-distance diagram from a quiet-Sun region is shown for comparison. (d) Power-spectrum diagram for the fast-moving wave. The green line corresponds to the same phase speed as the line in panel (b).
To better quantify the properties of the fast-moving wave, we obtain the time-distance relation of the wave by stacking together the cross-correlation functions for different travel-time lags, as shown in Fig. 2. There are two wave branches visible in the time-distance diagram (Fig. 2a-b), with the lower branch corresponding to the fast-moving wave, and the upper branch corresponding to the usual helioseismic waves. By comparing this time-distance diagram with the one obtained from a quiet-Sun region (Fig. 2c), we find that the fast-moving wave is a phenomenon only associated with sunspot. A linear fitting shows that the apparent phase speed for this fast-moving wave is 45.3 ± 1.7 km s-1, substantially faster than the speed of fast magnetoacoustic wave or Alfvén wave in the photosphere.
Figure 2d shows the k–ν power-spectrum diagram for this fast-moving wave. It shows that the dominant power is within the range of 2.5-4.0 mHz, indicating that the oscillation frequency of the wave falls into the category of five-minute oscillations. The dominant power shows a phase velocity close to 45 km s-1, in agreement with the fitting result in the space-time domain.
Figure 3 | (a) Schematic plot showing a scenario of a subsurface disturbance generating a helioseismic wave sweeping across the photosphere, forming the fast-moving wave observed in the photosphere. (b) Vertical snapshot showing the wave propagating away from the disturbance, located at 2 Mm away from the sunspot’s central axis at the depth of 5 Mm. The snapshot is taken at 7.5 min after the wave is excited. The wave shown in this figure is obtained from solving the ray-theory MHD equations using a realistic sunspot model for the frequency of 3 mHz. (c) Time-distance diagram seen in the photosphere for this wave. For comparison, a white dashed line, representing a speed of 45.3 km s-1, is plotted.
To explain this wave, we conjecture a disturbance occurring at approximately 5 Mm beneath the sunspot surface and 2 Mm away from the sunspot’s central axis (see Fig. 3a). Acoustic waves are excited by this disturbance and expand toward all directions. Due to the stratified structure of the sound-speed profile as a function of depth, and the existence of magnetic field that will alter, albeit slightly, the sound-speed profile both horizontally and vertically, the wavefront does not expand symmetrically toward all directions. The wavefront touches different locations of the photosphere at different times, forming effectively a fast-expanding ellipse at the surface due to the asymmetric propagation speed. Employing a realistic MHD sunspot model and following the ray-path approximation with magnetic field3, we calculate how a magnetoacoustic wave, at a frequency of 3.0 mHz, expands from the deep source and how its wavefront sweeps across the photosphere (see Fig. 3). The time-distance relation from this calculation shows an approximately 40 km s-1 surface speed of the wavefront when it is 10 Mm horizontally away from the source on the surface.
This newly detected fast-moving wave, although may not be a new type of wave, likely carries rich information from sunspots’ subsurface region, and may help to open a new window to diagnose sunspots’ internal structure and dynamics. For more details, please refer to our full paper4. We note that another paper5 reporting the same phenomenon was published at about the same time.
 Cameron, R., Gizon, L., & Duvall, T. L., Jr., 2008, SoPh, 251, 291
 Zhao, J., Kosovichev, A. G., & Ilonidis, S., 2011, SoPh, 268, 429
 Moradi, H., & Cally, P. S., 2008, SoPh, 251, 309
 Zhao, J., Chen, R., Hartlep, T., & Kosovichev, A. G., 2015, ApJL, 809, L15
 Löhner-Böttcher, J. & Bello González, N., 2015, A&A, 580, A53