M. Cristina Rabello-Soares1, Richard S. Bogart2, and Philip H. Scherrer2
1. Physics Department, Universidade Federal de Minas Gerais, Belo Horizonte, MG 30380, Brazil
2. W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305, USA
As acoustic waves are modified by magnetic field, helioseismology has the potential to study the structure of sunspots below the solar surface. There have been many observational and theoretical studies that have yielded a wealth of information, but, as basic features of sunspots are still being disputed, more work is needed. We analyze the effect of a sunspot in its quiet surroundings by applying a helioseismic technique on almost three years of Helioseismic and Magnetic Imager (HMI) observations obtained during solar cycle 24 to further study the sunspot structure below the solar surface.
We calculated the mean difference between the acoustic wave amplitude and flows observed in quiet regions (‘targets’) next to an active region and the ones surrounded only by quiet regions (‘comparisons’) over 38 Carrington rotations by applying ring-analysis to 5° regions in HMI Dopplergram images. We analyzed the variations with distance and propagation direction from the nearby active region as far as 8° away from the active region center. To check the systematic errors and the level of noise introduced by our analysis, the parameters of one of the comparison tiles (a quiet tile with only quiet tiles around it) for each target tile is randomly chosen and used instead of the target parameters and the calculations were repeated. These will be referred to as the control set.
Figure 1| The relative difference of the maximum power in the ring, at four different distances from the nearby active region for f (stars), p1 (triangles), p2 (crosses), and p3 (diamonds) modes. The colors show different directions: θ’=0° (in the direction of the nearby active region in black), θ’=45° (red), θ’=90° (perpendicular to it in blue), and θ’=135° (salmon). The small black squares close to zero are the results for the control set.
The mode amplitude is attenuated by the presence of the nearby active region for modes with frequency lower than about 4.2 mHz and it is amplified for higher frequencies. The amplitude difference depends on the direction of the wave in relation to the nearby active regions. This anisotropic variation is more important at 6° and 7° than at 5° or 8° away from the nearby active region (Figure 1). Although the maximum enhancement observed is as large as the maximum attenuation, it is largely independent of the wave direction. The largest amplification happens 6° away from the active region. On the other hand, waves that travel perpendicular to the nearby active are attenuated nearly 40% less than the ones propagating in its direction. The largest attenuation happens for p1 modes with frequency close to 3 mHz at 6° away from the nearby active region and traveling in its direction. The anisotropic component of the amplitude changes from attenuation to enhancement at a higher frequency than the isotropic term, around 4.8 mHz. Thus, although it is a small effect, waves with frequencies between 4.2 and 4.8 mHz moving perpendicular to the nearby active region are more amplified than waves traveling in its direction.
Figure 2| Mean angular speed for two different fitting methods: rdfitc (full circles) and rdfitf (diamonds). The small symbols are for the control set. The symbols have been slightly displaced horizontally to improve visibility. The straight lines are exponential fits to rdfitc (full line) and rdfitf (dashed line) angular velocities. Extrapolation of the rdfitc fit (full line) roughly agrees with the average of angular speed obtained by Ref.  at the sunspot umbra for all rotating sunspots during almost 40% of our data set.
Recently, Zheng et al.  found that sunspots tend to rotate counterclockwise in the southern hemisphere, and have the opposite behavior in the northern hemisphere, using HMI observations from 2014 January to 2015 February, which overlaps in part with our data set. Averaging their estimated angular speed for all rotating sunspots obtained during 2014 (in their Table 1), we obtain a net clockwise angular speed of 0.25° hr-1 at sunspot umbra. In our analysis, we also observe a mean clockwise flow around active regions which decreases with distance from close to 5 m s-1 to less than 1 m s-1 (Figure 2). We fitted an exponential function to the angular speed with a coefficient close to -0.7 degree-1. Extrapolating our fit, we get a angular speed at sunspot umbra similar to the above-mentioned average results.
Figure 3| Inferred flow variation parallel to (i.e., in the direction of) the nearby active region obtained for rdfitc. Thick arrows are for flows larger than 2.5σ and thin arrows are for 1.5-2.5σ. The size of the red arrow corresponds to a flow of 10 m s-1. For better visualization, outflows are in blue and inflows are in black. Additionally, the results were duplicated in the left and right sides of the active region.
We also analyzed the variation of the flow in the direction of the nearby active region with distance from near the surface to 7 Mm deep. Our results (Figure 3) agree with a large-scale circular flow around the sunspot in the shape of a cylindrical shell around the sunspot as proposed by Hindman et al.  supposing a downflow close to the sunspot and an upflow farther away connecting the near-surface inflow and the deep outflow. The center of the shell of this circular flow seems to be centered around 7° from the sunspot center, where we observe an inflow close to the surface down to ∼2 Mm, followed by an outflow at deeper layers until at least 7 Mm. Our results differ from Gizon et al.  as they observed outflows in the upper 4 Mm until as far as 120 Mm from the center of one sunspot (NOAA 9787). Their results are also in disagreement with Zhao et al. , even though both used the same helioseismic method.
For more information, please refer to our recent publication: Rabello-Soares, M. C., et al. 2018, ApJ, 859, 7.
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