V. Aparna1,2, Sanjiv K. Tiwari1,2, Ronald L. Moore3, Navdeep K. Panesar1,2, Brian Welsch4, Bart De Pontieu2, and Aimee Norton5
1. Bay Area Environmental Research Institute, NASA Research Park, Moffett Field, CA 94035, USA
2. Lockheed Martin Solar and Astrophysics Laboratory, 3251 Hanover Street, Building 203, Palo Alto, CA 94306, USA
3. NASA Marshall Space Flight Center, Huntsville, AL 35812, USA
4. Natural and Applied Sciences, University of Wisconsin-Green Bay, 2420 Nicolet Drive, Green Bay, WI 54311, USA
5. HEPL Solar Physics, Stanford University, Stanford, CA 94305-4085, USA
Solar convection sustains the Sun’s luminosity. Exploring convective processes thoroughly is essential to enhance our understanding of the solar dynamo[1]. In the presence of magnetic field, convective motions are inhibited by the Lorentz force, particularly in the direction perpendicular to the magnetic field. However, a systematic study quantifying the suppression of convection with increasing magnetic field has not been performed in the past.
We report the quantitative measure of the suppression of horizontal flux advection speeds with increasing magnetic field strength using HMI/SHARP CEA Bz magnetograms that have 12-minute cadence. We used six active regions (ARs) containing at least one sunspot, and field ranges covering strong-field sunspot regions, intermediate-strength plages to weak-field quiet Sun. We applied Fourier Local Correlation Tracking[2] (FLCT) to measure the flux-advection speeds by using a Gaussian kernel with an FWHM of 15 pixels. A continuum image and a magnetogram of an active region from our study along with tracked speeds overlaid on a magnetogram are shown in Figure 1.
Figure 1. Left: Continuum intensity image of AR 12108. Center: Magnetogram of the same AR at the same time. The orange contours roughly trace the boundary between penumbra and umbra (1500 G) and the green contours trace the approximate outer penumbral boundary (200 G). Right: Horizontal velocity vectors overlaid on the Bz magnetogram, the longest arrow measures 0.53 km/s.
Our result of the average of the horizontal speeds measured using six ARs are shown in Figure 2. It shows quantitatively the suppression of the horizontal velocities due to the vertical magnetic field. Each blue diamond in the plot is the mean horizontal speed in a 50 G wide bin in each frame of the 24-hour observation of the six ARs averaged. The highest speeds in the curve are seen at quiet regions above 150 G and measure around 110 m/s and the lowest are in the sunspot umbra around 10 m/s. The speeds are low in general and are characteristic of slower features, which are most evident at lower cadences. Similar analysis performed on HMI line-of-sight magnetograms at cadences 12-minute, 6-minute, 3-minute and 45-seconds show increasing magnitudes of speeds with cadence, suggesting that increasingly shorter lived and smaller-scale features are tracked with increasing cadence. Examples can be found in Ref. [3].
Figure 2. Left: mean of the mean speeds in Bz bins for the six ARs measured in this study (blue diamonds). The error bars (black) show the standard deviation of the values around the mean of means for each bin. The pink dashed line is the fourth-degree polynomial fit to the means. The coefficients of the fit are given in the legend on the top right in descending order of exponents. Right: mean-speed curves for all six ARs, with the curve for each AR represented in different-colored diamonds. The NOAA numbers of the ARs are given in the respective color in the legend in the bottom panel. The vertical dashed line of each color marks the strongest Bz bin for the AR of that color.
Speeds for the field range 1200-2300 G come from the plage regions and more significantly the sunspot penumbra and outer umbra. Here, the speeds are highly variable due to signatures from penumbral filaments, moving magnetic features, and umbral and penumbral waves. The flatness of the curve in Figure 2 however is because of averaging over the large ranges of speeds from such features. The speeds at the highest field ranges come from sunspot umbral regions where the horizontal motions are strongly suppressed. A slight bump is seen just before the speeds start tending to zero at the highest field strengths – we attribute this bump to p-mode waves arising from the penumbral and outer umbral regions.
The nuances of the speeds in the penumbral and umbral regions, which does not show an abrupt change in the speeds going from penumbra to umbra in Figure 2, is shown in Figure 3 with speeds (represented by asterisks) and field-strength (represented by triangles) plotted by azimuthally averaging around the spot center in increments of one pixel concentrically, using velocities at an instance in time. The speeds vary between 20 m/s and 300 m/s, consistent with earlier reports and showing that the plateau is an effect of averaging over this range of speeds.
Figure 3. Left: continuum image of the sunspot in AR 12480 (2016 January 12). Right: horizontal speed averaged (asterisks) on 1-pixel thick concentric circles over 2 hours from the center to the outer edge of the sunspot region shown in the left panel. Each average field strength (triangles) from the center to the outer edge of the sunspot has the same color as the average speed for that circle. The standard deviations around the averages are shown in black, thick and blue thin error bars for magnetic field strength and speeds, respectively. The standard deviations for the speeds (blue error bars) are divided by four for better display. The standard deviations for the magnetic field strength (black error bars) have their true size.
The quantitative effect of suppression of horizontal velocity with magnetic field is important for determining the energy input into coronal loops in Parker’s nano-flare heating model[4], and for coronal heating MHD simulations. Parker’s nano-flare heating model is governed by convective motions braiding the magnetic field lines rooted there and causing small-scale reconnections heating the local plasma in the coronal loops. The amount of braiding and the subsequent reconnections and heating events appear to depend on both the freedom of convection and magnetic field strength at the feet of the loops – in turn governing how bright or hot the loops get in coronal wavelengths[5]. We incorporate the convective freedom as a function of field strength presented here to determine how the two are related as a function of temperature of the coronal loops and loop length in a subsequent study.
References
[1] Nordlund, A., Stein, R. F., & Asplund, M. 2009, Living Rev Solar Phys, 6, 1, 2
[2] Fisher & Welsch, 2008, ASP Conf. Ser., 383, 373
[3] V. Aparna et al. 2025, ApJ, 987, 98
[4] Parker E. N. 1988., ApJ, 330, 474
[5] Tiwari S. K. et al. 2017, ApJL, 843, L20