Merlin M. Mendoza & Chia-Hsien Lin

Department of Space Science and Engineering, National Central University, Taiwan

Solar pores are dark regions in the continuum intensity which are associated with the concentration, dissipation, and transport of magnetic flux (e.g., [1], [2], [3]). Their observable quantities can provide us important constraints to improve simulations of active regions. In this work, we have investigated observable quantities such as the continuum intensity *I*, magnetic field inclination *θ*_{B}, and magnetic pressure *P*_{mag} to probe possible correlations as well as causations with the motion of the pore.

The 61 compact pores are identified from the Spaceweather HMI Active Region Patches (SHARP)^{[4]} from 2011 to 2018. Since the pores are selected from SHARP images, they are likely to be part of the magnetic system of the emerging active regions and formed from flux emergence.

Figure 1| Panels (a), (b), and (c) show the front (blue) and back (red) continuum intensities, magnetic field inclinations , and magnetic pressures in the outer (solid) and inner (dashed) edges of a moving pore in AR 11147. A portion of the SHARP image of AR 11147 is shown in panel (d) wherein a pore moving towards the right along with its smoothed trajectory (blue) is shown inside the dashed box. The red arrow on the lower right points toward the solar disk center.

The time variations of *I*, *θ*_{B}, and *P*_{mag} of one selected pore are plotted in Figure 1, which shows that *I* and *θ*_{B}, at the front and back sides of the pore are of similar magnitudes, while *P*_{mag} are significantly different. The statistical distributions of the front-back side differences of the three quantities, *∆I*, *∆θ*_{B}, and *∆P*_{mag}, of all 61 pores at every temporal point are shown in Figure 2. The differences are calculated at the inner and outer edges, and also for the inner – outer edge difference, as indicated in the superscripts. To enable comparison among different quantities, we scaled each histogram by the unsigned average of all the temporal points in that distribution. All the distributions show a single peak except for *∆P*_{mag}^{out} and *∆P*_{mag}^{in}, which show a double peak. This suggests that there may be a unique relationship between the motion of the pore and the magnetic pressure difference.

Figure 2| The histograms of front-back differences ∆I, ∆θ

_{B}, and ∆P_{mag}of each temporal point for all cases for the outer (a, b, and c) and inner edges (d, e, and f), and in-out edge differences (g, h, and i). For all panels, the top axes show the actual magnitudes of the quantities while the bottom axes are scaled by the average of the absolute values of all temporal points for each quantity. The mean value of the scaled version of each distribution is printed and marked by a black vertical line in the corresponding panel. In panels (c) and (f), the means of the actual magnitudes of the two peaks, are 197 Pa and −225 Pa (panel c) and 267 Pa and −215 Pa (panel f), and are marked by the blue and red lines, respectively.

To further investigate the relationship between the direction of pore movement and the direction of maximum magnetic pressure difference, we define two direction angles *ϕ*_{t} and *ϕ*_{dPo}, which represent the direction of the trajectory of the pore, and the direction of the maximum positive magnetic pressure difference at the opposite sides of the pore, respectively. *ϕ*_{dP} for the outer and inner layers, and edge difference are denoted as *ϕ*_{dPo}, *ϕ*_{dPi}, *ϕ*_{dPio}, respectively. In Figure 3, we show their scatter plots and 2D histograms for all temporal points of the moving pores. Panels (a), (c), (b) and (d) show four clusters of data points, indicating parallel and anti-parallel relationships between *ϕ*_{t} and *ϕ*_{dPo} and between *ϕ*_{t} and *ϕ*_{dPi}. The correlation coefficients of both parallel and anti-parallel cases are higher than 0.74. Panels (e) and (f) only show two horizontal clusters which indicates that the motion is unrelated to *ϕ*_{dPo}.

Our examinations of their causal relationships using transfer entropy (TE)^{[5]} indicate no significant causal relationships between *ϕ*_{t} and *ϕ*_{dPo} and vice versa. The high correlation but no causal relation may indicate that an unknown variable is possibly acting as a driver causing both the motion of the pore and the magnetic pressure differences.

Figure 3| The upper panels (a, c, and e) show the scatter plots of ϕ

_{t}vs. ϕ_{dPo}, ϕ_{t}vs. ϕ_{dPi}, and ϕ_{t}vs. ϕ_{dPio}, respectively. The cases of +⟨∆P_{mag}⟩ and −⟨∆P_{mag}⟩ are distinguished by the blue and red colors, respectively. Their corresponding two-dimensional histograms are shown in the lower panels (b, d, and f). The colorbars represent the number of temporal points.

For more details on this study, please visit: https://doi.org/10.3847/1538-4357/acbe43

### References

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[4] Scherrer, P. H., Schou, J., Bush, R. I., et al. 2012, *Solar Phys*, **275**, 207

[5] Wing, S., Johnson, J. R., & Vourlidas, A. 2018, *ApJ*, **854**, 85