151. Hemispheric Sign Preference of Magnetic Helicity Flux in Solar Cycle 24

Contributed by Sung-Hong Park. Posted on January 26, 2021

Sung-Hong Park1, K. D. Leka1,2, Kanya Kusano1.
1. Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Japan
2. NorthWest Research Associates, Boulder, CO 80301, USA

Over the past decades, extensive observations have revealed that left-handed/right-handed helical structures appear more frequently in the northern/southern hemisphere of the Sun, independent of solar cycles. This is the so-called hemispheric sign preference (HSP) of helicity. The degree of the HSP compliance has been found in the range of ~60-80% for various features[1] in the magnetized solar plasma, such as sunspots, filaments, and coronal loops. Many physical processes have been proposed to explain the observed HSP[2]:(1) Coriolis force, (2) differential rotation, (3) α-effect involved in turbulent dynamo models, (4) helical turbulent convection (called Σ-effect), and (5) local photospheric flows. We conjecture that several different processes may work together to produce the observed HSP. However, it is not clear which processes dominate or obscure the HSP. To answer this question, here we estimate magnetic helicity flux (dH/dt) across the photospheric surface for 4,802 samples of 1,105 unique active regions (ARs) observed during Solar Cycle 24. Details of the SDO/HMI data and methods used to obtain dH/dt estimates as well as their uncertainties can be found in Ref. [3].

Figure 1| Relative frequency distribution of magnetic helicity flux dH/dt values for ARs in the northern (blue) and southern hemispheres (red), respectively.

With the given set of our dH/dt estimates, we find that 63% and 65% of the investigated AR samples in the northern and southern hemispheres, respectively, follow the HSP (see Figure 1). The degree of the HSP compliance is calculated as the fraction of ARs that have negative/positive values of dH/dt if the given ARs are located in the northern/southern hemisphere. As shown in Figures 2 and 3, the HSP of dH/dt tends to gradually increase from ~50-60% up to ~70-80% for AR samples which (1) appear at the earlier inclining phase of solar cycle 24 or higher latitudes; (2) have larger values of |dH/dt|, the total unsigned magnetic flux Φ, and the average plasma flow speed <|v|>. In addition, as expected, the HSP is found to be lower in the case of ARs for which the sign of the average force-free parameter <α> is opposite to the sign expected from the HSP in each hemisphere.

Figure 2| Fraction of ARs in the northern (left column) and southern (right column) hemispheres, respectively, following the HSP of dH/dt, as a function of (a) date, (b) heliographic latitude, and (c) |dH/dt|. Error bars represent Poisson uncertainties in the HSP, each of which is calculated from the total number of AR samples in each bin.

We now offer interpretations of our observational findings on the HSP dependences of dH/dt with respect to various properties of ARs. First, the Coriolis force acting on a rising magnetic flux tube through the convection zone will generate the twist of magnetic field lines inside the flux tube which has a sign agreeing with the HSP. The twist will be more effectively induced by the Coriolis force in the case that a flux tube (1) rises through the convection zone at a higher latitude; (2) has larger magnetic flux so that expansion of the flux tube is faster. This scenario of the HSP enhancement is in good agreement with our observational findings that the HSP is positively correlated with the heliographic latitude, Φ, and <|v|>. Another important process that can generate and modify twist on a flux tube is the differential rotation. Meanwhile, the observed increase of the HSP with increasing latitude supports the scenario that the HSP can be enhanced by a larger differential rotation on the photosphere at a higher latitude by twisting the footpoints of magnetic fields and shearing a bipolar sunspot pair of an emerged Ω-shaped flux tube. Finally, the tachocline α-effect of flux-transport dynamos at the base of the convection zone will generate a twisted flux tube of which helicity sign follows the HSP. In some dynamo simulations4,5, the relative amplitude of the tachocline α-effect is much larger in the latitude range of 30-50 degrees compared to lower latitudes.

Figure 3| Same as Figure 2, but for the HSP of dH/dt as a function of (a) the total unsigned magnetic flux Φ, (b) the average force-free parameter <α>, and (c) the average flow speed <|v|> across the entire photospheric surface of the given AR sample.

To summarize, our observations support the enhancement of the HSP mainly by the Coriolis force acting on an expanding flux tube through the convection zone as well as the differential rotation on the solar surface and the α-effect at the base of the convection zone. For future work, we strongly urge research that employs advanced solar convective dynamo simulations to investigate the HSP trends found in this study and use them as their model validation.

For more information, please refer to Ref. [3].


[1] Wang, Y.-M. 2013, ApJL, 775, L46
[2] Bao, S. D., Sakurai, T., & Suematsu, Y. 2002, ApJ, 573, 445
[3] Park, S.-H., Leka, K. D., & Kusano, K. 2020, ApJ, 904, 6
[4] Dikpati, M., & Gilman, P. A. 2001, ApJ, 559, 428
[5] Gilman, P. A., & Charbonneau, P. 1999, AGU Geophysical Monograph Series, 111, 75

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