2. Testing Hemispheric Rule of Helicity with HMI Data

Contributed by Yang Liu. Posted on January 26, 2014

Yang Liu, J. T. Hoeksema, and X. Sun
W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305, USA

Magnetic twist in solar active regions (ARs) has been found to have a hemispheric preference in sign (hemispheric rule): negative in the northern hemisphere and positive in the southern. The preference reported in previous studies ranges greatly, from 58% to 82% (ref. 1-2). Full disk field-of-view, continuous observation coverage, high temporal and spatial resolutions, and consistent data quality, these specifications of vector magnetic field data taken by the HMI for more than 3 years allow for testing the hemispheric rule.

Figure 1 | Distribution of sign of twist in bipolar ARs as a function of latitude and time for Solar Cycle 24 from May 2010 to November 2013. The titles of the plots indicate the sample size (“AR Number”) and the degree of hemispheric preference (“Yes”) that refers to percentage of the ARs in the sample obeying the hemisphere rule. Top panel is for all ARs; middle is for ARs having the same signs of twist and writhe; bottom is for ARs having the opposite signs of twist and writhe.

Active regions are selected based upon availability of processed HMI vector magnetic field data. We analyzed each NOAA AR when at least 24 hours of vector data are available near central meridian passage. In total, 151 ARs are analyzed. We choose a Bz2 weighted force-free alpha3 as a proxy of the twist in the active region. Not surprisingly, 75%±7% of 151 ARs follow the hemispheric rule, well within the range of the preferences for ARs reported previously in similar studies. If the sample is divided into two groups – ARs having magnetic twist and writhe of the same sign and having opposite signs – the strength of the hemispheric preference differs substantially: 64%±11% for the former group and 87%±8% for the latter. This difference becomes even more significant in a sub-sample of 82 ARs having a simple bipole magnetic configuration (Fig. 1): 56%±16% for ARs having the same signs of twist and writhe, and 93% (a 95% confidence interval is 80%-98%) for ARs having the opposite signs. Magnetic writhe in an AR is calculated from its tilt angle.

Scenarios have been proposed to predict the sign-relationship between twist and writhe in ARs. If a flux tube originally possesses no twist, deformation of the tube during its rise through convection zone generates writhe in the tube, and at the same time generates the same amount of twist of the opposite sign to ensure conservation of helicity in the tube. In this scenario, the signs of the acquired twist and writhe are opposite, and the sign of the twist obeys the hemispheric rule4. On the other hand, if a flux tube initially has twist great enough to lead to kink instability, part of the twist is converted to writhe. In this case, the signs of the twist and writhe are the same5. It is not clear how this strong twist is generated in the first place. The dynamo process is one possibility. If it is the case, does above result suggest that the twist generated by the dynamo process has no (or weak) hemispheric preference?

The full paper is accepted by ApJ Letters.


[1] Pevtsov, A. A., Canfield, R. C., Metcalf, T. R., 1995, ApJL, 440, L109
[2] Bao, S., Zhang, H., 1998, ApJL, 496, L43
[3] Hagino, M., Sakurai, T., 2004, PASJ, 56, 831
[4] Longcope, D. W., Fisher, G. H., Pevtsov, A. A., 1998, ApJ, 507, 417
[5] Linton, M. G., Fisher, G. H., Dahlburg, R. B., Fan, Y., 1999, ApJ, 522, 1190

2 comments on “Testing Hemispheric Rule of Helicity with HMI Data

    1. Yang Liu

      good idea! would be easy to test. just wondering if there are enough active regions near the non-Hale boundary that allow for testing statistically .


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