# 114. What We Learned from a Long-term Study of Sunspot Physical Parameters

Contributed by Jing Li. Posted on November 20, 2018

Jing Li
Department of Earth, Planetary and Space Sciences, University of California at Los Angeles, Los Angeles, CA 90095-1567, USA

Well-measured sunspot physical parameters have great potential for revealing and answering questions related to solar cycles and magnetic flux emergence. Measurable parameters include magnetic tilt angles, magnetic flux, polarity pole separations, and magnetic areas. We have built on previous work[1] to measure such parameters using two decades of MDI and HMI magnetograms for 4385 sunspot groups, covering Cycles 23 and 24. We are particularly interested in the differences and similarities between Hale and anti-Hale sunspots, and in differences between separate hemispheres and solar cycles.

Figure 1| Example sunspot (NOAA 10693) vs. time. Each sunspot is represented by a set of parameters calculated around its disk central-meridian crossing, with ~60 time-resolved determinations per sunspot within shaded area. This is Figure 2 in Ref. [2].

The anti-Hale sunspots constitute 8.1±0.4% of all sunspots, and this fraction is the same in both hemispheres and cycles. They follow a Butterfly diagram similar to the Hale-sunspots (Fig 2), showing that the two types emerge in parallel. They also show similar magnetic flux distributions and latitudinal distributions, but the cumulative magnetic fluxes of the two populations differ greatly. Hale spots carry ~16 times more flux in total than the anti-Hale spots. It is not clear why 1 out of 12 sunspots should persistently violate the hemispheric polarity rule. Evidence shows that many of these sunspot groups are not evolved from the Hale population, but have irregular polarity arrangements in the beginning.

Excluding anti-Hale spots (which do not follow the law), we derive Joy’s law in three equivalent forms: $\sin\gamma=0.38\sin\phi$, $\gamma=0.39\phi$, and $\gamma=23.8\sin\phi$. They are all consistent with Coriolis force as the major cause of the law[3]. One difference between Hale and anti-Hale sunspots is that the former tilt toward the equator (average tilt angle $\bar\gamma=5.49^\circ\pm0.09^\circ$), while the latter tilt away from it ($\bar\gamma=-5.84^\circ\pm0.31^\circ$). The average pole separations are also significantly different. For Hale sunspots the mean pole separation is 4.18±0.07°, while for anti-Hale spots it is 2.74±0.15°, implying that anti-Hale sunspots have stronger magnetic tension than the Hale sunspots. Perhaps this is why anti-Hale sunspots do not follow Joy’s law; Coriolis force may not be sufficient to overcome magnetic tension in the anti-Hale systems and drive the magnetic loops into Joy’s law configurations.

Figure 2| Sunspot Butterfly diagram. Hale sunspots (blue: Cycle 23, orange: Cycle24), anti-Hale sunspots (black dots circled with green). This is Figure 6 in Ref [2].

We find that sunspot emergence is hemispheric asymmetric, with the southern hemisphere dominant in Cycle 23, and the northern hemisphere dominant in Cycle 24. However, averaged over the magnetic cycle (23 and 24, combined) the sunspot eruptions are numerically hemisphere-symmetric. Ratio (Nn(23)Ns(24))/(Ns(23)Nn(24)) ~ 1, is close to unity.

Statistically, sunspot magnetic fluxes grow with increasing pole separation. We find $\Phi(s)=7.59\times10^{20}s^{1.49}$ where $\Phi$ is the sunspot unsigned magnetic flux, and $s$ is the pole separation in degree. This result is consistent with $\Phi(s)=4.0\times 10^{20} s^{1.3}$ obtained by Wang & Sheeley within their uncertainties[4]. Also, tilt angles decrease with increasing pole separation (Fig. 3). Given the connections between the magnetic flux, pole separation and tilt angle, we find that magnetic flux decreases with increasing tilt angle, $\Phi(\gamma)=1.1\times10^{23}\times(0.87)^{|\gamma|}$. Our observations confirm the general impression that larger magnetic flux systems correspond to larger pole separation and smaller tilt angle[5].

Figure 3| Tilt angle as a function of pole separation. All sunspots are shown as “.’’ symbols. Orange and blue filled circles represent the average and median data points over a ~0.15 logarithmic bin pole separation. The solid line is the linear fit between absolute tilt angle and logarithmic pole separation. The dashed curve is a parabolic fit. This is Figure 14 in Ref. [2].

The data show rapid evolution of sunspot parameters during the disk crossing.  Future study will use the temporal variation of the sunspot parameters to show how and why the tilt, for example, varies so quickly upon sunspot emergence; how many sunspot groups stay as Hale and anti-Hale during their lifetimes, and how many of them interchange between two populations. This may shed light on how anti-Hale sunspots come to be.

### References

[1] Li, J., and Ulrich, R.K., 2012, ApJ, 130, 366
[2] Li, J., 2018, ApJ, 867, 89
[3] Wang, Y.-M., & Sheeley, N.R., Jr., 1991, ApJ, 375, 761
[4] Wang, Y.-M., and Sheeley, N.R., Jr., 1989, SoPh, 124, 81
[5] D’Silva, S., & Choudhuri, A.R., 1993, A&A, 272,621