Recovering Solar Toroidal Field Dynamics From Sunspot Location Patterns

We analyze both Kitt Peak magnetogram data and MDI continuum intensity sunspot data to search for the following solar toroidal band properties: width in latitude and the existence of a tipping instability (longitudinal m=1 mode) for any time during the solar cycle. To determine the extent which we can recover the toroidal field dynamics, we forward model artificially generated sunspot distributions from subsurface toroidal fields we assigned certain properties. We analyzed two sunspot distribution parameters using MDI and model data: the average latitudinal separation of sunspot pairs as a function of longitudinal separation, and the number of sunspot pairs creating a given angle with respect to the E-W direction. A toroidal band of 10 degrees width with a constant tipping of 5 degrees best fits MDI data early in the solar cycle. A toroidal band of 20 degrees width with a tipping amplitude decreasing in time from 5 to 0 degrees best fits MDI data late in the solar cycle. Model data generated by untipped toroidal bands cannot fit MDI high latitude data and can fit only one parameter at low latitudes. Tipped toroidal bands satisfy chi squared criteria at both high and low latitudes. We conclude this is evidence to reject the null hypothesis - that toroidal bands in the solar tachocline do not experience a tipping instability - in favor of the hypothesis that the toroidal band experiences an m=1 tipping instability. Our finding that the band widens from ~10 degrees early in the solar cycle to ~20 degrees late in the solar cycle may be explained in theory by magnetic drag spreading the toroidal band due to altered flow along the tipped field lines.Comment: This paper is accepted to Astrophysical Journal, September 2005 issu

The Dependence of Joy's Law as a Function of Flux Emergence Phase

Data from the Michelson Doppler Imager (MDI) and Helioseismic and Magnetic Imager (HMI) are analyzed from 1996 to 2023 to investigate tilt angles ($\gamma$) of bipolar magnetic regions and Joy's Law for Cycles 23, 24, and a portion of 25. The HMI radial magnetic field ($B_{r}$) and MDI magnetogram ($B_{los}$) data are used to calculate ($\gamma$) using the flux-weighted centroids of the positive and negative polarities. Each AR is only sampled once. The analysis includes only Beta ($\beta$)-class active regions since computing $\gamma$ of complex active regions is less meaningful. During the emergence of the ARs, we find that the average tilt angle ($\bar{\gamma}$) increases from 3.30$^{\circ}\pm$0.75 when 20\% of the flux has emerged to 6.79$^{\circ}\pm$0.66 when the ARs are at their maximum flux. Cycle 24 had a larger average tilt $\bar{\gamma}_{24}$=6.67$\pm$0.66 than Cycle 23, $\bar{\gamma}_{23}$=5.11$\pm$0.61. There are persistent differences in $\bar{\gamma}$ in the hemispheres with the southern hemisphere having higher ${\bar{\gamma}}$ in Cycles 23 and 24 but the errors are such that these differences are not statistically significant.Comment: 11 pages, 8 figures, 3 table

How much more can sunspots tell us about the solar dynamo?

Sunspot observations inspired solar dynamo theory and continue to do so. Simply counting them established the sunspot cycle and its period. Latitudinal distributions introduced the tough constraint that the source of sunspots moves equator-ward as the cycle progresses. Observations of Hale's polarity law mandated hemispheric asymmetry. How much more can sunspots tell us about the solar dynamo? We draw attention to a few outstanding questions raised by inherent sunspot properties. Namely, how to explain sunspot rotation rates, the incoherence of follower spots, the longitudinal spacing of sunspot groups, and brightness trends within a given sunspot cycle. After reviewing the first several topics, we then present new results on the brightness of sunspots in Cycle 24 as observed with the Helioseismic Magnetic Imager (HMI). We compare these results to the sunspot brightness observed in Cycle 23 with the Michelson Doppler Imager (MDI). Next, we compare the minimum intensities of five sunspots simultaneously observed by the Hinode Solar Optical Telescope Spectropolarimeter (SOT-SP) and HMI to verify that the minimum brightness of sunspot umbrae correlates well to the maximum field strength. We then examine 90 and 52 sunspots in the north and south hemisphere, respectively, from 2010 - 2012. Finally, we conclude that the average maximum field strengths of umbra 40 Carrington Rotations into Cycle 24 are 2690 Gauss, virtually indistinguishable from the 2660 Gauss value observed at a similar time in Cycle 23 with MDI

Magnetic Helicity, Tilt, and Twist

The final publication is available at Springer via http://dx.doi.org/10.1007/s11214-014-0082-2Since its introduction to astro- and solar physics, the concept of helicity has proven to be useful in providing critical insights into physics of various processes from astrophysical dynamos, to magnetic reconnection and eruptive phenomena. Signature of helicity was also detected in many solar features, including orientation of solar active regions, or Joy’s law. Here we provide a summary of both solar phenomena and consider mutual relationship and its importance for the evolution of solar magnetic fields.European Union (European Social Fund—ESF)Greek national fundsScience and Technology Facilities Council (STFC)Hungarian Research grantsNAS

Deciphering the Pre–solar-storm Features of the 2017 September Storm From Global and Local Dynamics

We investigate whether global toroid patterns and the local magnetic field topology of solar active region (AR) 12673 together can hindcast the occurrence of the biggest X-flares of solar cycle (SC)-24. Magnetic toroid patterns (narrow latitude belts warped in longitude, in which ARs are tightly bound) derived from the surface distributions of ARs, prior and during AR 12673 emergence, reveal that the portions of the south toroid containing AR 12673 was not tipped away from its north-toroid counterpart at that longitude, unlike the 2003 Halloween storms scenario. During the minimum phase there were too few emergences to determine multimode longitudinal toroid patterns. A new emergence within AR 12673 produced a complex nonpotential structure, which led to the rapid buildup of helicity and winding that triggered the biggest X-flare of SC-24, suggesting that this minimum-phase storm can be anticipated several hours before its occurrence. However, global patterns and local dynamics for a peak-phase storm, such as that from AR 11263, behaved like the 2003 Halloween storms, producing the third biggest X-flare of SC-24. AR 11263 was present at the longitude where the north and south toroids tipped away from each other. While global toroid patterns indicate that prestorm features can be forecast with a lead time of a few months, their application to observational data can be complicated by complex interactions with turbulent flows. Complex nonpotential field structure development hours before the storm are necessary for short-term prediction. We infer that minimum-phase storms cannot be forecast accurately more than a few hours ahead, while flare-prone ARs in the peak phase may be anticipated much earlier, possibly months ahead from global toroid patterns

The Decay Process of an {\alpha}-configuration Sunspot

The decay of sunspot plays a key role in magnetic flux transportation in solar active regions (ARs). To better understand the physical mechanism of the entire decay process of a sunspot, an {\alpha}-configuration sunspot in AR NOAA 12411 was studied. Based on the continuum intensity images and vector magnetic field data with stray light correction from Solar Dynamics Observatory/Helioseismic and Magnetic Imager, the area, vector magnetic field and magnetic flux in the umbra and penumbra are calculated with time, respectively. Our main results are as follows: (1) The decay curves of the sunspot area in its umbra, penumbra, and whole sunspot take the appearance of Gaussian profiles. The area decay rates of the umbra, penumbra and whole sunspot are -1.56 MSH/day, -12.61 MSH/day and -14.04 MSH/day, respectively; (2) With the decay of the sunspot, the total magnetic field strength and the vertical component of the penumbra increase, and the magnetic field of the penumbra becomes more vertical. Meanwhile, the total magnetic field strength and vertical magnetic field strength for the umbra decrease, and the inclination angle changes slightly with an average value of about 20{\deg}; (3) The magnetic flux decay curves of the sunspot in its umbra, penumbra, and whole sunspot exhibit quadratic patterns, their magnetic flux decay rates of the umbra, penumbra and whole sunspot are -9.84 * 10^19 Mx/day, -1.59 * 10^20 Mx/day and -2.60 * 10^20 Mx/day , respectively. The observation suggests that the penumbra may be transformed into the umbra, resulting in the increase of the average vertical magnetic field strength and the reduction of the inclination angle in the penumbra during the decay of the sunspot