Latitude-resolved Hinode spectro-polarimeter observations (2012–2021) established that the Sun's polar-field reversals of Cycle 24 were hemispherically asymmetric not only in timing (north-polar cap completed March 2013, south August 2014) but also in post-reversal evolution: the averaged north-polar radial flux density stayed at a weak level of about 0.5 Mx cm^-2 until the end of 2015 and peaked only at the 2019–2020 minimum, while the south-polar maximum arrived much earlier, in 2017. The proposed explanations — anomalous-tilt (non-Joy) and anti-Hale active regions with remnant flux surges for the north, and the prominent activity-complex poleward surge associated with AR 12192 for the south — remain unquantified. The open problem is to causally identify and quantify the flux-transport mechanisms that produced this asymmetric evolution, through surface-flux-transport (or dynamo) modeling with assimilated observed active regions, evaluated against the latitude-resolved polar observations, including counterfactual experiments and uncertainty estimates.

Background

The Sun's polar magnetic fields (fields above roughly 70° heliographic latitude in each polar cap) dominate the large-scale dipole and seed the next activity cycle, so their strength and reversal timing are key inputs to dynamo models and solar-cycle prediction. Each polar cap is predominantly unipolar during most of the 11-year cycle and reverses polarity near solar maximum, driven by remnant magnetic flux: when active regions (ARs, localized bundles of strong magnetic field emerging in sunspot belts) decay, their following-polarity flux (the part on the side toward the nearer pole) is transported poleward by meridional circulation, differential rotation, and supergranular diffusion, canceling the old-cycle polar field. This transport is usually described by a surface flux transport (SFT) model, which advects and diffuses the observed radial photospheric field. Active regions normally obey Hale's polarity law (the leading/following polarity arrangement is consistent within each hemisphere and cycle) and Joy's law (the leading side tilts toward the equator), both of which make poleward transport build the new-cycle polar field. Violations — anti-Hale (wrong polarity arrangement) and non-Joy (wrong-sign tilt) regions — transport flux of the 'wrong' sign poleward and can weaken or temporarily reverse the polar field; episodic bursts of this transport are seen as poleward surges in magnetic butterfly diagrams (time–latitude maps of the surface field). Polar flux density is measured in Mx cm^-2 (1 Mx = 10^-8 Wb), numerically equal to gauss for the radial component. Because Earth-bound telescopes observe from near the ecliptic plane, the poles are seen at grazing incidence, so measurements suffer limb projection, reduced signal-to-noise, and latitude-dependent instrumental systematics (characterized for Hinode polar data by Petrie 2022). Against this backdrop, Yang, Jiang et al. (2024) analyzed vector magnetograms from the Hinode satellite's Spectro-Polarimeter (SP, which measures the full polarization state of photospheric spectral lines) in 5° latitude bands over 2012–2021 and found: the north-polar reversal completed in March 2013 and the south's in August 2014; reversal proceeded successively from 70° toward the pole in each cap; the averaged north-polar radial flux density stayed weak (~0.5 Mx cm^-2) until the end of 2015, peaking (3.7 Mx cm^-2) only at the end-2019 minimum, whereas the south-polar maximum (−4.0 Mx cm^-2) came earlier, in 2017. Earlier work established the relevant mechanisms but not their quantitative roles in these two features: Sun et al. (2015) documented the Cycle 24 reversals and surge-driven reversal episodes with the Solar Dynamics Observatory's Helioseismic and Magnetic Imager (SDO/HMI, a full-disk filtergraph magnetograph); Janardhan et al. (2018) highlighted the unusually asymmetric reversal; Mordvinov & Kitchatinov (2019) showed from time–latitude (magnetic butterfly) analyses that decay of non-Joy and anti-Hale ARs produces remnant surges that disturb flux transport and contributed to polar-field weakening (qualitatively); Wang et al. (2020), assimilating observed ARs into an SFT model, reproduced the prominent southern poleward surge and showed that without the roughly year-long activity-complex emergence (Carrington rotations — numbered, approximately 27-day solar-rotation intervals — 2145–2159, 2013 December–2015 January, which included the super active region AR 12192) the southern polar field would have remained low or even reverted to the Cycle 23 polarity; Wang, Jiang & Luo (2025) extended such simulations from 2010 to 2024, finding that southern following-polarity surges were confined to 2011–2016 (about 46% of the hemisphere's unsigned AR flux emerged during CR 2141–2160) and that leading-polarity transport dominated after 2016; and Yang et al. (2024, ApJ 970, 183) used Hinode-constrained SFT simulations to infer a counter-cell meridional flow (a shallow reverse circulation near the poles) in the polar caps. None of these quantitatively disentangles the drivers of the two observed hemispheric anomalies that motivate this problem.

Problem Statement

Quantitatively determine the causal contributions of the candidate flux-transport mechanisms — anomalous-tilt (non-Joy) and anti-Hale active-region emergence, the timing and activity-longitude structure of activity-complex emergence, and the resulting poleward remnant-flux surges, in combination with the large-scale transport flows (meridional circulation, including any polar counter-cell, differential rotation, and turbulent diffusion) — to the two observed hemispheric anomalies of the Cycle 24 polar fields established by Yang et al. (2024) from Hinode/SP latitude-band observations: (i) the averaged north-polar radial flux density remaining weak (~0.5 Mx cm−20.5\ \mathrm{Mx\,cm^{-2}}) from the March 2013 reversal completion until the end of 2015, with the maximum delayed to the 2019–2020 solar minimum; and (ii) the south-polar flux-density maximum arriving early, in 2017, rather than at the minimum. A complete answer must (a) reproduce the observed latitude–time evolution of the polar radial flux density in both hemispheres (2012–2021) within stated observational uncertainties, including the latitude-dependent systematics of ecliptic-view polar measurements; (b) quantify, with uncertainty estimates, the contribution of each mechanism to the two timing features — e.g. via surface-flux-transport or dynamo simulations with assimilated observed active regions and counterfactual experiments that selectively remove or alter the anomalous ARs, the 2013 December–2015 January southern activity complexes, or the transport flows; and (c) establish whether these identified mechanisms suffice to explain both features or whether additional processes are required.

References

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