The recent anomalously weak polar field does not imply a weak field at solar cycle 25 minimum

Technical Summary: The Recent Anomalously Weak Polar Field Does Not Imply a Weak Field at Solar Cycle 25 Minimum

Problem Statement
Solar Cycle 25 has progressed past its sunspot number peak and is statistically stronger than Cycle 24. However, observational data from the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO) reveals an anomalously weak polar field, particularly in the northern hemisphere, which has been decreasing since mid-2025. This decline is driven by a prominent poleward surge of magnetic flux. Since the polar field strength at solar cycle minimum serves as a precursor for the amplitude of the subsequent cycle (Cycle 26), there is significant concern that the current weakening indicates an exceptionally weak Cycle 26. The central problem addressed is whether this short-term temporal decrease in the polar field necessitates a weak polar field at the Cycle 25 minimum, or if the long-term evolution will recover to a stronger state.

Methodology
The authors employ a Surface Flux Transport (SFT) model coupled with a statistical prediction of Active Region (AR) emergence to simulate the evolution of the solar large-scale magnetic field through the remainder of Cycle 25.

1. AR Emergence Prediction: The study adopts and refines the statistical prediction method from Jiang et al. (2018) and Jiang (2020).

   • Sunspot Numbers (SN): The monthly SN profile is modeled using the Hathaway et al. (1994) function for the ascending phase, with corrections for the declining phase based on Jiang et al. (2018). Random realizations are generated by adding time-dependent noise derived from the standard deviation of Cycles 12–24.
   • AR Properties: Bipolar ARs are generated with random daily emergence times satisfying the monthly SN count. Their latitudes follow a Gaussian distribution dependent on the cycle phase (generating a butterfly diagram), and their areas follow specific distributions.
   • Tilt Angle and Flux: The tilt angle follows a Joy's law linear form ($\alpha = T_n|\lambda| + \sigma(A) \cdot X$). The study incorporates updated observational results for tilt scatter (from Qin et al., 2025) and tilt quenching (from Jiao et al., 2021), applying a correction factor of 0.7 to account for inflow effects. Magnetic flux is calculated based on AR area using a power-law relation from Qin et al. (2025).
   • Ensemble Simulations: 100 random realizations of AR emergence are simulated to determine the expectation and uncertainty range (1$\sigma$) of the polar field evolution.

2. Surface Flux Transport Model:

   • The model solves the radial component of the induction equation on the photosphere, incorporating differential rotation (Snodgrass 1983), meridional flow (peak velocity 13 m s$^{-1}$), and turbulent diffusion ($\eta_T = 450$ km$^2$ s$^{-1}$).
   • The initial magnetic field is set using the HMI synoptic magnetogram from Carrington Rotation (CR) 2309 (April 2026).
   • Predicted ARs are inserted as bipolar Gaussian flux patches with opposite polarities, separated by an angular distance dependent on their area.

3. Source Analysis: To understand the specific mechanism behind the 2026 polar field decrease, the authors isolate ARs emerging in the northern hemisphere during CRs 2275–2285 (Sept 2023–June 2024). They perform a dedicated SFT simulation using only these ARs (without an initial field) to trace their specific contribution to the poleward surge.

Key Results

• Polar Field Prediction at Cycle 25 Minimum: Despite the current weakening, the ensemble simulations predict the polar field at the Cycle 25 minimum (end of 2031) to be $-5.62 \pm 1.61$ G in the north and $5.51 \pm 1.48$ G in the south.
• Comparison to Cycle 24: These predicted values are approximately 1$\sigma$ stronger than the polar field strength at the end of Cycle 24 (2.5 G). Consequently, the axial dipole moment is predicted to be $-2.70 \pm 0.76$ G, also stronger than the Cycle 24 minimum.
• Mechanism of Temporary Weakening: The analysis of the poleward surge causing the 2026 decrease reveals it originates from a group of high-latitude ARs (around 20$^\circ$) emerging during CRs 2275–2285. While these high-latitude ARs generate prominent poleward surges of the leading polarity that temporarily reduce the polar field strength, they do not result in a net negative contribution to the final polar field. The collective contribution of all ARs, including lower-latitude ones, results in a net increase to the polar field at the cycle minimum.
• Cycle 26 Estimation: Using the linear precursor relationship $S_{n+1} = 58.7 D_n$ (Jiang et al. 2018), the amplitude of Cycle 26 is estimated at $158 \pm 45$. This suggests Cycle 26 is likely to be moderate and comparable to Cycle 25 (which peaked at 160.9), rather than exceptionally weak.

Significance and Claims
The paper claims to resolve the apparent contradiction between the current weak polar field observations and the expected strength of the next solar cycle. The primary significance lies in demonstrating that short-term evolution of the polar field should not be simply correlated with the long-term properties of the solar large-scale field.

Specifically, the authors clarify that:

1. The poleward surge causing the current decrease is a transient effect driven by high-latitude ARs that, despite their temporary negative impact on the field strength, contribute a net positive increase to the polar field at the cycle minimum.
2. The current weak polar field is unlikely to lead to a weak Cycle 25 minimum or an exceptionally weak Cycle 26.
3. The SFT-precursor method, when accounting for the statistical properties of AR emergence and the specific nature of the poleward surge, provides a robust prediction that Cycle 26 will likely be a moderate cycle, continuing the trend of recovery from the weak Cycle 24.

The authors note that while the prediction for Cycle 26 is preliminary and subject to uncertainties in the precursor method (such as observational limits at high latitudes and the stochastic nature of ARs), the immediate conclusion regarding the Cycle 25 minimum is that the current weakening is not a precursor to a grand minimum or a significantly weak next cycle.