🔭 astrophysics

Variation of the sunspot area during the rising and declining phases of the solar cycle supports the toroidal flux loss due to flux emergence

By analyzing sunspot group areas and Bipolar Magnetic Region flux across multiple solar cycles, the study demonstrates that larger magnetic activity occurs during the rising phase than the declining phase, supporting the theory that nonlinear flux loss through emergence causes solar cycles to rise uniquely but decay in a similar manner.

Original authors: Bidya Binay Karak, Soumya Mishra, Anu Sreedevi

Published 2026-02-10

📖 3 min read☕ Coffee break read

CC BY 4.0

Original authors: Bidya Binay Karak, Soumya Mishra, Anu Sreedevi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Sun’s "Rollercoaster" Rhythm: Why Solar Cycles Rise Fast but Fall Slowly

Imagine the Sun is like a giant, cosmic drummer. Every 11 years or so, it goes through a "cycle": it starts quiet, gets incredibly loud and energetic (with sunspots and solar flares), and then slowly fades back into silence.

Scientists have long noticed something strange about this rhythm: The Sun’s "crescendo" (the rise) is unpredictable and varies wildly, but its "fade-out" (the decline) always follows almost the exact same pattern.

A new research paper explains why this happens using a concept called "The Leaky Bucket Theory."

1. The Setup: The Magnetic Bucket

Deep inside the Sun, there is a massive reservoir of magnetic energy (called the toroidal field). Think of this energy as water in a giant bucket.

When the water level in the bucket gets high enough, it starts to spill over the edges. In the Sun, when that magnetic "water" reaches a certain height, it bursts through the surface, creating sunspots—those dark, magnetic patches we see on the Sun’s face.

2. The Rising Phase: The High-Pressure Surge

When a new solar cycle begins, the "bucket" is being refilled very quickly.

In a Strong Cycle: The water is being poured in at a massive rate. The pressure is huge! Because there is so much "water," the spills (sunspots) are enormous and violent. This is why strong cycles produce massive sunspots and intense "space weather" (solar storms that can mess with our satellites and power grids).
In a Weak Cycle: The water is being poured in slowly. The pressure is low, so the spills are smaller and more manageable.

The takeaway: During the rising phase, the size of the sunspots tells you exactly how strong the cycle is going to be. It’s like looking at a rushing river to predict a flood.

3. The Declining Phase: The "Threshold" Effect

This is where the magic happens. The researchers found that no matter how much water was in the bucket originally, the decline phase always looks the same. Why?

Because of a "safety valve" effect. As the sunspots erupt, they "leak" the magnetic energy out of the Sun. Eventually, the energy level in the bucket drops down to a specific threshold level—just enough to keep a few small leaks going, but not enough to cause a flood.

Once the energy hits this "sweet spot" (the threshold), the Sun enters a state of controlled leaking.

Even if you started with a massive, overflowing bucket (a strong cycle), the eruptions eventually drain it down to that same baseline level.
Even if you started with a small bucket (a weak cycle), it also drains down to that same baseline.

By the time the cycle is ending, the "pressure" is the same for every cycle. This is why the sunspots during the decline phase are consistently smaller and follow a predictable, uniform pattern, regardless of whether the cycle was a "superstar" or a "dud."

Summary: The Big Picture

The researchers used 13 cycles of data (spanning over 150 years!) to prove that:

The Rise is Wild: The bigger the sunspots during the rise, the stronger the cycle. This is the "danger zone" for space weather.
The Fall is Uniform: Once the Sun reaches a certain level of magnetic exhaustion, it "decays" in a standardized way.

In short: The Sun’s "growth spurt" depends on how much energy it has, but its "old age" is governed by a universal limit.

This technical summary details the research paper titled "Variation of the sunspot area during the rising and declining phases of the solar cycle supports the toroidal flux loss due to flux emergence," authored by Karak et al. (2026).

1. Problem Statement

The solar cycle exhibits a fundamental asymmetry known as the Waldmeier Effect: while the amplitude (strength) of solar cycles varies irregularly, strong cycles rise more rapidly than weak ones, yet all cycles tend to decay at a similar rate and follow a common trajectory toward the equator.

The authors seek to provide observational evidence for a specific theoretical explanation of this phenomenon: the nonlinear loss of toroidal magnetic flux due to magnetic buoyancy. According to this theory (Biswas et al. 2022), the solar cycle's behavior is governed by the competition between the generation of toroidal flux in the convection zone (CZ) and its loss through flux emergence (sunspots). The central question is whether sunspot properties (area and magnetic flux) reflect this theoretical mechanism by showing cycle-dependent behavior during the rising phase and cycle-independent behavior during the declining phase.

2. Methodology

The study employs a multi-proxy approach using long-term and high-resolution datasets:

Sunspot Area Analysis: The authors utilize a cross-calibrated, homogeneous catalog of individual sunspot group areas spanning 13 solar cycles (1874–2025), compiled by Mandal et al. (2020).
Magnetic Flux Analysis: To supplement area data, they use space-borne magnetograms from MDI/SOHO (Cycle 23) and HMI/SDO (Cycle 24) via the AutoTAB (Automatic Tracking Algorithm for Bipolar Magnetic Regions) catalog. This allows for the tracking of Bipolar Magnetic Regions (BMRs) and their flux evolution.
Phase Segmentation: Solar cycles are identified using the International Sunspot Number (ISN) Version 2.0. Each cycle is divided into a rising phase (from minimum to the year of maximum activity) and a declining phase (from the year after maximum to the next minimum). To handle double-peaked cycles, the latter peak is used to define the transition.
Statistical Metrics: The authors calculate the mean and median sunspot areas and BMR fluxes for each phase and correlate these values with "cycle strength" (measured by total sunspot area).

3. Key Results

The study yields several critical observational findings:

Distinct Area Distributions: The distribution of daily total sunspot areas differs significantly between phases. The rising phase follows a Weibull distribution with a peak at higher area values, whereas the declining phase is better described by an exponential model with a peak at lower values and an extended tail toward smaller areas.
Phase-Dependent Asymmetry: In most cycles, the mean and median sunspot areas are statistically larger during the rising phase than during the declining phase.
Correlation with Cycle Strength:
- Rising Phase: There is a strong positive correlation between sunspot area (mean/median) and cycle strength. Stronger cycles produce statistically larger sunspots.
- Declining Phase: The sunspot area is largely uncorrelated with cycle strength.
Convergence in Late-Stage Decay: When analyzing only the last three years of the declining phase, the mean and median sunspot areas show almost no correlation with cycle strength and exhibit very little spread across different cycles.
Magnetic Flux Consistency: The BMR flux measurements from Cycles 23 and 24 mirror the sunspot area trends, showing higher mean and median flux values during the rising phase compared to the declining phase.

4. Significance and Conclusions

The findings provide robust observational support for the nonlinear flux loss model. The results confirm that:

The Theory is Validated: The observation that sunspot properties become cycle-independent during the decline supports the idea that the toroidal field in the CZ is being maintained near a specific threshold ( $B_c$ ) by the balance of generation and eruption, regardless of the initial cycle strength.
Space Weather Implications: Because the rising phase produces larger sunspots and higher magnetic flux, it is inherently more prone to driving intense and violent space weather events.
Refutation of Alternatives: The data suggests that the "diffusive cancellation at the equator" model (which predicts cycle-dependent decay) is less likely than the flux-emergence-driven decay model, as the latter better explains why strong cycles do not maintain large spots during their decline.