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Statistical and Kinematic Analysis of the Coupling between Coronal Mass Ejections and Solar Flares during the Solar Cycles 23–25

This study presents an improved statistical and kinematic framework that, by applying geometric corrections and phase-resolved classification to over 27,000 events across Solar Cycles 23–25, reveals a strong temporal correlation and distinct energetic characteristics between coupled coronal mass ejections and solar flares, supporting a unified model of magnetic reconnection-driven eruptive processes.

Original authors: A. M. Elnagar, Ramy Mawad, M. Youssef, S. A. Abdelmoneim, Hala Eldosoky

Published 2026-06-29

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CC BY 4.0

Original authors: A. M. Elnagar, Ramy Mawad, M. Youssef, S. A. Abdelmoneim, Hala Eldosoky

Original paper licensed under CC BY 4.0 (https://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 Big Picture: A Solar Dance

Imagine the Sun as a giant, chaotic dance floor. Two main stars of the show are Solar Flares (sudden, bright flashes of light, like a camera flash going off) and Coronal Mass Ejections (CMEs) (huge clouds of magnetic gas and plasma being thrown into space, like a cannonball).

For a long time, scientists have wondered: Do these two events happen together because they are part of the same explosion, or are they just random neighbors on the dance floor?

This paper, covering three solar cycles (roughly 30 years of solar activity), says: They are definitely partners. When a flare happens, a CME is usually right there with it, but they have a specific rhythm to their dance that previous studies missed.

The Problem: Looking at a 3D Object in 2D

The biggest hurdle the researchers faced was a "camera angle" problem.

The Analogy: Imagine watching a baseball game from the stands. If a pitcher throws a ball straight at you, it looks like a tiny dot getting bigger. If he throws it to the side, you see the whole arc.
The Reality: Our telescopes on Earth see the Sun from one angle. If a CME is thrown directly toward us or away from us, it looks slow and small. If it's thrown sideways, it looks fast and wide.
The Fix: The researchers built a new "mathematical 3D glasses" system. They took the 2D data and corrected it for the angle, revealing the true speed and size of the CMEs.
The Result: Once they put on these glasses, they realized the CMEs were actually 64.5% faster on average than we thought before. We were severely underestimating how fast these solar storms were moving.

The New Method: Better Matchmaking

In the past, scientists tried to pair Flares and CMEs just by checking if they happened at the same time. This was like trying to match couples at a party just by seeing who arrived at the same minute. It led to mistakes because many things happen at once during a busy solar party.

The authors created a smarter matchmaking algorithm:

Time Check: Did it happen within 3 hours of the flare?
Location Check: Did the CME come from the exact same spot on the Sun as the flare? (They converted the flare's location into a coordinate system that matches the CME's path).
The Result: Out of over 27,000 CMEs and 15,000 flares, they found 2,175 perfect pairs. This is a much cleaner, more reliable list than before.

The Discovery: The "Declining Phase" Surprise

The most interesting finding is when the CMEs hit their peak performance.

The Old Idea: Scientists thought the CMEs were fastest and most energetic right when the flare started (the "Impulsive Phase").
The New Reality: The researchers found that the CMEs actually get bigger, faster, and more massive during the Declining Phase (the time after the flare has peaked and is starting to fade).

The Analogy: Think of a firework.

The Impulsive Phase is the fuse burning and the initial bang.
The Declining Phase is when the shell actually shoots up into the sky and explodes into a massive, wide pattern.
The paper shows that the "shell" (the CME) keeps gathering speed and mass after the initial "bang" (the flare peak). The most violent, energetic eruptions happen while the flare is winding down, not just when it starts.

Two Different Types of Solar Storms

The study also separated the CMEs into two groups: those that had a partner flare, and those that didn't.

The Flare-Paired CMEs: These are the "Super Athletes." They are 38% faster, 149% heavier (more mass), and 530% more energetic than the ones without flares.
The Solo CMEs: These are the "Casual Walkers." They are slower, lighter, and less energetic.

This proves that when a flare and a CME happen together, it's a much more powerful event than when a CME happens on its own. They are physically linked by the same magnetic explosion.

The "Butterfly" Pattern

The researchers also checked if their new method messed up the big picture. They looked at where these events happened on the Sun over the years.

The Analogy: Solar activity has a famous "Butterfly Pattern." At the start of a solar cycle, storms happen at high latitudes (near the poles). As the cycle progresses, the storms migrate toward the equator, looking like butterfly wings.
The Result: Their new, stricter list of events still showed this perfect butterfly pattern. This proves their new method didn't accidentally pick only "easy" events; it captured the true nature of the Sun's behavior.

Summary of Key Takeaways

We were wrong about speed: Because of viewing angles, we thought CMEs were slower than they really are. Correcting for this makes them much faster.
Timing matters: The most energetic CMEs happen after the flare peaks, not during the initial explosion.
Partners are stronger: CMEs that happen with flares are vastly more powerful than those that happen alone.
Better matching: By using both time and 3D location, the researchers created a much more accurate list of which flares and CMEs are actually related.

In short, the Sun's eruptions are a complex, 3D dance where the "after-party" (the declining phase) is often more energetic than the "opening act."

Technical Summary: Statistical and Kinematic Analysis of the Coupling between Coronal Mass Ejections and Solar Flares during the Solar Cycles 23–25

Problem Statement
The physical relationship between Coronal Mass Ejections (CMEs) and solar flares remains a complex area of solar physics, characterized by uncertainties in event association and the limited treatment of flare evolution in previous statistical studies. While both phenomena are generally attributed to magnetic reconnection, their precise coupling is not one-to-one; many CMEs occur without flares and vice versa. A primary challenge in existing research is the reliable association of CMEs with specific flares. Previous studies often relied solely on temporal criteria, leading to ambiguities during highly active solar periods, or lacked a unified geometric reference system to compare flare locations (heliographic coordinates) with CME propagation directions (position angles). Furthermore, the impact of projection effects on CME kinematics and the evolution of CME properties across different stages of flare development (pre-flare, impulsive, declining, post-flare) required more rigorous, phase-resolved analysis.

Methodology
To address these limitations, the authors developed an improved statistical and kinematic framework analyzing data from Solar Cycles 23–25 (1996–2025). The study utilized the SOHO/LASCO CME Catalogue and the GOES X-ray flare catalogue, filtering for physically valid parameters. The core of the methodology involves a multi-step association algorithm:

Temporal Filtering: An initial broad search window ( $\pm 10$ hours) was applied around flare start times, followed by a refined window of $\pm 3$ hours based on the observed clustering of events near zero-time difference.
Spatial Association via Coordinate Transformation: To resolve the mismatch between flare heliographic coordinates and CME position angles, the authors transformed flare locations into a common heliocentric Cartesian coordinate system using solar ephemeris parameters ( $B_0$ and $L_0$ ). The flare position angle was then calculated and compared to the CME central position angle. A spatial association was established if the flare source lay within the CME's angular width ( $\Delta\psi \leq W/2$ ).
Projection Correction: Recognizing that coronagraph speeds are plane-of-sky measurements, the study applied a geometric correction using a cone-model approximation. This corrected the CME velocities based on the propagation angle relative to the observer's line of sight, derived from the associated flare's coordinates.
Phase-Resolved Classification: Associated events were categorized based on the flare's evolutionary stage at the time of CME launch: pre-flare, impulsive, declining, and post-flare.
Statistical Analysis: The study employed Pearson correlation coefficients, linear regression (log-log space for power-law relations), and Student's t-tests to evaluate relationships between CME properties (speed, mass, kinetic energy, width, acceleration) and flare parameters (flux, phase).

Key Contributions

Improved Association Framework: The paper introduces a robust method combining temporal filtering with geometric coordinate transformation and position-angle alignment, significantly reducing ambiguous associations compared to previous temporal-only approaches.
Phase-Resolved Kinematics: The study provides a detailed analysis of CME properties specifically tied to the evolutionary stages of the associated flare, rather than treating flares as single-point events.
Quantification of Projection Effects: The work rigorously quantifies the impact of projection effects on CME kinematics across three solar cycles, demonstrating the necessity of 3D geometric corrections for accurate speed estimation.
Population Differentiation: The analysis systematically compares flare-associated CMEs against non-associated events to identify distinct physical populations.

Results

Association Statistics: From over 27,000 CMEs and 15,000 flares, the algorithm identified 2,175 uniquely associated events. The temporal distribution showed a strong clustering within $\pm 3$ hours of flare onset.
Projection Correction Impact: Geometric correction increased the estimated mean CME speed by an average of 64.5% (from 544.9 km/s to 896.2 km/s), highlighting the substantial underestimation inherent in plane-of-sky measurements.
Phase Dependence:
- Speed and Energy: The highest mean CME speeds (1,639 km/s) and kinetic energies ( $9.0 \times 10^{31}$ erg) occurred during the declining phase of the flare, not the impulsive phase. The impulsive phase showed positive acceleration, while the declining and post-flare phases exhibited negative acceleration (deceleration).
- Mass and Width: Similarly, the largest CME masses ( $8.0 \times 10^{15}$ g) and angular widths (249°) were observed during the declining phase.
- Acceleration: Positive acceleration was confined to the impulsive phase, suggesting magnetic driving forces dominate early, while negative acceleration in later phases indicates the growing influence of solar-wind drag.
Solar Cycle Variations: CME speeds showed a strong dependence on solar activity, with Cycle 23 exhibiting the highest speeds (980 km/s) and Cycle 24 the lowest (789 km/s). In contrast, CME mass showed a weaker dependence on the solar cycle, exhibiting significant year-to-year variability.
Correlations: A moderate positive correlation ( $R=0.385$ ) was found between flare X-ray flux and CME kinetic energy. A stronger positive correlation ( $R=0.59$ ) existed between CME mass and angular width.
Population Differences: Flare-associated CMEs were systematically distinct from non-associated events, being approximately 38.6% faster, 149.2% more massive, and 530.8% more energetic. Statistical tests confirmed these differences are highly significant.

Significance and Claims
The paper claims to support a unified picture where CMEs and flares are coupled manifestations of magnetic reconnection. The authors assert that the physical properties of CMEs are not static but evolve significantly with the stage of flare development, with the most energetic eruptions (highest speed, mass, and energy) manifesting during the declining phase of the flare. This finding challenges the notion that CME acceleration is strictly tied to the flare peak, suggesting instead that magnetic energy transfer continues to shape the eruption as it propagates.

The study emphasizes that projection effects are a fundamental source of uncertainty in CME kinematics and that their correction is essential for realistic energy budget estimates. Furthermore, the clear statistical separation between flare-associated and non-associated CMEs suggests they represent distinct physical populations, with flare-associated events resulting from more efficient magnetic-energy conversion processes. The authors conclude that their improved association framework provides a robust basis for future investigations into solar eruptive processes and space weather, noting that the persistence of these trends across three solar cycles validates the physical reality of the observed couplings. The paper remains modest regarding Cycle 25 results, acknowledging it is only partially covered in the dataset, and notes limitations regarding the assumption of radial propagation in the projection correction model.