🔭 astrophysics

Validating a Non-conventional Method for Expansion of Coronal Mass Ejections (CMEs) and Investigating the Evolution of a CME Substructures Using Solar Orbiter and Wind Observations

This paper validates the Constant Acceleration Accounted Perspective (CAAP) method for estimating CME expansion speeds using simultaneous single-point observations from the aligned Solar Orbiter and Wind spacecraft, while also revealing significant temporal evolution in CME substructures, including apparent magnetic flux non-conservation and unexpected shock strengthening during propagation.

Original authors: Anjali Agarwal, Wageesh Mishra, Mathew J. Owens, Tanja Amerstorfer

Published 2026-04-13

📖 6 min read🧠 Deep dive

CC0 1.0

Original authors: Anjali Agarwal, Wageesh Mishra, Mathew J. Owens, Tanja Amerstorfer

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ 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

Imagine the Sun is a giant, fiery factory that occasionally sneezes massive clouds of magnetized gas into space. These sneezes are called Coronal Mass Ejections (CMEs). When they hit Earth, they can cause beautiful auroras but also disrupt satellites, power grids, and GPS.

To protect ourselves, scientists need to predict exactly how big these "sneezes" are, how fast they are moving, and how they change as they travel through space. This is where a new study comes in, offering a fresh way to look at these cosmic storms.

Here is the story of the paper, broken down into simple concepts with some everyday analogies.

1. The Problem: The "One-Person Band" Limitation

Imagine you are trying to guess the speed of a moving train, but you can only stand at one spot on the platform. You see the front of the train pass you, and then, hours later, you see the back of the train pass you.

The Old Way (Conventional Method): Scientists used to assume the train was moving at a steady speed the whole time. They would take the time it took to pass and the length of the train to guess how fast it was expanding.
The Flaw: But trains (and CMEs) don't always move steadily. Sometimes the front speeds up, sometimes the back slows down. If you only look at one spot, you might think the train is expanding at a steady rate when, in reality, it's stretching and squishing wildly. This leads to bad predictions about when the storm will hit Earth and how strong it will be.

2. The Solution: The "CAAP" Method

The authors of this paper proposed a new tool called CAAP (Constant Acceleration Accounted Perspective).

The Analogy: Think of CAAP like a smart video game physics engine. Instead of just guessing the speed, it assumes the train (the CME) is accelerating or decelerating at a steady rate as it passes you. By doing the math on this "steady change," it can calculate the exact speed of the front, the middle, and the back of the train at the same moment in time, even if you only have one camera watching it.

3. The Big Test: The "Cosmic Relay Race"

To prove their new method (CAAP) actually works, the scientists needed a special situation. They needed two "cameras" (spacecraft) lined up perfectly in a row, like two people standing on a track watching a runner.

The Setup: They used two spacecraft: Solar Orbiter (closer to the Sun) and Wind (further away).
The Rare Event: On November 3–5, 2021, a massive CME happened. Because the spacecraft were lined up perfectly:
- Solar Orbiter saw the back of the CME pass by.
- Wind saw the center of the CME pass by at almost the exact same time.
The Result: This allowed the scientists to measure the "instantaneous expansion speed" directly (like measuring the distance between the back and center of the runner in real-time). They compared this real measurement to what their CAAP method predicted using only the data from one spacecraft at a time.
The Verdict: The CAAP method was spot on! It matched the real measurements perfectly. This proves that even if we only have one spacecraft in the future, we can use CAAP to get a much more accurate picture of how a CME is expanding.

4. What Did They Learn About the Storm?

While testing their math, they discovered some surprising things about this specific CME storm:

The Shockwave Got Stronger: Usually, when a shockwave (the "bow wave" in front of the CME) travels away from the Sun, it gets weaker, like a sound fading in a large room. But this one got stronger as it moved from Solar Orbiter to Wind. It was like a runner suddenly sprinting faster as they ran away from the starting line.
- Why? It seems a fast stream of solar wind behind the CME pushed it from the back, compressing and speeding it up.
The "Sheath" Stayed the Same Size: The messy, turbulent gas between the shockwave and the main cloud (called the "sheath") didn't get bigger or smaller, which is unusual. It was like a crowd of people running behind a bus that stayed exactly the same width, even though the bus was speeding up.
The Cloud Grew (and Gained Magnetic Stuff): The main magnetic cloud (the "Magnetic Cloud" or MC) got significantly bigger as it traveled. Even stranger, it seemed to gain extra magnetic "fuel" (magnetic flux) along the way.
- Analogy: Imagine a balloon inflating as it flies through the air, but instead of just getting bigger, it also seems to be sucking in extra rubber from the air to make its skin thicker. This suggests the cloud was reconnecting with the surrounding solar wind, grabbing more magnetic energy.

5. The "Compass" Confusion

The scientists also tried to figure out which way the CME was pointing (its axis).

The Visual Check: Looking at the data, it looked like a highly tilted, twisted rope (like a corkscrew standing on its side).
The Math Check (MVA): When they used a standard mathematical tool to find the direction, it said the rope was lying almost flat.
The Conclusion: The math tool got confused because the spacecraft didn't pass right through the center of the cloud; they cut through it at an angle. It's like trying to guess the shape of a donut by only looking at a slice taken from the very edge—you might think it's a straight line!

Why Does This Matter?

Space weather forecasting is like trying to predict a hurricane. If you get the size and speed wrong, you might not warn people in time, or you might panic them unnecessarily.

Better Predictions: By proving the CAAP method works, scientists can now use it on any single spacecraft data to get a much better estimate of how fast a CME is expanding.
Safety: This helps us predict exactly when a storm will hit Earth and how long the "disturbance" will last, allowing power companies and satellite operators to prepare better.

In a nutshell: The scientists built a new mathematical "lens" (CAAP) that lets us see the true, changing speed of solar storms, even when we only have one camera to watch them. They tested it on a rare, perfectly lined-up solar storm and found it works perfectly, revealing that these storms can be surprisingly dynamic, sometimes speeding up and gaining strength as they travel toward us.

1. Problem Statement

Coronal Mass Ejections (CMEs) are primary drivers of space weather, and their expansion dynamics significantly influence their arrival time, radial size, and geoeffectiveness at Earth.

Limitation of Conventional Methods: Traditional methods for estimating CME expansion speed rely on single-point in situ observations. These methods typically assume a constant expansion speed (neglecting acceleration) and calculate expansion as half the difference between the Leading Edge (LE) and Trailing Edge (TE) speeds.
The Core Issue: Because LE and TE pass a single spacecraft hours apart (approx. 20 hours at 1 AU), conventional methods provide a time-independent average that fails to capture the instantaneous expansion speed at specific moments. This leads to inaccuracies in estimating radial size, magnetic field strength, and arrival times, particularly when CMEs exhibit non-linear speed profiles (acceleration/deceleration).
Need for Validation: A non-conventional method, the Constant Acceleration Accounted Perspective (CAAP), was recently proposed to estimate instantaneous expansion speed using single-point data by assuming constant acceleration. However, this method lacked validation against direct, simultaneous multi-point measurements.

2. Methodology

The study utilizes a rare observational opportunity involving two radially aligned spacecraft: Solar Orbiter (SolO) at 0.85 AU and Wind at 0.98 AU, separated by 0.13 AU radially and 2.3° angularly. The event analyzed is a CME occurring between November 3–5, 2021.

Unique Configuration: The geometry allowed for the simultaneous observation of the CME's Trailing Edge (TE) at SolO and its Center at Wind. This provided a direct, ground-truth measurement of the instantaneous expansion speed ( $V_{exp}^{inst}$ ).
CAAP Method Implementation:
- The authors applied the CAAP method to single-point data from both SolO and Wind independently.
- The method assumes constant acceleration ( $a$ ) for CME substructures (LE, Center, TE) during the spacecraft crossing.
- Acceleration values were derived from the mean acceleration between SolO and Wind using the measured propagation speeds of the same substructures at both locations.
- Using the kinematic equation $V_F(t_j) = V_F(t_i) + a_F \Delta t$ , the method estimated the propagation speeds of all substructures at the same instant, allowing for the calculation of instantaneous expansion speed.
Comparative Analysis:
- Direct vs. Estimated: The directly measured $V_{exp}^{inst}$ (from simultaneous SolO/Wind data) was compared against CAAP-derived estimates.
- Conventional vs. Non-conventional: CAAP results were compared against traditional time-independent expansion speed calculations.
Substructure Evolution: The study analyzed the evolution of the shock, sheath, and Magnetic Cloud (MC) between the two spacecraft using Minimum Variance Analysis (MVA) for axis orientation and standard plasma/magnetic field parameters for shock and sheath characteristics.

3. Key Contributions

Validation of CAAP: This is the first study to validate the CAAP method against simultaneous multi-point in situ observations, confirming its ability to accurately estimate time-dependent instantaneous expansion speeds using single-point data.
Revealing Acceleration Dynamics: The study identified that the CME substructures underwent acceleration (rather than the typical deceleration) while traveling from SolO to Wind, driven by a High-Speed Solar Stream (HSSS) compressing the rear of the MC.
Shock Amplification: Contrary to the expectation that interplanetary shocks weaken with distance, the study found the shock strengthened at Wind (higher Mach number and compression ratio) due to the accelerating driver and favorable background solar wind conditions.
Magnetic Flux Evolution: The analysis revealed a significant increase in magnetic flux (approx. 24% for poloidal flux) between SolO and Wind, indicating flux injection (likely via magnetic reconnection) rather than flux conservation.
Methodological Insight: The paper highlights that conventional methods significantly underestimate expansion speed (by ~30-40% in this case), leading to errors in predicting CME radial size and magnetic field strength.

4. Key Results

Expansion Speed Validation:
- Measured Instantaneous Expansion Speed: $68 \text{ km s}^{-1}$ (derived from simultaneous Wind Center and SolO TE speeds).
- CAAP Estimated Speed: $67 \text{ km s}^{-1}$ at Wind (and consistent at SolO).
- Conventional Method Estimate: $43 \text{ km s}^{-1}$ (SolO) and $33 \text{ km s}^{-1}$ (Wind).
- Conclusion: The CAAP method matches the ground-truth measurement closely, whereas the conventional method significantly underestimates the expansion.
Substructure Evolution:
- Shock: Speed increased from $515 \text{ km s}^{-1}$ (SolO) to $760 \text{ km s}^{-1}$ (Wind). The shock became a stronger Fast-Forward shock with higher compression ratios.
- Sheath: Duration and radial size remained nearly constant ( $\sim 17$ hours, $\sim 61 R_\odot$ ) despite the 0.13 AU propagation, suggesting a saturation effect or cancellation of competing factors.
- Magnetic Cloud (MC): Radial size increased from $39.3 R_\odot$ (SolO) to $53.5 R_\odot$ (Wind).
Magnetic Flux and Orientation:
- Flux Injection: The power-law index analysis ( $n_B$ vs. $2n_r$ ) indicated that magnetic flux was not conserved; it increased by ~24%, suggesting reconnection at the TE.
- Axis Orientation Discrepancy: Visual inspection suggested a highly inclined (ENW-type) flux rope, while MVA suggested a low inclination. The authors attribute this to the spacecraft sampling the MC obliquely (away from the central axis), rendering standard MVA axis estimation unreliable in this specific geometry.
Acceleration: All substructures (LE, Center, TE) showed positive acceleration ( $1.0 - 2.6 \text{ m s}^{-2}$ ) from SolO to Wind, attributed to momentum transfer from the HSSS at the rear.

5. Significance

Space Weather Forecasting: The study demonstrates that relying on conventional, time-independent expansion speeds leads to significant underestimation of CME radial size and overestimation of magnetic field strength. This impacts the accuracy of arrival time predictions and geomagnetic storm severity forecasts.
Methodological Advancement: The CAAP method offers a robust tool for estimating instantaneous expansion speeds even when only single-spacecraft data is available, provided reliable acceleration estimates can be obtained (e.g., from future sub-L1 missions or remote sensing).
Physical Understanding: The findings challenge standard assumptions about CME evolution, showing that CMEs can accelerate and shocks can strengthen in the inner heliosphere due to complex interactions with the ambient solar wind (specifically HSSS).
Future Directions: The paper underscores the critical need for placing in situ monitors at various sub-L1 distances to better constrain acceleration profiles and improve the reliability of space weather models. It also calls for further investigation into the mechanisms of magnetic flux injection and the limitations of MVA for highly inclined or distorted flux ropes.