🔭 astrophysics

Non-LTE Analysis of Pre-eruptive Prominence Plasma Parameters Effects on the Lyman-beta and Lyman-gamma Lines with Solar Orbiter SPICE Observations

This study utilizes Solar Orbiter SPICE observations of an off-limb prominence from April 2023 to generate 200 non-LTE models, demonstrating how key physical parameters such as central pressure, column mass, and temperature gradient influence the formation of hydrogen Lyman-beta and Lyman-gamma spectral lines.

Original authors: Yong Zhang (SUPA School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ UK), Nicolas Labrosse (SUPA School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ UK), Susann

Published 2026-04-16

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Original authors: Yong Zhang (SUPA School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ UK), Nicolas Labrosse (SUPA School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ UK), Susanna Parenti (Institut d'Astrophysique Spatiale, Bat 121, Université Paris-Saclay/CNRS 91405 Orsay Cedex France, Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191, Gif-sur-Yvette, France), Therese A. Kucera (Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD, 20771 USA)

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 Big Picture: A Solar "Before" Photo

Imagine the Sun as a giant, active stage. Sometimes, huge clouds of super-hot gas (called prominences) hang in the air above the surface, held up by invisible magnetic ropes. Usually, these clouds are calm, but sometimes they snap, erupt, and shoot out into space, causing "space weather" that can mess with our satellites and power grids.

On April 15, 2023, a spacecraft called Solar Orbiter took a special photo of one of these clouds just before it exploded. The scientists in this paper wanted to understand exactly what was happening inside that cloud right before the big bang.

The Problem: The "Black Box" Mystery

When we look at these clouds through a telescope, we see light. Specifically, they see two specific colors of light from hydrogen atoms, called Lyman-beta and Lyman-gamma.

Think of the prominence like a black box. You can see the light coming out of it (the output), but you can't see inside to measure the temperature, pressure, or density directly. The scientists knew the light coming out, but they didn't know exactly what combination of ingredients inside the box created that light.

The Solution: The "Virtual Lab"

To solve this, the scientists built a virtual laboratory inside their computers.

The Recipe: They created 200 different "recipes" for the solar cloud. Each recipe had slightly different amounts of heat, pressure, and gas density.
The Simulation: They ran a computer program (called PRODOP) that acted like a physics simulator. It asked: "If the cloud has this much pressure and that much heat, what would the light look like?"
The Comparison: They compared the computer-generated light to the actual light they saw from the Solar Orbiter.

The Detective Tool: The "Parallel Coordinate Plot"

This is the most creative part of the paper. Usually, scientists look at graphs one by one (e.g., "How does pressure affect light?"). But here, they used a tool called a Parallel Coordinate Plot.

The Analogy: Imagine a row of vertical poles, each representing a different ingredient (Temperature, Pressure, Mass, etc.).

Every single one of the 200 computer models is drawn as a colored string that weaves back and forth, touching every pole.
The color of the string represents the final result (how bright the light is).

How it helps:

If you look at the "Pressure" pole and see that all the bright red strings (very bright light) are clustered at the top, you instantly know: "High pressure makes bright light!"
If you look at the "Temperature" pole and see red strings scattered everywhere, you know: "Temperature doesn't really matter for brightness."

It's like looking at a tangled ball of yarn and instantly seeing which threads are the "winning" ones without having to untangle them one by one.

What They Discovered

By using this "string" method, they found the "secret ingredients" that control the light:

Pressure is King: The most important factor for how bright the light is was the central pressure. If the pressure is too high, the light gets too bright; if it's too low, it's too dim.
The "Steepness" Matters: They found that how quickly the temperature changes from the center of the cloud to the edge (the "gradient") also changes the light. A steeper change means dimmer light.
The "Goldilocks" Zone: By matching their 200 virtual models to the real photo, they could rule out the wrong answers.
- They found that the pressure in this specific cloud must be below a certain limit (0.48 dyn/cm²).
- They also figured out how "thick" the cloud is to light (optical thickness). The cloud wasn't as thick as some theories suggested; it was "thin" enough that light could pass through it relatively easily.

Why This Matters

Think of this like a doctor trying to diagnose a patient.

Before: They could see the patient had a fever (the bright light), but they didn't know if it was the flu, an infection, or heatstroke.
Now: By using their "virtual lab" and the "string graph," they can say, "Based on the fever pattern, the patient definitely has a specific type of infection, and their blood pressure is likely in this specific range."

This helps scientists understand the "ticking time bomb" phase of solar eruptions. If we can better understand the pressure and temperature right before an eruption, we might get better at predicting when a solar storm is coming, protecting our technology on Earth.

Summary

The paper is a detective story where scientists used a computer simulator and a colorful string graph to reverse-engineer the physics of a solar cloud. They figured out that pressure is the main dial controlling the light, and they successfully narrowed down the physical conditions of the cloud just hours before it exploded.

1. Problem Statement

Solar prominences are magnetically confined plasma structures suspended in the corona, often serving as precursors to Coronal Mass Ejections (CMEs). Characterizing their physical conditions (temperature, density, pressure, velocity) is critical for understanding solar activity and space weather.

The Challenge: While the Solar Orbiter's SPICE instrument provided the first dedicated off-limb observation of a prominence on April 15, 2023, observational data alone cannot uniquely constrain key physical parameters due to the complexity of radiative transfer.
The Gap: Previous studies (e.g., Zhang et al., 2026) identified dynamic changes in intensity and line width but lacked a detailed Non-Local Thermodynamic Equilibrium (Non-LTE) modeling framework to interpret how specific plasma parameters influence the formation of hydrogen Lyman lines ( $\beta$ and $\gamma$ ) in the pre-eruptive phase.

2. Methodology

The study employs a multi-step approach combining observational constraints with theoretical modeling and advanced data visualization.

A. Observational Data

Target: A quiescent prominence observed by Solar Orbiter/SPICE on April 15, 2023, prior to its eruption (07:03–08:09 UT).
Lines Analyzed: Hydrogen Lyman $\beta$ (102.57 nm) and Lyman $\gamma$ (97.25 nm).
Incident Radiation Constraint: To accurately model the boundary conditions, the authors used a SPICE full-disk mosaic from November 13–14, 2023 (the closest available date) to derive the incident Lyman $\beta$ profile. They scaled the default PRODOP code profile using the integrated intensity from this mosaic, as the instrumental broadening of SPICE prevented direct deconvolution of the line shape.

B. Non-LTE Modeling

Code: The 1D radiative transfer code PRODOP (Gouttebroze & Labrosse 2000) was used.
Geometry: The prominence was modeled as a 1D vertical slab including a Prominence-Corona Transition Region (PCTR).
Input Parameters: 200 random models were generated by varying key parameters within physically realistic ranges:
- Central Temperature ( $T_{cen}$ ): 5,000 – 15,000 K
- Central Pressure ( $p_{cen}$ ): 0.01 – 1.0 dyn cm $^{-2}$
- Column Mass ( $M$ ): $1.4 \times 10^{-7}$ – $1.4 \times 10^{-5}$ g cm $^{-2}$
- Temperature Gradient Steepness ( $\gamma$ ): 2 – 10
- Altitude, Radial Velocity, and Microturbulence were also constrained based on prior observations.
Outputs: Integrated intensity, collisional term ( $\epsilon B_{\nu_0}$ ), radiation term ( $(1-\epsilon)\bar{J}$ ), and optical thickness for Lyman $\beta$ and $\gamma$ .

C. Analysis Toolkit

Parallel Coordinate Plots: Used to visualize multivariate relationships. This method allows for the simultaneous comparison of multiple input parameters against output properties, identifying non-linear correlations and parameter sensitivities without fixing other variables.
Statistical Metrics:
- Correlation Coefficients: To quantify the strength of linear relationships.
- Elasticity Coefficients: Defined as $e_{xy} = (\Delta x/x) / (\Delta y/y)$ , measuring the sensitivity of an output property to relative changes in an input parameter.

3. Key Contributions

Methodological Innovation: The paper introduces and validates the use of parallel coordinate plots combined with elasticity coefficients as a robust diagnostic tool for Non-LTE modeling. This approach effectively identifies which parameters drive specific spectral features and quantifies their sensitivity, overcoming limitations of traditional 2D scatter plots.
Refined Incident Radiation: A novel method was developed to constrain incident radiation for off-limb prominence modeling using full-disk mosaic data, addressing the issue of instrumental broadening in SPICE observations.
Comprehensive Parameter Sensitivity Analysis: The study systematically maps how central pressure, column mass, temperature, and the PCTR temperature gradient ( $\gamma$ ) influence the Lyman $\beta$ and $\gamma$ line formation, distinguishing between collisional and radiative contributions.

4. Key Results

A. Parameter Sensitivities (Lyman $\beta$ and $\gamma$ )

Integrated Intensity: Strongly positively correlated with Central Pressure (Correlation $\approx$ 0.70) and Column Mass. It is negatively correlated with the temperature gradient steepness ( $\gamma$ ); a steeper gradient suppresses total emission.
Collisional vs. Radiative Terms: For both lines, the collisional term ( $\epsilon B_{\nu_0}$ ) and radiation term ( $(1-\epsilon)\bar{J}$ ) are of similar magnitude, indicating that both collisional excitation and radiative scattering are equally important for line formation.
Optical Thickness:
- Lyman $\beta$ : Highly sensitive to Column Mass (positive correlation) and Central Temperature (negative correlation). Higher temperatures lead to lower optical thickness.
- Lyman $\gamma$ : Primarily sensitive to Central Temperature. The correlation with column mass is weaker than in Lyman $\beta$ .

B. Parameter Constraints via Observation
By filtering the 200 random models to match the observed integrated intensities (within 3 standard deviations), the authors refined the physical parameters of the April 15, 2023 prominence:

Central Pressure: 95% of valid models have a pressure below 0.48 dyn cm $^{-2}$ . This is a robust constraint.
Optical Thickness:
- Lyman $\beta$ : Constrained to be below 4,800.
- Lyman $\gamma$ : Constrained to be below 1,000.
Non-Constrained Parameters: Central temperature, column mass, and $\gamma$ showed broad, non-biased distributions after filtering, indicating that Lyman $\beta$ and $\gamma$ alone are insufficient to uniquely constrain these specific parameters without additional spectral lines.

5. Significance

Diagnostic Potential: The study demonstrates that SPICE Lyman lines are powerful diagnostics for pre-eruptive prominence plasma. The derived constraints on pressure and optical thickness provide a baseline for understanding the thermodynamic state of prominences before eruption.
Future Multi-Line Diagnostics: The authors highlight that while pressure is well-constrained, other parameters require additional spectral lines (e.g., H $\alpha$ , Mg II) to break degeneracies. The framework established here serves as a blueprint for future multi-line Non-LTE analyses.
Space Weather Relevance: By improving the ability to infer thermodynamic and dynamic properties of prominences in the pre-eruptive phase, this work contributes to better forecasting of CMEs and their impact on space weather.

In conclusion, this paper successfully bridges the gap between high-resolution solar observations and theoretical radiative transfer modeling, providing a refined set of physical constraints for a specific prominence event and a robust methodological toolkit for future solar physics research.