🔭 astrophysics

Prominence Plasma Parameters Maps Inferred From Lyman $\beta$ and Lyman $\gamma$ Observations and Non-LTE Modelling

This paper presents a method to generate physically constrained maps of prominence plasma parameters, such as temperature and pressure, by using contribution functions to optimize non-LTE radiative transfer models against SPICE observations of Lyman $\beta$ and Lyman $\gamma$ lines from an off-limb prominence observed on April 15, 2023.

Original authors: Y. Zhang, N. Labrosse, T. A. Kucera, S. Parenti

Published 2026-04-16

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CC BY 4.0

Original authors: Y. Zhang, N. Labrosse, T. A. Kucera, S. Parenti

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

Imagine the Sun not just as a blazing ball of fire, but as a dynamic ocean of gas with hidden, floating islands. These islands are called solar prominences. They are massive clouds of cool, dense plasma suspended in the scorching hot atmosphere of the Sun. Understanding these clouds is like trying to understand the weather on Earth, but instead of rain and wind, we are dealing with magnetic fields and superheated gas that can trigger space storms affecting our satellites and power grids.

This paper is about a team of astronomers who acted like cosmic detectives. Their goal? To figure out exactly what these floating islands are made of, how hot they are, and how heavy they are, without ever being able to touch them.

Here is the story of how they did it, broken down into simple steps:

1. The Crime Scene: A Snapshot from Space

On April 15, 2023, a spacecraft called Solar Orbiter (a joint project between Europe and the US) took a very special picture. It used a high-tech camera named SPICE to look at a prominence hanging off the edge of the Sun.

Think of SPICE as a super-sensitive microphone that doesn't listen to sound, but to light. It listened to two specific "notes" (colors of light) coming from the prominence: Lyman-beta and Lyman-gamma. These are specific types of ultraviolet light emitted by hydrogen atoms. Just as a doctor listens to a heartbeat to guess a patient's health, the astronomers listened to these light "notes" to guess the health of the prominence.

2. The Problem: The "One Note, Many Causes" Puzzle

Here is the tricky part: The same amount of light can be produced by many different combinations of temperature and pressure.

Analogy: Imagine you hear a loud drum beat. Is it a small drum hit hard, or a big drum hit softly? You can't tell just by the volume.
In the Sun's case, a "loud" light signal could mean the gas is very hot but thin, or cool but very dense. The astronomers needed a way to solve this puzzle and find the exact recipe for every tiny spot on the prominence.

3. The Solution: The "Virtual Weather Station"

The team created a virtual simulation (a computer model) of the prominence. They didn't just guess; they used a clever strategy:

Step 1: The Lottery. They generated 1,000 random models of the prominence. Each model had a slightly different temperature, pressure, and density, like rolling dice to create 1,000 different "what-if" scenarios.
Step 2: The Match. They calculated what the light would look like for each of these 1,000 models and compared it to the real photo taken by the spacecraft.
Step 3: The Refinement. They found the models that were closest to the real photo. But here's the genius part: They realized that one model might match the "Lyman-beta" note perfectly but miss the "Lyman-gamma" note. So, they took the best parts of the "Lyman-beta" model and the best parts of the "Lyman-gamma" model and stitched them together to create a new, perfect model.

They used something called Contribution Functions as their guide. Think of this like a heat map inside the prominence. It told them exactly where inside the cloud the light was being made. If the light was coming mostly from the top layer, they knew to adjust the temperature of the top layer, not the bottom.

4. The Result: A 3D Map of the Invisible

By doing this for every single pixel (tiny dot) in the image, they created maps of the prominence's hidden properties.

The Mass Map: They figured out how much "stuff" (mass) was in each part of the cloud.
The Pressure Map: They calculated how hard the gas was pushing against itself.
The Temperature Map: They estimated how hot it was.

The Big Discovery:
They found that the "shape" of the light they saw in the photo matched the "shape" of the mass and pressure in their maps.

Analogy: It's like looking at a shadow on the wall and realizing that the shadow's shape perfectly matches the shape of a hidden object behind a curtain. The bright spots in the light corresponded to the heavy, high-pressure spots in the cloud.

5. Why Does This Matter?

This is a big deal for a few reasons:

Space Weather Forecasting: Prominences can erupt and shoot massive clouds of gas toward Earth, causing auroras but also damaging satellites. By understanding the "pressure" and "temperature" inside them, we might one day predict when they will erupt, just like meteorologists predict hurricanes.
A New Tool: This method allows scientists to turn a simple 2D picture of light into a detailed 3D understanding of the Sun's atmosphere. It's like turning a flat photograph of a cake into a recipe that tells you exactly how much flour, sugar, and heat went into every layer.

Summary

In short, the astronomers used a computerized "mix-and-match" game to decode the light from a solar cloud. By comparing thousands of fake clouds to the real one, they built a detailed map of the cloud's temperature and pressure. This helps us understand the "weather" of our Sun and how it might affect our technology here on Earth.

1. Problem Statement

Solar prominences are cool, dense plasma structures suspended in the hot solar corona. Understanding their physical conditions (temperature, pressure, column mass, and velocity) is critical for solar physics and space weather forecasting, as they are often precursors to Coronal Mass Ejections (CMEs).

While spectroscopic diagnostics exist, determining these parameters uniquely is challenging due to:

Non-LTE Environment: Prominence plasma is not in Local Thermodynamic Equilibrium, requiring complex radiative transfer modeling rather than simple diagnostic ratios.
Degeneracy: Different combinations of physical parameters (e.g., high pressure/low temperature vs. low pressure/high temperature) can produce identical integrated intensities in specific spectral lines.
Limitations of Single-Line Analysis: Previous studies often relied on single lines or simplified models that could not simultaneously constrain multiple parameters across a spatial region.

The specific challenge addressed in this paper is deriving spatially resolved maps of plasma parameters for a specific off-limb prominence observed by the SPICE instrument on Solar Orbiter (April 15, 2023), using the Lyman $\beta$ and Lyman $\gamma$ lines, which are sensitive to different thermodynamic conditions within the prominence.

2. Methodology

The authors developed a novel, physically constrained optimization method to generate parameter maps by matching observed integrated intensities with synthetic models.

Data Source

Instrument: Spectral Imaging of the Coronal Environment (SPICE) on board Solar Orbiter.
Event: Off-limb prominence observation on April 15, 2023 (pre-eruptive phase).
Lines: Lyman $\beta$ (102.5 nm) and Lyman $\gamma$ (97.2 nm).
Incident Radiation: Constrained using a full-disk mosaic from SPICE (November 13, 2023).

Modeling Framework

Code: PRODOP, a 1D non-LTE radiative transfer code designed for solar prominences (including Hydrogen, Helium, Calcium, and Magnesium lines).
Model Geometry: A 1D slab model oriented vertically, incorporating a Prominence-Corona Transition Region (PCTR).
Parameters: The model varies Central Temperature ( $T_{cen}$ ), Central Pressure ( $p_{cen}$ ), Column Mass ( $M$ ), and the PCTR temperature gradient ( $\gamma$ ).

The Optimization Algorithm

Instead of a standard grid search, the authors employed a contribution-function-guided refinement process:

Random Sampling: Generated 1,000 random models within physically constrained ranges (based on previous work by Zhang et al. 2026b).
Initial Selection: For each pixel, identified two "best" models from the random set:
- Model A: Best match for Lyman $\beta$ intensity.
- Model B: Best match for Lyman $\gamma$ intensity.
- Note: Initially, these were different models for the same pixel.
Contribution Function Analysis: Calculated the contribution functions ( $C$ ) for both lines. This function describes how specific layers within the slab contribute to the emergent intensity.
Hybrid Model Construction:
- Identified regions in the slab where the "worse-matching" line was sensitive (high $C$ ) but the "better-matching" line was insensitive (low $C$ ).
- Constructed new temperature ( $T_{new}$ ) and pressure ( $p_{new}$ ) profiles by linearly combining the profiles of Model A and Model B.
- Used coefficients ( $a_1, a_2$ ) restricted to $0 \le a \le 0.5$ to ensure the new model remained close to the better-matching baseline while adjusting the sensitive regions.
- Adjusted Column Mass ( $m_{new}$ ) using a broader coefficient range ( $a_3 \in [-0.5, 0.5]$ ) as it controls global density scale rather than local line formation.
Global Optimization: Tested combinations of coefficients ( $a_1, a_2, a_3$ ) to find the set that minimized the Mean Relative Difference ( $R_{avg}$ ) between synthetic and observed intensities across 9 representative pixels.

3. Key Contributions

Simultaneous Multi-Line Constraint: The method successfully constrains plasma parameters by simultaneously matching Lyman $\beta$ and Lyman $\gamma$ , overcoming the degeneracy issues inherent in single-line analysis.
Contribution Function-Guided Optimization: Unlike previous statistical approaches, this method uses the physical contribution functions of the spectral lines to guide the modification of temperature and pressure profiles, ensuring physical consistency.
Spatial Parameter Mapping: The study moves beyond point-wise analysis to generate full 2D maps of temperature, pressure, and column mass for the observed prominence region.
Validation of PRODOP: Demonstrates that the PRODOP code, when coupled with this optimization strategy, can reproduce observed EUV intensities with high fidelity.

4. Results

Model Performance: The optimized model set achieved a Mean Relative Difference ( $R_{avg}$ ) of 5% between synthetic and observed intensities for the 9-pixel test map, and 8% for the full region.
Derived Parameter Ranges:
- Column Mass: $1.6 \times 10^{-7}$ to $1.4 \times 10^{-5}$ g cm $^{-2}$ .
- Mean Pressure: 0.01 to 0.32 dyn cm $^{-2}$ .
- Mean Temperature: 9,885 to 30,238 K.
Spatial Correlations:
- The Column Mass and Mean Pressure maps showed strong structural correspondence with the observed Lyman intensity maps (high intensity regions correlated with high mass/pressure).
- The Mean Temperature map showed less structural variation. The authors attribute this to the lower sensitivity of Lyman $\beta$ and $\gamma$ intensities to temperature variations compared to mass and pressure in this specific regime.
Uncertainties: Estimated uncertainties were 86% for column mass, 72% for pressure, and 22% for temperature, highlighting the remaining degeneracy in temperature determination.
Synthetic Extensions: The authors successfully generated synthetic H $\alpha$ and Electron Density maps, which matched the morphology of the EUV observations, demonstrating the method's utility for predicting unobserved spectral lines.

5. Significance and Future Work

Scientific Impact: This work provides a robust quantitative bridge between spectroscopic diagnostics and non-LTE plasma modeling. It allows for the visualization of internal prominence structures (mass and pressure distributions) that are otherwise invisible.
Space Weather: By characterizing the pre-eruptive state of prominences, this method contributes to understanding the thermodynamic conditions that trigger solar eruptions.
Future Applications:
- The methodology can be extended to include additional spectral lines (e.g., from IRIS or Metis) to break degeneracies and improve temperature resolution.
- It enables the generation of synthetic observables for spacecraft that may lack specific spectral coverage, aiding in multi-mission comparative studies.
- The approach is applicable to future EUV spectroscopic datasets from missions like Solar Orbiter and Parker Solar Probe.

In conclusion, the paper presents a significant advancement in solar prominence diagnostics, moving from qualitative descriptions to quantitative, spatially resolved parameter mapping using a sophisticated non-LTE modeling framework.