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

(Solar Orbiter Nugget #89 by Yong Zhang¹, Nicolas Labrosse¹, Susanna Parenti^2,3 and Therese A. Kucera⁴​^​​​​​​)

Introduction

On 15 April 2023, the Spectral Imaging of the Coronal Environment (SPICE) on board Solar Orbiter performed its first dedicated off‑limb observation of a solar prominence. At the time, Solar Orbiter was at a heliocentric distance of 0.31 AU in an Earth‑quadrature configuration. SPICE observed a large quiescent prominence in the northern hemisphere that eventually erupted around 10:00 UT (Figure 1). Understanding the physical state of such prominences is essential for mapping the flow of mass and energy through the solar corona. However, the relatively cool and dense plasma makes it hard to measure basic physical quantities. We focus on the analysis of the pre‑eruptive phase (07:03–08:09 UT), when SPICE simultaneously observed the hydrogen Lyman β (102.57 nm) and Lyman γ (97.25 nm) lines. These lines are emitted by neutral hydrogen from the n=3 and n=4 levels to the ground state, with formation temperatures around a few 10⁴ K, making them excellent diagnostics of the cool plasma that constitutes prominences [2].

While the observational analysis [3] revealed variations in integrated intensity and line width across the prominence, the data alone could not uniquely determine the underlying physical conditions. To break this limitation, we performed detailed non‑local thermodynamic equilibrium (non‑LTE) radiative transfer modelling. The goals were to understand how different plasma parameters affect the formation of the Lyman β and Lyman γ lines and to use the SPICE observations to constrain those parameters. Furthermore, understanding these pre-eruptive conditions is crucial, as they set the stage for the subsequent eruption dynamics. This work will provide valuable insights into how SPICE observations can provide new diagnostics of these cool coronal plasmas, contributing to a deeper understanding of their role in solar activity and space weather.

Figure 1. The SPICE observation of the integrated intensity of the Lyman β and Lyman γ lines taken from 07:03:40 - 08:09:23 UT, 15 April 2023. The red rectangle is the prominence region we study.

Results

Influence of plasma parameters on observables

We used the 1D non‑LTE radiative transfer code PRODOP [4], which solves the statistical equilibrium and radiative transfer equations for hydrogen. The model assumes a 1D slab oriented vertically above the solar surface, incorporating the prominence-corona transition region (PCTR). We generated 200 random models sampling realistic ranges of central temperature (5000 ∼ 15000 K), central pressure (0.01 ∼ 1.0 dyn cm⁻²), column mass (1.4×10⁻⁷ g cm⁻² ~ 1.4×10⁻⁵ g cm⁻²), PCTR temperature steepness γ (2 ~ 10), altitude (20000 km ~ 60000 km), and radial velocity (0 km s⁻¹ ~ 40 km s⁻¹). The incident radiation from the solar disk was constrained using a SPICE full‑disk mosaic from November 2023, rescaling reference profiles [5] to match the observed integrated intensity.

To analyse the relationships between model parameters and line properties, we introduced parallel coordinate plots and the elasticity coefficient. These tools allow us to identify which parameters most strongly influence the integrated intensity, the collisional and radiative terms of the source function, and the optical thickness.

In a parallel coordinate plot, if we see a diversity of colours connected to different value ranges when we focus on one parameter’s axis, this means the parameter does not have much effect; on the other hand, if we see a certain colour concentrated on a certain value range, this means the parameter has some effect. For example, in Figure 2, we can see that in the axis of central pressure, column mass and γ, the colour seems to be more uniform in different parts. This suggests that these parameters have relatively high correlation coefficients (usually larger than 0.3) with integrated intensity. A parallel coordinate plot has the following advantages: (1) It helps us discover potential relations among different parameters; (2) It is an efficient way to show parameters’ relations; (3) We can track specific colors to identify the parameters that are used to construct different models; (4) We can understand the sensitivity of the property that determines the colors to different ranges of the other parameters shown in the plot. We also calculate the elasticity coefficient to show how the quantities we study (quantities in the first axis and depicted by the colour in our parallel coordinate plots) are sensitive to changes in other parameters.

Figure 2. The parallel coordinate plot of 6 parameters with the integrated intensity of the Lyman β  line.

The key findings are as follows. For both Lyman β and Lyman γ, the integrated intensity is primarily controlled by central pressure, column mass, and γ. Higher pressure or larger column mass increases the intensity, while a steeper temperature gradient (larger γ) reduces it. The collisional and radiative contributions to the source function are equally important, and both are dominated by central pressure. For the optical thickness, central temperature is the most important parameter: hotter cores produce much lower optical thickness.

Constraining the prominence plasma parameters

Figure 3. The probability distribution of the Lyman γ line optical thickness refined by observation.

We then used the observed integrated intensities to constrain the models. We do not refine all parameters but only parameters with clear biased distributions that show systematic tendencies for data to cluster in certain regions rather than being balanced or symmetric across the entire range (Figure 3). The mean observed Lyman β integrated intensity in the prominence region is 0.46 W m⁻² sr⁻¹ with standard deviation 0.21 W m⁻² sr⁻¹, and for Lyman γ it is 0.16 W m⁻² sr⁻¹ with standard deviation 0.08 W m⁻² sr⁻¹. Restricting the 200 models to those within three standard deviations of these means left 38 models. 36 of these models have a central pressure below 0.48 dyn cm⁻². The probability distribution shows a strong bias toward low pressures, with no models above 0.7 dyn cm⁻². We therefore conclude that the central pressure of this prominence is below 0.48 dyn cm⁻².

The optical thickness distributions also became biased: 95 % of the accepted models have Lyman β optical thickness below 4800 and Lyman γ optical thickness below 1000. Extremely optically thick models are thus excluded by the SPICE observations.

We find that the column mass and γ of these models seem to have a nearly equal possibility of being distributed in each value within the range after restricting the integrated intensity of the Lyman β and Lyman γ lines. This might be because the correlation coefficient and the elasticity coefficient between the integrated intensity and the column mass, and also that between the integrated intensity and γ , are not as large as those between the integrated intensity and the central pressure.

Conclusion

By combining Solar Orbiter/SPICE observations of a pre‑eruptive prominence with 1D non‑LTE radiative transfer modelling, we have identified the key physical parameters controlling the formation of the Lyman β and Lyman γ lines in this prominence. Central pressure, column mass, and the PCTR temperature gradient are the primary parameters of the integrated intensity, while central temperature dominates the optical thickness. Using the observed line intensities, we constrained the central pressure of the 15 April 2023 prominence to be below 0.48 dyn cm⁻², and the Lyman β and Lyman γ optical thicknesses to be below 4800 and 1000, respectively. This work introduces a method combining the parallel coordinate plot, the elasticity coefficient and the pattern of the probability distribution, to fully analyse relationships among multi-parameters and also constrain parameters by observed properties. This demonstrates an effective tool for multi‑parameter analysis in solar physics.

This nugget is based on the following work: https://academic.oup.com/mnras/article/546/4/stag222/8456384

Affiliations

• SUPA School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ UK
• 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
• Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD, 20771 USA

Acknowledgements: Solar Orbiter is a space mission of international collaboration between ESA and NASA, operated by ESA. SPICE data used in this work are available via DOI: 10.48326/idoc.medoc.spice.5.0.

References

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[3] Zhang, Y., et al. (2026). Monthly Notices of the Royal Astronomical Society, p. stag104  https://doi.org/10.1093/mnras/stag104

[4] Gouttebroze, P. (2000). Solar Physics, 195, 71–91. https://doi.org/10.1023/A:1005229231465

[5] Warren, H. P., et al. (1998). Astrophysical Journal, 505, 958–971. https://doi.org/10.1086/313151