Author: Shaun A. McLaughlin, Ryan O. Milligan Queen’s University Belfast.
The Lyman Continuum (LyC; <911.12Å) results from the free-bound transition of a free electron to the ground state of an ambient hydrogen nuclei. In the quiet-Sun, LyC forms at the top of the chromosphere/base of the transition region . Therefore, the LyC is sensitive to chromospheric energy perturbations induced during solar flares, and since thermalization occurs very rapidly at the higher densities located here, its spectrum may reflect the local plasma temperature . The LyC is a potentially powerful diagnostic tool of the chromospheric response to flare energy injection, but this potential is presently largely untapped.
Observational studies of the LyC have hypothesised two formation regions of the LyC during solar flares: a deeper-forming optically thick region that forms close to local thermodynamic equilibrium (LTE) and an overlying optically thin region in non-LTE that leads to an intensity enhancement in the LyC spectrum at shorter wavelengths (<750Å) [1, 2, 5].
In this nugget, we present the analysis of synthetic LyC emission generated using the RADYN code as part of the F-CHROMA project. These profiles were extracted from model solar atmospheres that had been subjected to a large range of heating functions. Having a strong theoretical understanding of the LyC is vital for the interpretation of the readily available LyC flare observations from the Extreme-Ultraviolet Experiment (EVE) on board the Solar dynamic observatory (SDO), with potentially upcoming flare observations from the Spectral Imaging of the Coronal Environment (SPICE) on board Solar Orbiter, and the EUV High-throughput Spectroscopic Telescope (EUVST) instrument aboard Solar-C which will provide spectroscopic LyC observations (460-1220Å).
LyC formation regions
RADYN is a well-established resource that has been extensively used to model the response of the solar atmosphere to flare energy injection. When simulating flares driven by electron beams (the ‘standard model’), the non-thermal electron distribution is modelled as a power law characterised by the spectral index, δ, the low energy cut-off, Ec, and energy flux density, F .
The left-hand panel of Figure 1 shows synthetic LyC spectra from RADYN at various times, where an Eddington-Barbier approximation  has been applied to the head of the continuum (800-911Å) and to wavelengths extending down to the He I edge (505-911Å). The right-hand panel shows the goodness of fit (GoF) parameter as a function of time for the two fits, where a smaller GoF value corresponds to a better fit. Generally, we can see from the GoF parameter that the Eddington-Barbier approximation fits the head of the LyC better than the tail. The head of the continuum is dominated by emission from an optically thick LyC layer, while LyC intensities at shorter wavelengths are enhanced due to the presence of an overlying optically thin region. Using contribution functions, we found that optically thin LyC emission comes from narrow regions of increased density, that formed due to chromospheric evaporation and condensation, known as chromospheric bubbles [5, 6].
Between t=5-6s, the GoF parameter is at a maximum for both fits. In the left-hand panel, we can see that the spectra have an unexpected profile at these times, where the head of the continuum appears suppressed. This is due to an overlying region of high opacity forming between the beam heating region and transition region that is minimally heated. This region maintains a large population of hydrogen atoms in the ground state that can absorb LyC photons emitted from the deeper forming optically thick LyC layer, resulting in the suppression of the continuum head. During these times, the spectra can no longer be approximated as a blackbody, and the Eddington-Barbier relation breaks down. At later times, this region dissipates, and the spectrum behaves as expected again .
Values for the non-LTE departure coefficient of the first level of hydrogen (b1) and the colour temperature (Tc) can be determined from the Eddington-Barbier relation. Values for b1 and Tc are quoted at the top of Figure 1 for the 800-911Å fits at the various times shown in the left-hand panel. During quiescent times, we found that the LyC was optically thick forming at the base of the transition region in non-LTE (b1~103). Whereas during solar flares, we found that this region becomes strongly coupled to local plasma conditions (b1~1), forming deeper in the atmosphere, due to the evaporation of the upper chromosphere exposing a deeper region of the chromosphere. Tc was found to increase from 8-9kK to 10-16kK. When b1 is close to unity, Tc is assumed to be close to the electron temperature of the plasma, Te. In Figure 2 we show that when b1 was at a minimum, Tc was approximately equal to Te, in agreement with the literature [1, 6]. At the times when the Eddington-Barbier approximation breaks down, the values for b1 and Tc were found to be spurious.
We have shown that during quiescent periods, the LyC is optically thick and forms at the top of the chromosphere in non-LTE. During solar flares, the optically thick layer of the LyC forms deeper in the atmosphere and is strongly coupled to local conditions. Optically thin layers of the LyC form at higher altitudes due to chromospheric evaporation and condensation, resulting in enhancements in the LyC intensities at shorter wavelengths in agreement with observations [1, 2, 6].
SPICE on board the Solar Orbiter mission that was launched in 2020, provides EUV coverage in the 704−790Å and 973−1049Å wavelength ranges. This provides partial coverage of LyC. Therefore, SPICE observations may be used to determine b1 and Tc below the LyC head. However, the range covered by SPICE may be reflective of the optically thin LyC layers [1, 2, 6].
Our analysis paves the way for an interpretation of LyC solar flare observations taken by current and future missions. For more details see McLaughlin et al. (2023) .
-  Machado, M. E., Milligan, R. O., & Simões, P. J. A. 2018, ApJ, 869, 63, doi: 10.3847/1538-4357/aaec6e
-  Machado, M. E., & Noyes, R. W. 1978, SoPh, 59, 129, doi: 10.1007/BF00154936
-  Allred, J. C., Kowalski, A. F., & Carlsson, M. 2015, ApJ, 809, 104, doi: 10.1088/0004-637X/809/1/104
-  Noyes, R.W., Kalkofen, W. The solar Lyman continuum and the structure of the solar chromosphere. Sol Phys 15, 120–138 (1970). https://doi.org/10.1007/BF00149479
-  Reid, A., Zhigulin, B., Carlsson, M., & Mathioudakis, M. 2020, ApJL, 894, L21, doi:10.3847/2041-8213/ab8d1e
-  Shaun A. McLaughlin et al 2023 ApJ 944 186, doi:10.3847/1538-4357/acaf66