An Optically Thin View of the Flaring Chromosphere: Nonthermal widths in a chromospheric condensation during an X-class solar flare

Spacetime diagrams of XR3, around the time of the fourth large scale HXR burst and heating episode in the transition region/chromosphere (inferred from brightenings of the IRIS SJI observations), are shown in Figure 2. Each panel is a different spectral line, where the intensity is integrated over the extent of the line. Top left is Cl i 1355.66 Å, top right is O i 1355.598 Å, bottom left is the Mg ii k line, and the bottom right is the Fe ii 2814.445 Å line. In each panel the strongest sources are highlighted by contours, the level of which is stated in the figure caption. Flaring emission in each line follows a similar evolution and morphology, with the ribbon propagating east along the slit with time (which is downward in the maps in Figure 2). The flare sources generally persist at a very strong level for less than two minutes, after which their intensity falls below the contour threshold. They do, however, have a more gradual decay following this initial decrease, staying brigher than the pre-flare for many minutes. Since outside of the penumbra/umbra the background continuum level is very much stronger, the Fe ii line is in absorption or only weakly in emission and difficult to discern, only showing as a prominent emission line in the lower part of the maps. From these maps of the source evolution three pixels were selected for detailed study later in the manuscript, indicated by the dotted horizontal lines.

Inspecting the spectra near the peak of the this heating episode reveals intensity enhancements, some line broadening, and modest Doppler shifts that mostly manifest as red wing asymmetries. Figure 3 shows spectrograms of the Cl i 1351.66 Å line, the O i 1355.598 Å line and the adjacent C i 1355.844 Å line, the Fe ii 2814.445 Å line, and the Mg ii NUV spectra including the h & k resonance lines (2796.34 Å, 2803.53 Å) and subordinate triplet (2791.6 Å, 2798.75 Å, 2798.82 Å). A zoomed-in view of the Mg ii k line is included also. The flare portion near $x=365-369$″ exhibits clear asymmetries, though we note that the overall width of the Mg ii lines are not as broad as some other flares (e.g. Kerr et al., 2015; Liu et al., 2015; Panos et al., 2018; Huang et al., 2019).

Selecting one of our sources within the region of interest, we show the time evolution of the response of each line to the flare in Figure 4 and Figure 5, which includes the Si iv 1402.77 Å line for added context. For each line an image shows the intensity as a function of wavelength (x-axes) and time (y-axes), where time is shown in seconds from a zero point that is stated above the colour bar of each panel. Cut-outs show examples of the spectral lines before, during, and after the flare, with dotted horizontal dashed lines in the images indicating the time of each cut-out. A description of each line is included in Appendix A.

Though the spectra exhibit red-wing asymmetries during the flare, we initially fit a single Gaussian component to each line. This enables us to measure the background values of the nonthermal widths, as well as to get a sense of the duration of any broadening. Even if the increase of the width of the Gaussian function fit to the lines was largely due to the presence of red-wing components (since the standard deviation, $\sigma$, would increase to accommodate the red wing), the lifetimes of the wider single Gaussian models are reflective of the lifetimes of the red wing asymmetry and are a useful metric to obtain.

A single Gaussian component was fit to the O i 1355.598 Å line and the nearby C i 1355.884 Å line, which is optically thick but we include that line solely to better constrain the continuum level. The O i line is narrow, and since IRIS performed on-board spectral summing, there are times at which the entire line is only a few pixels across. During the flare, however, the line spans a larger number of pixels.

Importantly, although it is typical to calculate the value of an analytic function only at the center wavelength of each pixel when fitting an analytic function such as a Gaussian profile to spectral data, in fact, the signal is the integrated flux across the wavelength range of each pixel. The typical approach thus assumes a linear approximation to the function over an individual wavelength bin. If there are only a few spectral pixels across the full width at half maximum (FWHM) of the profile, using only the center wavelength of each pixel can introduce significant errors, particularly with respect to line width and asymmetry parameters. For a detailed discussion of such errors, see Klimchuk et al. (2016), who provide an iterative algorithm to adjust the data to compensate for these errors when fitting analytic functions to the data. Here, we take a more direct approach: when fitting an analytic function to the observed spectral intensity, we numerically calculate the average of the analytic function across each bin, specifically:

where $F(x)$ is the analytic function, $x_{j}$ is the center wavelength of pixel $j$, $\Delta x$ is the pixel width, $N$ is the number of values of $x$ to use for numerically calculating the average, and the average over each pixel, $\bar{F}(x)$, is fit to the data (i.e., is used to calculate $\chi^{2}$) rather than $F(x)$. We use $N=5$, that is, we perform the calculation of the profile at five times higher sampling than the data in order to rapidly calculate the average across each pixel for the fitting procedure, therby obtaining accurate width information.

For a nice overview of line width descriptions see Rathore & Carlsson (2015). In brief, line widths are generally expressed by several conventions: the standard deviation of the Gaussian ($\sigma$), the FWHM ($W$), or by the (1/e) half-width, ($w$). These are related to each other in the following way:

An observed spectral line width also includes broadening due to the instrument itself, $W_{\mathrm{I}}$. The total observed FWHM line width is $W_{\mathrm{obs}}=2\sqrt{2\ln{2}}~{}\sigma_{\mathrm{obs}}$, and the nonthermal width of an optically thin line is

Note that for an optically thick line opacity effects result in widths and shapes that are not solely defined by the thermal and nonthermal widths as in Eq 3, but those values are still important in the line’s formation and characteristics.

Figure 6 shows spacetime maps of the observed FWHM (top row) and of the $w_{\mathrm{Nthm}}$ (bottom row), both in velocity units. The first column is our main region of interest, near the easternmost ribbon, and the second column shows a patch of the western ribbon. Patches of increased width are present, with morphology consistent with the enhanced intensity of flare ribbon sources seen in Figure 2. When measuring the nonthermal widths we assumed a value of $T=6$ kK (consistent with the range of values in the modelling work of Lin & Carlsson, 2015), which is likely too small for the flare, but at the moment we are primarily interested in obtained estimates of the non-flaring $w_{\mathrm{Nthm}}$ and the duration of the wider lines. For the instrumental width we assumed that the spectral point spread function was a Gaussian with a FWHM of 2.2 unbinned pixels in the FUVS channel, from the notes in the IRIS SSWIDL routine iris_nonthermalwidth.pro³³3https://hesperia.gsfc.nasa.gov/ssw/iris/idl/sao/util/tian/iris_nonthermalwidth.pro, giving $W_{\mathrm{I}}=28.6$ mÅ. In Appendix B we demonstrate that for a reasonable range of values of formation temperature or of $W_{\mathrm{I}}$ the derived $w_{\mathrm{Nthm}}$ does not change drastically.

In the region of interest, which is in the penumbra/umbra, the background values are $w_{\mathrm{Nthm}}\sim 2-4$ km s^-1, whereas farther west in a quiet-Sun region the background values are somewhat higher, $w_{\mathrm{Nthm}}\sim 4.5-6$ km s^-1. These are both somewhat lower than the values measured by Carlsson et al. (2015), who reported nonthermal widths of $7.3$ km s^-1, but that study looked at plage. The lifetime of each enhancement was around $\Delta t\sim 30-90$ s. Selecting three pixels in the region of interest for closer study we show lightcurves in Figure 7, in which the red curves are $w_{\mathrm{Nthm}}$, and the black curves/grey shaded areas the integrated intensities across the line (from the data, not from the Gaussian model). Recall that here the increased widths of the Guassian functions fit to the O i line in the flare ribbon are largely due to the presence of the red-wing component. Despite initially decaying with a similar timescale as the width of the Gaussian model, the intensity does not return to background levels for many minutes. The lifetime of the intensity peak is around $60-90$ s, and exhibits a slow rise some 1.5-2.5 minutes before reaching its peak.

The Mg ii transitions also broaden, which are shown on the second column of Figure 7. Instead of fitting a Gaussian to the Mg ii spectra, which are optically thick and very non-Gaussian in shape, we measure the line’s quantiles (e.g. Kerr et al., 2015; Ruan et al., 2018; Peat et al., 2021, where for example the wavelength corresponding to the 88-th quantile is written $Q_{88}$), and define the width as the distance between 88-th and 12-th quantiles, $W_{Q}=Q_{88}-Q_{12}$. This is analogous to the FWHM if the line were Gaussian in shape. The width begins to increase during the flare, reaching typical values of $W_{Q}=[0.4-0.6]$ Å around the time of peak intensity. Interestingly, $W_{Q}$ peaks shortly after the intensity peak.

As indicated earlier, many of the spectra exhibited a red-wing asymmetry (resulting in very large $\chi_{\nu}^{2}$ values), so for three pixels within the region of interest (slit pixel # $[47,48,49]$) we fit two Gaussian components each to O i 1355.598 Å, C i 1355.844 Å, Cl i 1351.66 Å, and Fe ii 2814.445 Å, around the times of the flaring emission. A single Gaussian component was fit for every exposure, but if the asymmetry of the line was above a certain threshold⁴⁴4A measure of asymmetry for each profile was calculated using the metric described in Polito et al. (2019), where the intensity difference in the red and blue wings is compared to the peak intensity (in our case we measured the intensity between $\lambda=[0.04-0.14]$ Å in each wing). If the asymmetry was above the typical background value for each line then the profile was flagged for multiple-component fitting an attempt to fit two Gaussian components was performed. One component was labelled the ‘stationary’ component, and was restricted to have a small centroid shift typically $\pm 5$ km s^-1 from the rest wavelength, but varied sometimes after a visual inspection of the results. The shifted component that produced the red-wing asymmetry was labelled the ‘condensation’ component, and was restricted to have a centroid larger than the rest wavelength of the line. A visual inspection confirmed both the presence of red wing component as well as the quality of the fit. Reduced $\chi^{2}$ metrics, $\chi_{\nu}^{2}$, were calculated also, and for the O i window $\chi_{\nu}^{2}$ was calculated for both the full window (i.e. including C i), and separately for O i. If the quality of the fit for a particular exposure was not good (based on a larger $\chi^{2}_{\nu}$, or a fit that did not capture an obvious red wing component upon visual inspection), the bounds and initial guess were varied to obtain a better result with smaller $\chi^{2}_{\nu}$.

Examples of fitting the O i 1355.598 Å line are shown in Figure 8, where each panel shows a single exposure of O i 1355.598 and C i 1355.844 Å from IRIS (black lines), with the pixel along the slit (‘yind’) and time index (‘xind’) noted, both of which refer to the pixel numbers in the level-2 IRIS data. Error bars (photon counting plus dark current noise) are included as blue vertical lines at each wavelength. For each exposure the fit residuals (model - data) are shown below (note that the data and model fits are shown on a logarithmic scale, but residuals are on a linear scale).

In some instances the C i 1355.844 Å appeared to exhibit an asymmetry for quite some time prior to the onset of a measurable asymmetry in O i 1355.598 Å or the other lines. This may be because C i 1355.844 Å is a stronger line than O i 1355.598 Å, but Cl i is fairly strong also and tended to be co-temporal with O i. Perhaps optical depth effects are playing a role here. Once present, the condensation component grew in strength, but never had a peak intensity dominant over the stationary component. It then decreased in peak intensity until it was no longer discernible as a component. Typical lifetimes were $60-90$ s. After its disappearance, there were occasional re-emergences after a short gap ($\sim 5-30$ s), that were weak and persisted only a few exposures ($\sim 5-15$ s). As mentioned earlier the Cl i line may have a non-negligible opacity in the stationary component (e.g. Shine, 1983), but we operate under the assumption that the condensation component was optically thin in order to fit that part of the line and extract metrics from it. Similarly, Fe ii 2814.445 Å may be optically thick in the pre-flare (e.g. Kowalski et al., 2017; Graham et al., 2020), though we investigate this in the modelling sections of this paper.

Using the guess and bounds for each initial successful two-component Gaussian fit to the profiles, we then employed a Monte Carlo approach: 10,000 realisations were made for each spectral line from each exposure, drawing randomly from a Poisson distribution with mean equal to the observed intensity within each wavelength bin plus a random uniform sampling of the dark current plus readout noise. The total line intensity, nonthermal widths, and Doppler shift of both components were measured for each realisation. Going forward, quoted values of each of those line metrics are the 50% quantile of an exposure’s distribution, with the upper (lower) limits being the 84% (16%) quantiles.

Comparing the O i 1355.598 Å fit results for each of the three pixels within the region of interest in Figure 9 we can see fairly consistent behaviour within each source. In that figure the total line intensity is the top row, with the total line intensity defined as $I_{OI}=\sqrt{2\pi}I_{p}\sigma/\Delta\lambda$, where $I_{p}$ is the amplitude and $\sigma$ the standard deviation of the Gaussian component (in wavelength units), and $\Delta\lambda$ is the wavelength grid spacing (required to normalise $\sigma$ to be a number of pixels rather than in units of Å). The second row is the Doppler shift of the line, $V_{\mathrm{Dopp}}$, calculated from the shift of the centroid of the Gaussian component from the rest wavelength, and the third row is the nonthermal width $w_{\mathrm{Nthm}}$. The first column is the condensation component, and the second column is the stationary component.

The total intensity of the condensation component grows over $\sim 40$ s to a peak, and decays over approximately a further $40$ s (plus or minus a few exposures for each pixel). While the stationary component grows in intensity over a similar timescale, it does not decrease following the peak, remaining bright over the time frame analysed here. Doppler shifts are between $2-12$ km s^-1 for the condensation component (with the range based on a histogram of all three pixels). That is actually rather slow in comparison to general flare-induced chromospheric downflows which can be up to several 10s of km s^-1. The stationary component shows only marginal Doppler shifts around the rest wavelength, including slight blueshifts, which is not unexpected if this is indeed representing a mostly stationary layer. Warren et al. (2016) report that in the B-class flare they studied that O i 1355.598 Å showed almost no change in Doppler motions, and generally exhibited a small blueshift of $V_{\mathrm{{Dopp}}}\sim-2$ km s^-1, which the authors attributed to uncertainty with the wavelength calibration. Similarly, Warren et al. (2016) note almost no change in line width, which is consistent with the stationary component that we observe, where $w_{\mathrm{Nthm}}$ is comparable to the background values discussed earlier. However, the condensation component does show an increase above the background, reaching $w_{\mathrm{Nthm}}\sim 5-12$ km s^-1 (with the range based on a histogram of all three pixels), though with some slightly larger or smaller values at times. There is a fair amount of scatter within that range, which is likely due to the assumption of a constant $T=10$ kK and due to the narrowness of the line which makes fitting difficult. In a future study, the ideal would be to not include spectral summing.

We made the assumption that the shifted components of Cl i 1351.66 Å and Fe ii 2814.445 Å were optically thin (allowing us to extract similar metrics as we did for O i 1355.598 Å), and that they also form at the same temperature as O i since they originate within the chromospheric condensation. These assumptions seem to be largely borne out, with comparable values of $V_{\mathrm{Dopp}}$ and $w_{\mathrm{Nthm}}$ for each line. Considering all three lines there was a typical nonthermal velocity around $w_{\mathrm{Nthm}}=10$ km s^-1. Where there are differences, such as Cl i and Fe ii having a larger initial Doppler shift, these could be due to those species forming earlier within the condensation’s evolution, or being generally brighter and thus detectable earlier. Also, there could be a small temperature gradient between the lines such that a fixed $T=10$ kK is not fully appropriate. Figure 10 shows the comparisons of $V_{\mathrm{Dopp}}$ (first column) and $w_{\mathrm{Nthm}}$ (second column) for the three lines, which are represented by different colours and symbols. Each row is a different slit pixel.

Two flare simulations were produced using the RADYN+FP codes, driven by injected nonthermal electron distributions inferred from observations, but with the caveat that the pre-flare atmosphere is not wholly representative of the pre-flare state in the observations. These are intended as a general guide, and not to represent an apples-to-apples model-data comparison of these flare sources.

RADYN+FP is the combination of the RADYN radiation hydrodynamics code (Carlsson & Stein, 1995, 1997; Abbett & Hawley, 1999; Allred et al., 2005; Allred et al., 2015) and the nonthermal particle transport code FP (Allred et al., 2020), which together model the response of the solar atmosphere to energy injection via a distribution of nonthermal particles. RADYN solves the coupled equations of non-local thermodynamic equilibrium radiation transfer, non-equilibrium atomic level populations, and hydrodynamics, including the feedback among those equations. These equations are solved for one half of a symmetric loop, on an adaptive grid capable of resolving the strong shocks and gradients that typically appear during flares. Energy injection via the injected nonthermal particles then heats the plasma, which evolves and subsequently has a feedback on the energy losses of the particles as the simulation progresses. Nonthermal collisional excitation and ionisation of hydrogen and helium by the particle beam is included in the solution, which are important sources of ionisation during the flare impulsive phase. Backwarming by the optically thin flare-heated corona and transition region are all included in the solution, which can heat and photoionise the chromosphere. RADYN was recently upgraded with an improved treatment of electric-pressure (Stark) damping of the Hydrogen lines, with the exception of the Ly$\alpha$ & Ly$\beta$ transitions (Kowalski et al., 2022). Though RADYN now has the ability to suppress conduction via non-local effects and turbulence (Allred et al., 2022) we do not model those effects in our experiments, to avoid adding additional unconstrained parameters. Instead, thermal conduction is Spitzer, saturated at the free-streaming limit. FP can model the propagation and thermalisation of a distribution of particles of any mass and charge (i.e. electron, proton, or heavy ion beams, or combinations thereof), including processes such the beam-neutralising return current. The injected distribution can be of any form, but here we use the standard assumption of a power-law with slope $\delta$, low-energy cutoff $E_{c}$ and total energy flux, $F$.

RADYN, and now RADYN+FP, has become a workhorse of the flare modelling community, where it has been used to understand atmospheric evolution, energy transport mechanisms, and radiative processes during solar flares. For an in-depth discussion of how RADYN and other flare loop models have been employed over the last decade to help understand IRIS observations see Kerr (2022) and Kerr (2023).

Ashfield et al. (2022) studied this same flare, from which they determined a loop of length $L=85$ Mm of a source nearby the ribbon that we analyse here. We adopt this same length in our experiments such that the RADYN pre-flare atmosphere was a $L_{1/2}=42.5$ Mm half-loop. A reflecting boundary condition was used at the top of the loop, to mimic incoming disturbances from the other leg of the loop. The pre-flare structure was a VAL3C-like atmosphere (Vernazza et al., 1981), with 300 grid cells and apex values of $T=1$ MK and $n_{e}=6.2\times 10^{8}$ cm^-3, constructed using the atmosphere described in Carlsson et al. (2023), stretched to $L_{1/2}=42.5$ Mm from an initial 10 Mm. Bound-bound transitions of H i, He i, He ii, and Ca ii were solved assuming complete frequency redistribution (CRD), though the Lyman series were treated as pure Doppler (though with Stark broadening from Allred et al., 2015) profiles to mimic partial frequency redistribution (PRD) of the Lyman lines for the purposes of energy balance (see Leenaarts et al., 2012). We acknowledge here that the observations were of umbral/penumbral flare sources, which would have a cooler lower atmosphere than we model here. To treat such an atmosphere properly, particularly as concerns continuum emission, would require careful consideration of molecular opacity, which we have not yet included in RADYN. Therefore our models represent more general flare simulations, with other properties guided by the observations.

Analysis of the hard X-ray observations from this event, using RHESSI or Fermi/Gamma Ray Burst Monitor (GBM; Meegan et al., 2009) data, imply a very soft spectrum, with a slope of $\delta=7-8$ (e.g. Kleint et al., 2017; Kowalski et al., 2019). Imaging the RHESSI 25-50 keV X-rays suggests a strong coronal source present near $\sim$17:06UT (Ashfield et al., 2022), though there are hints that this extends down to footpoints (Kleint et al., 2017). There are additional bursts of hard X-rays observed by Fermi around the time of our source of interest $\sim$17:16-17:20 UT. Due to the strong coronal source and apparent lack of strong footpoints observed at $25-50$ keV, Ashfield et al. (2022) suggested that this flare was mostly thermal in nature, and proceeded to model the event by injecting energy directly at their loop apex (with timescales guided by the lifetime and intensity of AIA 1600 Å pixels co-spatial with the IRIS ribbon). However, for a few reasons we decided to model this event by injecting a distribution of nonthermal particles⁵⁵5Also, since we aim test the impact of including enhanced microturbulent broadening inside a condensation, so all we really need are flares that produce downflows, without being overly concerned as to how the energy ultimately reached the chromosphere. See Kowalski et al. (2019) for details, but in summary: (1) the Fermi data suggested a somewhat high value of the low-energy cutoff, $E_{c}=35$ keV, so that, indeed, images of 25-50 keV X-rays may have been largely thermal in nature, with the dominant source in the corona (the dynamic range of RHESSI means that in the presence of a strong source, weaker sources are not detectable); (2) features in the Fermi $35-41$ keV and $58-72$ keV lightcurves are co-temporal with the appearance of newly brightened source areas in the chromosphere, suggestive of a direct link between energetic electrons and deposition of energy into the lower atmosphere (see also Graham et al., 2020); and (3) there was a rapid variability in $>35$ keV HXR lightcurves, so they are more likely to to be nonthermal in nature. The total power carried by nonthermal electrons at the times of interest were derived from the Fermi observations, which can be divided over the flaring area to obtain the energy flux. Kowalski et al. (2019) determined a range of possible energy fluxes, $F=2\times 10^{10}-2\times 10^{11}$ erg s^-1 cm^-2. We chose two values of energy flux within this range, such that the two flare simulations were driven by injection of a nonthermal electron distribution with $\delta=8$, $E_{c}=35$ keV, and $F=[5\times 10^{10},2\times 10^{11}]$ erg s^-1 cm^-2 (hereafter we refer to these as 5F10 and 2F11 experiments, respectively), with a constant injection rate lasting 30 s.

The evolution in space and time of the two flares is shown in Figure 11, where the lefthand column is the 5F10 simulation, and the righthand is the 2F11 simulation. Though the temperature panels are saturated at $T=1$ MK, this is just to allow more details to be seen in the cooler lower atmosphere, both simulations resulted in coronal temperatures exceeding $T=10$ MK (including in the lower corona near the flare transition region), and the 2F11 simulation produced $T>45$ MK. As would be expected, the 2F11 simulation drove more rapid and dramatic changes, with a much more compressed flare transition region and chromosphere.

Smearing of profiles by unresolved large ($>150-200$ km s^-1) macroscopic flows, or including rather large values of microturbulence throughout the chromosphere have been suggested as a resolution to the question of the broadening of Mg ii resonance lines during solar flares. Neither is compatible with our observations or modelling. Our flare models are clearly missing certain ingredients. We briefly speculate as what those may be, which are not mutually exclusive nor exhaustive.

One missing ingredient may be additional heating at great depths. Temperature gradients between the core-to-wing formation heights may be too steep in current modelling, such that the core is too intense relative to the wings. Easing that gradient, either by increased density to raise the wing formation height closer to the line core formation height, or by additional heating of the lowest parts of the atmosphere that is not currently taking place in our electron-beam models. Heating the chromosphere to a greater depth would enhance the line wing’s source function at those depths (the core forms in the upper chromosphere), naturally increasing the emergent intensity (in the Eddington-Barbier approximation, the emergent intensity at some wavelength is reflective of the source function at the height at which $\tau_{\lambda}=1$). Broadening due to the stratification of the line source function is often referred to as ‘opacity broadening’ (see e.g. Rathore & Carlsson, 2015), and increased opacity broadening due to mass-loading of the quiet chromosphere has recently been explored as an explanation for the width of quiescent Mg ii profiles in MHD models (Hansteen et al., 2023). Further evidence that heating to greater depth is required in flares includes the outstanding problem of where and how the NUV and optical continua are formed (i.e. the question of white light flares), and the requirement to heat the temperature minimum region or upper photosphere, inferred from spectral inversions (e.g. Metcalf et al., 1990a; Metcalf et al., 1990b) and spectropolarimetry (e.g. Jurčák et al., 2018). Certain observations point to a mid-upper chromospheric origin of the optical continuum due to the presence of a Balmer jump, whereas other sources are consistent with heating of the upper photosphere or temperature minimum region. Indeed, some semi-empirical modelling suggests that to explain both the observed NUV and optical data we need heating of the full extent of the photosphere through transition region (e.g. Kleint et al., 2016). For more discussion see the introduction to Kerr & Fletcher (2014) and Section 3 of Kerr (2023). Investigation into the continuum-to-line ratio for Fe ii (e.g. Kowalski et al., 2019) in this flare could help guide the models, which currently predict ratios too small compared to the observations.

Another potential missing ingredient is broadening due to interactions between ambient Mg ii ions and the nonthermal particles within the electron or proton beams. RADYN includes nonthermal collisions for H and He, but we do not model the effects on Mg ii. Hawley et al. (2007) speculated that the discrepancy between their stellar flare observations and models of Mg ii resonance lines may be in some part due to the addition of nonthermal collisions to the total collisional rate, since the PRD implementation uses the depopulation rate of the h & k lines when calculating the coherency rates in the PRD solution. Enhancing the collisional rates may result in increased redistribution of core photons to the wings. As well as nonthermal collisions, the energetic electrons in the beam could produce broadening due to turbulent electric fields from beam-induced plasma waves, that result in an additional Stark-type effect (Airapetyan & Nikogosyan, 1988; Gavrilenko, 1999; Tomozov, 1990), or during charge-exchange between nonthermal particles and ambient plasma (Gomez et al., 2022). The effect of these latter processes on Mg ii is unknown, but certainly present interesting avenues to explore.