Solar Flare Ribbon Fronts II: Evolution of heating rates in individual flare footpoints

A major model-data discrepancy is that the observed ribbon front lifetimes can be up to one or two orders of magnitude longer than the synthetic ribbon front spectra which are only a few seconds. We found in Kerr et al. (2021) that a simulation with a very weak injection of nonthermal electrons could result in only enhanced absorption of He I 10830 Å (i.e., without subsequent emission), and in Polito et al. (2023a) that two regimes of energy fluxes were required to explain ribbon fronts versus bright ribbons. Based on those points, here we perform a series of rather simple experiments aiming to achieve persistent ribbon front-like behaviour that subsequently transitions to bright ribbon fronts with explosive evaporation. Though seemingly simple, these experiments carry implications for energy release and particle acceleration processes in localised regions of the flare ribbons. They also present a somewhat contrarian view to the prevailing thought on energy injection timescales, that we discuss briefly here.

In our experiments we model flares in which we inject a weak flux of nonthermal electrons for $t_{\mathrm{dur}}=100$ s, before raising this flux over a period of 100s to values required to produce the observed bright ribbon behaviour. We stress, though, that our primary focus was obtaining realistic durations of the ribbon front phase and so the temporal profile of the ‘main’ heating phase was rather ad-hoc. This was designed to determine how quickly the flare footpoint would transition from ribbon front to bright ribbon, and ultimately produce chromospheric evaporation. Some further experiments were performed that varied the duration of the weak heating phase from $t_{\mathrm{dur}}=25-150$ s.

These timings (i.e. around 200s total heating) are rather long compared to what has become the general community’s consensus, which more typically assumes bombardment by electron beams into individual locations on the order of a few seconds to tens of seconds (see e.g. discussions in the review by Kerr, 2022). This is based on both observations of the chromospheric response (i.e. the rapid apparent motion of bright fare ribbons as new field lines reconnect) as well as hard X-ray footpoint motion, and the appearance of structure in hard X-ray lightcurves which can be interpreted as elementary bursts of energy injection (see e.g. the recent example by Collier et al., 2024).

Despite the body of evidence that suggests a relatively short duration of injection of energetic electrons into discrete areas, we are content that our experiments with long duration heating are appropriate to explore the properties of these ribbon front flare sources. This is especially true as prior experiments with short duration heating have been unable to reproduce ribbon front behaviours with the appropriate lifetimes. Our weak heating phase was observationally driven, based on lifetimes of ribbon front sources. The main heating phase, though arguably longer than the actual main heating phase in real flares, was intended to show that ribbon fronts transition to bright ribbons even if the increased energy flux is modest. Further, since Polito et al. (2023a) found that not every ribbon front source ultimately produced chromospheric evaporation, the ramp-up in energy flux in our experiments will demonstrate that explosive evaporation occurs only when the energy flux becomes strong. As we will see in the remainder of this manuscript, our new experiments (1) successfully reproduce ribbon front lifetimes, (2) result in a transition to bright ribbon sources as soon as the energy flux is increased, (3) that when the energy flux in the main heating phase is large enough explosive evaporation is produced.

Current hard X-ray observations do not preclude the extended weak heating phase we propose. In the ribbon front phase of our model the nonthermal electron flux is orders of magnitude weaker than that of the main heating phase which produces the bright ribbons. Since the dynamic range of prior solar hard X-ray observatories has been small, the X-rays produced during ribbon front lifetimes would not be detectable in the presence of brighter X-ray sources elsewhere on the flare ribbons. Nor is the X-ray spatial resolution sufficient to isolate these small localised flare ribbon front sources from the rest of the bright ribbon. Finally, we note that although the general consensus is that the bright ribbon sources only have a few seconds to tens of seconds of nonthermal particle bombardment, there is healthy debate as to what keeps flare sources cooling slowly compared to the rapid cooling in flare loop models. There have been suggestions than some other form of energy is deposited for a longer period of time (see e.g. Qiu & Longcope, 2016; Zhu et al., 2018; Ashfield et al., 2022). Although our main heating phase is 100s of electron bombardment, this could in principle be a few seconds of nonthermal electrons, followed by the yet unknown source of energy flux.

To simulate the flaring atmosphere we employed the RADYN+FP numerical code, which is the combination of the field-aligned radiation hydrodynamic (RHD) code RADYN (Carlsson & Stein, 1992, 1995, 1997; Abbett & Hawley, 1999; Carlsson & Stein, 2002; Allred et al., 2005, 2015; Carlsson et al., 2023), coupled with the nonthermal particle transport code FP (Allred et al., 2020). RADYN solves the equations of hydrodynamics, plane-parallel non-local thermodynamic equilibrium (NLTE) radiation transfer, and non-equilibrium atomic level populations, including charge conservation. FP solves the propagation and thermalisation of a distribution of energetic particles through a specified atmosphere, which in our case is the evolving RADYN flares. Feedback between each aspect of the problem is included self-consistently. Energy injected by the nonthermal particles affects the thermodynamic structure of the atmosphere, which varies the atomic level populations and emitted radiation. In turn this also affects the thermodynamic state through non-local radiative heating and cooling, which affects the energy deposition profile. The changing temperature of the atmosphere is included in the solution of the particle transport, which solves the full Coulomb collisional operator, making no cold- or warm-target assumption. Instead it is valid for both extremes and everything in between. FP was merged with RADYN in 2021, replacing the prior imbedded Fokker-Planck based module from Allred et al. (2015).

RADYN has become a workhorse of the flare community given its ability to model the response of solar chromosphere and transition region at very high spatial resolution (sub-meter where necessary), and to included the important effects of NLTE radiation transport. We do not provide an exhaustive description of the code here, instead we direct readers to recent general descriptions of the code in Allred et al. (2015) and Carlsson et al. (2023), and to recent detailed reviews of the ways in which RADYN has been used in tandem with observations from IRIS to explore flare physics Kerr (2022, 2023). Some salient points regarding RADYN’s capabilities and limitations when modelling He that are relevant to our study are noted below, the majority of which are similar to, and discussed in more detail in, Kerr et al. (2021).

The model He atom employed in our experiments is a 9-level-with-continuum. The upper and lower levels of He I 10830 Å included but without substructure of the ${}^{3}P$ state. Processes important for populating orthohelium are included. The photoionisation-recombination route is achieved by an irradiating EUV spectrum from the transition region and corona, which uses the local density and temperature of each grid cell when constructing an integrated downward-directed radiation field (note that irradiation by lines modelled in detail by RADYN, such as He II 304 Å are not included but we believe that this is only a minor effect). The nonthermal collisional ionisation-recombination route is modelled by adding to the rate equations nonthermal collisional ionisation of He I and He II (following the recipes of Arnaud & Rothenflug, 1985). The effects of the beam-neutralising return current are included when modelling the nonthermal particle distribution. Thermal collisional ionisation-recombination, direct collisional excitation routes, and collisions between the upper and lower levels are included, which become more important when the flare chromosphere is sufficiently hot.

Our experiments used the same initial atmosphere as in Kerr et al. (2021), which is an 11Mm half-loop (with 191 grid points), with an apex temperature of $T=3.15$ MK and electron density $n_{e}=7.6\times 10^{9}$ cm^-3. Flare energy was injected in the form of a distribution of nonthermal electrons with spectral index $\delta=[3,5,7]$, and low-energy cutoff $E_{c}=[10,15,20,25,30]$ keV. The energy flux injected varied with time, but was the same for each experiment. Given the indications from Kerr et al. (2021) that a weak energy flux may sustain a longer period of enhanced absorption, we set the duration of weak-heating to be $t_{\mathrm{dur}}=100$ s (similar to the observations of Xu et al., 2016) with a constant energy flux of $F=5\times 10^{8}$ erg s^-1 cm^-2, followed by an ad-hoc ramp up over the next $100$ s to more typical flare energy fluxes, reaching $F=1\times 10^{11}$ erg s^-1 cm^-2 by $t=200$ s. A schematic of the evolution of the energy flux is shown in Figure 2. Since we are primarily concerned with demonstrating the requirement of a weak-heating phase for some flare sources, and the difference between the synthetic spectra during their ribbon front phase and the main/bright ribbon phase, the particular details of strong-heating phase are not as important for our current experiments. We elected to slowly ramp up the energy injection in order to determine if there were any obvious signatures that appeared in the synthetic spectra as they transitioned from ribbon front-like to typical-flare spectra.

In addition to this parameter study we modelled five flares with varying $t_{\mathrm{dur}}=[25,50,75,125,150]$ s, all with $\delta=5$ and $E_{c}=25$ keV. The subsequent heating of those additional flares then followed the gray shaded area of Figure 2, just offset in time, such that the strong-heating phase injected the same total energy flux in each simulation.

Figure 3 shows three typical snapshots of the stratification of temperature, electron density, bulk velocity (upflows are negative), and the ratio of the populations of the upper-to-lower levels of He I 10830 Å (2p ³P versus 2s ³S), for $\delta=[3,5,7]$, $E_{c}=25$ keV, and $t_{\mathrm{dur}}=100$ s. One snapshot shows $t=50$ s, during our supposed weak-heating (ribbon front) phase, one snapshot shows $t=165$ s, midway through the ramp-up of the strong-heating phase, and the final snapshot shows $t=196$ s, when the injected energy flux was at its maximum (where we would expect bright ribbon behaviour). During the weak-heating phase gentle chromospheric evaporation is present, with velocities on the order $v\sim 10-20$ km s^-1. Modest temperature increases are present throughout the chromosphere, with softer nonthermal electron distributions (larger $\delta$; smaller $E_{c}$) producing somewhat warmer and denser upper chromospheres. Harder nonthermal electron distributions produce both temperature and electron density enhancements to greater depth. While there are enhanced populations of the He I 2p ³P level relative to the He I 2s ³S level in the upper chromosphere (where the line forms) for all flares, the ratio is notably larger for softer beams. During the strong-heating phase the atmosphere evolves more dramatically, as one would expect, with orders of magnitude increases in electron density, explosive chromospheric evaporation and chromospheric condensations on the order a few 10s km s^-1.

To provide additional model validation, we complement the He I 10830 Å synthetic spectra from RADYN+FP  with synthetic Mg II NUV spectra from RH15D (Uitenbroek, 2001; Pereira & Uitenbroek, 2015). This code includes the effects of partial frequency redistribution (PRD), important for Mg II even in the elevated density of the flare chromosphere (Leenaarts et al., 2013a; Kerr et al., 2019a), and overlapping transitions. We used the hybrid PRD approximation of Leenaarts et al. (2012). RH15D solves the multi-line, multi-species NLTE radiation transfer and atomic level population equations given an input atmosphere (in our case, the RADYN flare atmospheres processed at 1 s snapshots). The species modelled in NLTE are: H, C I+C II, O I, Si I+Si II & Mg II, with several others included as LTE background opacity. Background opacity was also provided by modelling the many thousands of lines in the Kurucz linelists²²2http://kurucz.harvard.edu/linelists.htm, between $\lambda=[20-8000]$ Å. A constant value of microturbulence was added at each grid cell, with the value $v_{\mathrm{turb}}=7$ km s^-1 based on Carlsson et al. (2015), and the same as used in (Polito et al., 2023a). This is somewhat smaller than the flare values observed by Kerr et al. (2024), but since those values were obtained at flare peak we did not know when the transition from background to flare values in the chromosphere should take place so we chose to keep this constant. While the Mg II spectra will be more narrow than observed, this is a known problem (e.g. Kerr et al., 2024) and does not affect our conclusions.

For Mg II we used the 11-level-with-continuum atomic model of Leenaarts et al. (2013a). Though RH15D does not model non-equilibrium effects we have previously demonstrated that these likely have a minimal impact on the Mg II solution (Kerr et al., 2019b), aside from the initial switch on and cessation of flare energy injection. Relaxation timescales are $\tau_{\mathrm{relax}}<0.1$ s during the bulk of the fare, rising to $\tau_{\mathrm{relax}}\sim 0.1-2$ s during the initial bombardment and first couple of seconds of the cooling phase. Omitting PRD effects for Mg II were much more impactful. Further, we keep the H populations and electron densities fixed, such that they include nonthermal and non-equilibrium effects, mitigating omitting these effects from other species. Zhu et al. (2019) improved the treatment of Stark damping for Mg II, which we employ here.

All of our flare simulations exhibited the expected behaviour of enhanced He I 10830 Å absorption (dimming), followed by a subsequent brightening. However, unlike the experiments of Huang et al. (2020) or Kerr et al. (2021), many of our flares exhibited He I 10830 Å dimming that persisted for dozens of seconds, up to $t\sim 100$ s, with harder nonthermal electron distributions producing enhanced He I 10830 Å absorption for longer periods. That is, the dimming persisted for the entirety of the weak-heating phase in several of our flare simulations, and for durations similar to the observations of Xu et al. (2016).

Lightcurves of the He I 10830 Å line, integrated in the range $[\lambda_{0}-0.04~{}\AA]\rightarrow[\lambda_{0}-0.54~{}\AA]$, mimicking the wavelength range of the passband in the Xu et al. (2016) BBSO observations, are shown in Figure 4 for each of the 15 simulations with $t_{\mathrm{dur}}=100$ s. The contrast of the wavelength-integrated flaring intensity ($I_{\mathrm{flare}}$) to the pre-flare intensity ($I_{{0}}$) was defined as: ($I_{\mathrm{flare}}-I_{{0}})/I_{{0}}\times 100$. It is immediately clear that the period of dimming is strongly dependent on the properties of the injected nonthermal electron beam, with harder nonthermal electron distributions resulting in longer duration dimming. Softer nonthermal distributions, though generally lasting longer than the few seconds of dimming in Huang et al. (2020) and Kerr et al. (2021), transition to emission more rapidly.

The slow ramp-up to more typical flare energy fluxes results in more structure than the lightcurves shown in Kerr et al. (2021), some of which are reminiscent of the Xu et al. (2016) with a local minima (though the lines are still in emission) and multiple peaks over time. This seems to occur for flares with larger $E_{c}$ in our parameter grid, and is due to the presence of downward directed mass flows (chromospheric condensations) which Doppler shift the spectra outside of the selected window, towards redder wavelengths.

Despite the fact that Doppler shifts result in structure in the lightcurves, the periods of enhanced absorption do occur over the full spectral line profiles, and do persist for the timescales indicated in Figure 4. Even though small Doppler motions are present during the dimming period, they are modest and insufficient to create an artificial dimming feature. This is illustrated in Figure 5, which shows the He I 10830 Å profiles as a function of time from three simulations, with cutouts at a few snapshots. In that figure it is also clear that there can be a transitory time, where parts of the line profile are undergoing enhanced absorption, parts are similar to the pre-flare, and parts are enhanced relative to the pre-flare. Appendix A shows the wavelength-time panels for each simulation with $t_{\mathrm{dur}}=100$ s.

The duration of the weak-heating phase has a direct impact on the lifetime of the He I 10830 Å ribbon front-like behaviour. Shortening $t_{\mathrm{dur}}$ reduces the time taken for the line to show a positive contrast, and lengthening $t_{\mathrm{dur}}$ increases the time taken for the line to transition from absorption to emission. In fact, for the harder nonthermal electron distributions, the lifetime of the dimming equals the duration of the weak-heating phase, as shown in the He I 10830 Å lightcurves in Figure 6 where we vary $t_{\mathrm{dur}}=[25,50,75,100,125,150]$ s. This implies that, in a rough sense, the length of the observed dimming period informs us about the duration of weak precipitation of nonthermal particles. There is of course some level of ambiguity as we saw for some intermediate cases (e.g. $\delta=5$; $E_{c}=20$ keV) that He I 10830 Å is driven into emission prior to the start of the strong-heating phase.

Here we explore the formation properties of the line and the plasma conditions in the He I 10830 Å line forming region of the atmosphere, building upon some prior efforts in Huang et al. (2020), to understand when the line is driven into emission. That is, can we state confidently what the differences in plasma conditions are at the ribbon front versus the main bright ribbons?

The contribution function to the emergent intensity, $C_{I}(\lambda,\mu,z)$, can be defined as:

Huang et al. (2020) averaged the plasma properties over a broad range of heights where $C_{I}$ was elevated. Here, we follow a similar, but more robust, approach where we carefully identify the range of heights that most significantly contribute to He I 10830 Å emission and perform a weighted average over that range (following the approaches of Kowalski et al., 2017; Zhu et al., 2019; McLaughlin et al., 2023; Kerr et al., 2024). The normalised cumulative distribution function of $C_{I}$ was constructed, and the heights at which the bulk of the emission is formed was identified. For our purposes we defined this as being the heights bounding $10\%-95\%$ of the line’s contribution (similar results were obtained for $5\%-95\%$, and $20\%-95\%$). Then, the average plasma properties between those (time-varying) heights was measured, weighted by $C_{I}$, which can be sharply peaked.

Since $C_{I}$ is a function of wavelength we selected the line core as the reference point with which to asses plasma conditions, defined as the wavelength at which $z(\tau_{\lambda}=1)$ was maximised. That is, the wavelength at which the line’s optical depth was largest (this does not necessarily mean the line was optically thick throughout the flare). Doppler motions can shift the wavelength of the line core when they are co-spatial with regions of high orthohelium density.

Temperature, electron density, bulk velocity, and the optical depth in the line core emitting region were all measured as a function of time, and compared to the contrast of the wavelength-integrated intensity of the full line ($\lambda_{0}\pm 1.5$ Å), shown in Figure 7. Each panel shows how one of the properties varies with temperature, with colour representing the contrast of the line (the magnitude of the negative contrasts is generally smaller than when using the BBSO wavelength-integration range). This figure is the aggregate of our whole simulation grid, with each symbol in effect representing a single snapshot from whichever simulation it happens to originate from. Here the intention is not to show a time evolution, which we glean from other figures and analysis (from which we also know that a negative contrast represents the notional ribbon front phase of each simulation). Rather, the intention is to understand what general atmospheric conditions lead to either a negative or positive contrast, by combining the full simulation dataset.

During periods of enhanced absorption the atmosphere is generally cooler and less dense than periods of strong emission, with some overlap between smaller negative and smaller positive contrasts. The, rough, threshold between positive and negative He I 10830 Å contrast is $n_{e}\sim 3.5\times 10^{12}$ cm^-3 and $T\sim 13.5$ kK (which is essentially the same temperature as estimated by Huang et al., 2020, but a larger electron density). Of note is that we find that the He I 10830 Å line can be strongly in emission even if $T<13.5$ kK if the upper chromospheric electron density is sufficiently elevated, which in our simulations means $n_{e}>3\times 10^{13}$ cm^-3. At $T>18$ kK we find only emission.

Opacity in the line core varies over time in the simulations, and over the particular evolution of each flare atmosphere, but generally it increased during the flare such that the optical depth approached or exceeded unity, meaning that optical depth effects play a role in line formation. This is true both during the periods of dimming or enhancement but $\tau>0.5$ only when the line is strongly enhanced, which is intuitive given the larger densities when that is the case.

Finally, we note that periods of dimming are generally associated with a gentle upflow of the line forming region, with $v_{z}\sim[-10,0]$ km s^-1. Downflows are present in some of the simulations, up to $v_{z}=30$ km s^-1.

So, the ribbon front-like He I 10830 Å behaviour is present when the line forming region in the mid-upper chromosphere is still relatively cool, and is undergoing gentle evaporation, while the brighter flare ribbons are associated with a much warmer and denser upper chromosphere.

Kerr et al. (2021) noted the increased population of He I 2s ³S through the chromosphere due to nonthermal collisional ionisation of He, that increases the opacity and produces the dimming. There is also an enhancement of He I 2p ^P level, but during the dimming period the ratio of the upper-to-lower level in the upper chromosphere decreases since He I 2s ³S is preferentially populated. At the time that the line switches to being enhanced this ratio reverses, and the line is driven into emission. This seemingly happens at $T>13.5$ kK and $n_{e}>3.5\times 10^{12}$ cm^-3 (or a cooler plasma but with $n_{e}>>3.5\times 10^{12}$ cm^-3), and is at least partially due to increased collisional ionisation from the lower-to-upper level.

In general the Mg II spectra follow a common evolution through the weak-heating phase and the ramp-up to peak energy injection. Quantitative differences, and the rate of their evolution, in the various spectral line characteristics such as the intensity, depth of central reversals, and other properties (discussed in detail in Section 4.2) arise with varying the injected nonthermal electron beam parameters. Figure 8 shows the evolution of Mg II line in the $\delta=5$, $E_{c}=30$ keV simulation. Appendix A shows the temporal evolution for the other experiments, along with the Mg II 2798 Å subordinate blend

Upon initial energy injection the Mg II k line increases in intensity, and the depth of its central reversal increases. The line core is slightly blueshifted, and the line becomes asymmetric with more intense red peak (k2r) relative to blue peak (k2v). As the energy flux injected increases the Mg II k line intensity similarly increases, and the central reversal becomes shallower. At times the reversal almost fully fills in, particularly close to flare peak, and at other times it effectively merges with the k2v component such that the line appears with a broad blue shoulder. In response to chromospheric condensations the lines become redshifted or exhibit redshifted components alongside mostly stationary components. All the subordinate lines behave similarly to the Mg II k line, though have a tendency to transition to being single-peaked once the weak-heating phase has ended. For some simulations (those with softer nonthermal electron distributions) the subordinate triplet appears single peaked even during the weak-heating phase.

Our quantitative model-data comparison of Mg II ribbon front behaviour follows the framework of Polito et al. (2023a), where we extract the wavelength positions of the k2r, k2v, and k3 components of the Mg II k line, and use those to build quantitative metrics (described in more detail below), which can be compared to the results of the four observed solar flares studied by Polito et al. (2023a). The impacts of IRIS instrumental effects on the analysis that follows was investigated for a range of representative exposure times and cadences. While the main conclusions and trends did not change, the reduced spectral resolution and smearing in exposure time did result in some minor quantitative differences in comparison to the native RH15D spectra. See Appendix B for an overview of the impact of IRIS instrumental effects on the synthetic spectra.

For each Mg II profile we extract several metrics that characterise their response to the flare during the various stages of flare energy injection. These metrics are the same as used by Polito et al. (2023a). They are the depth of the central reversal, $D_{\mathrm{CR}}$, the asymmetry of the k2 peaks, $A_{\mathrm{k2}}$ (where a positive value means more intense k2r versus k2v peak), the separation of the k2 peaks, $S_{\mathrm{k2}}$, and the Doppler shift of the k3 component (i.e. the Doppler shift of the line core), $v_{\mathrm{Dopp,k3}}$:

We find similar results as with He I 10830 Å, which is that the weak-heating phase of simulations with harder nonthermal electron distributions produce Mg II spectra consistent with ribbon front observations. In fact, the same simulations that typify ribbon fronts in He I 10830 Å can be characterised as ribbon fronts in Mg II.

Slight blueshifts of the line core (k3) were present, up to $\sim-(10-12)$ km s^-1, which transition to redshifts by the peak of the strong-heating phase, albeit in a somewhat noisy manner in some simulations (Figure 9, left column). This is due to the presence of multiple components in the line, one slightly blueshifted or stationary and one redshifted. The algorithm to identify k3 can sometimes jump between these components. Observations generally are redshifted in the main ribbon, but this often manifests as an asymmetric red-wing not always as a shifted k3. These Doppler shifts are consistent with the observational analysis of ribbon front Polito et al. (2023a) in which the distribution of k3 Doppler shifts peaked at $-10$ km s^-1 (though some of those observed profiles could exhibit even larger blueshifts up to $-20$ km s^-1). The magnitude of $V_{\mathrm{Dopp}}$ did not seem to depend strongly on $E_{c}$ or $\delta$, though a faster evolution back towards rest was associated with softer nonthermal distributions.

Red peak (k2r) asymmetries were present during the weak-heating phase, though were only strong for a brief time (Figure 10, left column). The harder nonthermal electron beams only produced mildly asymmetric profiles, with values consistent with the bulk of the observed distribution of $A_{\mathrm{k2}}\sim 0-0.2$. The tail of the observed distribution of asymmetries with larger values of $A_{\mathrm{k2}}$ is seemingly suggestive of softer nonthermal electron beams. Most of the simulations actually began exhibiting blue peak asymmetries during the weak-heating phase. During the ramp-up to peak energy deposition $A_{\mathrm{k2}}$ could be either blue or red dominant.

The k3 Doppler shift and the peak asymmetry are perhaps not as ‘clean’ as He I 10830 Å, since the Mg II spectra do not persist with ribbon front-like characteristics for the entirety of the weak-heating phase, beginning their transition to what might be considered more consistent with regular bright ribbon characteristics earlier. However, the k2 peak separation and the depth of the central reversal may offer a better diagnostic of the lifetime of any weak-heating phase.

For the majority of the weak-heating phase the k2 peak separation increases from the pre-flare value, and remains fairly constant in the harder nonthermal electron beam simulations, with values $S_{\mathrm{k2}}\sim 35-40$ km s^-1 (Figure 10, right column). Their temporal evolution tracks the lifetime of the He I 10830 Å ribbon front-like behaviours pretty well, with the softer nonthermal electron beam simulations more rapidly transitioning to a smaller k2 peak separation. The same simulations that persist with enhanced absorption of He I 10830 Å until the start of the ramp-up of energy injection have a larger k2 peak separation throughout the weak-heating phase. The observations of Polito et al. (2023a) suggest a broader range of values of $S_{\mathrm{k2}}$ than present in our simulations.

The central reversal deepens in every simulation at the onset of energy deposition, but in the case of softer nonthermal electron distributions the reversal switches to being shallower than the pre-flare quite rapidly. A trend of deepening reversal depth is present in the harder nonthermal electron distributions, in which $D_{\mathrm{CR}}$ only reduces in magnitude once the energy flux injected begins to increase. During the latter half of the simulations the profiles have very shallow central reversals and occasionally become single peaked. We might expect only single peaked profiles during the bright ribbon phase, but these have proven tricky to produce in RHD simulations, requiring large electron densities (e.g. Rubio da Costa & Kleint, 2017; Zhu et al., 2019). It is possible that a more aggressive ramp-up time, and larger energy flux following the weak-heating phase could lead to those conditions but here we are primarily interested in the ribbon front period.

Of the range of ribbon front-like behaviours, the increase of intensity accompanied by increased depth of the central reversal best typifies the duration of the weak-heating phase.

As noted in the previous section, the profiles as observed with IRIS could appear different due to instrumental effects. We repeated the analysis of Mg II line characteristics for the profiles converted to IRIS quality. The trends identified do not change but certainly some of the finer scale temporal differences are not seen, and some of the noisier behaviour is reduced since multiple components (redshifted plus stationary) are not present as often. The magnitude of the Doppler shift of k3 is largely unaffected. There are some quantitative differences in the depth of the reversal since the profiles appear artificially shallower at IRIS resolution. Similarly the profiles may appear single peaked more often. The only notable difference in timing is that the $\delta=5$, $E_{c}=20$ keV simulation transitions from deeper-to-shallower central reversal sooner. Peak separation only differs by a few km s^-1. Red peak asymmetries are accentuated somewhat but the temporal trend is unchanged. Summing over spectral pixels ($2\times 2$ binning) does introduce short lived local maxima and minima.

The obvious question is, what do these ribbon front Mg II profiles tell us about the evolution of the plasma, and why do we need a period of weak energy injection by hard nonthermal electron distributions to produce those conditions? Using a similar approach as in Section 3.2, the plasma properties averaged over the formation height of k2v, k2r and k3 were obtained and contrasted during the different stages of energy deposition.

In this section we follow closely the foundational investigations of Mg II profile characteristics by Leenaarts et al. (2013a), Leenaarts et al. (2013b), and Pereira et al. (2013). Those authors studied a quiet Sun 3D RMHD simulation, and cautioned that their results are indicative primarily of those conditions and that more active scenarios could differ significantly. For that reason, where appropriate, we confirm any inferences based on their conclusions by applying elements of their analysis to our flare simulations. An obvious caveat is that their conclusions were based on hundreds of thousands of spectra, whereas we have 4515 (15 1D RHD flare simulations each with 301 snapshots, representing 1s cadence).

Conspicuously absent from our exploration of the origin of the various ribbon front characteristics is the Mg II line widths which can broaden to an even greater degree in ribbon fronts than in bright ribbon segments. This is because our flare models are still unable to reproduce the observed degree of broadening (see e.g. Kerr et al., 2024), indicating that we are missing some key physics.