Draft versionMarch 7, 2018Preprint typeset using LATEX style emulateapj v. 12/16/11

SPECTROSCOPIC INVERSIONS OF THE Ca ii 8542 Å LINE IN A C-CLASS SOLAR FLARE

D. Kuridze1,5, V. Henriques1,2, M. Mathioudakis1, J. Koza3, T. V. Zaqarashvili4,5,6, J. Rybak, A. Hanslmeier4 and F. P. Keenan1

1Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, UK; e-mail: d.kuridze@qub.ac.uk2Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, NO-0315 Oslo, Norway

3Astronomical Institute, Slovak Academy of Sciences, 059 60 Tatranska Lomnica, Slovakia4IGAM, Institute of Physics, University of Graz, Universitatsplatz 5, 8010 Graz, Austria

5Abastumani Astrophysical Observatory at Ilia State University, 3/5 Cholokashvili avenue, 0162 Tbilisi, Georgia and6Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria

(Dated: received / accepted)Draft version March 7, 2018

ABSTRACTWe study the C8.4 class solar flare SOL2016-05-14T11:34 UT using high-resolution spectral imaging in theCa ii 8542 Å line obtained with the CRISP imaging spectropolarimeter on the Swedish 1-m Solar Telescope.Spectroscopic inversions of the Ca ii 8542 Å line using the non-LTE code NICOLE are used to investigatethe evolution of the temperature and velocity structure in the flare chromosphere. A comparison of the tem-perature stratification in flaring and non-flaring areas reveals strong footpoint heating during the flare peakin the lower atmosphere. The temperature of the flaring footpoints between continuum optical depth at500 nm, log τ500 ≈ −2.5 and − 3.5 is ∼ 5 − 6.5 kK, close to the flare peak, reducing gradually to ∼ 5 kK.The temperature in the middle and upper chromosphere, between log τ500 ≈ −3.5 and − 5.5, is estimated to be∼ 6.5 − 20 kK, decreasing to pre-flare temperatures, ∼ 5 − 10 kK, after approximately 15 minutes. However,the temperature stratification of the non-flaring areas is unchanged. The inverted velocity fields show that theflaring chromosphere is dominated by weak downflowing condensations at the Ca ii 8542 Å formation height.

1. INTRODUCTION

It is now widely accepted that the chromosphere is a keyto our understanding of solar flares due to the large amountof radiative losses that originate in it (Fletcher et al. 2011).Chromospheric radiation can provide vital diagnostics for thestructure and dynamics of plasma parameters, such as tem-perature, velocity, density, pressure and magnetic field in theflaring atmosphere.

The method of choice for studies of the one-dimensionalvertical stratification of solar and stellar atmospheres has beenthe use of semi-empirical models that attempt to reproduce theobserved profiles in LTE or non-LTE radiative transfer (e.g.see the review by Mauas 2007). Such an approach has beensuccessful for the quiet-Sun (QS) atmosphere, for which static1D models, developed under an assumption of hydrostaticequilibrium, reproduce chromospheric spectral lines and con-tinua (Gingerich et al. 1971; Vernazza et al. 1981; Fontenlaet al. 1990, 1991, 1993, 2006, 2009; Rutten & Uitenbroek2012).

The first set of static semi-empirical models of a flaringphotosphere and chromosphere was developed by Machado& Linsky (1975). These authors modelled the wings of theCa iiH&K lines and concluded that the temperature minimumregion in flares is both hotter and formed deeper in the atmo-sphere than the QS models. Machado et al. (1980) developedmodels for a bright and a faint flare, that reproduce lines andcontinua of H i, Si i, C i, Ca ii, and Mg ii, and show a sub-stantial temperature enhancement from the photosphere up tothe transition region. Semi-empirical models of a white-lightflare also show that flare related perturbations can affect thewing and continuum formation heights, as well as the con-tinuum emission originating in the photosphere (Mauas 1990;Mauas et al. 1990; Mauas 1993).

Gan & Fang (1987) and Gan et al. (1993) used Hα line pro-files to construct semi-empirical models for two flares which

showed evidence for chromospheric condensations, whichcan reproduce the well-observed Hα line profile asymmetriesin flares. Moreover, Gan & Mauas (1994) found that con-densations can increase the back-warming of the atmosphere,leading to the heating of the photosphere and enhancementof the continuum emission. The evolution of chromosphericvelocity fields during solar flares was also studied by Falchi& Mauas (2002) and Berlicki et al. (2005). Falchi & Mauas(2002) constructed 5 semi-empirical models for different flareevolution times, which reproduce the profiles of the Hδ, Ca iiK and Si i 3905 Å lines. Velocity fields were included to re-produce the asymmetric line profiles. Berlicki et al. (2008)performed semi-empirical modeling of the solar flaring at-mosphere above sunspots using NLTE radiative transfer tech-niques. They found that the flaring layers (loops) are domi-nated by chromospheric evaporation leading to a significantincrease of gas pressure. Flare models obtained with forwardradiative hydrodynamic codes such as RADYN (Carlsson &Stein 1997) can also reproduce the observed asymmetric lineprofiles and temperature increase in the lower solar atmo-sphere (Kuridze et al. 2015, 2016).

A powerful way to construct atmospheric models with asemi-empirical approach, is to fit the observed Stokes pro-files using inversion algorithms (de la Cruz Rodrıguez & vanNoort 2016). Through such inversions, the ionisation equilib-rium, statistical equilibrium and radiative transfer equationsare solved numerically to synthesize the Stokes profiles un-der a set of pre-defined initial atmospheric conditions. Dif-ferences between the observed and synthetic profiles are usedto modify, at a height usually determined by a response func-tion, an initial model atmosphere that is used to reproduce theobserved spectral signatures.

Several inversions have been performed in the Ca ii H lineusing the LTE Stokes Inversion based on Response functionscode (SIR, Ruiz Cobo & del Toro Iniesta 1992). A first-order

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NLTE correction was applied to obtain the temperature strati-fication of the QS and active region chromosphere (Beck et al.2013, 2015). However, the development of NLTE radiativetransfer codes, such as HAZEL (Asensio Ramos et al. 2008),HELIX+ (Lagg et al. 2009) and NICOLE (Socas-Navarroet al. 2015) combined with the increased computational poweravailable, also make NLTE inversions possible (see the reviewby de la Cruz Rodrıguez & van Noort (2016)).

The Ca ii infrared (IR) triplet line at 8542 Å is well suitedfor the development of chromospheric models due to its sen-sitivity to physical parameters, including magnetic field, inthe solar photosphere and chromosphere (Cauzzi et al. 2008;Pietarila et al. 2007; Quintero Noda et al. 2016). Further-more, the optimization of NICOLE for Ca ii 8542 Å allowsthe use of this feature for the computation of semi-empiricalatmospheric models. For more details about the spectropo-larimetric capabilities of Ca ii 8542 Å the reader is referred toQuintero Noda et al. (2016).

Inversions with NICOLE have been successfully performedfor spectro-polarimetric Ca ii 8542 Å observations of umbralflashes in sunspots (de la Cruz Rodrıguez et al. 2013), andgranular-sized magnetic elements (magnetic bubbles) in anactive region (de la Cruz Rodrıguez et al. 2015a). In thispaper we use NICOLE to invert high-resolution Ca ii 8542Å spectral imaging observations to construct models for thelower atmosphere of a solar flare. Multiple inversions wereperformed for the observed region covering flare ribbons andfor non-flaring areas at different times during the event. Fromthe constructed models we investigate the structure, spatialand temporal evolutions of basic physical parameters in theupper photosphere and chromosphere during the flare.

2. OBSERVATIONS AND DATA REDUCTION

The observations were undertaken between 11:38 and 12:49UT on 2016 May 14 close to the West limb (877′′, −66′′),near the equator with the CRisp Imaging SpectroPolarimeter(CRISP; Scharmer 2006; Scharmer et al. 2008) instrument,mounted on the Swedish 1-m Solar Telescope (SST; Scharmeret al. 2003a) on La Palma. Adaptive optics were used through-out the observations, consisting of a tip-tilt mirror and a 85-electrode deformable mirror setup that is an upgrade of thesystem described in Scharmer et al. (2003b). The observa-tions comprised of spectral imaging in the Hα 6563 Å andCa ii 8542 Å lines. All data were reconstructed with Multi-Object Multi-Frame Blind Deconvolution (MOMFBD; vanNoort et al. 2005). The CRISP instrument includes three dif-ferent cameras. One camera acquires wideband (WB) imagesdirectly from the prefilter and two narrowband (NB) camerasplaced after a 50/50 polarizing beam splitter acquire narrow-band (transmitted and reflected) horizontal and vertical polar-ization components, each combination of camera, wavelengthand component being an object for reconstruction (for setupdetails see e.g. de la Cruz Rodrıguez et al. 2015b). The WBchannel provides frames for every time-step, synchronouslywith the other cameras, and can be used as an alignmentreference. The images, reconstructed from the narrowbandwavelengths, are aligned at the smallest scales by using themethod described by Henriques (2013). This employs cross-correlation between auxiliary wideband channels, obtainedfrom an extended MOMFBD scheme, to account for differentresidual small-scale seeing distortions. We applied the CRISPdata reduction pipeline as described in de la Cruz Rodrıguezet al. (2015b) which includes small-scale seeing compensa-

tion as in Henriques (2012). Our spatial sampling was 0′′.057pixel−1 and the spatial resolution was close to the diffractionlimit of the telescope for many images in the time-series overthe 41 × 41 Mm2 field-of-view (FOV). For the Hα line scanwe observed in 15 positions symmetrically sampled from theline core in 0.2 Å steps. The Ca ii 8542 Å scan consistedof 25 line positions ranging from −1.2 Å to + 1.2 Å from theline core with 0.1 Å steps, plus 1 position at −1.5 Å. A fullspectral scan for both lines had a total acquisition time of 12s, which is the temporal cadence of the time-series. However,we note that the present paper includes only the analysis ofthe Ca ii 8542 Å data which had a duration of 7 seconds perscan. The transmission FWHM for Ca ii 8542 Å is 107.3 mÅwith a pre-filter FWHM of 9.3 Å (de la Cruz Rodrıguez et al.2015b). A two-ribbon C8.4 flare was observed in active re-gion NOAA 12543 during our observations. Throughout theanalysis we made use of CRISPEX (Vissers & Rouppe vander Voort 2012), a versatile widget-based tool for effectiveviewing and exploration of multi-dimensional imaging spec-troscopy data.

Figure 1 shows a sample of the flare images in the Ca ii 8542Å line core and wing positions. Our observations commenced4 minutes after the main flare peak (∼11:34 UT). Light curvesgenerated from the region marked with the orange box in Fig-ure 1 show the post-peak evolution of the emission in the linecore and wings (right panel of Figure 1). Although we missedthe rise phase and flare peak, at 11:38 UT two bright ribbonsassociated with post-flare emission are clearly detected withgood spatial and temporal coverage.

3. INVERSIONS

We used the NICOLE inversion algorithm (Socas-Navarroet al. 2015) which has been parallelized to solve multi-level,NLTE radiative transfer problems (Socas-Navarro & TrujilloBueno 1997). This code iteratively perturbs physical param-eters such as temperature, line-of-sight (LOS) velocity, mag-netic field and microturbulence of an initial guess model at-mosphere to find the best match with the observations (Socas-Navarro et al. 2000). The output stratification of the electronand gas pressures, as well as the densities, are computed fromthe equation-of-state using the temperature stratification andthe upper boundary condition for the electron pressure underthe assumption of hydrostatic equilibrium.

NICOLE includes a five bound level plus continuum Ca iimodel atom (Leenaarts et al. 2009) with complete frequencyredistribution, which is applicable for lines such as Ca ii 8542Å (Uitenbroek 1989; Quintero Noda et al. 2016; Wedemeyer-Bohm & Carlsson 2011). The synthetic spectra were calcu-lated for a wavelength grid of 113 datapoints in 0.025 Å steps,4 times denser than the CRISP dataset. Stratification of the

Table 1Number of nodes and input atmosphere models used during each cycle (Cy)

of the inversion.

Physical parameter Cy 1 Cy 2 Cy 3Temperature 4 nodes 7 nodes 7 nodesLOS Velocity 1 node 5 nodes 5 nodes

Microturbulence 1 node 1 node 1 nodeMacroturbulence none none noneInput atmosphere FAL-C model from Cy 1 model from Cy 2

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Figure 1. The Ca ii 8542 Å line wing and core images obtained with the CRISP instrument on the SST at 11:38:20 UT on 2016 May 14. The orange boxindicates the flaring region analysed in this paper. The temporal evolution of the region averaged over the area marked with the yellow box is presented in the farright panel.

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Figure 2. The top row shows the images at 11:38 UT (4 minutes after the flare peak) and the bottom row images at 11:45 UT. SST images of the flaring region inthe Ca ii 8542 Å line core are shown in the left panels. NICOLE outputs showing the temperature and the LOS velocity maps in the interval log τ ∼ −3.5 and − 5.5are provided in the middle and right panels, respectively. Blue contours show the area analysed in this paper which has intensity levels greater than 30% of theintensity maximum. ’FL’, ’FF’, ’QS’ mark the selected pixels at the flare loop, flare footpoint, and quiet Sun, respectively discussed in the text in more detail.The red and blue colors in the dopplerograms represent positive Doppler velocities (downflows) and negative Doppler velocities (upflows), respectively. Thewhite dotted line indicates the location where vertical cut of the atmosphere is made for detailed analyses.

atmospheric parameters obtained by the inversions are givenas a function of the logarithm of the optical depth-scale at500 nm (hereafter log τ). The response function of the Ca ii8542 Å line is expanded to log τ ∼ 0 and − 5.5 (see QuinteroNoda et al. 2016, for details). As our Ca ii 8542 Å line scan is−1.5 Å to + 1.2 Å from line core, the analysis of the responsefunctions show that it provides diagnostics in the layers be-tween log τ ∼ −1 and − 5.5 (see Figure 6 in Quintero Nodaet al. 2016).

To improve convergence, the inversions were performed inthree cycles, expanding on the suggestion of Ruiz Cobo &del Toro Iniesta (1992) and as implemented in de la CruzRodrıguez et al. (2012). In the first cycle and for the firstscan, the inversions were performed with 4 nodes in temper-ature and 1 in LOS velocity, with the initial guess model be-ing the FAL-C atmosphere (Fontenla et al. 1993). The con-vergence of the models obtained from the first cycle was im-proved by applying horizontal interpolation to recompute the

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Figure 3. Observed (black) and best-fit synthetic (red dotted) Ca ii 8542 Å line profiles together with temperature and velocity stratifications for the three selectedpixels indicated as FL, FF QS in Figure 2.

inverted parameters of the pixels with low quality of fits. Asecond cycle was then performed with an increased number ofnodes (7 for temperature and 4 for LOS velocity), and the in-terpolated initial guess model constructed from the first cycle.The synthetic profiles obtained from the second cycle tend tohave deeper absorptions than the observations, even for thequiet Sun. The comparison between the FTS disk center so-lar atlas profile (Neckel 1999), convolved with a model theCRISP transmission profile with FWHM=107.3 mÅ providedby de la Cruz Rodrguez (2015b), and the average SST/CRISPflat-field disk-center profile does not show an adequate co-incidence of resulting profiles. This indicated a broader orasymmetric instrumental profiles than the respective modelused in NICOLE (the synthetic profiles are convolved withthe instrumental profile before comparison with the observa-tions and before the final output). Therefore, in the third cy-cle we convolved the instrumental profile with a Gaussian ofFWHM=141 mÅ and performed an inversion with the samenumber of nodes and an initial guess model constructed fromthe second cycle. This led to a better match between the ob-served and synthetic spectra. Table 1 summarizes the numberof nodes and initial temperature models used in the three cy-cles. We also convolved the atlas profile with an asymmetricLorentzian transmission profile model for the CRISP trans-mission profile with FWHM = 0.080 Å. This also providesrequired similarity between the atlas and the observed flat-

field profiles suggesting that indeed the transmission profilecould be asymmetric. We run the inversions with the asym-metric Lorentzian profile and the resulted atmospheres werethe same as obtained with the CRISP instrumental profile con-volved with a symmetric Gaussian with FWHM = 141 mÅ.

As our observations do not include full Stokes imagingspectroscopic data, we run NICOLE only for Stokes I pro-files. Therefore, in both cycles, the magnetic field vector andthe weights for other Stokes parameters were set to zero. Weinverted a 200 × 200 pixel2 area (8.2×8.2 Mm2) covering theflare ribbons as well as some non-flaring regions (see left pan-els of Figure 1). Although our time-series comprises of 346spectral scans, we only choose the best scans in terms of spa-tial resolution. This limits the total number of scans to 35,with a cadence of approximately 1 minute in the time interval11:38 to 12:09 UT.

4. ANALYSIS AND RESULTS

Figure 2 presents a Ca ii 8542 Å line core image of theregion selected for inversions (marked with the orange boxin Figure 1). The NICOLE output showing the temperatureand the LOS velocity maps are also presented. Tempera-ture and velocity maps are integrated and averaged betweenlog τ ≈ −3.5 and − 5.5, corresponding to middle and upperchromospheric layers, respectively. The top row shows theimages close to the flare peak (∼11:38 UT) and the bottomimages 7 minutes later. A temperature map of the inverted re-

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Figure 4. The temporal evolution of the temperature and velocity stratifications for the flaring and non-flaring pixels marked with QS and FF in Figure 2,respectively.

gion close to flare peak shows temperature enhancements forthe two flare ribbons. The LOS velocity map of the same re-gion in the top-right panel of Figure 2 reveals downflows atthe flare ribbons, while the temperature map in the bottom-middle panel indicates that the size of the flare ribbons andthe heated areas have decreased dramatically 7 minutes later.

Figure 3 shows the line profiles and temperature/velocitystratifications of 3 pixels indicated as FL, FF, QS in Figure 2,with the pixels in different parts of the region under investi-gation. The best-fit synthetic profiles obtained from the in-version at 11:38:20 UT are also shown. There are basically 3different shapes of line profile over the selected region duringthe flare: absorption, emission and those with central reversal.In the non-flaring areas (QS), Ca ii 8542 Å shows the well-known absorption line profile. The line profiles of the flaringloops (FL) connecting the flare footpoints (ribbons) have cen-tral reversals, whereas profiles of the flare footpoints (FF) arein full emission without a central reversal. Figure 3 shows thatthe observed spectra are generally reproduced by the syntheticbest-fit spectra. The QS temperature is close to the FAL-C temperature profile, whereas the FL has a higher chromo-spheric temperature at log τ ∼ −2.5 and − 5.5 (middle panelsof Figure 3), with the flare footpoints showing the largest tem-peratures.

In Figure 4 we present the temporal evolution ofthe temperature and velocity stratifications for the flar-ing and non-flaring pixels. The temperature of the foot-points is enhanced across the chromosphere between op-tical depths of log τ ∼ −2.5 and − 5.5. As time pro-

gresses, the temperature in the lower chromosphere be-tween log τ ∼ −2.5 and − 3.5 decreases gradually fromT ∼ 5 − 6.5 kK to T ∼ 5 kK. In the middle and upper chromo-sphere, between log τ ∼ −3.5 and − 5.5, the temperature de-crease from T ∼ 6.5 − 20 kK to T ∼ 5 − 10 kK during about15 minutes (top left panel of Figure 4). The velocity fieldfor the flaring pixel is dominated by weak upflows which de-crease gradually with time, while the temperature and velocityof the non-flaring areas are lower and unchanged in the chro-mosphere at log τ ∼ −1 and − 5.5 (right panels of Figure 4).

In Figure 5 we show the evolution of the temperature strat-ifications using density maps which have been produced withthe superimposition of individual pixels from the flaring re-gion marked with blue contours in Figure 2. It must benoted that the stratification of the pixels with low quality offit, such as non-physically low or high temperature plateausor dips and peaks, were ignored and are not included in thedensity plots. Our density maps confirm that the most in-tensively heated layers are in the middle and upper chromo-sphere at optical depths of log τ ∼ −3.5 and − 5.5, reachingtemperature between ∼6.5 - 20 kK. The temperature stratifi-cation of the layers below log τ ∼ −2.5 remains unchangedduring the flare and is consistent with the QS FALC modelused as the initial atmosphere for the inversions (Figure 5).In the top-left panel of Figure 6 we show a vertical cut ofthe net flare temperature enhancement close to the flare peak(∼11:38 UT), where an average temperature stratification ob-tained from quiet, non-flaring areas has been subtracted. Thetwo bright regions at ∼2 and 7.5 Mm show the temperatureenhancements of the flare ribbons.

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Figure 5. Density maps showing the evolution of the temperature stratification during the flare. Each map is produced by superimposing the stratification ofaround 2000 individual models, selected for quality of fit at each time. The selected region is marked with blue contours in Figure 2. The blue dashed line depictsthe FALC model, used as the initial atmosphere for the inversions.

As noted in Section 3, NICOLE calculates the basic ther-modynamical parameters that define the internal energy ofthe system, such as the density and electron pressure, us-ing the equation-of-state, temperature stratification and upperboundary condition under the assumption of hydrostatic equi-librium. To estimate the energy content of the flaring chromo-sphere, we compute the internal energy e using the relation-ship:

e =1

γ − 1pρ, (1)

where p and ρ are the gas pressure and density, respectively,and γ=5/3 is the ratio of specific heats (Aschwanden 2004;Beck et al. 2013). The top right panel of Figure 6 shows avertical cut of the excess energy density per unit mass closeto flare maximum at 11:38 UT, which is the internal energy,e(x, y, τ), computed for each pixel minus an average internalenergy, eq(x, y, τ) estimated from quiet, non-flaring areas. Athree-dimensional (3D) rendering of this excess energy den-sity for an inner part of the inverted datacube is also shown inthe bottom left panel of Figure 6. It illustrates that the energydensity enhancement coincides with the locations of flare rib-bons where the temperature enhancements are detected. Theratio of total internal energy of this part of the inverted surface(S ≈ 5.3 × 6.7 Mm2) over the internal energy for an equally-sized surface of the QS as a function of optical depth is pre-sented in the bottom middle panel of Figure 6. This showsthat the energy of the flaring region is increased in the rangeof optical depths log τ ∼ −2.5 − 5.5 compared to the internalenergy of the QS. The ratio has a peak at log τ ≈ −5 wherethe internal energy of the inverted flare region is increased bya factor of cose to 3 over the QS. As time progresses, the ra-tio decreases gradually to ∼1 after about 15 minutes, meaningthat the atmosphere (energetically speaking) has reached QSlevels. The total energy of the chromospheric volume shownon the bottom left panel of Figure 6 (integrated over the range

of optical depth log τ ≈ −3 − 5.5) is estimated to be ∼1024

erg close to the flare peak, decreasing linearly to a QS energylevel of ∼ 6 × 1023 erg after approximately 15 minutes (bot-tom right panel of Figure 6). We note that due to the highviewing angle of the observed region the vertical extend ofthe model atmospheres shown and described in Figure 6 doesnot correspond to the true geometrical height of the lowersolar atmosphere. NICOLE derives the geometrical heightfrom optical depth height scale and the temperature plus den-sity/pressure stratifications and the same optical depth τ doesnot refer to the layers at the same geometrical height in thedifferent models. Therefore, temperature/energy excess de-rived through the models does not show accurately the energydistribution as a function of geometrical height, but it does soas a function of optical depth.

5. DISCUSSION AND CONCLUSIONS

We have presented spectroscopic observations of the Caii 8542 Å line in a C8.4-class flare. The line profiles of theflare ribbons are in total emission without a central reversal,whereas those of flaring loops, which connect the flare foot-points, show central reversals (Figure 3). In the quiet Sunthe line is in absorption (Figure 3). The analysis of syntheticchromospheric spectral line profiles produced with radiativehydrodynamic models have shown that the changes in tem-perature, radiation field and population density of the energystates make the line profile revert from absorption into emis-sion with or without a central reversal (Kuridze et al. 2015,2016). In a recent investigation, Kuridze et al. (2016) studiedthe flare profiles of the Na i D1 line which also forms in theoptically thick chromosphere. The heating of the lower so-lar atmosphere by the non-thermal electron beam makes theNa i D1 line profiles go into full emission. However, whenthe beam heating stops, the profiles develop a central rever-sal at the line cores. Unfortunately, as there is no energy fluxfrom electrons in NICOLE, it cannot be used to investigate

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Figure 6. Top left: A vertical cut of the temperature stratification with the quiet, non-flaring temperature subtracted. The maps are produced along the locationsindicated by the white dotted line in Figure 2. Top right: The vertical cut of the excess energy density per unit mass, which is the internal energy e(x, y, τ)computed for each pixel, minus an average internal energy eq(x, y, τ) estimated from quiet, non-flaring areas. Bottom left: 3D rendering of the excess energydensity produced for an inner part (only S ≈ 5.3 × 6.7 Mm2) of the inverted datacube. The maps have been smoothed over 10 pixels (∼400 km) along the x-axis.Bottom middle: evolution of the ratio of the area-integrated internal energy for the inverted region shown on the bottom left panel over an equally-sized area ofQS. Bottom right: evolution of the total energy (dashed line) integrated over an inverted region presented on the bottom left panel of Figure 6. The total energyof the same-size QS volume is overplotted as dotted line.

how the emission and centrally reversed profiles of Ca ii 8542Å line are formed. However, the analysis of the syntheticline profiles from the RADYN simulations shows that for astrong electron beam heating (model F11) the Ca ii 8542 Åline profiles are in full emission, but develop a central rever-sal after beam heating at the relaxation phase of the simula-tion (Kuridze et al. 2015). For a weak flare run (model F9),the synthetized Ca ii 8542 Å profile exhibits a shallow reversalduring the beam heating phase that deepens during the relax-ation phase.

The comparison of synthetic line profiles and their temper-ature stratifications from different models obtained from theinversions presented here indicates that the depth of the cen-tral reversal depends on the temperature at the core formationheight (∼ −5.5 < log τ < −3.5), i.e. a higher temperature pro-duces a shallower central reversal (Figure 3). This could ex-plain why flare ribbons, which are believed to be the primarysite of non-thermal energy deposition and intense heating,have profiles in full emission, whereas flaring loops, whichare secondary products of the flare and hence less heated ar-eas, have central reversals.

We constructed semi-empirical models of the flaring atmo-sphere using the spectral inversion NLTE code NICOLE toinvestigate its structure and evolution. Models were generatedat 35 different times during the flare, starting at 4 minutes af-ter the peak. The construction of the models is based on acomparison between observed and synthetic spectra. Closeto the line core, where the self-reversal is formed, we find a

small discrepancy between the synthetic and observed spectraof the flare ribbons (Figure 3). The synthetic profiles have asmall absorption in the core, in contrast to the observed pro-files which are in full emission (bottom left panel of Figure 3).This influences the narrow layer of core formation height andhence does not have strong effect on the overall output model.A possible reason of the observed discrepancy could be thelower ionization degree of Ca ii in the flaring atmosphere com-pared to the ionization used in NICOLE (Wittmann 1974).Furthermore, the models constructed close to the flare peakare characterized by high quality of fit and provide a bettermatch with the observed spectra. This is because, as timefrom flare maximum progresses, the well-defined shapes ofemission and centrally-reversed line profiles become flatterand feature more irregular shapes, which causes NICOLEto encounter difficulties finding atmospheres that reliably fitsuch profiles.

Our analysis of the constructed model shows that the mostintensively heated layers in the flaring lower atmosphereare the middle and upper chromosphere at optical depths oflog τ ∼ −3.5 and − 5.5, respectively, with temperatures be-tween ∼6.5 - 20 kK. The temperatures of these layers aredecreasing down to typical QS values (∼5 - 10 kK) afterabout 15 minutes (Figure 5). In the photosphere, belowlog τ ≈ −2.5, there is no significant difference between quies-cence and flaring temperature stratifications (Figure 5). Thisagrees with some of the previous results (e.g. Falchi & Mauas(2002)), which show that during the flare the atmosphere isunchanged below ∼600 km. However, it must be noted that as

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the observations presented in this work started 4 minutes afterthe flare peak, it is possible that the temperature in the deeperlayers of the atmosphere was affected during the impulsivephase.

The velocity field indicates that the observed field-of-view(FOV) is dominated by weak downflows at optical depths oflog τ ∼ −1 and − 5.5 associated with the post-flare chromo-spheric condensations (Figures 2 and 3). Centrally-reversedCa ii 8542 Å profiles show excess emission in the blue wing(blue asymmetry) with a red-shifted line center (middle leftpanel of Figure 3). Similar to blue asymmetries observed inHα, Na i D1 and Mg ii flaring line profiles (Abbett & Haw-ley 1999; Kuridze et al. 2015, 2016; Kerr et al. 2016), theasymmetry found in Ca ii 8542 Å seems to be related to thevelocity gradients associated with the chromospheric conden-sations. The core of the Ca ii 8542 Å profile presented inthe left middle panel of Figure 3 is red-shifted owing to thedownflows at the height of core formation (middle right panelof Figure 3). Velocity decreases downward toward the wingformation regions, producing a positive velocity gradient withrespect to the height inward. This gradient can modify theoptical depth of the atmosphere in such a way that higher-lying (core) atoms absorb photons with longer wavelengths(red wing photons), and the blue asymmetry in the centrally-reversed peak is formed. We note that semi-empirical modelsof the flaring atmosphere above sunspots Berlicki et al. (2008)indicate that at the early phase of the flare the flaring layers(loops) are dominated by chromospheric upwlows (evapora-tions) rather than downflows as detected in our study. Thisdifference may be due to the difference in phases of the flaresas we detect the downflows in the late phase (4 minutes afterthe flare peak).

Using the gas density and pressure stratification obtainedfrom NICOLE, under the assumption of hydrostatic equilib-rium, we investigated the evolution of the total internal en-ergy of the lower solar atmosphere covering the Ca ii 8542Å formation height. Our analysis shows that the total en-ergy of the chromosphere close to the flare maximum (∼11:38UT) is significantly increased in the range of optical depthslog τ ∼ −3.5 − 5.5 compared to the internal energy of theQS (Figure 6). A maximum enhancement was detected atlog τ ≈ −5 where the total internal energy, integrated over aselected area of the flare, is a factor of 3 greater than the inte-gral over the same area of a QS region. This internal energychanges reduces to the relaxed, QS state, after approximately15 minutes. The total energy of the inverted box shown onthe left panel of Figure 6 is estimated to be ∼1024 erg close tothe flare peak, and decreases linearly to the QS energy level∼ 6 × 1023 erg after 15 minutes (bottom right panel of Fig-ure 6). We note that hydrostatic equilibrium may not be avalid assumption for accurate estimations of the thermody-namical parameters, and hence the energy for a highly dynam-ical process such as a solar flare. However, we emphasise thatmodern inversion algorithms currently only use the assump-tion of hydrostatic equilibrium to obtain pressures and densitystratifications and we believe that quantities such as the evo-lution of the energy ratio with time should be unaffected bythis approximation.

To our knowledge, we have presented the first spectroscopicinversions, in NLTE, of the solar chromospheric line (Ca ii8542 Å) to produce semi-empirical models of the flaring at-mosphere. The temperature stratification obtained from theinversion are in good agreement with other semi-empirical

NLTE flare models constructed without inversion codes, andwith atmospheres obtained with forward modeling using ra-diative radiative hydrodynamic simulations (Machado et al.1980; Falchi & Mauas 2002; Allred et al. 2005; Kuridze et al.2015; Rubio da Costa et al. 2016). This suggests that NLTEinversions can be reliably applied to the flaring chromosphere.

The research leading to these results has received fund-ing from the European Communitys Seventh Framework Pro-gramme (FP7/20072013) under grant agreement No. 606862(F-CHROMA). The Swedish 1-m Solar Telescope is operatedon the island of La Palma by the Institute for Solar Physics(ISP) of Stockholm University at the Spanish Observatoriodel Roque de los Muchachos of the Instituto de Astrofısicade Canarias. The SST observations were taken within theTransnational Access and Service Programme: High Resolu-tion Solar Physics Network (EU-7FP 312495 SOLARNET).This research has made use of NASAs Astrophysics Data Sys-tem. This project made use of the Darwin Supercomputerof the University of Cambridge High Performance Comput-ing Service (http:// www.hpc.cam.ac.uk/ ), provided by DellInc. using Strategic Research Infrastructure Funding fromthe Higher Education Funding Council for England and fund-ing from the Science and Technology Facilities Council. Theauthors benefited from the excellent technical support of theSST staff, in particular from the SST astronomer Pit Sutterlin.This work was supported by the Science Grant Agency projectVEGA 2/0004/16 (Slovakia) and by the Slovak Research andDevelopment Agency under the contract No. SK-AT-2015-0022. This article was created by the realization of the projectITMS No. 26220120029, based on the supporting operationalResearch and development program financed from the Euro-pean Regional Development Fund. A.H. thank the AustrianFWF (project P 27765) for support. The work of T.V.Z. wassupported by by the Austrian Fonds zur Forderung der wis-senschaftlichen Forschung (FWF) project P 28764-N27 andby the Shota Rustaveli National Science Foundation projectDI-2016-17.

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