Spectroscopic Inversions of the Ca II 8542 Line in a C-class SolarFlare

Kuridze, D., Mathioudakis, M., de Jorge Henriques, V. M., Kozak, J., Zaqarashvili, T. V., Rybak, J., ... Keenan, F.P. (2017). Spectroscopic Inversions of the Ca II 8542 Line in a C-class Solar Flare. The Astrophysical Journal,846, 1-9. [9]. https://doi.org/10.3847/1538-4357/aa83b9

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Spectroscopic Inversions of the Ca II 8542 Line in a C-class Solar FlareD. Kuridze1,5 , V. Henriques1,2 , M. Mathioudakis1 , J. Koza3 , T. V. Zaqarashvili4,5,6 ,

J. Rybk3 , A. Hanslmeier4, and F. P. Keenan11 Astrophysics Research Centre, School of Mathematics and Physics, Queens University Belfast, Belfast BT71NN, UK; d.kuridze@qub.ac.uk

2 Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, NO-0315 Oslo, Norway3 Astronomical Institute, Slovak Academy of Sciences, 059 60 Tatranska Lomnica, Slovakia4 IGAM, Institute of Physics, University of Graz, Universittsplatz 5, A-8010 Graz, Austria

5 Abastumani Astrophysical Observatory at Ilia State University, 3/5 Cholokashvili Avenue, 0162 Tbilisi, Georgia6 Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, A-8042 Graz, AustriaReceived 2017 May 24; revised 2017 July 28; accepted 2017 July 31; published 2017 August 28

Abstract

We study the C8.4-class solar flare SOL2016-05-14T11:34 UT using high-resolution spectral imaging in the Ca II8542 line obtained with the CRISP imaging spectropolarimeter on the Swedish 1 m Solar Telescope.Spectroscopic inversions of the Ca II 8542 line using the non-LTE code NICOLE are used to investigate theevolution of the temperature and velocity structure in the flaring chromosphere. A comparison of the temperaturestratification in flaring and non-flaring areas reveals strong footpoint heating during the flare peak in the loweratmosphere. The temperature of the flaring footpoints between log 2.5 and 3.5500t - - , where 500 isthe continuum optical depth at 500 nm, is 5 6.5 kK~ close to the flare peak, reducing gradually to 5 kK~ . Thetemperature in the middle and upper chromosphere, between log 3.5500t - and5.5, is estimated tobe 6.520 kK, decreasing to preflare temperatures, 510 kK, after approximately 15 minutes. However, thetemperature stratification of the non-flaring areas is unchanged. The inverted velocity fields show that the flaringchromosphere is dominated by weak downflowing condensations at the formation height of Ca II 8542.

Key words: radiative transfer Sun: atmosphere Sun: chromosphere Sun: flares Sun: photosphere techniques: imaging spectroscopy

1. Introduction

It is now widely accepted that the chromosphere is a key toour understanding of solar flares, because of the large amountof radiative loss that originates in it (Fletcher et al. 2011).Chromospheric radiation can provide vital diagnostics for thestructure and dynamics of plasma parameters, such astemperature, velocity, density, pressure, and magnetic field inthe flaring 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., seethe 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; Fontenla et al.1990, 1991, 1993, 2006, 2009; Rutten & Uitenbroek 2012).

The first set of static semi-empirical models of a flaringphotosphere and chromosphere was developed by Machado &Linsky (1975). These authors modeled the wings of the Ca IIH&K lines and concluded that the region of minimumtemperature in flares is both hotter and formed deeper in theatmosphere than in the QS models. Machado et al. (1980)developed models for a bright flare and a faint one thatreproduce lines and continua of H I, Si I, C I, Ca II, and Mg II,and show a substantial temperature enhancement from thephotosphere up to the transition region. Semi-empirical modelsof a white-light flare also show that flare-related perturbationscan affect the formation heights of the wings and continuum, aswell as the continuum emission originating in the photosphere(Mauas 1990, 1993; Mauas et al. 1990).

Gan & Fang (1987) and Gan et al. (1993) used H lineprofiles to construct semi-empirical models for two flares thatshowed evidence for chromospheric condensations, which canreproduce the well-observed asymmetries in H line profiles inflares. Moreover, Gan & Mauas (1994) found that condensationscan increase the back-warming of the atmosphere, leading toheating of the photosphere and enhancement of the continuumemission. The evolution of chromospheric velocity fields duringsolar flares was also studied by Falchi & Mauas (2002) andBerlicki et al. (2005). Falchi & Mauas (2002) constructed fivesemi-empirical models for different flare evolution times, whichreproduce the profiles of the H, Ca II K, and Si I 3905 lines.Velocity fields were included to reproduce the asymmetric lineprofiles. Berlicki et al. (2008) performed semi-empiricalmodeling of the solar flaring atmosphere above sunspots usingNLTE radiative transfer techniques. They found that the flaringlayers (loops) are dominated by chromospheric evaporation,leading to a significant increase in gas pressure. Flare modelsobtained with forward radiative hydrodynamic codes such asRADYN (Carlsson & Stein 1997) can also reproduce theobserved asymmetric line profiles and increase in temperature inthe lower solar atmosphere (Kuridze et al. 2015, 2016).A powerful way to construct atmospheric models with a semi-

empirical approach is to fit the observed Stokes profiles usinginversion algorithms (de la Cruz Rodrguez & van Noort 2016).Through such inversions, the ionization equilibrium, statisticalequilibrium, and radiative transfer equations are solved numeri-cally to synthesize the Stokes profiles under a set of predefinedinitial atmospheric conditions. Differences between the observedand synthetic profiles are used to modify, at a height usuallydetermined by a response function, an initial model atmospherethat is used to reproduce the observed spectral signatures.

The Astrophysical Journal, 846:9 (9pp), 2017 September 1 https://doi.org/10.3847/1538-4357/aa83b9 2017. The American Astronomical Society. All rights reserved.

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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-orderNLTE correction was applied to obtain the temperaturestratification of the chromosphere of the QS and active region(Beck et al. 2013, 2015). However, the development of NLTEradiative transfer codes, such as HAZEL (Asensio Ramos et al.2008), HELIX+ (Lagg et al. 2009), and NICOLE (Socas-Navarro et al. 2015), combined with the increased computa-tional power available, also make NLTE inversions possible(see the review by de la Cruz Rodrguez & van Noort 2016).

The Ca II infrared (IR) triplet line at 8542 is well suited forthe development of chromospheric models, due to itssensitivity to physical parameters, including magnetic field, inthe solar photosphere and chromosphere (Pietarila et al. 2007;Cauzzi et al. 2008; Quintero Noda et al. 2016). Furthermore,the optimization of NICOLE for Ca II 8542 allows the use ofthis feature for the computation of semi-empirical atmosphericmodels. For more details about the spectropolarimetriccapabilities of Ca II 8542 the reader is referred to QuinteroNoda et al. (2016).

Inversions with NICOLE have been successfully performedfor spectropolarimetric Ca II 8542 observations of umbralflashes in sunspots (de la Cruz Rodrguez et al. 2013), andgranular-sized magnetic elements (magnetic bubbles) in anactive region (de la Cruz Rodrguez et al. 2015a). In this paperwe use NICOLE to invert high-resolution Ca II 8542 spectralimaging observations to construct models for the loweratmosphere of a solar flare. Multiple inversions were performedfor the observed region covering flare ribbons and for non-flaring areas at different times during the event. From theconstructed models we investigate the structural, spatial, andtemporal evolutions of basic physical parameters in the upperphotosphere 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), nearthe equator at =0.54 with the CRisp Imaging Spectro-Polarimeter (CRISP; Scharmer 2006; Scharmer et al. 2008)instrument, mounted on the Swedish 1 m Solar Telescope (SST;Scharmer et al. 2003a) on La Palma. Adaptive optics were usedthroughout the observations, consisting of a tiptilt mirror and an85-electrode deformable mirror setup that is an upgrade of thesystem described in Scharmer et al. (2003b). The observationscomprised spectral imaging in the H6563 and Ca II 8542

lines. All data were reconstructed with multi-object, multi-frameblind deconvolution (MOMFBD; van Noort et al. 2005). TheCRISP instrument includes three different cameras. One cameraacquires wideband (WB) images directly from the prefilter, andtwo narrowband (NB) cameras placed after a 50/50 polarizingbeam splitter acquire narrowband (transmitted and reflected)components of horizontal and vertical polarization, eachcombination of camera, wavelength, and component being anobject for reconstruction (for setup details, see, e.g., de la CruzRodrguez et al. 2015b). The WB channel provides frames forevery time step, synchronously with the other cameras, and canbe used as an alignment reference. The images, reconstructedfrom the narrowband wavelengths, are aligned at the smallestscales by using the method described by Henriques (2013). Thisemploys cross-correlation between auxiliary wideband channels,obtained from an extended MOMFBD scheme, to account fordifferent residual small-scale seeing distortions. We applied theCRISP data reduction pipeline as described in de la CruzRodrguez et al. (2015b), which includes small-scale seeingcompensation as in Henriques (2012). Our spatial sampling was0 057 pixel1 and the spatial resolution was close to thediffraction limit of the telescope for many images in the timeseries over the 4141 Mm2 field of view. For the H line scanwe observed in 15 positions symmetrically sampled from theline core in 0.2 steps. The Ca II 8542 scan consisted of 25line positions ranging from 1.2 to+1.2 from the line corein 0.1 steps, plus one position at 1.5. A full spectral scanfor both lines had a total acquisition time of 12 s, which is thetemporal cadence of the time series. However, we note that thepresent paper includes only the analysis of the Ca II 8542 data,which had a duration of 7 s per scan. The transmission FWHMfor Ca II 8542 is 107.3 m with a prefilter FWHM of 9.3(de la Cruz Rodrguez et al. 2015b). A two-ribbon C8.4 flare wasobserved in active region NOAA 12543 during our observations.Throughout the analysis we made use of CRISPEX (Vissers &Rouppe van der Voort 2012), a versatile widget-based tool foreffective viewing and exploration of multi-dimensional imagingspectroscopy data.Figure 1 shows a sample of the flare images in the Ca II

8542 line core and wing positions. Our observationscommenced 4 minutes after the main flare peak (11:34UT). Light curves generated from the region marked with theorange box in Figure 1 show the post-peak evolution of theemission in the line core and wings (right panel of Figure 1).Although we missed the rise phase and flare peak, two brightribbons associated with post-flare emission are clearly detectedat 11:38 UT with good spatial and temporal coverage.

Figure 1. Images in the Ca II 8542 line wing and core obtained with the CRISP instrument on the SST at 11:38:20 UT on 2016 May 14. The orange box indicatesthe flaring region analyzed in this paper. The temporal evolution of the region averaged over the area marked with the yellow box is presented in the far right panel.

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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 para-meters such as temperature, line-of-sight (LOS) velocity,magnetic field, and microturbulence of an initial guess modelatmosphere to find the best match with the observations (Socas-Navarro et al. 2000). The output stratifications of the electronand gas pressures, as well as the densities, are computed fromthe equation of state using the temperature stratification and theupper boundary condition for the electron pressure under theassumption of hydrostatic equilibrium.

NICOLE includes a Ca II model atom consisting of fivebound levels plus continuum (Leenaarts et al. 2009) withcomplete frequency redistribution, which is applicable for linessuch as Ca II 8542 (Uitenbroek 1989; Wedemeyer-Bhm &Carlsson 2011; Quintero Noda et al. 2016). The syntheticspectra were calculated for a wavelength grid of 113 data pointsin 0.025 steps, four times denser than the CRISP data set.Stratification of the atmospheric parameters obtained by theinversions is given as a function of the logarithm of the opticaldepth scale at 500nm (hereafter log t). The response functionof the Ca II 8542 line is expanded to log 0t ~ and 5.5 (seeQuintero Noda et al. 2016 for details). As our CaII8542 linescan is 1.5 to+1.2 from line core, the analysis ofthe response functions shows that it provides diagnostics in thelayers between log 1 and 5.5 (see Figure 6 in QuinteroNoda et al. 2016).

To improve convergence, the inversions were performed inthree cycles, expanding on the suggestion of Ruiz Cobo & delToro Iniesta (1992) and as implemented in de la CruzRodrguez et al. (2012). In the first cycle and for the first scan,the inversions were performed with four nodes in temperatureand one in LOS velocity, with the initial guess model being theFAL-C atmosphere (Fontenla et al. 1993). The convergence ofthe models obtained from the first cycle was improved byapplying horizontal interpolation to recompute the invertedparameters of the pixels with a low quality of fits. A secondcycle was then performed with an increased number of nodes(seven for temperature and four for LOS velocity) and theinterpolated 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 solar atlas profile ofthe Fourier transform spectrometer (FTS) disk center (Neckel1999), convolved with a model of the CRISP transmissionprofile with FWHM=107.3 m provided by de la CruzRodrguez et al. (2015b), and the average SST/CRISP flat-fielddisk-center profile does not show an adequate coincidence ofresulting profiles. This indicates a broader or more asymmetricinstrumental profile than the respective model used in NICOLE(the synthetic profiles are convolved with the instrumentalprofile before comparison with the observations and before thefinal output). Therefore, in the third cycle we convolved theinstrumental profile with a Gaussian of FWHM=141 m andperformed an inversion with the same number of nodes and aninitial guess model constructed from the second cycle. This ledto a better match between the observed and synthetic spectra.Table 1 summarizes the number of nodes and initial temperaturemodels used in the three cycles. We also convolved the atlasprofile with an asymmetric Lorentzian model of the transmission

profile for the CRISP transmission profile with FWHM=0.080. This also provides the required similarity between theatlas and the observed flat-field profiles, suggesting that indeedthe transmission profile could be asymmetric. We ran theinversions with the asymmetric Lorentzian profile and theresulting atmospheres were the same as obtained with the CRISPinstrumental profile convolved with a symmetric Gaussian withFWHM=141 m.Our observations do not include full Stokes imaging

spectroscopic data, so we run NICOLE only for Stokes Iprofiles. Therefore, in both cycles, the magnetic field vectorand the weights for other Stokes parameters were set to zero.We inverted an area of 200200 pixel2 (8.28.2 Mm2)covering the flare ribbons as well as some non-flaring regions(see left panels of Figure 1). Although our time seriescomprises 346 spectral scans, we choose only the best scansin terms of spatial resolution. This limits the total number ofscans to 35, with a cadence of approximately 1 minute in thetime interval 11:38 to 12:09 UT.

4. Analysis and Results

Figure 2 presents a Ca II 8542 line core image of theregion selected for inversions (marked with the orange box inFigure 1). The NICOLE output showing the temperature andthe LOS velocity maps is also presented. Temperature andvelocity maps are integrated and averaged betweenlog 3.5t - 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 bottom rowshows images 7minutes later. A temperature map of theinverted region close to flare peak shows temperatureenhancements for the two flare ribbons. The LOS velocitymap of the same region in the top right panel of Figure 2reveals downflows at the flare ribbons, while the temperaturemap in the bottom middle panel indicates that the size of theflare ribbons and the heated areas has decreased dramatically7 minutes later.Figure 3 shows the line profiles and temperature/velocity

stratifications of three pixels indicated as FL, FF, and QS inFigure 2, with the pixels in different parts of the region underinvestigation. The best-fit synthetic profiles obtained from theinversion at 11:38:20 UT are also shown. There are basicallythree different shapes of line profile over the selected regionduring the flare: absorption, emission, and those with centralreversal. In the non-flaring areas (QS), Ca II 8542 shows thewell-known absorption line profile. The line profiles of theflaring loops (FLs) connecting the flare footpoints (FFs)(ribbons) have central reversals, whereas profiles of the FFare in full emission without a central reversal. Figure 3 showsthat the observed spectra are generally reproduced by thesynthetic best-fit spectra. The QS temperature is close to the

Table 1Number of Nodes and Input Atmosphere Models Used

during Each Cycle of the Inversion

Physical Parameter Cycle 1 Cycle 2 Cycle 3

Temperature 4 nodes 7 nodes 7 nodesLOS velocity 1 node 5 nodes 5 nodesMicroturbulence 1 node 1 node 1 nodeMacroturbulence none none noneInput atmosphere FAL-C model from Cycle 1 model from Cycle 2

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FAL-C temperature profile, whereas the FL has a higherchromospheric temperature at log 2.5t ~ - and 5.5 (middlepanels of Figure 3), with the FF showing the highesttemperatures.

In Figure 4 we present the temporal evolution of thetemperature and velocity stratifications for the flaring and non-flaring pixels. The temperature of the footpoints is enhancedacross the chromosphere between optical depths of log t ~

2.5- and5.5. As time progresses, the temperature in the lowerchromosphere between log 2.5 and3.5 decreases gradu-ally from T56.5 kK to T 5 kK~ . In the middle and upperchromosphere, between log 3.5 and5.5, the temperaturedecreases from T 6.520 kK to T 510 kK during about15 minutes (top left panel of Figure 4). The velocity field forthe flaring pixel is dominated by weak upflows that decreasegradually with time, while the temperature and velocity of thenon-flaring areas are lower and unchanged in the chromosphere atlog 1 and5.5 (right panels of Figure 4).

In Figure 5 we show the evolution of the temperaturestratifications using density maps that have been produced withthe superimposition of individual pixels from the flaring regionmarked with blue contours in Figure 2. It must be noted that thestratifications of the pixels with a low quality of fit, such asunphysically low or high temperature plateaus or dips andpeaks, were ignored and are not included in the density plots.Our density maps confirm that the most intensively heated

layers are in the middle and upper chromosphere at optical depthsof log 3.5 and5.5, reaching temperatures between 6.5and 20 kK. The temperature stratification of the layers belowlog 2.5 remains unchanged during the flare and isconsistent with the QS FAL-C model used as the initialatmosphere for the inversions (Figure 5). In the top left panel ofFigure 6 we show a vertical cut of the net temperatureenhancement of the flare close to its peak (11:38 UT), wherean average temperature stratification obtained from quiet, non-flaring areas has been subtracted. The two bright regions at 2and 7.5 Mm show the temperature enhancements of the flareribbons.As noted in Section 3, NICOLE calculates the basic

thermodynamic parameters that define the internal energy ofthe system, such as the density and electron pressure, using theequation of state, temperature stratification, and upperboundary condition under the assumption of hydrostaticequilibrium. To estimate the energy content of the flaringchromosphere, we compute the internal energy e using therelationship

ep1

1, 1

g r=

-( )

where p and are the gas pressure and density, respectively,and =5/3 is the ratio of specific heats (Aschwanden 2004;

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 in theCa II 8542 line core are shown in the left panels. NICOLE outputs showing the temperature and the LOS velocity maps in the interval between log 3.5 and5.5 are provided in the middle and right panels, respectively. Blue contours show the area analyzed in this paper, which has intensity levels greater than 30% of theintensity maximum. FL, FF, and QS mark the selected pixels at the flare loop, flare footpoint, and quiet Sun, respectively, and are discussed in the text in moredetail. 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 a vertical cut of the atmosphere is made for detailed analyses.

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Beck et al. 2013). The top right panel of Figure 6 shows avertical cut of the excess energy density per unit mass close toflare maximum at 11:38 UT, which is the internal energy,e x y, , t( ), computed for each pixel minus an average internalenergy, e x y, ,q t( ), estimated from quiet, non-flaring areas. Athree-dimensional (3D) rendering of this excess energy densityfor an inner part of the inverted data cube is also shown in thebottom left panel of Figure 6. It illustrates that the enhancementin energy density coincides with the locations of flare ribbonswhere the temperature enhancements are detected. The ratio oftotal internal energy of this part of the inverted surface(S 5.3 6.7 Mm2) to the internal energy for an equallysized surface of the QS as a function of optical depth ispresented in the bottom middle panel of Figure 6. This showsthat the energy of the flaring region is increased in the range ofoptical depths log from 2.5~- to 5.5 compared to theinternal energy of the QS. The ratio has a peak at log 5t -where the internal energy of the inverted flare region isincreased by a factor of close to three over the QS. As timeprogresses, the ratio decreases gradually to 1 after about15 minutes, meaning that the atmosphere (energeticallyspeaking) has reached QS levels. The total energy of the

chromospheric volume shown in the bottom left panel ofFigure 6 (integrated over the range of optical depth log from 3.5 to 5.5) is estimated to be 1024 erg close to theflare peak, decreasing linearly to a QS energy level of 6~ 1023 erg after approximately 15 minutes (bottom right panel ofFigure 6). We note that, due to the high viewing angle of theobserved region, the vertical extent of the model atmospheresshown and described in Figure 6 does not correspond to thetrue geometrical height of the lower solar atmosphere. NICOLEderives the geometrical height from the optical depth scale andthe temperature plus density/pressure stratifications, and anoptical depth refers to layers at different geometrical heightsin different models. Therefore, a temperature/energy excessderived through the models does not show accurately theenergy distribution as a function of geometrical height, but itdoes so as a function of optical depth.

5. Discussion and Conclusions

We have presented spectroscopic observations of the Ca II8542 line in a C8.4-class flare. The line profiles of the flareribbons are in total emission without a central reversal, whereasthose of FLs, which connect the FFs, show central reversals

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

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(Figure 3). In the quiet Sun the line is in absorption (Figure 3).The analysis of synthetic chromospheric spectral line profilesproduced with radiative hydrodynamic models has shown thatthe changes in temperature, radiation field, and populationdensity of the energy states make the line profile revert fromabsorption into emission with or without a central reversal(Kuridze et al. 2015, 2016). In a recent investigation, Kuridzeet al. (2016) studied the flare profiles of the Na I D1 line, whichalso forms in the optically thick chromosphere. The heating ofthe lower solar atmosphere by the nonthermal electron beammakes the Na I D1 line profiles go into full emission. However,when the beam heating stops, the profiles develop a centralreversal at the line cores. Unfortunately, as there is no energyflux from electrons in NICOLE, that cannot be used toinvestigate how the emission and centrally reversed profiles ofthe Ca II 8542 line are formed. However, the analysis of thesynthetic line profiles from the RADYN simulations showsthat for a strong electron beam heating (model F11) theCa II 8542 line profiles are in full emission but develop acentral reversal after beam heating in the relaxation phaseof the simulation (Kuridze et al. 2015). For a weak flare run(model F9), the synthesized Ca II 8542 profile exhibits ashallow reversal during the beam heating phase that deepensduring the relaxation 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 centralreversal depends on the temperature at the core formation

height ( 5.5 log 3.5t~- < < - ), i.e., a higher temperatureproduces a shallower central reversal (Figure 3). This couldexplain why flare ribbons, which are believed to be the primarysite of nonthermal energy deposition and intense heating, haveprofiles in full emission, whereas FLs, which are secondaryproducts of the flare and hence less heated areas, have centralreversals.We constructed semi-empirical models of the flaring

atmosphere using the spectral inversion NLTE code NICOLEto investigate its structure and evolution. Models weregenerated at 35 different times during the flare, starting at 4minutes after the peak. The construction of the models is basedon a comparison between observed and synthetic spectra. Closeto the line core, where the self-reversal is formed, we find asmall 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 observedprofiles, which are in full emission (bottom left panel ofFigure 3). This influences the narrow layer of core formationheight and hence does not have a strong effect on the overalloutput model. A possible reason for the observed discrepancycould be the lower degree of ionization of Ca II in the flaringatmosphere compared to the ionization used in NICOLE(Wittmann 1974). Furthermore, the models constructed close tothe flare peak are characterized by a high quality of fit andprovide a better match with the observed spectra. This isbecause, as time from flare maximum progresses, the well-defined shapes of emission and centrally reversed line profilesbecome flatter and feature more irregular shapes, which causes

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.

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NICOLE to encounter difficulties in finding atmospheres thatreliably fit such profiles.

Our analysis of the constructed model shows that the mostintensively heated layers in the flaring lower atmosphere are themiddle and upper chromosphere at optical depths of log 3.5 and5.5, respectively, with temperatures between 6.5and 20 kK. The temperatures of these layers decrease to typicalQS values (510 kK) after about 15 minutes (Figure 5). In thephotosphere, below log 2.5t - , there is no significantdifference in temperature stratifications between quiescence andflaring (Figure 5). This agrees with some of the previous results(e.g., Falchi & Mauas 2002), which show that during the flare theatmosphere is unchanged below 600 km. However, it must benoted that, because the observations presented in this work started4 minutes after the flare peak, it is possible that the temperature inthe deeper layers of the atmosphere was affected during theimpulsive phase.

The velocity field indicates that the observed field of view isdominated by weak downflows at optical depths oflog 1 and5.5 associated with the post-flare chromo-spheric condensations (Figures 2 and 3). Centrally reversedCa II 8542 profiles show excess emission in the blue wing(blue asymmetry) with a redshifted line center (left middle panelof Figure 3). Similar to blue asymmetries observed in H, Na ID1, and Mg II flaring line profiles (Abbett & Hawley 1999;Kuridze et al. 2015, 2016; Kerr et al. 2016), the asymmetry foundin Ca II 8542 seems to be related to the velocity gradientsassociated with the chromospheric condensations. The core of theCa II 8542 profile presented in the left middle panel of Figure 3is redshifted owing to the downflows at the height of coreformation (right middle panel of Figure 3). Velocity decreasesdownward toward the wing formation regions, producing apositive velocity gradient with respect to the height inward. Thisgradient can modify the optical depth of the atmosphere in such a

way that higher-lying (core) atoms absorb photons with longerwavelengths (red wing photons), and the blue asymmetry in thecentrally reversed peak is formed. We note that semi-empiricalmodels of 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 upflows (evaporations)rather than downflows as detected in our study. This differencemay be due to the difference in phases of the flares as we detectthe downflows in the late phase (4 minutes after the flare peak).Using the stratification of gas density and pressure obtained

from NICOLE, under the assumption of hydrostatic equili-brium, we investigated the evolution of the total internal energyof the lower solar atmosphere covering the formation height ofCa II 8542. Our analysis shows that the total energy of thechromosphere close to the flare maximum (11:38 UT) issignificantly increased in the range of optical depth log from

3.5~- to 5.5 compared to the internal energy of the QS(Figure 6). A maximum enhancement was detected atlog 5t - , where the total internal energy, integrated over aselected area of the flare, is a factor of three greater thanthe integral over the same area of a QS region. This internalenergy reduces to the relaxed, QS state after approximately15 minutes. The total energy of the inverted box shown in theleft panel of Figure 6 is estimated to be 1024 erg close to theflare peak, and to decrease linearly to the QS energy level of

6 1023~ erg after 15 minutes (bottom right panel ofFigure 6). We note that hydrostatic equilibrium may not be avalid assumption for accurate estimations of the thermodynamicparameters, and hence for the energy for a highly dynamicalprocess such as a solar flare. However, we emphasize thatmodern inversion algorithms currently use the assumption ofhydrostatic equilibrium only to obtain pressures and densitystratifications, and we believe that quantities such as theevolution of the energy ratio with time should be unaffected bythis approximation.

Figure 5. Density maps showing the evolution of the temperature stratification during the flare. Each map is produced by superimposing the stratification of around2000 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 depicts the FAL-Cmodel, used as the initial atmosphere for the inversions.

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The Astrophysical Journal, 846:9 (9pp), 2017 September 1 Kuridze et al.

To our knowledge, we have presented the first spectroscopicinversions, in NLTE, of the solar chromospheric line (Ca II8542) to produce semi-empirical models of the flaringatmosphere. The temperature stratification obtained from theinversion is in good agreement with other semi-empiricalNLTE flare models constructed without inversion codes, andwith atmospheres obtained with forward modeling usingradiative 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 fundingfrom the European Communitys Seventh FrameworkProgramme (FP7/20072013) under grant agreement No.606862 (F-CHROMA). The Swedish 1 m Solar Telescope isoperated on the island of La Palma by the Institute for SolarPhysics (ISP) of Stockholm University at the SpanishObservatorio del Roque de los Muchachos of the Instituto deAstrofsica de Canarias. The SST observations were takenwithin the Transnational Access and Service Programme: HighResolution Solar Physics Network (EU-7FP 312495 SOLAR-NET). This research has made use of NASAs AstrophysicsData System. This project made use of the Darwin Super-computer of the University of Cambridge High PerformanceComputing Service (http://www.hpc.cam.ac.uk/), providedby Dell Inc. using Strategic Research Infrastructure Fundingfrom the Higher Education Funding Council for England andfunding from the Science and Technology Facilities Council.The authors benefited from the excellent technical support of

the SST staff, in particular from the SST astronomer PitStterlin. This work was supported by the Science GrantAgency project VEGA 2/0004/16 (Slovakia) and by theSlovak Research and Development Agency under the contractNo. SK-AT-2015-0022. This article was created by therealization of the project ITMS No. 26220120029, based onthe supporting operational research and development programfinanced from the European Regional Development Fund. A.H.thank the Austrian FWF (project P 27765) for support. Thework of T.V.Z. was supported by the Austrian Fonds zurFrderung der wissenschaftlichen Forschung (FWF) project P28764-N27 and by the Shota Rustaveli National ScienceFoundation project DI-2016-17 and by the Austrian Scientific-technology collaboration (WTZ) project SK 12/2016.

ORCID iDs

D. Kuridze https://orcid.org/0000-0003-2760-2311V. Henriques https://orcid.org/0000-0002-4024-7732M. Mathioudakis https://orcid.org/0000-0002-7725-6296J. Koza https://orcid.org/0000-0002-7444-7046T. V. Zaqarashvili https://orcid.org/0000-0001-5015-5762J. Rybk https://orcid.org/0000-0003-3128-8396F. P. Keenan https://orcid.org/0000-0001-5435-1170

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Figure 6. Top left: vertical cut of the temperature stratification with the quiet, non-flaring temperature subtracted. The maps are produced from the locations indicatedby the white dotted line in Figure 2. Top right: vertical cut of the excess energy density per unit mass, which is the internal energy e x y, , t( ) computed for each pixelminus an average internal energy e x y, ,q t( ) estimated from quiet, non-flaring areas. Bottom left: 3D rendering of the excess energy density produced for an inner part(only S 5.3 6.7 Mm2) of the inverted data cube. The maps have been smoothed over 10 pixels (400 km) along the x-axis. Bottom middle: evolution of the ratioof the area-integrated internal energy for the inverted region shown in the bottom left panel over an equally sized area of QS. Bottom right: evolution of the totalenergy (dashed line) integrated over an inverted region presented in the bottom left panel. The total energy of the same-size QS volume is overplotted as a dotted line.

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1. Introduction2. Observations and Data Reduction3. Inversions4. Analysis and Results5. Discussion and ConclusionsReferences