Solar Flare Chromospheric Line Emission: Comparison Between IBIS High-resolution Observations and Radiative Hydrodynamic Simulations
Fatima Rubio da Costa, Lucia Kleint, Vahé Petrosian, Alberto Sainz Dalda, Wei Liu
aa r X i v : . [ a s t r o - ph . S R ] A p r D raft version S eptember
21, 2018
Preprint typeset using L A TEX style emulateapj v. 5 / / SOLAR FLARE CHROMOSPHERIC LINE EMISSION: COMPARISON BETWEEN IBIS HIGH-RESOLUTIONOBSERVATIONS AND RADIATIVE HYDRODYNAMIC SIMULATIONS F atima R ubio da C osta , L ucia K leint , V ah ´ e P etrosian , A lberto S ainz D alda and W ei L iu , Draft version September 21, 2018
ABSTRACTSolar flares involve impulsive energy release, which results in enhanced radiation in a broad spectral andat a wide height range. In particular, line emission from the chromosphere can provide critical diagnostics ofplasma heating processes. Thus, a direct comparison between high-resolution spectroscopic observations andadvanced numerical modeling results can be extremely valuable, but has not been attempted so far. We presentin this paper such a self-consistent investigation of an M3.0 flare observed by the Dunn Solar Telescope’s(DST)
Interferometric Bi-dimensional Spectrometer ( IBIS ) on 2011 September 24 that we have modeled withthe radiative hydrodynamic code RADYN. We obtained images and spectra of the flaring region with IBIS inH α II Reuven Ramaty High Energy Solar Spectroscope Imager ( RHESSI )in X-rays. The latter was used to infer the non-thermal electron population, which was passed to RADYNto simulate the atmospheric response to electron collisional heating. We then synthesized spectral lines andcompared their shapes and intensities with those observed by IBIS and found a general agreement. In particular,the synthetic Ca II α profile is fainter inthe core than the observation. This indicates that H α emission is more responsive to the non-thermal electronflux than the Ca II Subject headings:
Sun: flares; chromosphere — line: profiles — radiative transfer — hydrodynamics (HD) INTRODUCTION
Energy release (e.g., by magnetic reconnection) in solarflares in general results in particle acceleration, plasma heat-ing, and plasma wave (or turbulence) generation. Most ofthe released energy is transported by the accelerated parti-cles downward along magnetic field lines and deposited inthe dense chromosphere by Coulomb collisions with ambientplasma in the so-called thick target model (e.g., Brown 1971;Petrosian 1973; Lin & Hudson 1976). Some energy may betransported by thermal conduction from directly heated coro-nal plasma (e.g., Zarro & Lemen 1988; Battaglia et al. 2009),and possibly by plasma waves (e.g., Fletcher & Hudson 2008;Haerendel 2009). Observational signatures of the energy de-position include radiation in X-rays via bremsstrahlung ofthe electrons, gamma-rays via interaction of accelerated ionswith background ions, various lines (e.g., H α ) and continuumemission from the heated plasma. These observations can pro-vide useful diagnostics and help constrain mechanisms of en-ergy release and particle acceleration, a fundamental questionfor solar flares.Strong chromospheric lines, such as H α and Ca II Department of Physics, Stanford University, Stanford, CA 94305,USA; Email: [email protected] University of Applied Sciences and Arts Northwestern Switzerland,5210 Windisch, Switzerland Stanford-Lockheed Institute for Space Research, Stanford University,HEPL, 466 Via Ortega, Stanford, CA 94305, USA Lockheed Martin Solar and Astrophysics Laboratory, 3251 HanoverStreet, Palo Alto, CA 94304, USA W. W. Hansen Experimental Physics Laboratory, Stanford University,Stanford, CA 94305, USA for the correct interpretation of the observations and evolutionof line intensities and profiles. Spectroscopic observations ofsuch emission are primarily obtained from ground-based fa-cilities, which have several advantages over space telescopes.Among these are the flexibility of real-time adjustments ofpointing and exposure times, and wide ranges of available ob-serving modes and filters. However, because of the limitedfield-of-view (FOV) (as a trade-o ff for high spatial resolution),our limited capability in predicting flares and seeing and ourlimited weather conditions, such ground-based spectroscopicobservations of flares are rare (e.g. Kleint 2012; Deng et al.2013; Fischer et al. 2012) and thus very valuable.Numerical modeling of flare line emission is a necessarystep to interpret observational data and subsequently, to con-strain flare mechanisms. Early modeling of atmospheric lineemission were based on empirical flaring atmosphere mod-els (e.g., Canfield et al. 1984; Fang et al. 1993) or on radia-tive transfer simulations of an electron-beam heated chromo-sphere (e.g., Fisher et al. 1985; Gan & Fang 1990; Ding et al.1998). Ding & Fang (2001) and Berlicki (2007) later stud-ied how the precipitation of electrons from the corona af-fects the line profiles. Kaˇsparov´a et al. (2009) focused onsubsecond scale variations and solved 1-D radiative hydrody-namics of a solar atmosphere subjected to a subsecond elec-tron beam heating to study the H α line emission. More so-phisticated later models involved non-LTE radiative hydrody-namic calculations on timescales up to several tens of sec-onds: Allred et al. (2005) injected a power-law electron beamat the apex of a loop and tracked the atmospheric responseand how the H α line evolved in time in response to the flux ofelectrons.In this paper we present a self-consistent, detailed com-parison of line profiles from high-resolution spectroscopicflare observations and advanced radiative transfer hydrody-namic simulations using observationally inferred electronspectra as inputs. Such a comprehensive investigation hasnot been attempted in the past and can o ff er new insightsto flare dynamics. Specifically, we obtain H α and Ca II Reuven Ramaty High Energy Solar Spectroscope Im-ager ( RHESSI ; Lin et al. 2002), which are then used asinputs to the RADYN code (Carlsson & Stein 1992, 1997;Allred et al. 2005) to perform radiative transfer hydrodynamicsimulations. Line profiles are synthesized from the simulationresults and compared to the IBIS observations, completing afull circle of the investigation.This paper is organized as follows. We describe the relevantobservations in Section 2 and the RADYN code in Section 3.We then present the simulation results and comparisons withobservations in Section 4 and finally the conclusions and dis-cussion in Section 5. OBSERVATIONS
On 2011 September 24, an M3.0 class flare occurred inthe NOAA active region (AR) 11302. As shown in Fig-ure 1, this flare started at 19:09 UT, reaching its maximumat 19:21 in the
GOES
RHESSI detected HXRs from the beginning of the impulsivephase (19:08) up to 19:24 UT. DST / IBIS observed footpointemission from the chromosphere in H α and Ca II SDO ) observed the flare in (extreme) ultra-violet(UV); the 1700 Å images of the flare ribbons were used toestimate the cross-sectional area of the flare loop.
Chromospheric Line Observations by IBIS
IBIS is a dual Fabry-Perot system, capable of full-Stokesdual beam polarimetry of di ff erent spectral lines. The spec-tral lines and six polarization states are scanned sequentiallyand reconstructed into images of the Stokes vector during thedata reduction process. During our observations, we scannedthe chromospheric H α II I F ig . 1.— Temporal evolution of the flux measured on 24 September 2011.(a) GOES
SXR flux measured every 3 seconds, showing the M3.0 flare andthe preceding and succeeding M2.8 and M5.8 flares from the same AR; (b)
RHESSI count rates in colored solid lines and
GOES are above 2500 DN, which is equal to a flux of 31250 DNs − . This corresponds to ≈
50% of the maximum intensity.Contours of this intensity level are illustrated in Figure 2. H α Observations
The H α line is one of the most commonly observed linesin flares because of its high contrast and thus provides usefuldiagnostics. However, its interpretation is complex becausethe emission originates from a broad range of heights, fromthe upper photosphere to the lower chromosphere, and it issensitive to the flux of non-thermal electrons precipitating tothe chromosphere (Kaˇsparov´a et al. 2009).There have been only a few published observations whichshow the temporal evolution of the H α profiles from the startof a flare because of the di ffi culty in setting and holding thespectrograph slit on a flare footpoint (e.g. Kviˇcala et al. 1961;Canfield & Gunkler 1985; Radziszewski et al. 2007, 2011;Deng et al. 2013). With IBIS we obtained three H α scans withgood seeing, starting after the impulsive phase, at 19:22:40UT, 19:24:15 UT and 19:32:09 UT; each of them lasted 27seconds and included 24 wavelength points in a wavelengthrange of ± Ca II The Ca II infrared triplet ( λ = P / , / levels and the lower metastable 3d D / , / levels.(There are no allowed electric dipole transitions to the groundstate.).The Ca II ff ected by chromospheric motions.Despite this and the fact that in the near infrared wavelengthsthe terrestrial atmospheric turbulence is reduced, the Ca II in-frared triplet observations are still scarce and only possiblewith ground-based instruments. In this paper we use imag-ing spectroscopy in the Ca II ± SDO of AR 11302 at19:24 UT (top). The box denotes the FOV of IBIS, which wascentered on a small pore west of the active region and cov-ered one of the flare ribbons. The bottom row shows exampleimages from IBIS with their wavelengths labeled. While theblue wing images (6561.2 Å and 8541.1 Å) show a filament inthe lower left corner and a brightening due to the ribbon emis-sion, the images near the line cores (6562.9 Å and 8542.0 Å)resemble the emission of AIA 304. During our observations,the ribbon is seen to expand and the filament becomes smallerand weaker in intensity.
RHESSI
ObservationsRHESSI had full coverage of the impulsive phase of theflare and part of the decay phase until its sunset, which startedat 19:23:52 UT (see Figure 1).Using the CLEAN algorithm, we reconstructed images at25-50 keV integrated over 52 s intervals from 19:08:52 to19:35:44. These images revealed two HXR footpoint sourcesand a loop top source at later times (see Figure 3). The west-ern footpoint is brighter and moves faster than the eastern one,which is located in a stronger magnetic field. Such asymmet-ric footpoint emission is understood as a result of asymmetricmagnetic mirroring (e.g., Wang et al. 1995; Jin & Ding 2007;Liu et al. 2009; Yang et al. 2012).
Inferring the non-thermal electron distribution
We can infer the non-thermal electron distribution and thusits energy flux by analyzing
RHESSI
X-ray spectra. Themoderate count rates of this M3.0 flare allow imaging spec-troscopy of spatially resolved sources only during the HXRpeak of the impulsive phase. To cover the temporal evolu-tion of the flare, we thus chose to fit the spatially integratedspectra, which are dominated by the western HXR footpoint(see Figure 3) that coincides with the flare kernel position ob-served by IBIS. This provides reasonable diagnostics for theelectron energy flux as an input to our RADYN simulation ofthat kernel.Because each of
RHESSI ’s nine germanium detectors hasslightly di ff erent characteristics and makes independent mea-surements, we analyzed the spectra of individual detectorsseparately. We then used the means and standard deviationsof the fitting parameters to obtain the best-fit parameter anduncertainties. This has several advantages (e.g., avoiding en-ergy smearing) over the conventional approach of directly fit-ting the average count spectra of all detectors (for details, see,Liu et al. 2008; Milligan & Dennis 2009). We excluded de-tectors 2 and 7 because of their abnormally high thresholdand / or low energy resolution (Smith et al. 2002). We also ex-cluded detector 6 due to its consistently higher χ values ofthe fitting results than those of the other detectors. For eachof the remaining six detectors, we obtained photon spectra byintegrating 30 s intervals from 19:09:30 to 19:13:00 UT and60 s intervals from 19:13:00 to 19:23:52 UT until the space-craft night. Using the standard Object Spectral Executive (OSPEX)software package (Brown et al. 2006), we applied correctionsfor albedo, instrumental emission lines, pulse pileup and thedetector response matrix (DRM). We fitted the spectra witha thermal component plus a thick-target, non-thermal compo-nent consisting of a broken power law, F ( E ) = ( δ − F c E c (cid:16) EE c (cid:17) − δ (1)for energies E > E c and a power law with a fixed index δ = − E < E c . Here F c = R ∞ E c F ( E ) dE is the total electron fluxabove E c .Figure 4(a) shows a spectrum of detector 4, as an example,during the impulsive phase, from which we can clearly seethe dominance by the thermal component at low energies andby the non-thermal component at high energies. The greenand blue lines show the fitted thermal and non-thermal com-ponents, respectively, and the red line is the total fit, summingall the components.The temporal evolution of the power-law index δ and en-ergy cuto ff E c of the non-thermal component are shown inFigures 5(a) and 5(b). We find a soft-hard-soft spectral evo-lution, with the hardest spectra (lowest δ ) occurring at 19:12–19:15 UT.From RHESSI we obtain the total rate of injection of elec-trons. To estimate the flux of electrons (or energy flux E ( E ) = E × F ( E )) within the loop, it requires the knowledge of itscross-sectional area. The spatial resolution ( ≥ ′′ ) of thecombined RHESSI detectors 3–9 used for HXR imaging isinsu ffi cient for resolving the flare footpoints. We thus ap-proximated this area with SDO / AIA 1700 Å (1 . ′′ RHESSI
HXRfootpoint, as shown in Figure 6. Similar cospatiality betweenH α kernels and HXR footpoints has also been reported (e.g.Liu et al. 2007). However, we also notice some small 1700 Åkernels without a corresponding HXR source, which could becaused in part by RHESSI ’s limited dynamic range of the or-der of 1:10.As the flare evolves, the contours associated with the AIA1700 Å easternmost footpoint are not anymore cospatiallyaligned with the
RHESSI ff erent locations than1700 Å emission [see e.g. Figure 6(c) and (d)]. One possi-bility is that such HXRs are emitted from the loop-top source[see Figure 3(f)]. Nevertheless, this mismatch could result inan overestimate of the flare loop cross-sectional area and thusunderestimate of the electron energy flux. We estimated thatthe uncertainty in the inferred area is about 16%.Images taken between 19:11 and 19:13 UT contain severalsaturated pixels, which we discarded by imposing an upperthreshold of 16000 DN. The resulting areas were then inter-polated to the time intervals used for RHESSI spectral fittingand are shown in Figure 5(d). Finally, by dividing the electronpower by the estimated loop cross-sectional area, we obtainedelectron energy flux, whose temporal evolution is shown inFigure 5(e). RADYN SIMULATIONS F ig . 2.— Overview of AR 11302 seen by SDO (top row) Helioseismic and Magnetic Imager (HMI) in continuum and AIA in 304 Å, and by IBIS (bottom row)in white light, H α (three wavelengths) and Ca II SDO images denotes the FOV of IBIS, which covers the western flareribbon. The red contours in the 6562.9 Å image show the area that was averaged to obtain an average intensity profile of the ribbon.
We used the RADYN code of Carlsson & Stein (1997),including the modifications of Abbett & Hawley (1999) andAllred et al. (2005), to simulate the radiative-hydrodynamicresponse of the lower atmosphere to energy deposition bynon-thermal electrons in a single flare loop.
General Description of the RADYN Code
The code solves simultaneously the equations of hydrody-namics, population conservation, and radiative transfer im-plicitly on a one-dimensional adaptive grid (Dorfi & Drury1987), as described by Carlsson & Stein (1992).For radiative transfer calculations, atoms important to thechromospheric energy balance are treated in non-LTE. Theseinclude six-level plus continuum hydrogen, six-level plus con-tinuum, singly ionized calcium, nine-level plus continuum he-lium, and four-level plus continuum, singly ionized magne-sium. Line transitions treated in detail are listed in Table 1of Abbett & Hawley (1999). Complete redistribution is as-sumed for all lines, except for the Lyman transitions in whichpartial frequency re-distribution is mimicked by truncatingthe profiles at 10 Doppler widths (Milkey & Mihalas 1973).Other atomic species are included in the calculation as back-ground continua in LTE, using the Uppsalla opacity package of Gustafsson (1973).Additions of hydrodynamic e ff ects due to gravity, ther-mal conduction, and compressional viscosity to the originalRADYN code were described by Abbett & Hawley (1999).Later additions by Allred et al. (2005) included photoioniza-tion heating by high-temperature, soft X-ray emitting plasma,optically-thin cooling due to thermal bremsstrahlung and col-lisionally excited metal transitions, and conductive flux limitsto avoid unphysical values in the transition region of largetemperature gradients. Simulation Setup
We assumed a single quarter circle loop geometry in aplane-parallel model atmosphere, discretized in 191 gridpoints. The model loop is 10 Mm in height. We assume asymmetric boundary condition at the loop apex ( z =
10 Mm).We note from the observations (Figure 6) that the footpointsappear to move during the flare but not more than its diam-eter so that our assumption of a single loop is a reasonableapproximation.The initial atmosphere (Figure 7) was adopted from theFP2 model of Abbett & Hawley (1999), which is generatedby adding a transition region and corona to the model atmo- F ig . 3.— RHESSI
SDO / AIA 304 Å images, during the impulsive phase of the flare, from 19:10:18 to 19:14:20. The contoursrepresent the 95, 70 and 30% of the maximum intensity at each time interval. The white box represents the FOV of IBIS. sphere of Carlsson & Stein (1997). The temperature was fixedat 10 K at the loop top and no external heating was provided.This allowed the the atmosphere to relax to a hydrodynamicequilibrium state.Initially the bottom boundary is located in the upper pho-tosphere; the chromosphere is at 0.9 Mm from the bottom ofthe loop and the transition region is at a distance of 1.56 Mmfrom the bottom. During the evolution of the atmosphere weassume open boundaries at the bottom and apex of the loop,extrapolating if necessary.The non-thermal electron heating was calculated from thepower-law spectrum provided by
RHESSI spectral fits (seeFigure 5). It was included in RADYN as a source of exter-nal heating in the equation of internal energy conservation ( Q term of equation (3) in Abbett & Hawley (1999)) and has beenupdated every integration time interval based on RHESSI data.Intermediate times have been interpolated.
Chromospheric Response to Non-Thermal Electrons
In general, the hydrodynamic evolution of the atmo-sphere is qualitatively similar to the F09 case reported byAbbett & Hawley (1999). Here we focus on a narrow regionwithin a distance range of z = α and Ca II Formation and Evolution of Spectral Lines
In order to compare the synthetic H α and Ca II − has been applied to compen-sate for the lack of small scale random motions in the model(de la Cruz Rodr´ıguez et al. 2012).Since the atmosphere at the beginning of the run is in anequilibrium condition, we treat the line profile at this time asthe quiet Sun profile, which is subtracted from the intensityprofiles at other times, obtaining the so-called excess line pro- F ig . 4.— (a) RHESSI photon spectrum from detector 4 taken at 19:11:28-19:11:58, during the impulsive phase. The green and blue lines represent thefitted thermal and non-thermal power-law components respectively. Othercontributions to the spectrum are not shown. The red line is the final fit,taking into account all the components. The two vertical dotted lines markthe energy range over which the spectral fit was performed. (b) Residuals ofthe fit normalized to 1 σ at each energy. file (Henoux et al. 1998; Matsumoto et al. 2008), which willallow us to better interpret how the flux of electrons a ff ectsthe flare emission. The observed H α and Ca II ff ects the chromospheric emission, we write the for-mal solution of the transfer equation for emergent intensity(Carlsson & Stein 1997): I ν = µ Z τ ν S ν e − τνµ d τ ν = µ Z z S ν χ ν e − τνµ dz = µ Z z C i dz , (2)where χ ν is the monochromatic opacity per unit volume; S ν is the source function, which is defined as the ratio betweenthe emissivity to the opacity of the atmosphere; τ ν is themonochromatic optical depth and the integrand C i is the socalled intensity contribution function, which represents theemergent intensity emanating from height z . Evolution of the H α Line Profile
The top row of Figure 9 shows the synthesized H α excessprofiles, which are asymmetric early during the flare and be-come almost symmetric later when the atmosphere relaxes.The line profile including the quiet Sun emission (red solidline in the right column of Figure 9) shows a dip in the linecore.By integrating the intensity along the line profile, and sub-tracting the quiet Sun emission, we estimated the evolution ofthe H α excess flux in time. Figure 5(f) shows the H α lightcurve, where flux has been averaged during the integrationtime of each RHESSI spectrum. As the plasma is pushed F ig . 5.— Variation of the non-thermal electron spectral parameters obtainedfrom fitting the RHESSI data. (a) Mean spectral index; (b) Low cuto ff energy;(c) Non-thermal power; (d) Area of the AIA 1700 Å footpoints; (e) Electronenergy flux obtained by dividing the power by the footpoints area. (f) H α syn-thetic light curve obtained with RADYN ( ∆ λ = II ∆ λ = x -axis represent the integration time of the spectrum (panels (a)-(e))and in the y -axis the standard deviation resulting from the combination of the6 RHESSI detectors. In panels (f) and (g), flux values have only been plottedat the integration interval for clarity. The red and green vertical lines repre-sent the time range during which the H α and Ca II upwards, the chromospheric evaporation takes place and theH α flux decreases. After 19:14:24 the atmosphere is morestable and the H α flux varies with the flux of the injected non-thermal electrons.Between 19:10 and 19:13, the density population at the en-ergy level n of the hydrogen atom decreases by almost a fac-tor of two with respect to the density population at the en-ergy level n (see Figure 10; therefore the ratio n / n at thistime range decreases. The fact that a H α photon is emitted bythe transition from n to n , that explains the decrease of theH α flux at these times. Calcium atoms have a similar behav-ior, which explains the similar decrease shown in Figure 5(g).The top row of Figure 11 shows the intensity contributionfunction, C i (increasing from bright to dark), for H α at thesame times as in Figure 9. The line frequencies are in veloc-ity units, where positive velocities represent plasma movingupwards, towards the corona and negative velocities denote F ig . 6.— SDO / AIA 1700 Å images showing the evolution of the flare ribbons. The red contours represent the footpoints areas having 75% of the maximumintensity and the blue contours, the 30% of the
RHESSI ig . 7.— Initial atmosphere FP2, from Abbett & Hawley (1999), in hydro-dynamic equilibrium.F ig . 8.— Chromospheric spatial distribution of the temperature, electrondensity and velocity (at di ff erent time steps). Positive velocities correspondto upflowing plasma and negative velocities to downflowing plasma. Theback solid line is the initial atmosphere in hydrodynamic equilibrium. TheX-axis is in logarithmic scale. material moving downwards. The blue line represents the at-mospheric velocity stratification and the black line, the lineprofile (including the quiet Sun emission, as the red profilesof Figure 9). The green line represents the height at which τ ν =
1, showing us that the height formation of H α wings iscoming from the lower chromosphere ( ≈ α emission profile becomes broad and centrally reversed duenot only to non-thermal e ff ects when the atmosphere is bom-barded by energetic electrons (Canfield et al. 1984), but alsoto the temperature spatial distribution and the sudden behav-ior change of the source function in a very thin atmosphericlayer. Evolution of the Ca II The synthesized Ca II α and duringthe flare the line becomes almost symmetric, specially in thecore.To obtain the temporal evolution of the Ca II II α , peaking bothfluxes at the same time.Following equation 2, the intensity contribution function C i for the Ca II C i becomes stronger in the coreof the line and presents a symmetric behavior in the wings,being sensitive to plasma velocity changes. The monochro-matic optical depth (green line) shows us that the formationof the wings is constant in time and located below 0.2 Mm;the height formation of the core moves towards lower heightsfor almost seven minutes. Afterwards it is stable at 1.05 Mm. COMPARING OBSERVED AND SYNTHETIC LINE PROFILES
RHESSI entered night at 19:23:52 UT, whereas the firstavailable IBIS observation with decent seeing started at19:22:UT. The two observations thus overlapped for ≈ RHESSI spectral information as input, withthe line profiles observed by IBIS at 19:22:40 UT for H α andat 19:22:15 UT for Ca II Calibration of the quiet Sun profiles
To be able to compare the observed line profiles with thesynthetic profiles, we first have to calibrate the spectral linesof IBIS and RADYN to the same reference system. Weuse the continuum emission of the Fourier Transform Spec-trometer (FTS) atlas taken at the McMath-Pierce Telescope F ig . 9.— Time evolution of the averaged H α (top row) and Ca II ig . 10.— Height stratification of the ratio between the hydrogen energylevel n and the energy level n . (Brault & Neckel 1999) as reference. By doing so, both ob-served and synthetic profiles can be calibrated and normalizedto the continuum.In order to calibrate the lines to the continuum of the FTSatlas, we multiplied the quiet Sun line intensity by a factor,such that the distance between the line and the FTS atlas isminimum at the continuum (see Figure 12).As mentioned in Section 2.1 the H α and Ca II • In general, 1D simulation (even if they take into ac-count the dynamics of the atmosphere) cannot catch allthe structuring and small scales that are present in thechromosphere. • If the spatial resolution of the simulation is not highenough, the width of the average (spatio-temporal) pro-file is lower because the hydrodynamic simulations donot contain the necessary small-scale turbulence andthe small scale motions are missing in the model. AsLeenaarts (2010) mentions, the increase in grid resolu-tion causes an increase in amplitude of the velocity vari-ations in the mid and upper chromosphere, and hence awidening of the average profile. • Because of higher opacities, synthetic lines usuallyshow a much darker line core than the FTS atlas. Thismay be attributed to a low heating rate in simulations.Figure 12 shows the resulting IBIS and RADYN lines fitto the FTS atlas after the calibration. The vertical error barsassociated to the IBIS profile in Figure 12(a) show the di ff er-ence between the observed and the synthetic emission duringthe flare at di ff erent wavelength positions. The intensity dif-ference between both H α lines in the wings is due to the poorfit of the IBIS H α profile to the continuum, because it is avery broad line and the observations covered only a wave-length range of 4 Å.After the quiet Sun profiles were calibrated and normalizedto the continuum, we applied the normalization factor to theflaring line profiles and compared them in Figure 13 with theIBIS H α and Ca II α and Ca II F ig . 11.— Intensity contribution function for H α (top) and Ca II τ ν = ig . 12.— Comparison of the calibrated H α (left) and Ca II ff erence between both profiles during the flare at that particularwavelength position. For a better comparison of the shape of both line profiles,the synthetic profile has been shifted by 0.05 erg s − cm − Å − in order to align the wings of both lines. The line hasbeen scaled to fit at the core, as shown by the green line ofFigure 13. H α Line Profiles
Figure 13(a) compares the H α excess line profile ob-tained from RADYN (red) and observed by IBIS (blue) from19:22:40 to 19:23:07 UT. As mentioned in Section 4.1, theintensity shift between both profiles at the wings of the line isdue to the uncertainty of the continuum fit.The core of the simulated line is ≈
23% less bright thanthe observation and the wings are slightly narrow, as dis- cussed in Section 4.1. The core of H α is sensitive to the tem-perature pattern due to the low mass of the hydrogen atom(Leenaarts et al. 2012) which can contribute to the di ff erencein the core emission. The green profile in Figure 13(a) is thesynthetic profile scaled to fit at the core and at the continuumof the IBIS profile and the vertical error bar represents thedi ff erence between the observed and the synthetic emission atdi ff erent wavelength positions, calculated for this time.The standard NLTE line formation assumption of statisticalequilibrium does not properly fit the observations because ofthe slow collisional and radiative transition rates when com-pared to the hydrodynamical timescale. In addition, at leastthe Lyman- α and β lines need to be modeled with partialfrequency redistribution (PRD) because of their strong influ-0 F ig . 13.— Comparison of the H α and Ca II α line is 1.07 Å, while for Ca II ff erence between observedand synthetic profiles during the flare at that particular wavelength position. ence on the H α line (Leenaarts 2010). Inclusion of thesee ff ects might significantly increase the H α opacity. Thus,proper modeling of the H α line requires full time-dependentradiative transfer with PRD in tandem with the hydrody-namic evolution, a Herculean task that has not been donein 1D hydrodynamic simulations since so far all 1D simula-tions perform radiative transfer assuming complete redistribu-tion (Allred et al. 2005; Kaˇsparov´a et al. 2009; Varady et al.2010).As Leenaarts et al. (2012) explains, PRD e ff ects can be ap-proximated by truncating the Lyman line profiles. RADYNtruncates the Lyman line profiles at ±
64 km s − away fromthe line center frequency. This is a reasonable approximation,with the e ff ect that we get higher heights of formation than ifwe assumed PRD. Ca II Figure 13(b) compares IBIS (blue line) and RADYN (redline) at the time range 19:22:15 - 19:22:42 UT, showing agood agreement between both profiles. The green line pro-file is the synthetic profile scaled to fit at the core and at thecontinuum of the IBIS profile.As mentioned by Smith & Drake (1987), assuming com-plete spectral redistribution for the scattered photons may bea poor approximation for the Ca II II ff ects are important, especiallyin the core of the line. Considering these two statements andthat both lines di ff er in the core in ≈ only 2.4%, our syntheticCa II τ ν =
1, (green line in Figure 11) we get that theCa II α is formed at 0.2 Mm in thewings of the line and 1.15 Mm at the core. Even if both lines had almost a similar formation height range and the same at-mospheric conditions, Ca II α . Since the 3d D / , / levels are metastable,they can only be populated from below by collisional excita-tion, strengthening the sensitivity of the Ca II infrared tripletto local temperature. On the other hand, the lower energylevel of H α is 10 eV higher than Ca II ff erent behavior of the two lines. SUMMARY AND DISCUSSION
We have presented in this paper a self-consistent, data-driven radiative hydrodynamic simulation of an M3.0 flareand its comparison with high-resolution spectroscopic obser-vations by the IBIS instrument. By fitting X-ray spectra ofthis flare observed by
RHESSI , we inferred the flux of the non-thermal accelerated electrons, which was used as an input tothe RADYN code. The RADYN code incorporates carefultreatments of atomic and molecular physics together with ra-diative transfer and hydrodynamics, allowing us to study theevolution of the flaring atmosphere as well as the detailedchromospheric emission. We synthesized the H α and Ca II II α synthetic line is ≈
23% fainter in the core thanthe observations. Both synthetic lines have similar shapes asthe observed line, but the synthetic lines exhibit a typical flat-tening in the core due to an overestimate of the opacity, asdiscussed in Section 4.1.There are several limitations in our approach, which couldbe improved in the future. For example, solar flares are com-plex and dynamically three-dimensional in nature. The cur-rent 1D models are not yet capable of handling this properlyand solving the equations of non-equilibrium and non-LTEoptically thick radiative transfer in multiple dimensions. Theinclusion of a quasi thermal component in the electron dis-tribution, in addition to the non-thermal component, and aproper treatment of the electron transport process can play an1important role in the estimation of the electron heating rate(e.g., Liu et al. 2009). Moreover, taking into account the un-certainties in the
RHESSI fitting parameters and the measure-ment of the area may reduce the di ff erences between the syn-thesize and observed line profiles.As noted by Leenaarts (2010), the dominant chromosphericenergy loss on the quiet Sun is through radiation in stronglines, and a comprehensive model of the chromosphere cannotbe constructed without the inclusion of the underlying pho-tosphere and upper convection zone and the overlying lowercorona. Our RADYN code lacks detailed treatment of thephotospheric radiation, which could potentially contribute tothe small discrepancies between the synthetic and observedlines. A better reproduction of the observations may requirehigher resolution, larger computational domains, an improvedtreatment of radiation and non-equilibrium hydrogen ioniza-tion. To improve the modeling of the hydrogen transitions andin particular H α , 3D NLTE time-dependent radiative transfercodes including PRD would be a considerable undertaking.By increasing the flux of the injected electrons a factor oftwo, the atmosphere evolves faster at initial times and as resultthe line profiles show red-wing asymmetries at early times. During the impulsive phase of the flare, the H α emission in-creases by a factor of 1.2 and Ca II α and a factor of 1.1 for Ca II α and Ca II InterfaceRegion Imaging Spectrograph ( IRIS ; De Pontieu et al. 2014)would give a more detailed information about the response ofthe chromosphere during a solar flare.The authors thank M. Carlsson for the stimulating discus-sions. Work performed by F.R.dC., V.P. and W.L. is sup-ported by NASA grants NNX13AF79G and NNX14AG03G.L.K. and A.S.D. are supported by NASA LWS grantNNX13AI63G.
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