Solar Flare Composition and Thermodynamics from RESIK X-ray Spectra
B. Sylwester, J. Sylwester, K. J. H. Phillips, A. Kepa, T. Mrosek
aa r X i v : . [ a s t r o - ph . S R ] A p r Solar Flare Composition and Thermodynamics from RESIK X-ray Spectra
B. Sylwester and J. Sylwester Space Research Center, Polish Academy of Sciences, Kopernika 11, 51-622 Wrocław, Poland bs,[email protected]
K. J. H. Phillips Earth Sciences Department, Natural History Museum, London SW7 5BD, United Kingdom [email protected]
A. Ke¸pa and T. Mrozek , Astronomical Institute, University of Wrocław, ul. Kopernika 11, 51-622 Wrocław, Poland ak,tmrozek @cbk.pan.wroc.pl
Received ; accepted Scientific Associate 2 –
ABSTRACT
Previous estimates of the solar flare abundances of Si, S, Cl, Ar, and K from theRESIK X-ray crystal spectrometer on board the
CORONAS-F spacecraft were madeon the assumption of isothermal X-ray emission. We investigate the effect on these es-timates by relaxing this assumption and instead determining the differential emissionmeasure (DEM) or thermal structure of the emitting plasma by re-analyzing RESIKdata for a
GOES class M1.0 flare on 2002 November 14 (SOL2002-11-14T22:26)for which there was good data coverage. The analysis method uses a maximum-likelihood (Withbroe–Sylwester) routine for evaluating the DEM. In a first step, calledhere AbuOpt, an optimized set of abundances of Si, S, Ar, and K is found that is con-sistent with the observed spectra. With these abundances, the differential emissionmeasure evolution during the flare is found. The abundance optimization leads to re-vised abundances of silicon and sulfur in the flare plasma: A (S) = 6 . ± . and A (Si) = 7 . ± . (on a logarithmic scale with A (H) = 12 ). Previously determinedabundances of Ar, K, and Cl from an isothermal assumption are still the preferredvalues. During the flare’s maximum phase, the X-ray-emitting plasma has a basicallytwo-temperature structure, with the cooler plasma with approximately constant tem-perature (3–6 MK) and a hotter plasma with temperature − MK. Using imagingdata from the
RHESSI hard X-ray spacecraft, the emission volume of the hot plasmais deduced from which lower limits of the electron density N e and the thermal contentof the plasma are given. Subject headings:
Sun: corona — Sun: flares — Sun: X-rays, gamma-rays — Sun:abundances
1. Introduction
Observations of solar soft X-ray spectra are essential for the diagnostics of hot plasmasassociated with flares and active regions. The fluxes of emission lines and continua dependsensitively on electron temperature or rather, since the plasma is not in general isothermal, thedistribution of emission measure with electron temperature. For rapidly varying conditions,X-ray spectra can also be used to find the plasma’s ionization state or the presence of nonthermalelectrons. If combined with images taken at similar energy ranges, lower limits of electrondensities and the energy content of the emitting plasma can also be found.The RESIK (REntgenovsky Spektrometr s Izognutymi Kristalami: Sylwester et al. (2005))instrument, a crystal spectrometer aboard the Russian
CORONAS-F d = 6 . ˚A) for channels 1 and2 (spectral ranges for an on-line source 3.40 ˚A–3.80 ˚A, 3.83 ˚A–4.27 ˚A) and two quartz crystals(quartz , d = 8 . ˚A) for channels 3 and 4 (spectral ranges 4.35 ˚A–4.86 ˚A, 5.00 ˚A–6.05 ˚A).Instrumental fluorescence background emission, often a problem with previous solar X-rayspectrometers, was minimized through the adjustment of pulse-height analyzer settings over themission lifetime; ultimately, for the period 2002 December 24 to 2003 March 23, the fluorescence 4 –background was entirely eliminated for channels 1 and 2 and its amount reduced and accuratelyestimated for channels 3 and 4. To maximize the instrument’s sensitivity, no collimator was used;although this introduced the possibility of overlapping spectra from two or more X-ray sources onthe Sun, in practice this very rarely occurred.RESIK was intensity-calibrated to a higher accuracy than was possible for previous solarcrystal spectrometers (the procedure is described by Sylwester et al. (2005)), so enabling elementabundances to be derived for elements whose spectral lines feature in RESIK spectra. Previously,such analyses (see e.g. Sylwester et al. (2010b)) have used the assumption of an isothermalplasma for the X-ray emission and with temperature and emission measure given by the flux ratioof the two emission bands of GOES . The justification for this was that plots of the measured linefluxes during flares divided by the
GOES emission measure ( EM GOES ) against
GOES temperature( T GOES ) showed points distributed either along the theoretical G ( T e ) function or the functiondisplaced by a constant amount. The G ( T e ) function is the line emission per unit emission measureas a function of electron temperature T e calculated, e.g., from the CHIANTI atomic database andsoftware package (Dere et al. 1997; Landi et al. 2012) for an assumed element abundance. Theamount of the displacement gives the factor by which the assumed abundance must be adjusted togive agreement with the measured RESIK line fluxes. A particularly tight distribution of pointsaround the calculated G ( T e ) curve was obtained for the case of the Ar XVII lines in RESIK’schannel 2, and a rather broader scatter of points for K and Cl since the line emission for theselow-abundance elements was weak. Thus an argon abundance estimate with very small statisticaluncertainty ( A (Ar) = 6 . ± . on a logarithmic scale with A (H) = 12 ) resulted, in closeagreement with other argon abundance estimates from solar proxies (Sylwester et al. 2010a). TheRESIK Si and S abundance estimates are based on strong lines of H-like and He-like Si and Sseen in RESIK’s channels 3 and 4, but the distribution of points given by line flux divided by EM GOES against T GOES was less impressive than that for the Ar
XVII lines. It was speculated(Sylwester et al. 2012, 2013) that the subtraction of crystal fluorescence was not as accurately 5 –done as was thought or that the results were affected by some lines occurring very near the endof the range of either channel 3 or channel 4. Here we investigate whether the assumption of anisothermal emitting plasma might instead be more significant in leading to biased results, thethinking being that the temperature derived from the two
GOES channels is more representative ofthe hotter Ar
XVII lines than that of the H-like or He-like Si and S ions, an idea described furtherin Section 3.In this work, we discuss RESIK spectra for the particular case of the M1.0 flare on 2002November 14 with
GOES soft X-ray maximum at 22:26 UT (SOL2002-11-14T22:26 using theIAU standard flare-naming convention). We first used an iterative procedure (AbuOpt) to deriveoptimized element abundance estimates of Si, S, Ar, and K, since these elements are representedby lines in RESIK spectra and so their abundances will influence the nature of the RESIK spectra.The optimization is done with a maximum likelihood routine (the Withbroe–Sylwester routine)which determines the differential emission measure (DEM). The optimized abundances of Siand S in particular differ from our previous estimates based on an isothermal assumption. Withthe Withbroe–Sylwester routine, and with the optimized abundances of Si, S, Ar, and K, theevolution of the differential emission measure (DEM) over the flare duration was then found.With X-ray images of this flare from
RHESSI , estimates of the emitting volume V are made, andfrom these, lower limits to the electron densities and thermal energy content of the flaring plasmaare determined. The physical significance of the new Si and S abundances are discussed in respectof the well known first ionization potential (FIP) effect, in which the abundances of elements withlow ( . eV) FIP in coronal plasmas are apparently enhanced over photospheric abundances.
2. Observations
The SOL2002-11-14T22:26 flare occurred in active region NOAA 10195 located at S14E65,a region that had recently rotated on to the south-east limb and became flare-productive on 2012 6 –November 14. During the November 14 flare under discussion, the X-ray emission, indicated byboth RESIK and
GOES , showed a sudden enhancement starting at 22:15 UT with maximum atabout 22:26 UT, followed by a slow decay extending until spacecraft night, at 22:56 UT. Some124 individual RESIK spectra (total integrated time 26.5 minutes) are included in the spectrumshown in Figure 1 (top left panel) which is averaged over the entire flare duration. The top rightand lower panels ( e , g , n ) show RESIK spectra averaged over time intervals (given in the caption)during the rise, maximum, and decay phases of the flare. The changing relative line fluxes of theS XV lines near 5.04 ˚A (channel 4) and S XVI
Ly- α line at 4.73 ˚A, connected by dotted lines,are evident, indicating as expected that the maximum temperature is attained near the flare peakphase. Three RESIK spectra were taken during the previous spacecraft orbit (from 21:15:16 UTto 21:18:52 UT) when no soft X-ray flare was in progress and the total X-ray activity was muchlower ( GOES
C1 level); the average of these spectra is shown near the zero level of panel n ,clearly showing that the spectra shown in Figure 1 are almost entirely due to the flare. The chiefspectral line features are due to transitions in H-like and He-like ions of Si, S, Ar, and K and areformed by thermal plasmas with temperature range 2 MK to 20 MK. Among those of note are theHe-like K (K XVIII s − s s, s p ) lines (see Sylwester et al. (2010b)) and H-like and He-likeAr lines in channel 1; the He-like Ar (Ar XVII s − s s, s p ) lines (Sylwester et al. 2010a) andthe He-like S (S XV ) s − s p line in channel 2; the S XV s − s p and H-like S (S XVI ) Ly- α lines (Sylwester et al. 2012) and He-like Cl (Cl XVII ) lines (Sylwester et al. 2011) in channel 3;and S XV s − s s, s p lines and H-like Si (Si XIV ) and He-like Si (Si
XIII ) lines and someSi
XII dielectronic satellites (Sylwester et al. 2012, 2013) in channel 4. Further details about theselines including wavelengths are given in the papers cited and in Table II of Sylwester et al. (2005).Figure 2 shows the normalized X-ray light curves for the flare in
RHESSI and
GOES withcolor codes for different energy bands (the two
GOES bands and three selected from available
RHESSI bands). The harder X-rays seen with
RHESSI peak early in the flare development, withthe 12 – 25 keV and 25 – 50 keV emission showing sharp impulsive bursts at 22:24:42 UT and 7 – I rr ad i an c e [ P ho t. c m − s − Å − ] K XV III w , x , y , z A r XV II w , x , y , z S XV w S XV I L y α S XV w , x , y , z S i X I V L y ß S i X III w S i X III w e I rr ad i an c e [ P ho t. c m − s − Å − ] g n Fig. 1.— (Top left:) Averaged RESIK spectrum for the SOL2002-11-14T22:26 flare over theperiod 22:22:45–22:53:31 UT (total exposure time 26.5 minutes). Different colors are used for thefour RESIK channels. Principal line identifications of the chief features are given; the notationused is for the He-like ions (K
XVIII , S XV , Si XIII ) are w = 1 s S − s p P , w s S − s p P , w s S − s p P . (Top right and lower panels:) Three representative spectrataken during the rise (22:22:46–22:24:48 UT, upper right e ), maximum (22:25:46–22:26:46 UT,lower left g ), and decay (22:34:06–22:36:36, lower right n ) phases of the flare, with integrationtimes 2, 1, and 2.5 minutes (the letters refer to the intervals shown in Figure 2). The pre-flarespectrum is shown near the zero level of panel n . The inclination of the dotted track linking theS XV (5.04 ˚A) and the hotter S XVI (4.73 ˚A) line features is an indication of the emitting plasma’schanging temperature. 8 – R e l a t i v e i n t en s i t y a b c d e f g h i j k l m n o p q r s Fig. 2.— Normalized
RHESSI and
GOES light curves for the SOL2002-11-14T22:26 flare. The
GOES fluxes in the 1 – 8 ˚A and 0.5 – 4 ˚A ranges are shown as black continuous and dashed linesrespectively. The
RHESSI light curves are shown by colored lines: pink (6 – 12 keV), green (12 –25 keV), and blue (25 – 50 keV). The key letters above each time strip denote intervals over whichRESIK spectra were integrated for DEM analysis. The grey strip indicates a passage through apolar van Allen radiation belt when the RESIK high-voltages were turned off and no observationswere made. 9 –Fig. 3.— Four
RHESSI images of SOL2002-11-14T22:26 flare obtained with the PIXON algo-rithm in the energy range 6 – 7 keV. Times (UT) are indicated at the top of each panel. The top twoimages were taken during hard X-ray impulsive emission, the lower left image at the soft X-raymaximum, and the lower right image during the decay phase. The contours are drawn at levels 0.5,0.7 and 0.9 of the maximum intensity in each image. Solar north is at the top of each image, solareast to the left; the x (east–west) and y (north–south) co-ordinates are in arcseconds. The dottedgrid lines show solar longitude and latitude at ◦ intervals. The integration time for the last imagewas 12 s, the first three images 4 s (i.e. one rotation of the RHESSI spacecraft). The low-intensityfeature to the south of the main feature in the last image is reproducible and so is likely to bereal, but its weakness does not significantly add to the total emission. The extent of the main flareemission at the 50% iso-contour level is approximately 5400 km. 10 –22:25:27 UT, during the soft X-ray emission rise seen with
GOES . This figure also shows 19 timeintervals (marked by key letters a to s ) over which RESIK spectra were integrated and used forfurther analysis, in particular the inversion of line fluxes to obtain differential emission measurefor which spectra of high statistical quality are necessary. (Letters e , g , and n in the panels ofFigure 1 refer to those shown in Figure 2.) Figure 3 shows RHESSI images of the flare, with theupper two images were taken during the first and second hard impulsive X-ray peaks, the lowertwo images during the soft X-ray maximum (22:26:48 UT) and the decay phase (22:28:52 UT).The image reconstructions were performed using the PIXON method and
RHESSI grids 3, 4,5, 6, 8, and 9; this was done for the 6 – 7 keV energy range, which is effectively the lowestaccessible to
RHESSI and so is larger than the energy range of the RESIK spectra (2.0–3.6 keV).In the analysis below, we are interested in the
RHESSI image dimensions so the relative meritsof image construction routines are of some importance. These are discussed by Dennis & Pernak(2009). The PIXON method is the only way to image extended sources in the presence of compactsources, as in the case here, and there is much less background compared with the CLEANroutine which is also available. There is the possibility of “over-resolution” (i.e. the source sizeis under-represented) with PIXON, but only if the total signal in the image exceeds 6000–7000photon counts: in the case of the images shown in Figure 3, the total signal is slightly less than2000 counts. The contours on the images in Figure 3 are drawn at levels 0.5, 0.7 and 0.9 of themaximum emission in each image. Approximately 60 such images over the flare duration showan additional weak feature to the south of the main structure; this does not add to estimates of theimage extent which, at the 0.5 contour level, is almost constant at 5400 km.
3. Spectral analysis method
A commonly used method of deducing electron temperature T e and volume emission measure EM = R N e dV for X-ray flare emission assumed to be isothermal uses the flux ratio of the GOES
11 –1–8 ˚A and 0.5–4.0 ˚A bands based on the work of White et al. (2005). However, an isothermalassumption is not generally valid for the interpretation of X-ray spectra with many lines formedover a broad temperature range, different temperatures being obtained according to the fluxratio of the lines chosen. More generally, the emission measure within intervals of temperatureis described by the differential emission measure, DEM (Withbroe 1975; Levine & Pye 1980;McTiernan et al. 1999; Landi & Chiuderi Drago 2008). Thus, for an optically thin, multi-thermalplasma such as the X-ray flare discussed here, the observed flux F i of each line or spectral interval i can be expressed as (Sylwester et al. 1980): F i = A i Z ∞ T =0 f i ( T ) ϕ ( T )d T (1)where A i represents the assumed abundance of an element contributing to the flux of a particularline or spectral interval. We assume A i to be constant over emitting volume V , while f i ( T ) , theemission function (more commonly known as the G ( T ) function for individual lines) is calculablefrom atomic excitation theory for chosen spectral intervals i . The differential emission measurefunction ϕ ( T ) , defined by DEM ≡ ϕ ( T ) ≡ N e d V d T , (2)may be determined by solving under certain conditions from the analysis of a full system ofequations like Equation (1) for i spectral intervals. Although the problem is recognized as beingill-conditioned (Craig & Brown 1976), methods of solution exist that give solutions for ϕ ( T ) and their uncertainties that satisfy the input data to within observational uncertainties and canbe ascribed physical meaning. Here, we followed the iterative maximum-likelihood, Bayesianroutine called the Withbroe–Sylwester method and described by Sylwester et al. (1980). It hasbeen tested previously on synthetic spectra and assumed DEM functions to see whether the DEMsare recovered after the inversion (e.g. Sylwester & Sylwester (1998, 1999); Ke¸pa et al. (2006)). 12 –Table 1: Wavelength bands used for studies of the elemental abundances and DEMNo Range [ ˚A] Main contributor (cont. = continuum)1 3.480 - 3.630 cont. + K XVIII p +sat.2 3.630 - 3.800 cont. + Ar XVIII p , S XVI p, p XVII p +sat, S XV p XV sat.5 4.340 - 4.430 cont. + S XV p +sat6 4.430 - 4.520 cont. + Cl XVI p +sat7 4.680 - 4.750 cont. + S XVI p , + Si XIV p XIV p XV p +sat + cont.10 5.220 - 5.320 Si XIII p +sat. + cont.11 5.320 - 5.470 Si XIII p +sat. + cont.12 5.475 - 5.640 Si XII sat. + cont.13 5.640 - 5.715 Si
XIII p + cont.14 5.715 - 5.850 Si XII sat. + cont.15 5.900 - 5.950 continuumThe analysis proceeds in two steps. In the first (called AbuOpt), optimized values for theabundances of elements that make large contributions to the line features in RESIK spectra arefound. We selected the input data which consisted of observed fluxes in 15 narrow spectralintervals in RESIK spectra for each of the 19 time intervals ( a to s ) shown in Figure 2; mostinclude strong emission lines while a few are almost entirely continuum radiation (the sumof free–free and free–bound). The wavelength ranges of the intervals and details of principalemission features included (lines or continuum) are specified in Table 1. The main lines arethose due to H-like or He-like Si, S, and Ar and associated dielectronic satellite lines, with the 13 –He-like K lines generally appearing as weak (the He-like Cl lines are much weaker still and havepractically no effect on the analysis). In the table, we use the notation “ p ” for the transition s S − s p P in He-like ions and “ p ” for Ly- α in H-like ions; “sat.” for dielectronic satellitelines; and “cont.” for continuum. We then applied the Withbroe–Sylwester DEM inversion methodto these input data to achieve an optimum fit between the observed and calculated fluxes. Thisrequires the evaluation of the emission functions f i ( T ) for these intervals – lines plus continuumor continuum alone – which can be calculated from the CHIANTI (v. 7.0) code. These dependon temperature and element abundance (Equation 1). We investigated the effect of varying theabundances of Si, S, Ar, and K. To do this, and to avoid a time-consuming calculation, wepre-calculated a grid of theoretical spectra with temperatures in the range 1–100 MK (101 stepsin equal intervals of log T ) and 21 values of the abundances of four elements (Si, S, Ar, andK) ranging from zero to 16 times the CHIANTI “coronal” value. With one exception, the otherelement abundances, which affect the free–bound continua only, were kept at their coronal valuesas specified in
CHIANTI ; the effect of varying these abundances is relatively minor – see theanalysis of Phillips et al. (2010). The exception is the element Cl which has very low abundance;for this we took our abundance estimate A (Cl) = 5 . ± . (from Sylwester et al. (2011) basedon an isothermal analysis of Cl XVI lines in RESIK channel 3). There are, as a result of thiscalculation, 84 ( × ) pre-calculated spectra for each of 101 temperatures in the RESIK spectralrange (the spectral resolution was chosen to be 0.001 ˚A).With these calculated spectra, we ran the Withbroe-Sylwester DEM method on the inputdata consisting of fluxes in the 15 narrow spectral intervals, the DEM ( ϕ ( T ) ) function varyingfreely for each of the 21 abundance values for Si, S, Ar, and K. After 1000 iterations, the valueof normalized χ was obtained describing the difference between the measured and fitted fluxesin terms of measurement uncertainties (assuming Poissonian statistics of the photon counts).Figure 4 shows examples for Si, S, Ar, and K for the 19 time intervals (represented by curves withdifferent colors) and the spectrum averaged over all 19 intervals (black curve with dots). Clear 14 –minima in the value of χ / min( χ ) as a function of element abundance are apparent for Ar, S,and Si; the K abundance is too small to have any effect on the value of χ below a thresholdcorresponding to a potassium abundance of − of the hydrogen abundance. We interpret theplots to mean that the abundance corresponding to the minimum in χ is the optimum one, i.e. forwhich the agreement between the observed set of spectral fluxes and the theory is the best.In Figure 5 we plot derived optimum abundance values against time for Si, S, Ar, and K.Uncertainties in the abundance determinations are assigned that correspond to the abundance rangedefined by min( χ ) + 1 (Bevington & Robinson 2003). There is little evidence for time-changingabundances apart from a slight tendency of A (S) to be a little smaller at earlier times. Theabundances (linearly averaged over the 19 time intervals) obtained are: A (K) = 6 . ± . , A (Ar) = 6 . ± . , A (S) = 6 . ± . , and A (Si) = 7 . ± . (abundances are expressedon a logarithmic scale with A (H) = 12 ). As a result, we assume from hereon that the Si, S, Ar,and K abundances are time- and temperature-independent, at least for the flare considered here.In future analysis, this assumption may be relaxed to account for possible abundance differenceswith temperature.As indicated earlier, most of our previous analyses of RESIK flare spectra were basedon an isothermal assumption, with the emitting temperature and emission measure taken from GOES ( T GOES , EM GOES ). For the Ar abundance, determined from the prominent Ar
XVII lines in channel 2, a very tight distribution of observed points given by the “ G ( T ) ” plot, i.e.line flux divided by EM GOES plotted against T GOES , was obtained, resulting in an abundancedetermination with small uncertainty: A (Ar) = 6 . ± . (Figure 2 of Sylwester et al. (2010a)).This value is in close agreement with other determinations from solar proxies (e.g. H II regions,Jupiter’s atmosphere) and is considered by us to be fairly definitive. The value obtained in thiswork is slightly higher. It also has larger uncertainty which would indicate prima facie that forthis particular flare the isothermal abundance interpretation is more likely to be correct. But as 15 – B e s t − f i t Log [ χ / m i n ( χ ) ] K Ar B e s t − f i t Log [ χ / m i n ( χ ) ] S Si Fig. 4.— Plot of the quality of the fit, expressed as the ratio of normalized χ to the minimumvalue of χ , of the observed and theory fluxes for all 19 time intervals during the flare (coloredto distinguish them: blue for rise phase spectra, red, orange, or green for decay phase) as a func-tion of assumed element abundance for K, Ar, S and Si. The black curve with dots is derivedfrom the average spectrum over the 19 time intervals. The vertical dotted blue lines correspondto the CHIANTI “coronal” abundance (Feldman 1992), and the dashed red lines to the
CHIANTI “photospheric” abundances (Asplund et al. 2009). 16 –indicated in Section 1, it appears, from the agreement of the observed points with the calculated G ( T ) plot shown by Sylwester et al. (2010a), that the characteristic temperature of the plasmaemitting the Ar XVII lines is well described by the temperature estimated from the two
GOES channels. We therefore interpret this to mean that the isothermal abundance determination is tobe preferred. For potassium, the estimated abundance from this work is a factor 4.5 higher thanthat from our previous determination ( A (K) = 5 . ± . : Sylwester et al. (2010b)) assumingisothermal emission and has larger uncertainty. The larger uncertainties again suggest that thevalue from our earlier isothermal analysis to be preferred; the similar temperature of formationof the K XVIII lines to that of the Ar
XVII lines suggests that the
GOES temperature accuratelydescribes the K
XVIII line emission also.For the lower-temperature S ions (both H-like and He-like ions were considered), theisothermal analysis of RESIK spectra by Sylwester et al. (2012) was not particularly satisfactory,with large scatter of points on the G ( T ) plot, even though there are several strong lines withwhich the analysis is possible. Sylwester et al. (2012) determined A (S) = 7 . ± . , i.e.higher than the presently determined value ( A (S) = 6 . ± . ) and with larger uncertainty. Are-analysis of the SOL2002-11-14T22:26 flare spectra alone on an isothermal assumption gives A (S) = 7 . ± . (S XV w and nearby lines at 5.04 ˚A) and A (S) = 7 . ± . (S XV w line at4.08 ˚A). Our interpretation here is that the less satisfactory agreement of the observed points withthe calculated G ( T ) function is due to the fact that the S XV emission functions have characteristictemperatures that are less than those derived from the ratio of the GOES channels. In this case,a DEM analysis of the emitting flare plasma gives a more reliable abundance determination. Insummary, our preferred value for the S abundance for this flare is the one determined in thepresent analysis, viz. A (S) = 6 . ± . .The argument for the S abundance determination holds a fortiori for the Si abundance,since the lines on which the determinations are principally made, He-like and H-like Si (Si XIII
17 –and Si
XIV ), have lower characteristic temperatures than the S lines. From an isothermalassumption (Sylwester et al. 2013), we determined A (Si) = 7 . ± . (Si XIII lines), and A (Si) = 7 . ± . (Si XIV lines), both estimates being about a factor 2 more than is estimatedfrom the present work ( A (Si) = 7 . ± . ) and having larger uncertainties. In this case,therefore, our preferred value for the Si abundance is the one given by this analysis. (Note that forcomparison with recent abundance estimates for RS CVn stars (Huenemoerder et al. 2013), valuesof S and Si abundances were used from a DEM analysis of a flare on 2002 December 26 with theisothermal values of Ar and K for the same flare.)An illustration of the foregoing argument with reference to the G ( T ) functions for theprincipal RESIK lines is provided by a plot that we constructed of RESIK and RHESSI spectraduring a flare against photon energy together with a theoretical spectrum from
CHIANTI calculatedwith
GOES values of temperature and emission measure estimated at the time of the spectrum.A very close agreement of the
CHIANTI spectrum with the RESIK channels 1 and 2 spectra wasfound. However, the temperature of the
CHIANTI spectrum was too low to describe the
RHESSI spectrum but on the other hand too high to describe the RESIK spectrum in channels 3 and 4. AsRESIK channels 1 and 2 include the Ar
XVII and K
XVIII lines, it appears that these lines are welldescribed by
GOES temperature and emission measure but the S and Si lines in RESIK channels3 and 4 are not; for these lines a lower-temperature component is needed to fit their fluxes.With optimized averaged abundances for S and Si and the isothermal abundancedeterminations for Ar and K, the DEM distribution for the 19 time intervals of the flare could nowbe calculated. Abundances of elements other than these were taken from the
CHIANTI “coronal”abundances of Feldman et al. (1992), except for Cl as already described. With the ionizationfractions of Bryans et al. (2009), the Withbroe–Sylwester procedure was then used for the DEMinversion, the convergence continuing until iteration
10 000 . The uncertainties of the inversionwere determined from 100 Monte Carlo runs, where the input line fluxes for every time step were 18 – −8−7−6−5−4 GO ES f l u x [ W m − ] A bundan c e [ l og ] K +− 0.46 A bundan c e [ l og ] Ar +− 0.11 A bundan c e [ l og ] S +− −0.06 A bundan c e [ l og ] Si +− −0.08 Fig. 5.— The time variations of derived absolute abundance of K, Ar, S and Si. The abundanceswere determined using the abundance–optimization (AbuOpt) approach described in the text. Theerror bars on abundance determination are based on the results presented in Figure 4 and cor-respond to the range of values for min( χ ) + 1 . . Thin black horizontal lines represent timeaveraged values of elemental abundances together with their RMS error bands (dotted horizontallines). In the top panel, the GOES light curves integrated over the times of individual RESIKspectra collection are shown. The horizontal blue dotted lines correspond to “coronal” abun-dances (Feldman (1992)), while the dashed red lines correspond to “photospheric” abundances(Asplund et al. (2009)). 19 –randomly perturbed with corresponding statistical uncertainties. The evolutionary changes ofthe DEM are indicated in the left and right panels of Figure 6. The left panel shows the DEMdistribution as a contour plot, while calculated DEMs for selected times during the flare (intervals a , g , i , l , q in Figure 2) are shown in the right panel. It is evident that for all times the bulk of theemitting plasma has a temperature of − MK contributing to a cooler component. A hotter component is present near the flare’s maximum phase with temperature of ∼ − MK asis clear from Figure 6, but the emission measure is always more than two orders of magnitudesmaller. For comparison, the temperature derived from the flux ratio of the two bands of
GOES ,assuming isothermal emission, is shown on this plot as the curve running from top to bottom;the
GOES temperature is generally a little higher than the cooler component indicated by theDEM analysis except at the flare peak when it does not quite attain the temperature of the hottercomponent. The temperature of the cooler component is perhaps somewhat larger than that typicalof non-flaring regions, but the
GOES emission in the previous
CORONAS-F spacecraft orbit (atabout the C1 level) indicates a temperature of about 5 MK, a reflection of the presence of severalnon-flaring active regions on the Sun at the time. A DEM analysis of the RESIK emission duringthe previous orbit in fact shows the bulk of the emission to have a temperature of ∼ . MK.The total emission measures of the cooler and hotter components indicated in Figure 6(left panel) were evaluated and plotted in Figure 7 (top panel). The emission measures of bothcomponents evolve with time, reaching a maximum in each case at about the time of the
GOES maximum emission (22:26 UT), with that of the cooler component larger by a factor of about100. The decrease of the emission measure of both components is somewhat faster than that of EM GOES evaluated from the flux ratio of the two
GOES bands.The temperature of the cooler component is low enough that it is unlikely to contributesignificantly to the 6 – 7 keV emission seen in the
RHESSI images shown in Figure 3. If weinterpret the
RHESSI emission to be due mainly to the hotter component seen in RESIK spectra, 20 – M i nu t e s i n t o t he e v en t f r o m [ : : U T ] agilq T GOES a g i l q Log E M [ c m − K − ] Fig. 6.— (Left:) Contour plot of the differential emission measure during the SOL2002-11-14T22:26 flare, darker colors indicating greater emission measure. The horizontal scale is thelogarithm of temperature, and time increases upwards, measured from 22:14:41 UT. Horizontaldotted lines define the time intervals a , g , i , l , and q (see Figure 2) and the smooth curve runningfrom top to bottom is the temperature derived from the ratio of the two GOES channels on anisothermal assumption. (Right:) Emission measure distributions for the intervals indicated in theleft plot, derived from the Withbroe–Sylwester routine. Vertical error bars indicate uncertainties.A cooler (temperature ∼ − MK) component is present over all the time interval shown, withhotter component ( ∼ MK) at the peak of the
GOES light curve. 21 –
Log E M [ c m − ] Log N e E T H [ e r g s ] Fig. 7.— The time evolution of (top) the total emission measure for the cooler (
T < MK, inblack) and hotter (
T > MK in red) plasma (the blue solid line is the emission measure EM GOES from the flux ratio of the
GOES bands); (center) electron densities derived from the emissionmeasure of the hotter component and average size of the
RHESSI images; (bottom) thermal energy E th , defined by Equation (3) (the blue curve is E th as deduced from GOES ). 22 –we may obtain densities and other information about the flaring plasma. A series of approximately60
RHESSI . × cm . Combined with the peak emission measure of the hotter component( × cm − ), this gives an electron density N e = 2 . × cm − . The detailed time variationsare indicated in Figure 7 (center panel). Estimates of the thermal energy E th , E th | N e =const = 3 k B R T ϕ ( T ) dT qR ϕ ( T ) dT √ V (3)where k B is Boltzmann’s constant, presented in Figure 7 (bottom panel), show that E th reachesa maximum of ∼ × erg, rather typical for a medium-class flare such as the one underdiscussion.
4. Discussion and Conclusions
One of the primary intentions of this analysis of RESIK spectra and other data for theM1 flare under discussion has been to test a calculation procedure for obtaining differentialemission measure using spectral fluxes from the RESIK instrument on
CORONAS-F . Data fromthis well-calibrated instrument have been used in the past to derive abundances of elementswhose lines occur in the RESIK X-ray range (3.4–6.1 ˚A), viz. Si, S, Ar, K, and Cl. For flaredata we have previously used the approximation that the emitting plasma is isothermal withtemperature given by the flux ratio of the two bands of
GOES . This appears to be a goodassumption for the case of Ar, K, and Cl abundance determinations, which particularly in thecase of Ar have small uncertainties and agree well with abundance determinations from other, 23 –unrelated, methods. Previous determinations of the Si and S abundances from RESIK spectrausing the same procedure appear to be less accurate: the estimates have larger uncertainties,and the characteristic temperatures of the emission functions of H-like and He-like ions of theseelements are significantly less than that from the flux ratio of the
GOES bands. Here we usea procedure (called AbuOpt) in which the abundances of Si, S, Ar, and K are first optimizedusing the maximum-likelihood, Bayesian Withbroe–Sylwester inversion technique for obtainingdifferential emission measure from line fluxes is used. The Withbroe–Sylwester routine was thenrun with optimized abundances to obtain the time evolution of the DEM. The result (shown as atime sequence in Figure 6) is a DEM distribution with well-defined cooler ( ∼ − MK) andhotter ( − MK) components. If the hotter component is assumed to describe the emissionseen by
RHESSI , the spatial dimensions combined with the total emission measure of the hottercomponent lead to estimates of electron density and thermal energy. Compared with recentestimates of N e from extreme ultraviolet line ratios, these represent lower limits, but give anindication of the physical characteristics of the flaring plasma.Values of element abundances derived from both an isothermal assumption and from theAbuOpt method described here were discussed in §
3. It appears that our previous estimatesfor Ar and K based on an isothermal assumption are reliable, having smaller uncertainties,and are preferred values, but for S and Si, the abundance estimates from the present work – A (S) = 6 . ± . and A (Si) = 7 . ± . – are to be preferred for the flare analyzed here.Our Si abundance estimate is significantly lower than our estimates from an isothermalanalysis of RESIK flare spectra (Sylwester et al. 2013), viz. A (Si) = 7 . ± . from the Si XIV
Ly- β line at 5.217 ˚A and A (Si) = 7 . ± . from the Si XIII w line at 5.688 ˚A. There are veryfew determinations of the Si abundance from X-ray flare spectra that our values can be comparedwith, the only reliable one being that of Veck & Parkinson (1981) who used the OSO-8 graphitecrystal spectrometer to derive A (Si) = 7 . +0 . − . from the Si XIII w line and . +0 . − . from 24 –the Si XIV
Ly- α line. An isothermal assumption was used, with the temperature derived fromthe slope of the nearby continuum which is evident in the spectra from this instrument. Clearly,our present estimates are nearer to the Veck & Parkinson (1981) values than those from ourisothermal analysis. Photospheric abundance estimates (Asplund et al. 2009) from 3-D and 1-DLTE analyses, one with non-LTE corrections, give A (Si) = 7 . ± . , so abundance estimatesfrom our present X-ray flare result and from the Si XIV result of Veck & Parkinson (1981) are notsignificantly larger (factor . ± . ) than photospheric despite the enhancement expected fromthe low FIP value for Si (8.15 eV); at any rate the enhancement is less than the factor 4 indicatedby Feldman et al. (1992) and Feldman (1992).The S abundance estimate obtained here is only 0.03 different from the determination ofVeck & Parkinson (1981) from the OSO-8 instrument: they give A (S) = 6 . +0 . − . determinedfrom the intense S XV w, y, z lines at ∼ ˚A. Again, our result and the Veck & Parkinson (1981)result are unexpected on the standard FIP picture for this element which has a FIP (10.4 eV)marginally considered to be high (i.e. more than 10 eV). Recent photospheric estimates rangefrom A ( S ) = 7 . ± . (Asplund et al. 2009) to . ± (0 . stat ± (0 . syst (Caffau et al.2011). If the uncertainty estimates for all these determinations are to be considered literally,there would appear to be a slight inverse FIP effect for S, i.e. our flare abundance estimate is . ± . times photospheric. An inverse FIP effect is difficult to reconcile with theoretical models(e.g. H´enoux (1998)) with the exception of that based on ponderomotive forces associated withpropagating Alfv´en waves proposed by Laming (2004, 2009, 2012). An inverse FIP effect, whichis observed in cool main sequence stars (Wood et al. 2012), can possibly be explained by wavespropagating upwards from the chromosphere and reflecting back down as opposed to propagatingdownwards from the corona and reflecting back upwards.Extreme-ultraviolet spectral lines observed by the Extreme-ultraviolet Imaging Spectrometer(EIS) on Hinode have recently been used to give Si/S abundance ratios in active regions and other 25 –non-flaring features from the intensity ratio of Si X X . . . , so on the basis of the EIS results is typical of an established active region. The2002 November 14 flare occurred in an active region that had recently appeared on the Sun’ssouth-east limb, so its history is not well determined; all one can say is that it was flare-prolific onNovember 14, with a complex magnetic geometry.The electron densities in this analysis are typical of those estimated from a combination ofimage data and volume emission measures, but are less than those from density-sensitive spectralline ratios. These are in short supply in the X-ray region, but a number of Fe XXI lines in theextreme ultraviolet spectrum seen with the Extreme Ultraviolet Variability Experiment (EVE)instrument on
Solar Dynamics Explorer have recently been identified, enabling electron density tobe found as a function of time in two
GOES class X flares (Milligan et al. 2012). These indicatedensities of up to cm − , a factor 5 higher than the M1.0 flare discussed here. Our estimatesof both N e and the thermal energy are thus likely to be lower limits with undetermined fillingfactors, perhaps of order 1/25.We plan to use the AbuOpt approach together with the Withbroe-Sylwester DEM analysismethod to study element abundances and the thermodynamics of several other flares observed byRESIK to see whether the reduced Si and S abundances found here still hold, and whether anyvariations in element abundance are related to flare characteristics such as GOES class.We acknowledge financial support from the Polish National Science Centre grant number2011/01/B/ST9/05861 and the European Commissions grant FP7/2007-2013: eHEROES, ProjectNo. 284461. The data analysis was performed using the
CHIANTI atomic code, a collaborativeproject involving George Mason University, University of Michigan (USA) and University of 26 –Cambridge (UK). The launch and operation of RESIK was possible thanks to generosity of theRussian team of scientists and engineers from the IZMIRAN Institute led by Professor V. D.Kuznetsov. 27 –
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