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ISSN 1063-7737, Astronomy Letters, 2009, Vol. 35, No. 1, pp. 45­56. c Pleiades Publishing, Inc., 2009. Original Russian Text c S.V. Shestov, A.M. Urnov, S.V. Kuzin, I.A. Zhitnik, S.A. Bogachev, 2009, published in Pis'ma v Astronomicheski Zhurnal, 2009, Vol. 35, No. 1, i pp. 927­939.

Electron Density Diagnostics for Various Plasma Structures of the Solar ° Corona Based on Fe XI­Fe XIII Lines in the Range 176­207 A Measured in the SPIRIT/CORONAS-F Experiment
S. V. Shestov
1

1, 2 *

, A. M. Urnov1 , S. V. Kuzin1 , I. A. Zhitnik1 , and S. A. Bogachev

1

Lebedev Physical Institute, Russian Academy of Sciences, Leninskii pr. 53, Moscow, 119991 Russia 2 Moscow Physicotechnical Institute, Dolgoprudnyi, Moscow oblast, 141700 Russia
Received May 26, 2008

° Abstract--The relative intensities of Fe XI­Fe XIII lines in the range 176­207 A have been measured for various plasma structures of the solar corona using data from the XUV spectroheliograph of the SPIRIT instrumentation onboard the CORONAS-F satellite with an improved spectral sensitivity calibration. Electron density diagnostics of a plasma with temperatures 0.8­2.5 MK has been carried out in active regions, quiet-Sun and off-limb areas, and, for the first time, in extremely intense solar flares. The density range is (1.6­8) â 109 cm-3 for flares, (0.6­1.6) â 109 cm-3 for active regions, and 5 â 108 cm-3 for quiet-Sun areas. The calibration accuracy of the spectral sensitivity for the spectroheliograph has been analyzed based on spectral lines with density-independent intensity ratios. PACS numbers : 95.55.Fw; 95.75.Fg; 96.60.P-; 96.60.Tf; 95.85.Mt; 95.30.Ky DOI: 10.1134/S106377370901006X Key words: CORONAS-F, SPIRIT, XUV spectra, flares, active regions, density diagnostics.

INTRODUCTION The electron temperature and density are the most important parameters of astrophysical and laboratory plasmas. These are needed to construct theoretical models for various plasma structures of the solar corona--flares, active regions, coronal holes, off-limb structures, etc. The extreme ultraviolet (XUV) spectral range is most informative for the determination of these coronal plasma parameters (diagnostics), since many strong emission lines of a number of chemical elements with various degrees of ionization (from He II to Fe XXIV) fall within it. The most direct data on the physical conditions in the coronal plasma can be obtained by spectroscopic methods from spectral lines in the XUV spectral range. The complex structure and the presence of metastable energy levels in multielectron ions (such as Fe VIII­Fe XVII) cause the populations of certain levels (and, hence, the intensities of the corresponding lines) to depend on the plasma electron density. The density determined from the intensity ratio of two spectral lines of an ion does not require any additional assumptions about the abundances, ionization equilibrium, temperature, and geometry of the source and
*

E-mail: sshestov@dgap.mipt.ru

specifies the density in the plasma whose temperature corresponds to this ion. The methods of density determination from line intensity ratios were applied to the data obtained in various space experiments using both slit spectrographs and spectroheliographs: to the spectra of the full solar disk in a period without flares taken in Aerobee rocket experiments (Behring et al. 1976; Malinovsky and Heroux 1973), to the spectra of flares taken with the spectroheliograph onboard the Skylab station (Dere et al. 1979), and to the spectra of quiet-Sun areas and active regions taken in SERTS rocket experiments (Brosius et al. 1998; Keenan et al. 2007). Analysis of the data from the spectroheliograph onboard the Skylab station is complicated by the fact that the solar images in neighboring spectral lines overlap--the solar size along the dispersion ax° is is 25 A. Although the images in neighboring lines do not overlap in slit spectrographs (as in the SERTS and CDS/SOHO experiments), the recording of spectral lines in higher diffraction orders is a factor that complicates the interpretation of experimental data. For example, the main catalog of ° spectral lines in the range 170­225 A used to test the Fe X­Fe XIII atomic data (Del Zanna and Mason 2005; Keenan et al. 2007) was produced in the
45


46

SHESTOV et al.

SERTS-95 experiment (Brosius et al. 1998) in the second diffraction order of the spectrograph, which is strongly blended with lines of the first diffraction order. It should be emphasized that the optical systems of the instruments in the experiments mentioned above introduced significant uncertainties in identifying the spectra and measuring the relative intensities of spectral lines (Keenan et al. 2005, 2007). Although a large number of spectroscopic experiments have been carried out, the number of recorded flare spectra is small. The flares are difficult to record because of their compact sizes and short lifetimes. When spectrographs with a limited field of view are used (as in the SERTS and CDS/SOHO experiments), the probability of recording a flare is low, because the entire Sun cannot be observed at once. So far the main catalog of spectral lines in flares is the catalog of spectra taken in the 1970s with a slitless spectroheliograph onboard the Skylab station (Dere 1978). These limitations were overcome in the SPIRIT experiment (Zhitnik et al. 2002) onboard the CORONAS-F satellite (Oraevsky and Sobelman 2002). The SPIRIT instrumentation included two independent XUV spectroheliographs that recorded monochromatic images of the full solar disk in the spectral ° ranges 176­207 and 280­330 A. Systematic observations of the Sun with the SPIRIT instrumentation were performed from September 2001 to December 2005. Several tens of thousands of spectroheliograms, including more than a hundred spectroheliograms containing solar flares, were taken. The spectra of extremely intense X-class solar flares at various phases of their development were taken for the first time. In this paper, we present the technique and results of our density measurements for plasma structures in the solar corona based on Fe XI­Fe XIII spec° tral lines in the range 176­207 A recorded with the SPIRIT XUV spectroheliograph. For our analysis, we used the spectra of 28 various objects: ten spectra of X-class flares, two spectra of M-class flares, ten spectra of active regions, one spectrum of an off-limb area, and five spectra of quiet-Sun areas. We determined the calibration accuracy of the spectral sensitivity for the spectroheliograph and made a comparison with the theoretical calculations used in the CHIANTI software (Dere et al. 1997; Landi et al. 2006) and in other more recent works on Fe XI (Keenan et al. 2005), Fe XII (Del Zanna and Mason 2005), and Fe XIII (Keenan et al. 2007) lines. Our data were compared with the SERTS-95 experimental data (Brosius et al. 1998). The ways of increasing the measurement accuracy are pointed out.

THE XUV SPECTROHELIOGRAPH ONBOARD THE CORONAS-F SATELLITE CORONAS-F, the second satellite of the Russian­Ukrainian program to investigate the solar activity, operated in orbit from mid-2001 to late 2005. There was the SPIRIT instrumentation designed at the Lebedev Physical Institute, Russian Academy of Sciences, onboard the satellite. The main goal of the SPIRIT experiment was to study the structure and dynamics of active processes in the solar corona (such as flares, active regions, coronal mass ejections, etc.). The method of imaging spectroscopy was implemented in the SPIRIT instrumentation: the solar images were simultaneously obtained in various parts of the soft X-ray and XUV spectral ranges with high spatial, spectral, and temporal resolutions (Zhitnik et al. 2002). The SPIRIT instrumentation consisted of a telescope assembly designed to image the Sun in narrow spectral intervals of the XUV spectral range and a spectroheliograph assembly. The latter consisted of two X-ray Mg XII spectroheliographs that formed monochromatic images of the Sun at a wavelength ° of 8.42 A and two independent XUV spectroheliographs that formed monochromatic images of the Sun in approximately 150 spectral lines of the ranges ° 176­207 and 280­330 A. The XUV spectroheliographs were based on a slitless scheme with a planar grazing-incidence diffraction grating. The optical scheme and parameters of the XUV spectroheliographs are given in Beigman et al. (2005). When the slitless scheme is used, monochromatic images of the full solar disk are formed on the spectroheliograph detector. The peculiarities of the scheme include the absence of emission in higher diffraction orders, while the width of the solar image along the dispersion axis was ° 0.5 A, which reduces the overlap of the images in neighboring spectral lines. Using this optical scheme in the SPIRIT XUV spectroheliographs allowed one to take more than 100 spectroheliograms containing solar flares, including ten spectroheliograms in ° the range 176­207 A containing extremely intense -class flares. The basic peculiarities of the spectral range 176­ ° 207 A include the presence of spectral lines formed in a wide temperature range, from 0.5 to 20 MK (e.g., Fe VIII and Fe XXIV, respectively). The presence of many lines of iron ions and the density dependence of their intensities allow diagnostics to be carried out by methods that are insensitive to the coronal abundances and in a wide density range, 108 ­1012 cm3 . A total of 65 lines, most of which belong to Fe X­ Fe XIII, are observed in the spectral range 176­ ° 207 A. The catalog of spectral lines compiled from the
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47

spectrum of an M5.6 flare observed on September 16, 2001, by the SPIRIT XUV spectroheliograph is given in Shestov et al. (2008), where the identification of 51 lines was suggested. EXPERIMENTAL DATA In this paper, we chose 28 various objects of the solar corona for our analysis: flares, active regions, quiet-Sun areas, and off-limb areas. We used ten spectra of X-class flares taken at various phases of their development, two spectra of -class flares, ten spectra of active regions in a period without flares, five spectra of quiet-Sun areas, and one spectrum of an off-limb area. A complete list of all the observations used with comments is presented in Table 1. EXPERIMENTAL DATA PROCESSING The data for each object were processed according to the following procedure: spectroheliogram preprocessing (background subtraction and rotation), onedimensional spectrum extraction, wavelength calibration, and allowance for the spectral sensitivity of the spectroheliograph (Shestov et al. 2008). In the extracted one-dimensional spectrum, the background was resubtracted and the parameters of individual lines were determined: the wavelength, peak intensity, and width. In this paper, we used a refined spectral sensitivity function of the spectroheliograph that differs from that used in Shestov et al. (2008). The refined spectral sensitivity function is tested in this paper. Since the main errors in the intensities of spectral lines arise at the stages of background subtraction and line parameter determination, let us consider them in more detail. After preprocessing, the one-dimensional spectrum still contains a background that can be the sum of the detector's dark current, scattered light, and, possibly, continuum solar radiation. A procedure similar to that used for the SERTS data (Thomas and Neupert 1994) was developed to subtract the back° ground. We eliminated 0.6-A-wide regions around strong spectral lines from the spectrum and averaged the remaining signal using a sliding filter 35 pixels in width. The averaged signal was passed through a Fourier filter that transmitted low spatial frequencies with a width up to 1/20. The filtered signal was considered to be the background and was subtracted from the original spectrum. For some of the spectra, the background subtraction procedure was repeated iteratively, if required. The entire background subtraction procedure was optimized in parameters (the widths of the region being eliminated, the sliding filter, the Fourier filter, etc.). As an example, the original
ASTRONOMY LETTERS Vol. 35 No. 1 2009

one-dimensional spectrum (for the flare recorded on September 7, 2005) and the derived background are shown in Fig. 1. To determine the positions and parameters of spectral lines, we used the method of fitting the spectrum in a chosen narrow wavelength range. This method proved to be efficient in analyzing strongly blended spectra (Thomas and Neupert 1994; Beigman et al. 2005; Shestov et al. 2008). According to this method, the emission intensity distribution in the chosen spectral region 1 ­2 can generally be written as i() = P + Q
N

(1)
2

+
i=1

Ai exp -

1 2

- i 0 i

,

[1 ,2 ], where P + Q describes the local background; N is the number of spectral lines; Ai , i , and i are 0 the peak intensity, wavelength, and width of spectral line i, respectively. The line shape is assumed to be Gaussian; the total line intensity can be calculated using the formula (2) Ii = 2Ai i . In fitting, the parameters P, Q, Ai ,i ,and i are cho0 sen using the 2 test. In this case, there is noise in the experimental spectrum that is determined by the detector noise and its distribution is assumed to be Gaussian. In most cases, the error of the 2 method in determining each of the line parameters Ai ,i ,i 0 is small (up to 1%) and has a lower value than the spread in these parameters obtained by varying the parameters of the background subtraction procedure (the widths of the sliding filter, the Fourier filter, etc.). Therefore, as the errors in the line parameters Ai ,i ,i , we took their spread obtained at various 0 background parameters. The error in the total line intensity was calculated using the formula Ii = Ai + i , where F = F /F is the relative error of F . The errors in the total line intensities determined in this way generally do not exceed 5% for "strong" ° lines (like Fe XI 180.41 A) and 20% for "weak" lines ° (like Fe XIII 196.54 A). We measured the parameters (Ai ,i ,i ) and total 0 intensities Ii of the chosen spectral lines (for the list, see below) for all of the objects given in Table 1. (3)


48 Table 1. List of observed objects No. Time, UT Object QS QS QS QS QS AR AR AR AR AR AR AR AR AR AR F F F F F F F F F F F F

SHESTOV et al.

Comments

1 07:27 Feb. 11, 2002 2 02:02 July 16, 2004 3 02:02 July 16, 2004 4 5 7 16:47 Mar. 4, 2002 16:47 Mar. 4, 2002 12:13 Oct. 2. 2001

6 13:20 Sep. 11, 2005

° Hot region (Fe XXIV192.03 A line is present). M1.6 flare was observed at 10:21 (GOES data)

8 07:27 Feb. 11, 2002 9 21:30 June 7, 2002 10 21:30 June 7, 2002 11 18:15 June 17, 2002 12 07:02 Aug. 21, 2002 13 07:02 Aug. 21, 2002 14 07:02 Aug. 21, 2002 15 22:51 Sep. 6, 2005

Impulsive X1.1 flare was observed at 05:34 (GOES data)

° On-limb hot region (Fe XXIV 192.03 Aline ispresent). ° 16 22:51 Sep. 6, 2005 Off-limb Off-limb hot region (Fe XXIV 192.03 A line is present). M3.2 flare (max--13:11) 4.8 flare (max--01:49) + M2.2 (max--02:20) X1.4 flare (max--02:06, onset--02:02) X17 flare (max--17:40) X17 flare X17 flare X5.5 flare X6.2 flare --//-- --//-- --//-- --//-- 18 02:17 Sep. 16, 2005 19 02:02 July 16, 2004

17 13:20 Sep. 11, 2005

20 18:17 Sep. 7, 2005 21 20:04 Sep. 7, 2005 22 21:35 Sep. 7, 2005 23 21:48 Sep. 8, 2005 24 23:19 Sep. 8, 2005 25 20:29 Sep. 9, 2005 26 21:59 Sep. 9, 2005 27 19:48 Sep. 13, 2005 28 21:19 Sep. 13, 2005

X5.5 flare (max--21:06) X6.2 flare (max--20:03) X1.5 flare (max--19:28) X1.5 flare (max--20:04)

Note. QS, quiet-Sun areas; AR, active regions; Off-limb, an off-limb area; and F, a flare region. The time is the initial time at which the spectroheliogram was taken. The quiet-Sun areas and active regions recorded simultaneously were observed at different locations of the solar disk. For the flares, the X-ray class and time of flare maximum are given based on GOES data.

CHOOSING SPECTRAL LINES FOR DIAGNOSTICS The catalog by Shestov et al. (2008) contains data for 31 Fe XI­Fe XIII lines. Since most of them are strongly blended or have a low intensity, for our analysis we chose the lines with minimum blending

whose parameters could be reliably determined from experimental data. We used a total of 18 lines: Fe XIII: 196.54, 200.02, 201.13, 202.04, 203.16, ° 203.80, 203.83, 204.95 A, ° Fe XII: 186.85, 186.89, 192.39, 193.51, 195.12 A, ° Fe XI: 179.76, 180.41, 188.23, 188.30, 192.83 A.
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10 000 Intensity, arb. units 8000 6000 4000 2000 0 175 180 185 190 195 Wavelength, å 200 205 210

Fig. 1. Background subtraction procedure: the original spectrum (thin line), the regions used to calculate the background (medium line), and the derived background (thick line). The figure is drawn for an X17 flare recorded on September 7, 2005, at 20:04.

These spectral lines can be grouped in pairs into two groups: --the intensity ratios do not depend or depend weakly on the density and temperature under typical coronal conditions (a density of 109 cm-3 and a temperature of 106 K); --the intensity ratios depend strongly on the density and can be used to determine the density. The spectral lines from the first group were used to test the calibration accuracy of the spectroheliograph's spectral sensitivity and to detect blends; the spectral lines from the seconde group were used to determine the density. Below, we describe in detail the calibration testing and the density measurement for each ion.

Fe XIII Lines
The Fe XIII lines belonging to the 3s2 3p2 ­3s2 3p3d electronic transitions fall within the spectral range ° 176­207 A. The Fe XIII lines observed in an M5.6 flare (Shestov et al. 2008) are listed in Table 2. The ° 203.80 and 203.83 A lines are unresolvable and below designated as (203.83+.80) Testing the calibration accuracy based on Fe XIII lines. Six pairs of spectral lines whose intensity ratios depended weakly on the density and temperature were used to test the calibration of the spectroheliograph. The results are presented in Fig. 2. For each pair, the object numbers (according to Table 1) are along the x axis and the intensity ratios are along the y axis. The symbols correspond to the SPIRIT measurements; the vertical bars mark the experimental errors. The dotted straight line indicates the ratio obtained in the SERTS-95 experiment; the solid straight lines mark the range of ratios corresponding to the density range 108 ­1010 cm-3 calculated using CHIANTI.
ASTRONOMY LETTERS Vol. 35 No. 1 2009

The 200.02/(203.80 + .83) ratios in 20 of the 28 cases (70%) coincided with their theoretical values, within the measurement error limits; the maximum deviation in the other cases does not exceed 50%. This suggests that the calibration accuracy of the spectroheliograph's spectral sensitivity is high in the ° range 200­204 A and that the theoretical calculations agree with the experimental data. In half of the cases, the 204.95/200.02, 204.95/(203.80 + .83), and 204.95/201.13 line intensity ratios also coincided with their theoretical values, within the error limits. We associate the large deviations of these ratios for objects nos. 20, 23, 25, and 28 with an overestimated ° intensity of the 204.95 A line due to the presence of defects on the original spectroheliograms. Note that the intensity of the 204.95 line gave an overestimated ratio (including that for the lines with a common upper level, 204.95/201.13) in the SERTS-95 experiment. This may suggest that the 204.95 line in the SERTS experiment is blended with a line in the first diffraction order. The 203.16/200.02 line ratio differs from its theoretical value, on average, by a factor of 2.5. Since other ratios correspond to the theoretical calculations for a large number of objects, we may conclude that either the atomic data are inaccurate or the 203.16 line was identified erroneously (e.g., according to NIST data,1 the spectral line with = ° 202.42 A corresponds to the 3s2 3p2 3P1 ­3s2 3p3d 3P0 transition). Table 3 compares the calculated and experimentally measured line intensity ratios. The Keenan and CHIANTI columns in the table give the theoretical values from Keenan et al. (2007) and those calculated using CHIANTI for the density log ne = 9.4
1

http://physics.nist.gov/PhysRefData/


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SHESTOV et al.

Table 2. Fe XIII lines observed in the M5.6 flare on September 16, 2001 (see Shestov et al. 2008) ° Wavelength A 196.54 200.02 201.13 202.04 203.16 203.80 203.83 204.26 204.95 3 s2 3 p 3 s2 3 p 3s 3p
2

Transition
21 23 23

CHIANTI 4­26 2­25 2­23 1­20 2­22 3­25 3­24 2­21 3­23

Blending ° Fe XII 196.64 A ° Fe XII 201.14 A

D2 ­3s2 3p3d 1F3 P1 ­3s2 3p3d 3D P1 ­3s 3p3d D
2 3 2 1

3 s2 3 p 3 s2 3 p 3s 3p 3 s2 3 p 3s 3p 3 s2 3 p
2 2

23 23

P0 ­3s2 3p3d 3P1 P1 ­3s2 3p3d 3P0
2 3 2 3 2 1

23 23 23 23

P2 ­3s 3p3d D P2 ­3s2 3p3d 3D P1 ­3s 3p3d D P2 ­3s2 3p3d 3D
2 1

° Fe XIII 203.83 A ° Fe XIII 203.80 A

Note. Wavelength is given based on CHIANTI data; Transition is a spectroscopic designation of the spectral line; CHIANTI are the numbers of the lower and upper levels of the transition used in CHIANTI; Blending indicates what the line is blended with.

Table 3. Comparison of the theoretical and observed intensity ratios of the Fe XIII lines independent of plasma parameters Line ratio Keenan CHIANTI With common upper level 201.13/204.95 200.02/(203.80+.83) 200.02/201.13 203.16/200.02 203.80/203.83 204.95/200.02 204.95/(203.80+.83) 3.7


SERTS-95 1.7 ± 0.3 0.16 ± 0.06 0.65 ± 0.11 0.51 ± 0.10 0.20 ± 0.04 0.88 ± 0.17 0.17 ± 0.09


SPIRIT 3.4 ± 0.9 0.20 ± 0.07 0.49 ± 0.22 0.22 ± 0.02 -- 0.71 ± 0.25 0.12 ± 0.04

3.3 Weakly dependent on parameters

0.20 0.74 0.49 0.32 0.37 0.07

0.18 0.75 0.53 0.33 0.40



0.07

Note. Keenan--based on data from Keenan et al. (2007), CHIANTI--calculated using CHIANTI for the density log ne = 9.4, SERTS-95--based on SERTS-95 experimental data (Keenan et al. 2007), SPIRIT--our measured mean. ° Recalculated using 203.80 and 203.83 A line data.

(the mean density measured in the SERTS-95 experiment). Note that Keenan et al. (2007) used a more complete model of the Fe XIII ion (13 electronic configurations and 301 fine-structure levels versus 6 electronic configurations and 97 levels for CHIANTI). The SERTS-95 column gives the ratios measured in an active region in the SERTS-95 experiment (Keenan et al. 2007). The SPIRIT column gives the mean ratios that we measured. For each pair of lines, the ratio was measured over all measurements; the mean spread in measurements is given as the errors. Density measurement based on Fe XIII lines. We used the (203.80 + .83)/202.04, 196.54/202.04,

and 200.02/202.04 line ratios to determine the density. The theoretical density dependences of these ratios are shown in Fig. 3. The calculations were performed using CHIANTI for the temperature range log T = 6.0­6.4, which corresponds to a Fe XIII abundance with respect to the Fe ions of more than 2% (see Mazzotta et al. 1998). Note that the same dependences in Keenan et al. (2007), who used a more complete atomic model than that in CHIANTI, have a larger spread in temperature. This can lead to a spread in density up to 0.2 dex (1 dex corresponds to a change in the decimal logarithm by one). The results of our density determination for various
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51

1.0 0.8 0.6 0.4 0.2 0 1.2 1.0 Fe XIII line intensity ratio 0.8 0.6 0.4 0.2 0 2.5 2.0 1.5 1.0 0.5 0 5 10 15 20 5 10 15 20 25 5 10 15 20 25
Fe XIII 200.02/(203.80 + .83) SPIRIT
CHIANTI 5.2 SERTS-95

1.2
Fe XIII 200.02/201.13

1.0 0.8 0.6 0.4 0.2 30 0 1.0
Fe XIII 203.16/200.02

5

10

15

20

25

30

Fe XIII 204.95/201.13

0.8 0.6 0.4 0.2 30 0 1.0 0.8 0.6 0.4 0.2 25 30 0 Object number 5 10 15 20 25 30 5 10 15 20 25 30

Fe XIII 204.95 /200.02

Fe XIII 204.95/(203.80 + .83)

Fig. 2. Fe XIII line intensity ratios that do not depend or depend weakly on the density measured in the SPIRIT (symbols) and SERTS-95 (dotted line) experiments and theoretical CHIANTI values (solid line). The errors of individual measurements are given for the SPIRIT data. The range of values that the intensity ratio can take for the spread in density 108 ­1010 cm-3 is given for CHIANTI. The object numbers (according to Table 1) are along the x axis and the line intensity ratios are along the y axis.

structures of the solar corona based on SPIRIT data are presented in Fig. 4. In this figure, the object numbers (according to Table 1) are along the x axis and the logarithm of density is along the y axis. Different symbols correspond to different pairs of spectral lines; the vertical bars mark the experimental errors. The densities are (3­6) â 108 cm-3 for the quietSun areas (objects nos. 1­5) and (0.6­ 1.6) â 109 cm-3 for the active regions (objects nos. 6­15). The active region no. 12, where the density is 2.8 â 109 cm-3 , as measured from all three pairs of Fe XIII lines, constitutes an exception; this
ASTRONOMY LETTERS Vol. 35 No. 1 2009

may be attributable to the flare observed one an a half hours earlier (GOES data). The density in the high-temperature off-limb area (object no. 16) is 8 â 108 -3 . The density in the flares (objects nos. 17­ 28) is (1.6­8) â 109 -3 . The density in the X17 flare observed on September 7, 2005, near maximum (object no. 20) measured from various pairs of Fe XIII lines lies within the range 6 â 109 ­1.3 â 1010 cm-3 . However, there are large experimental errors here, because the signal in the original spectroheliogram is weak. The absence of systematic differences in the den-


52 Table 4. Fe XII lines used here ° Wavelength, A 186.85 186.89 192.39 193.51 195.12 3s 3p D 3s2 3p3 4D 3s2 3p3 4S 3s 3p S 3s 3p S
2 34 2 34 2 32

SHESTOV et al.

Transition
3/2 5/2

CHIANTI
2 2 2

Blending ° Fe XII 186.89 A ° Fe XII 186.85 A

­3s 3p ( P )3d F5/ ­3s2 3p2 (3P )3d 2 F7/
2 2 23 23 4 4

2

23

2­36 3­39 1­30 1­29 1­27

3/2 3/2 3/2

­3s2 3p2 (3P )3d 4 P1/ ­3s 3p ( P )3d P3/ ­3s 3p ( P )3d P5/

2 2 2

° Fe XII 195.18 A

Note. For the notation, see Table 2.

sities obtained from the 196.54/202.04 line ratio and from the other two pairs of lines suggests that there is ° virtually no blending of the Fe XIII 196.54 A line and that the calibration of the spectroheliograph's spec° tral sensitivity is accurate in the range 196­205 A.

Fe XII Lines The Fe XII spectral lines belonging to the 3s2 3p3 ­3s2 3p2 3d electronic transitions fall within ° the spectral range 176­207 A. The catalog that we compiled based on the spectrum of an M5.6 flare (Shestov et al. 2008) contains data for 16 Fe XII lines. Most of the lines are strongly blended and many of them have low intensities. In fact, the ° 186.89+.85 A (unresolvable) lines and the 192.39, ° 193.51, and 195.12 A triplet lines that were used here
4 log Te = 6.2 log Te = 6.0 log Te = 6.4

3

(203.80 + .83)/202.04

2

196.54/202.04

1
200.02/202.04

0 7

8

9

10 log n

11
e

12

13

Fig. 3. Fe XIII (203.80+.83)/202.04, 196.54/202.04, and 200.02/202.04 line intensity ratios versus logarithm of the electron density. The ratios were calculated using CHIANTI for various temperatures.

(see Table 4) are intense enough for the parameters to be determined reliably. The intensities of the 192.39, ° 193.51, and 195.12 A triplet lines have similar density dependences, while their experimentally measured ratios are close to the theoretical ones 1 : 2.1 : 3.1. This suggests that the calibration of the spectrohelio° graph's spectral sensitivity near 195 A is accurate and ° that the 195.12 A line is blended weakly, in agreement with the theory: blending takes place at high densities (1010 cm-3 or higher). Density measurement based on Fe XII lines. We used the (186.89+.85)/193.51 line ratio, whose density dependence (calculated using CHIANTI) is shown in Fig. 5, to determine the density. The calculations were performed for the temperature range log T = 6.0­6.4, which corresponds to a relative Fe XII abundance of more than 2%. The spread in density due to the presence of a plasma with different temperatures can reach 0.2 dex. The density measured from the Fe XII (186.89+.85)/193.51 line ratio together with the density determined from Fe XIII lines for various structures in the solar corona are presented in Fig. 6. For the non-flare objects (nos. 1­16), the density derived from Fe XII lines, on average, corresponds to that obtained from Fe XIII lines (the random deviations reach 0.2­0.3 dex, i.e., a factor of 1.5­2.0). For the flares, the density determined from Fe XII lines is considerably higher than that derived from Fe XIII lines (exceeds the latter by a factor of 3­6). The absolute value of the density determined from Fe XII lines for the flares often exceeds log ne = 10. Note that similar discrepancies are observed in other experiments. The density determined for a quiet-Sun area from the Fe XII line intensity ratio for the data from Behring et al. (1976), Malinovsky and Heroux (1973), and the SERTS-95 experiment is log ne = 8.9, 8.8, and 9.0, respectively (see the review by Storey et al. 2005) and agrees with the data obtained from the lines of other ions. However, the density determined for an active region in the SERTS-95 experiment
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Fe XIII line intensity ratio


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11

Quiet Sun

Active regions

Offlimb

Flares

10 log n
e

Fe XIII (203.80 + .83)/202.04 Fe XIII 200.02/202.04 Fe XIII 196.54/202.04

9

8 0

5

10

15 20 Object number

25

30

Fig. 4. Density measurements in various structures of the solar corona based on Fe XIII line intensities. The object numbers (according to Table 1) are along the x axis and the logarithm of density is along the y axis.

is log ne = 10.5, which is considerably higher that the density inferred from other ions, log ne = 9.4 (for details, see Brosius et al. 1998).

Fe XI Lines
The Fe XI lines corresponding to the 3s2 3p4 ­2s2 3p3 3d transitions fall within the spectral ° range 176­207 A. Our catalog (Shestov et al. 2008) provides data for 14 Fe XI lines. However, most of these lines either are strongly blended or have low intensities. The lines used here are listed in Table 5. ° ° The 188.23 A and 188.30 A lines are unresolvable and below designated as 188.23+.30. Testing the calibration accuracy based on Fe XI lines. The (188.23+.30)/180.41 and 192.83/(188.23+.30) line intensity ratios were used to test the spectroheliograph's calibration. The results are presented in Fig. 7. For each pair of lines, the object numbers (according to Table 1) are along the x axis and the intensity ratio is along the y axis. The symbols correspond to the SPIRIT measurements and the vertical bars mark the experimental errors. The dotted straight line indicates the ratio obtained in the SERTS-95 experiment; the solid straight lines mark the range of ratios corresponding to the density range 108 ­1010 cm-3 calculated using CHIANTI. The (188.23+.30)/180.41 intensity ratio in 11 of the 28 cases (40%) coincided with their theoretical values, while the SERTS-95 experimental ratio turned out to be a factor of 4 smaller than the theoretical one (although the experimental error was 70%). ° This may be because the 180.41 A line in the SERTS experiment was blended with a line in the first diffraction order (Keenan et al. 2005). The 192.83/(188.23+.30) ratio for the non-flare objects (nos. 1­16) is close to its theoretical value,
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° while the Fe XI 192.83 A line in the flares is blended ° with the hot Ca XVII 192.82 A line (log T = 6.8). Therefore, the ratios are larger than the theoretical ones. This is indicative of a good calibration accuracy of the spectroheliograph's spectral sensitivity in the ° range 180­193 A and, given the results obtained from Fe XII and Fe XIII lines, in the entire spectral range of the spectroheliograph. Table 6 compares the calculated and experimentally measured intensity ratios. The Keenan and CHIANTI columns in the table give the theoretical ratios from Keenan et al. (2005) and those calculated using CHIANTI for the density log ne = 9.4 (the mean density measured in the SERTS-95 experiment). The SERTS-95 column gives the ratios
3.0 2.5 Fe XII line intensity ratio 2.0 1.5 1.0 0.5 0 7 log Te = 6.2 log Te = 6.0 log Te = 6.4
(186.89 + .85)/193.51

8

9

10 log n

11
e

12

13

Fig. 5. Fe XII (186.89+.85)/193.51 line intensity ratio versus logarithm of the electron density. The ratio was calculated using CHIANTI for various temperatures.


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Quiet Sun

Active regions

Off-l limb

Flares

10 log n
e

Fe Fe Fe Fe

XIII (203.80 + .83)/202.04 XIII 200.02/202.04 XIII 196.54/202.04 XII (186.89 + .85)/193.51

9

8 0

5

10

15 20 Object number

25

30

Fig. 6. Density measurements in various structures of the solar corona based on Fe XII­Fe XIII line intensities. The object numbers (see Table 1) are along the x axis and the logarithm of density is along the y axis.

1.0
Fe XI (188.23 + .30)/180.41

2.0
Fe XI 192.83/(188.23 + .30)

Fe XI line intensity ratio

0.8 0.6

1.5

SPIRIT CHIANTI 5.2 SERTS-95

1.0 0.4 0.2 0.5

0

5

10

15

20

25 30 0 5 Object number

10

15

20

25

30

Fig. 7. Same as Fig. 2for theFe XI lines.

measured in an active region in the SERTS-95 experiment (Keenan et al. 2005). The SPIRIT column gives the mean ratios that we measured. For each pair of lines, the ratio was averaged over all measurements; the mean spread in measurements is given as the errors. Density measurement based on Fe XI lines. We used the 179.76/180.41 line intensity ratio to measure the density. The density dependence of this ratio is shown in Fig. 8. The calculations were performed using CHIANTI for the temperature range log T = 5.9­6.3, which corresponds to a Fe XI abundance with respect to the Fe ions of more than 1%. The error in the density due to the presence of a plasma with various temperatures can reach 0.2 dex. The results of our density measurements for various structures in the solar corona are presented in Fig. 9. In this figure, the object numbers (according to Table 1) are along the x axis and the decimal logarithm of density is along the y axis. The symbols

correspond to different pairs of spectral lines. The vertical bars denote the measurement errors. In most of the objects, the density derived from Fe XI lines is slightly higher (up to 0.2 dex) than the mean density obtained from Fe XIII lines. For the flare objects (nos. 17­28), the density measured from Fe XI lines correspond to the density inferred from Fe XIII lines, suggesting that the density determined from Fe XII lines was overestimated. RESULTS AND CONCLUSIONS In this paper, we presented the technique for measuring the intensities of spectral lines in the range ° 176­207 A based on data from the XUV spectroheliograph of the SPIRIT instrumentation onboard the CORONAS-F satellite. We measured the intensities of Fe XI­Fe XIII lines in various plasma structures of the solar corona: in active regions, quiet-Sun areas, off-limb areas, and, for the first time, in extremely intense solar X-class flares. We used an improved
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ELECTRON DENSITY DIAGNOSTICS Table 5. Fe XI lines used here ° Wavelength, A 179.76 180.41 188.23 188.30 192.83
2 41 2 43

55

Transition 3s 3p D2 ­3s 3p ( D)3d F3 3s 3p P2 ­3s 3p ( S )3d D
2 34 3 3 2 32 1

CHIANTI 4­46 1­42 1­38 1­39 2­38

Blending ° Fe X 180.41 A ° Fe XI 188.30 A and Fe X 188.18 ° Fe XI 188.23 A and Fe X 188.19 ° Ca XVII 192.82 A

3s2 3p4 3P2 ­3s2 3p3 (2D)3d 3P2 3s2 3p4 3P2 ­3s2 3p3 (2D)3d 1P1 3s 3p P1 ­3s 3p ( D)3d P2
2 43 2 32 3

° A ° A

Note. For the notation, see Table 2.

Table 6. Comparison of the theoretical and observed Fe XI line intensity ratios that are independent of plasma parameters Line ratio (188.23+.30)/180.41 192.83/(188.23+.30) Keenan 0.70 0.16


CHIANTI 0.69 0.15

SERTS-95 0.16 ± 0.11 0.11 ± 0.08


SPIRIT 0.45 ± 0.07 0.17 ± 0.03

Note. Keenan--based on data from Keenan et al. (2005), CHIANTI--calculated using CHIANTI for density log ne = 9.4, SERTS95--based on SERTS-95 experimental data (see Keenan et al. 2005), SPIRIT--the mean measured in this paper. ° Calculated from 188.23 and 188.30 A line data.

calibration of the spectroheliograph's spectral sensitivity and analyzed the calibration accuracy based on density-independent line intensity ratios. We carried out electron density diagnostics for a plasma with a temperature of 0.8­2.5 MK based on spectral lines with density-dependent intensity ratios. Five ratios of Fe XI (179.76/180.41), Fe XII (186.89+.85)/193.51), and Fe XIII (196.54/202.04, 200.02/202.04, and (203.83+.80)/202.04)) lines were chosen to determine the density. The plasma density was measured for 28 objects in the solar corona: ten X-class flares, two M-class flares, ten active regions, five quiet-Sun areas, and one off-limb area. The results of our density measurements are presented in Fig. 9. The densities for the quiet-Sun areas (objects nos. 1­5) are (3­6) â 108 cm-3 . The measurement error reaches 0.7 dex (related to the low line intensity in the original spectroheliograms); the spread in density derived from various pairs of lines reaches 0.4 dex. The densities for the active regions (objects nos. 6­15) are (0.6­1.6) â 109 cm-3 . The measurement error is 0.4 dex; the spread in density obtained from various pairs of lines is the same. For the active region No. 12, the density is 2.8 â 109 cm-3 ;all five pairs of lines show such an "overestimated" density. The density in the high-temperature off-limb area (object no. 16) is 8 â 108 cm-3 ; the measurements based on various pairs of lines agree with one another.
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The densities in the flares lie within the range (1.6­8) â 109 cm-3 ; the measurement error is generally smaller than the spread derived from various pairs of lines. In most cases, the density derived from Fe XII lines is considerably higher than that determined from lines of other ions and often exceeds 1010 cm-3 . This

0.8
179.76/180.41 log Te = 6.1 log Te = 5.9 log Te = 6.3

Fe XI line intensity ratio

0.6

0.4

0.2

0 7

8

9

10 log n

11
e

12

13

Fig. 8. Fe XI 179.76/180.41 line intensity ratio versus logarithm of the electron density. The ratio was calculated using CHIANTI for various temperatures.


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Quiet Sun

Active regions

Offlimb

Flares

10 log n
e

Fe XIII (203.80 + 83)/202.04 Fe XII (186.89 + 85)/193.51 Fe XI 179.76/180.41

9

8 0

5

10

15 20 Object number

25

30

Fig. 9. Density measurements in various structures of the solar corona based on Fe XI­Fe XIII line intensities. The object numbers (according to Table 1) are along the x axis and the logarithm of density is along the y axis.

may be because the atomic data for Fe XII are inaccurate. We found no systematic differences in the densities measured for the same object using different pairs of lines, except an overestimated density determined from Fe XII lines in flares. The difference in the densities for the same object may suggest that the density distribution is highly nonuniform in the plasma of the object under study. ACKNOWLEDGMENTS This work was supported by Basic Research Program no. 16 of the Presidium of the Russian Academy of Sciences, the "Optical Spectroscopy and Frequency Standards" Program of the Section of Physical Sciences of the Russian Academy of Sciences, and the Russian Foundation for Basic Research (project nos. 08-02-01301- and 06-0216298). REFERENCES
1. W. E. Behring, L. Cohen, U. Feldman, et al., Astrophys. J. 203, 521 (1976). 2. I. L. Beigman, S. A. Bozhenkov, I. A. Zhitnik, et al., Pisma. Astron. Zh. 31, 39 (2005). 3. J. W. Brosius, J. M. Davila, and R. J. Thomas, Astrophys. J. Suppl. Ser. 199, 255 (1998). 4. G. Del Zanna and H. E. Mason, Astron. Astrophys. 433, 731 (2005).

5. K. P. Dere, Astrophys. J. 221, 1062 (1978). 6. K. P. Dere, E. Landi, H. E. Mason, et al., Astron. Astrophys. Suppl. Ser. 125, 149 (1997). 7. K. P. Dere, H. E. Mason, K. G. Widing, et al., Astrophys. J. Suppl. Ser. 40, 341 (1979). 8. F. P. Keenan, K. M. Aggarwal, R. S. Ryans, et al., Astrophys. J. 624, 428 (2005). 9. F. P. Keenan, D. B. Jess, K. M. Aggarwal, et al., Mon. Not. R. Astron. Soc. 376, 205 (2007). 10. E. Landi, G. Del Zanna, P. R. Young, et al., Astrophys. J., Suppl. Ser. 162, 261 (2006). 11. M. Malinovsky and L. Heroux, Astrophys. J. 181, 1009 (1973). 12. P. Mazzotta, G. Mazzitelli, S. Colafrancesco, et al., Astron. Astrophys., Suppl. Ser. 133, 403 (1998). 13. V. N. Oraevsky and I. I. Sobelman, Pis'ma Astron. Zh. 28, 457 (2002) [Astron. Lett. 28, 401 (2002)]. 14. S. V. Shestov, S. A. Bozhenkov, I. A. Zhitnik, et al., Pis'ma Astron. Zh. 34, 38 (2008) [Astron. Lett. 34, 33 (2008)]. 15. P. J. Storey, G. Del Zanna, H. E. Mason, et al., Astron. Astrophys. 433, 717 (2005). 16. R. J. Thomas and W. M. Neupert, Astrophys. J. 91, 461 (1994). 17. I. A. Zhitnik, S. V. Kuzin, A. M. Urnov, et al., Pis'ma Astron. Zh. 31, 39 (2005) [Astron. Lett. 31, 37 (2005)].

Translated by V. Astakhov

ASTRONOMY LETTERS

Vol. 35 No. 1

2009