Density diagnostics of solar emission lines from nitrogen-like ions

0273—1177/88 $0.00 + .50 Copyright © 1989 COSPAR

Adv. Space Res. Vol. 8, No. 11, pp. (11)179—(11)183, 1988 Printed in Great Britain. All rights reserved.

DENSITY DIAGNOSTICS OF SOLAR EMISSION LINES FROM NITROGEN-LIKE IONS B. N. Dwivedi* and P. K. Raju** *Depar~zentof Applied Physics, Institute of Technology, Banaras Hindu University, Varanasi 221005, India *

*Indian Institute of Astrophysics, Bangalore 560034, India

ABSTRACT

Steady state level population of 13 levels of nitrogen-like ions; Ne IV,Mg VI, Si VIII, and S X have been computed as a function of electron density and temperature.We have accounted for collisional and spontaneous radiative processes. Photo—excitations among the ground term levels have also been considered. Using the computed level populations line intensities have been obtained as a function of electron density and temperature. This study indicates that line intensity ratios for nitrogen-like ions can be used as a density monitor of the solar plasma. Absolute line fluxes from these ions at earth distance have been computed and compared with values obtained using various satellite and rocket measurements. INTRODUCTION The study of solar EUV emission lines has been widely used to derive the electron density and temperature of the solar plasma. Lines emitted from beryllium-like ions have been extensively used to probe the solar transition region and the astrophysical plasma /1, 2, 3, 4, 5, 6/. The lines in the boron—like ions have also been used as a density monitor of the solar plasma /7, 8, 9, 10, 11, 12, 13/. The density diagnostics of solar emission lines from carbon—like ions /14, 15/ and oxygen—like ions /16/ have been studied in detail. However, the method of determining the electron density from emission lines is not new and has been used since long /17/ for 0 II lines3of n~trogen sequence. The density sensitivity for the 0 II line ratio occurs around 10 cm and is useful for probing gaseous nebulae. If more highly ionized ions in the nitrogen sequence are considered, examples have been found that are useful at solar densities /18, 19/. Forbidden lines of the ions of Mg VI, Si VIII, S X and Ar XII have been considered by Feldman et al. /19/. In the present investigation we have considered the first 13 levels of nitrogen-like ions. According to the ionization equi~ibrium calculations Jordan /20/, Mg VI }~as maximum relative ion abundance at 4 x 10 K, Si VIII at 8 x 10 K and S X at 1.4 x 10 K. Lines emitted from these ions are therefore useful in probing the solar chromosphere-corona transition region and the inner corona. The schematic energy level diagram comprising the first 13 levels of nitrogen-like ions has been shown in Figure 1. The various physical processes considered in the present investigation include the electron collisional excitations and spontaneous radiative de—excitations for permitted transitions; electron excitations and de-excitations,spontaneous radiative de—excitations among the ground term levels. LINE EMISSION The line emission from a given volume element in the solar atmosphere in a steady state is given by the expression 3 Sr4 ~_1) E(j,i) =LA~~ E1~N~(ergs cm Where E. is the energy of transition between upper level j and lower level i, A.. is the rad?~tive transition probability and N. is the number density of the ions in e,tè~ted level j. Thus the number density as a fii~nction of electron density and temperature has been evaluated by solving all the detailed balance equations for the atomic levels shown in Figure 1. The integrated line fluxes have been computed using the model atmosphere of Elzner /22/. .

(11)179

(11)180

B. N. Dwivedj and P. K. Raju

_____

—

Is

.~

12

—

4

2a2p

—

12~

ii

I

II I

1t111 ~JJJJ

il

I -

i

I

3

—Th

—

_Jj

_50

10

9

2

.~

~Ii

‘‘ii

222~Li ~

COLLISIONAL

•/

4p

~

7 6

_______

TRANSITIONS

RADIATIVE TRANSITIONS

Fig.1.

Energy—Level

Diagram for NI—like ions

RESULTS AND DISCUSSION The density determination from nitrogen-like ions becomes possible because of the first five levels of the ground term being metastable. The collisional and the radiative deexcitation rates for these levels compete at electron densities in the relevant range. Therefore, the level populations and consequently the line intensity ratios become density dependent. Since the occupation of higher levels is essentially governed by the levels of the ground term, the variation of occupation of the ground state levels is reflected in the variation of line emission with the electron density. The variation of ground state level populations as a function of electron density have been studied and are found to compare well with the reported values in the literature /23/. The detailed result will be reported elsewhere. In Figures2 and 3, we have shown various line intensity ratios as a function of electron density only for Si VIII and S X for sake of brevity. The results of the other ions studied will be reported elsewhere. The results on the temperature dependence of li~ne intensity ratios would be reported elsewhere. Feldman et a]. /19/ have specifically studied the forbidden lines of nitrogen like ions for density determination. They indicate S X forbidden lir~s as 3a useful density diagnostic of the inner corona and find an electron density of 10 cm for the quiet as well as active conditions which is rather surprising. Our calculations show 9that3the electron densities derived fr~m F~g VI, Si VIII and S X line ratios are 1.6 x 10 ciii ; 6.20 x 10 cm and 3.15 x14L0 cnn respectively. These values correspond to an electron pressure of about 5 x 10 which compares well to the various studies reported in the literature. The forbidden lines from these ions have been discussed in detail /19/. In the present work we have studied the possibility of using emission lines from the allowed transitions in some detail. There are not many lines in this class from these ions with calibrated intensities suitable for density determinations. In order to check whether the density sensitivity of line ratios falls into a range that are useful for solar atmosphere, we have calculated the relevant intensity ratios using a spherically symmetric model for the quiet sun /22/. The intensity ratios thus obtained are shown by dots in Figures 2 and 3. They fall on the density sensitive portion of the curves, thereby providing a direct method for determining Ne• The computed line fluxes from the entire solar disk at earth’s distance for various strong and weak lines have been listed in Tables 1 and 2 along with observed values wherever available. Calculated line fluxes from these ions may he useful in resolving difficulties

Density Diagnostics from Nitrogen-Like Ions

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(11)181

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12

Log Ne Fig.2. Log of Intensity Ratios E(j,i)/E (6,1) of Si VIII at the electron temperature Te, as a function of Log Ne. Dots correspond to the calculated ratios based on the Model of Elzner / 22/.

~

—

12

Log Ne Fig.3. Same as Figure 2 but for S X lines.

associated with line identification, masking or blending due to lines arising from the ions of other isoelectronic sequences. Such a study provides first hand information to predict for future observations the lines that have hitherto not been observed. Moreover, this study could also act as a test or constraint on the model atmosphere when compared with observational data. In our opinion this kind of study might also help interpretation of observational data in the right perspective /11, 13, 25/. With longer exposure it should be possible to observe some of the weaker lines as well. The discrepancies between the calculated and observed flux values could be ascribed to uncertainties in the atomic parameters, relative abundances, model atmosphere and ionization equilibrium on one hand and in measurements on the other. The average electron density distribution in the inner corona has been determined by using white-light observation of Saito /26/. At a height of 20” above the white-light limb,8 Saito’s 3. This analysis density predicts is however an equatorial averaged solar over regions minimum of electron different density temperatures. of 3.68 xThe10 value cm- obtained by us using line 8rati9s and corresponding theoreti&al line fluxes shows an electron density of 3.15 x 10 cm at a temperature of 1.6 x 10 K of the inner corona. Feldman et al. /]~9/ wh3ile justifying their work, are surprised to derive the same electron density of 10 cm for both quiet and active regions. However, they find that coronal forbidden lines in many other active region spectra, that were not suitable for analysis of S X lines, are substantially more intense than the lines in quiet sun spectra. Thus one finds it difficult to arrive at a conclusion whether such an analysis of the data and the interpretation therefrom could be final. The present investigation may help resolve such a puzzle with the availability of data from future solar missions with greater spectral and spatial resolutions. CONCLUS ION The solar emission lines of the nitrogen—like ions Mg VI, Si VI!! and S X in the EUV region are sensitive to electron density. Therefore, the solar extreme ultraviolet lines from these ions are useful to probe the emitting regions of the solar atmosphere. However, observational data with greater spectral resolution, which future missions might provide, could verify our calculations. Furthermore, we find that there are many lines from these ions which have observable flux values but no observational data are presently available. The calculated fluxes based on a working model for solar Chromosphere-corona transition region and the corona may help in resolving difficulties associated with line identificati on.

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B. N. Dwivedi and P. K. Raju

Computed Line Fluxes from the entire Solar Disk at Earth’s distance TABLE 1 SiVIII-lon, N(Si)/N(H) = 5.01 x 1O5 (Relative Abundance of Silicon, Kato/21/)

Transition

Flux (1O~ergs cu2 ~_1)

Wave length

R

Calculated

13, 13, 12, 12, 12, 12, 10, 10, 10, 9, 9, 9, 8,

2 4 2 3 4 5 2 3 4 2 3 5 1

214.75 232.84 216.79 216.92 235.24 235.56 276.84 277.05 307.65 276.89 277.10 309.26 314.31

0.43 0.08 0.13 1.20 0.06 0.30 0.53 0.06 0.07 0.09 1.32 0.18 1.34

7, 6, 5, 4, 2,

1 1 1 1 1

316.21 319.83 944.44 949.24 1445.78

2.56 3.82 0.36 0.16 0.24

TABLE 2.

Transition

12, 12, 9, 9, 8, 7, 6, 5, 4, 3, 2,

3 5 3 5 1 1 1 1 1 1 1

.~a ~b

6”,.~ 1~3d 11~,2•4d 22”, 3~8d

SX-Ion, N(S)/N(H) = 1.99 x 10~(Relative Abundance of Sulphur, Kato /21/) 2 s4) Flux (10~ergs cm Calculated Observed*

lth

180.78 196.84 228.64 255.07 257.13 259.49 264.24 776.58 787.78 1196.92 1213.62

0.21 0.06 0.24 0.04 0.79 1.53 2.15 0.10 0.05 0.08 0.14

*

Notes for the Tables 1 and 2

a b c d

Observed Observed Observed Observed

line line line line

Observed*

fluxes fluxes fluxes fluxes

from from from from

b ~ d 5.2~17~,1.5d 4.9,20 ,2.0

1.4C

Malinovsky and Heroux /27/ Behring et al. /28/ Sandlin et al. /29/ Austin et al. /30/

.

Density Diagnostics from Nitrogen-Like Ions

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REFERENCES 1. R.H.Munro, A.K.Dupree, and G.L.Withbroe, Solar Phys., 19, 347 (1971). 2. C.Jordan, In: Highlights of Astronomy, ed. C.de Jager, D.Reidel Pub. Co., 1971, p.519. 3. A.H.Gabriel and C.Jordan, in: Case Studies in Atomic Collision Physics, eds. E.McDaniel M.C. McDowel, Holland Astron. Pub. Co.,Astroph~ys., 1972, p.210. 4. and M.Louiergue and North H.Nussbaumer, 51, 163 (1976). 5. P.L.Dufton, A.E.Kingston, J.G.Doyle, and K.G.Widing, Mon. Not. Roy. Astron. Soc., 205, 81 (1983). 6. F.P.Keenan, K.A.Berrington, P.G.Burke, A.E.Kingston, and P.L.Dufton, Mon. Not. Roy Astron. Soc., 207, 459 (1984). 7. G.Elwert and P.K.Raju, Astrophys. Space Sd., 38, 369 (1975). 8. D.R.Flower and H.Nussbaumer, Astron.Astrophys., 45, 145 (1975). 9. D.R.Flower and H.Nussbaumer, Astron.Astrophys., 45, 349 (1975). 10. J.E.Vernazza and H.E.Mason, Astrophys. J., 226, 720 (1978). 11. B.N.Dwivedl and P.K.Raju, Solar Phys., 68, 111 (1980). 12. H.P.Saha and E.Trefftz, Solar Phys., 87, 233 (1983). 13. B.N.Dwivedi, Solar Phys. Lett., in press (1988). 14. H.E.Mason and A.K.Bhatia, Mon. Not. Roy. Astron. Soc., 184, 423 (1978). 15. P.K.Raju and B.N.Dwivedi, Pramana 13, 319 (1979). 16. P.K.Raju and B.N.Dwivedi, Solar Phys., 60, 269 (1978). 17. L.H.Aller, C.W.Ufford and J.H.Vleck, Astrophys. J., 109, 42 (1949). 18. P.K.Raju, Bull. Astron. Soc. India 6, 45 (1978). 19. U.Feldman, G.A.Doschek, J.T. Mariska, A.K.Bhatia, and H.E.Mason, Astrophys. J., 226, 674 (1978). 20. C.Jordan, Mon. Not. Roy. Astron. Soc., 142, 501 (1969). 21. T.Kato, Astrophys. J. Suppl., 30, 397 (1976). 22. L.R.Elzner, Astron. Astrophys., 47, 9 (1976). 23. M.Kafatos and J.Lynch, Astrophys. 3. Suppl., 42, 611 (1980). 24. G.A.Doschek, U.Feldman, A.K.Bhatia and H.E.Mason, Astrophys. J., 226, 1129 (1978). 25. B.N.Dwivedi and P.K.Raju, Bull. Astron. Soc. India 13, 387 (1985). 26. K.Saito, Ann. Tokyo Astro. Obs. Ser.2 12, 53, (1970). 27. M.Malinovsky and L.Heroux, Astrophys. 3., 181, 1009 (1973). 28. W.E.Behring, L.Cohen. U.Feldman and G.A.Doschek, Astrophys. J., 203, 521 (1976). 29. G.D.Sandlin, G.E.Bruckner and R.Tousey, Astrophys. 3. 214, 898 (1977). 30. W.E.Austin, J.D.Purcell, R.Tousey, ana K.G.Widing, Astrophys. J., 145, 373 (1966).