Adv. SpaceRes.Vol. 8, No. 11, pp. (11)185—(i1)188,1988 0273—1177/88$0.00+ .50Printed in GreatBritain. All rights reserved. Copyright © 1989 COSPAR

ELECTRON DENSITIES IN THE SOLARATMOSPHERE FROM EUV EMISSION LINES

B. N. DwivediDepartmentof Applied Physics, Institute of Technology, Banaras HinduUniversity, Varanasi 221005, India

ABSTRACT

The solar EUV emission lines from boron—like (Mg VIII and Si X), carbon-like (Mg VIIand Si IX) and oxygen-like (Si VII and S IX) ions have been used to derive electrondensities in the solar atmosphere. The line intensity ratios using Kopp and Orrall modeltall on the density—sensitive portion of the line intensity ratio curves which are thereforeused as density monitors of the quiet sun and the coronal holes. The electron densities

9 —3 8 —3 8 —3 8 —3of 1.6 x 10 cm , 9.7 x 10 cm , 5.2 x 10 cm and 5.1 x 10 cm are estimatedat the electron temperatures of 5 x 1O

5 K, 8 x 10~ K, io6 K and 1.6 x i06 K,

respectively for the quiet Sun whereas the corresponding electron densities of 7.4 x io8—3 8 —3 8 —3 8 —3

cm , 4.8 x 10 cm , 2.6 x 10 cm and 1.8 x 10 cm for the coronal holes. TheEUV emission lines, used in this study and which are hitherto not observed, havesufficient intensity for observation by future solar missions.

INTRODUCTION

The EUV spectrum of the Sun has become available with greater spectral and spatial reso-lution from rockets, unmanned and manned spacecrafts. The physical conditions of thesolar plasma can be best understood from an analysis and interpretation of its linespectrum. The electron density and temperature can be derived from the intensity ratiosof certain spectral lines. Line intensity ratios can be found that are sensitive primarilyto electron density. If the temperature of formation of the lines is also known, the localelectron pressure (N Te) of the plasma can be calculated. If the density-sensitive linepairs can be found eover a range of temperatures, the pressure throughout the plasmacan be determined and this result is important from the hydrodynamical point of view.

The C III seems to be the first ion considered for application to the solar transitionregion /1,2/. Ions in the beryllium sequence have rich emission-line spectra in the X-and EUV region /3/. Observations of the relative strengths of these lines in a given ionhave been widely used to probe the solar and astrophysical plasma /4,5,6,7,8,9/. Linesemitted from boron—like /10,11,12,13,14,15,16/, carbon—like /17,18/, nitrogen—like /19,20,21/ and oxygen-like /22/ ions have been studied in detail for density diagnostics of thesolar atmosphere.

If the computed line intensity ratio is found to vary with electron density, one findsit useful for density diagnostics. Moreover, the observed line intensity ratio should fallwell within the density-sensitive portion of the curve in order to reliably determinethe electron density. However, the observed lines with calibrated intensities have tobe distinctly free from any ambiguity with regard to the blending, masking or otherobservational problems. Therefore one finds very few observed lines with calibratedintensities to exploit them for density determinations. One of the ways to look at theproblem is to use a model atmosphere to compute the corresponding line intensities tofind out the theoretical values of Ne~ Such a study is also useful in identifying close

lines arising from different ions prevalent in the atmosphere and provides first handinformation to predict lines with observable intensity which have hitherto not beenobserved for future observations. This study also acts as a test or constraint on themodel atmospherewhen compared with the observational data.

We have, therefore, used a model atmosphere of Kopp and Orrall /23/ for the quiet Sunand the coronal holes to estimate the line intensities in order to use them for densitydeterminations. Kopp and Orrall have used a combined theoretical and observational

.37¼SR8:ii—M(11)185

(11)186 B. N. Dwivedi

approach to construct models of the inner corona applicable to quiet open-field regionsand coronal holes. These models extend from the top of the transition region at r 1.003

out to r = 3 R. Briefly, the temperature and density models are calculated by inte-

grating the full energy equation (with heating, thermal conductivity, radiative lossesand solar wind convection included), subject to hydrostatic equilibrium, in both radialand more divergent geometries. The unknown heating term is parameterized bytwo physical quantities: the mechanical flux incident at the base; and characteristicscale height for the dissipation of this flux. Boundary conditions at the base are fixedby EUV—derived models of the transition region. Using these models, the line intensitiesfrom Mg VIII and Si X(boron-like), Mg VII and Si IX (carbon—like) and Si VII and S IX(oxygen—like) have been computed. Electron densities are then derived for the quietSun and the coronal holes, are found to be in good agreement with the available obser-vational data.

Line Intensities

The line emission per unit volume is given by the expression

E(j,i) = A~1h v.. N~ (erg cm

3s~) N

— 1.59 x 10 ______ ion el N— .. e

x(~) N. N Nion el H

where NH = 0.8 Ne has been used. The integrated line intensity at the sun is given by

I(j,i) = 7.95 x io_2 !E*(j,i) N dh (erg cm2 Sr’ N

where E*(j,i) = 1.59 x i08 A.. . _______ ion el ________

N. N Nion el HN.

ion . .

is the relative ion abundance and taken from 3ordan /24/. Electron density Ne and

electron temperature Te as a function of height have kindly been provided by Kopp /25/N

in the tabular form. The relative abundances N for Mg, Si and S have been takenH

from Kato /26/. N. is the level density for the upper level of the transition. The

necessary steady state equilibrium equations for various levels accounting for differentphysical processes as well as the atomic data used here have been the same as reportedby Raju and Dwivedi /18,22/ and Dwivedi and Raju /14,27/.

RESULTS AND DISCUSSION

Density sensitivity of line intensity ratios considered in this study arises because ofthe existence of metastable levels. In Figures 1 and 2, we have shown the variationof some of the line intensity ratios only for Mg VII and Si X lines as a function ofelectron density. The results of the other ions have not been shown for want of spaceand will be reported elsewhere. The values of the temperature indicated in these figuresare those at which the relative ion abundances of the elements are reported to be themaximum. In order to study the temperature dependenceof line intensity ratios, we havecarried out computation at two different temperatures on either side of the temperatureat which the relative ion abundance of the element is maximum. We find that the lineintensity ratios discussed here are rather insensitive of temperature variation.

There are not many observed lines from these ions with calibrated intensities suitablefor density determinations. In order to determine the electron density from the quietSun and coronal hole regions, the computed line intensities using Kopp and Orrall modelhave been used. The line intensity ratios thus obtained are shown by dots in Figures1 and 2 for the quiet Sun and coronal holes. The crosses in these figures correspondto the line intensity ratios in the model atmosphere of Elzner /28/ for the sake ofcomparison. The electron densities thus derived are listed in Table 1 using Mg VII andSi X lines which seem to be quite reasonable and compare well with the observationaldata wherever available. The line intensity ratios and the derived electron densitiesfrom Mg VIII, Si IX, Si VII and S IX have not been given here and will be reportedelsewhere. Nonetheless, the average electron densities obtained from the EUV emissionlines studied have been listed in Table 2.

CONCLUSION

The study of emission lines from the ions considered could provide supplementary andcomplementary information leading to a more comprehensive study of the solar atmosphere.

ElectronDensitiesfrom EUV Lines (11)187

0.4I (230.40)

0.2

0.5- Cu

09 0.6 1(272.00)0.0SI S

—0.2 0 CH - COr~a(hole0 0.4 — . ~.9 OsCO 95 - Quiet Sonas

10~)1 0.3~ CH

US Uu~etSon1(01902)0 Os

• -0.6 _______IC 347.431.9

~ 4)4.92) / c~- Coronu) hole 0.1 1(134.0?)

0.0 -

1)240.74)—1.0 ((419.00—0.1 1(038.00—1.2/ 1(41492)

-0.2 -__________________________ I I

6 9 10 11 12 7 B 9 10 11 12

Log N0 Icr~%’) Log N0 tcnT’)

Fig. 1 FiFigs. 1 and 2. Electron density dependence of Mg VII and X density—sensitive lineintensity ratios. Dots and crosses correspond to the computed intensity ratios based onthe model atmosphere of Kopp and Orrall/23/ and Elzner /28/, respectively.

TABLE 1. Computed line intensity ratios and derived electron densities using Kopp andOrrall model

Quiet Sun Coronal holeLine intensityratio Intensity N (cm

3) Intensity N (cm3)e eratio ratio

Mg VII-ion

1(319.02) 0.89 1.6 x I09 0.57 7.4 x io81(434.92) O.66~ 1.0 x

1(280.74) 0.37 1.5 x l0~ 0.22 7.4 x 1081(434.92) 0.27k 9.6 x io8

Si X-ion

1(258.40) 2.37 4.6 x i08 2.0 1.7 x io81(272.00) 2.l0~ 2.3 x io8

2.45* 5.4 x 108

1(347.43) 2.10 5.0 x 108 3.14 2.1 x 1081(356.07) 2.83k 2.9 x io8

2.790* 3.2 x io8

1(638.00) 1.61 5.8 x i08 2.38 1.7 x io81(653.00) 2.0k 2.9 x 108

+Computed line intensity ratio using Elzner model /28/0Observed line intensity ratio from Malinovsky and Heroux /29/**Observed line intensity ratio from Vernazza and Reeves /30/

With the availability of observational data, which future solar missions might provide,the electron densities deriv& for the quiet Sun and the coronal hole regions may serveas a useful testing ground for the model of Kopp and Orrall. Most of the lines used inthis study are found to be with observable intensity and should be observed. The electrondensities derivedin this study are found to be quite reasonable and should await obser-vational support by future solar missions.

(11)188 B. N. Dwivedi

ACKNOWLEDGEMENT

The author is grateful to Dr. P.K. Raju of Indian Institute of Astrophysics in Bangalore,India, for his valuable advice and encouragement.

TABLE 2. Average electron densities derived from the line intensity ratios of EUVemission lines from Mg VII, Mg VIII, Si VII, Si IX, Si X and S IX ions

Electron DensityElectron Temperature (N ) —3

(T) e cme Quiet Sun Coronal Hole

5 x l0~ K 1.6 x 1O9 7.4 x io8

8 x l0~ K 9.7 x io8 4.8 x io8

106 K 5.2 x l0~ 2.6 x 108

1.6 x i06 K 5.1 x io8 1.8 x l0~

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