E X C I T A T I O N E Q U I L I B R I U M FOR LOW L Y I N G L E V E L S IN

CII , N l l t , O i v , N e w , M g v l H , S i x , A N D S i l l

S U R E S H C H A N D R A

Department of Physics, D.N. College, Gulaothi 245408, India

(Received 23 March; in revised form 10 June, 1978)

Abstract. The populations of the excited state 2P3/z relative to the ground s t a t e 2pi/2 have been investigated in C n, N m, O Iv, Ne vl, Mg viii, Si x, and Si II by considering all the radiative and collisional processes including the collisional transitions to the higher states which cascade to the upper level. The relative populations are used for the calculation of the line emissivities. The intensities of 76 320, 30 258 and 14 302 lines of Ne vl, Mg vm, and Six ions respectively in the chromosphere- corona transition region are also calculated.

1. Introduction

The calculations for the excitation equilibrium of Fe, Ni, and Ca ions were carried out by Zirker (1970). These were severely hampered as: (1) the proton excitation rates which are important at high temperatures were neglected, (2) the collisional excitation to the higher levels which cascade to the upper level of the line were not taken into account, and (3) the adequate atomic data were not available. After these calculations, several workers made calculations for the densities of the excited states of the ions, e.g. Blaha (1971), Fe xzv; Flower and Pineau des Forets (1973), Fe xm; Rozelot et al. (1974), Fe xt. Recently Mason (1975) has discussed the excitation of Fe x, Fe xl, Fe xIv, Ca xII, Ca xm, and Ca x v by considering all the radiative and collisional processes including cascade via the excited configuration and the effect of autoionizing levels on the electron collisional excitation rate. She also included the spin-orbit type interaction, and spin-spin interactions.

In the present investigation I have calculated the population of 2P3/2 level relative to 2P1/2 level within the ground configuration of C H, N m, O Iv, Ne vI, Mg viii, Si x, and S in ions by considering the excitation processes: the photoex- citation, collisional excitation, proton excitation, excitation to the higher states which cascade to the upper level, the dielectronic excitation which cascade to the upper level, and the deexcitation processes: radiative deexcitation, collisional deexcitation, as a function of temperature for electron densities Are = 107, 108, 109,

and 10 l~ These results are employed for the calculation of: (1) the line emissivities of the C ii, N m, O iv, Ne vT, Mg vm, Si x, and Si ii ions, and (2) the line intensities of Ne vl, Mg vm, and S i x ions in the chromosphere-corona transition region.

2. Line Emissivity

The line emissivity JL (in erg cm -3 s -~ sterad -~) is given by

JL = 1.27 • 10 -13 NjA(L i) W(i, j) , (1)

Solar Physics 58 (1978) 291-297. All Rights Reserved Copyright O 1978 by D. Reidel Publishing Company, Dordrecht, Holland

292 SURESH CHANDRA

where A(j, i) (s -1) is the spontaneous transition probability, W(i, ]) (eV) the energy difference between the corresponding levels, Ni, the population density of the ion concerned in the upper state j, can be expressed as

Nj N1NE NH N = Ne. (2) N1Nz NH Ne

Here N~ is the electron density, NE/NH the elemental abundance relative to hydrogen, NffNE the ion abundances and NH/N~(=0.8) is the density of the protons relative to the electrons. The ion abundances which have been calculated by considering all the possible ionization and recombination processes and includ- ing the density effect are readily available in a tabular form (Jordan, 1969). The population of the excited state relative to the ground state (NJNa =-N2/N1) are determined by the steady state equation

NI(A~2 + C12+P12+ C12c + C12e) = N2(A2t + C21), (3)

where A 12 is the photo excitation rate which is related to the spontaneous transition probability, A21, by

A12 = A2~Dg2g71 [exp (W(1, 2)/kTr)- 1] -~ . (4)

Here the black body radiation temperature Tr and the dilution factor D are taken as 6000 K and 0.3 respectively, g~ and g2 are the statistical weights of the lower and upper levels and k is the Boltzmann constant.

The electron collisional excitation rates C12 are calculated with the help of a well known relation

8.63 x 10 -6 1)(1, 2)Ne = exp [ - W(1, 2)/kT]. (5) C12 T1/2g 1

Here fi(1, 2) is the collision strength for the transition and is assumed to be independent of energy.

Px2 are the proton excitation rates and are important only for the transitions in the ground configuration (Seaton, 1964) and at high temperatures. The proton excitation rate coefficients required for the calculations are readily given in the tabular form by Bely and Faucher (1970).

C12c are the rates for the collisional excitation to the higher states which cascade to the upper level and are given by

1.7 • 10 -3 f(1, k) ~ , , W(1, k)] C12~= N~ (6)

Here f(1, k) is the dipole oscillator strength for the transition between the ground state and the higher state k. The gaunt factor g is about 0.6 for the transitions in which the principal quantum numbers remain the same and is about 0.2 for the transitions in which the principal quantum number changes (Mason, 1975). C(k, 2) is known as cascade coefficient and represents the probability that the ion in the

E X C I T A T I O N E Q U I L I B R I U M F O R L O W L Y I N G L E V E L S 293

higher state k will decay to the level 2 and is given by

A (k, 2) C(k, 2)=- a(k, 2)+A(k, 1)'

C12d are the rates for the dielectronic excitation to the higher states which cascade to the upper level and are given by (Ansari and Alam, 1975)

C~2u = 8.22 • IO-4B(Z)T -3/2 Z A(x)f(1, k )W ~/2 (1, k) C(k, 2)• k

0.015Z l-l/ • ]_1.1613 • lO4 W(1, k )T-l[ [ . . ~ _ ~ j J (7)

with

B(Z) = z~/Z(z + 1) 2 (Z2+ 13.4) -~/2 ,

A(x) = (1 + 0.105x + 0.015x2)-1; w(1, k)

X - - 13.6(Z + 1)

and Z = m + 1.

is the charge on the ion concerned. Although the contribution of C12 d is m

negligible in the present case it contributes however significantly for the lines in the

UV and X-ray regions. C2~ are the collisional deexcitation rates and are related to the collisional

excitation rates by

C2a = C12gig21 exp [W(1, 2)/kT] . (8)

3. Line Intensity

The intensity of the line (in erg cm -~ s -~) observed at the Earth's distance is given by (Pottasch, 1963)

• 10 -17 W(i, j ) f NjAji dh, (9) I 1.74

where the integration is performed over the line forming region. In the chromos- phere-corona transition region (electron pressure p a r a m e t e r = 6 x l 0 1 4 , the conductive flux factor = 1012) Equation (9) reduces to

" A N E ( Nj N1 T 1/2 I=5.02W(i,I) ii-~--~H J-~aNE Ne dr. (10)

4. The Atomic Data

The atomic data used here have been adopted from various sources. The collision strengths are taken from Blaha (1968, 1969). The transition probabilities and Oscillator strengths for the excitation to the higher levels have been taken from the

294 SURESH CHANDRA

compilations of Wiese et al. (1966, 1969). Energy levels are taken from the tables of Moore (1949). The elemental abundances relative to hydrogen used here have been experimentally determined by Dupree (1972).

TABLE I

Values of N2/N1 and Jr_ for C 1I

Log T N2/N1 JL

Ne= 107,108 , 107 109,1010

3.8 1.98 1.725(-21) a 3.9 2.05 1.522(-19) 4.0 2.13 3.976(-18) 4.1 2.24 1.317(-17) 4.2 2.36 1.562(-17) 4.3 2.52 1.704(-17) 4.4 2.73 1.645(-17) 4.5 3.02 1.046(-17) 4.6 3.43 4.627(-18) 4,7 3.99 2.050(-18) 4.8 4.74 7.874(-19) 4.9 5.66 3.187(-19) 5.0 6.73 5.110(-20)

a The numbers in brackets are the power to 10.

Log T

TABLE II

Values of N2/N1 and JL for N m

N21N1 IL

Ne = 107, 108 107 109 ' 10 TM

4.3 2.02 4.4 2.09 4.5 2.18 4.6 2.33 4.7 2.57 4.8 2.95 4.9 3.48 5.0 4.18 5.1 5.04 5.2 6.02 5.3 7.08 5.4 8.17

9.725(-20)" 3.032(-18) 3.896(-17) 1.734(-16) 3.254(-16) 4.096(-16) 3.754(-16) 2.206(-16) 9.429(-17) 2.248(-17) 2.147(-18) 1.133(-19)

a See note of Table I.

E X C I T A T I O N E Q U I L I B R I U M F O R L O W L Y I N G L E V E L S 295

5. Results and Discussion

The relat ive popula t ions of the excited states have been calculated as a funct ion of

t empera tu re for the e lectron densi t ies Are = 107, 108, 109, and 10 l~ The results are

p resen ted in Tables I through VII. The results are also used for the calculat ion of

the line emissivities (Equa t ion (1)) and the line intensi t ies (Equat ion (11)) (for

Ne vi, Mg v m , and Si x) for the electron densit ies m e n t i o n e d above and the results

are also p resen ted in Tables I through VII.

TABLE III

Values of N2/Na and JL for O IV

Log T N2/N1 ,IL

Ne= 107,108 107 109,101~

4.7 2.17 4.8 2.37 4.9 2.72 5.0 3.15 5.1 3.77 5.2 4.57 5,3 5.49 5,4 6.49 5.5 7.55 5.6 8.63

9.120(-17)" 1.313(-15) 1.017(-14) 2.638(-14) 4.267(-14) 4.197(-14) 2.469(-14) 7.499(-15) 1.098(-15) 7.056(-17)

a See note of Table I.

TABLE IV

Values of Nz/NbJL, and I for Ne vI

tog T "N2/N1

Ne= 107

&

108 109 101~ 107 108 109 101~

5.2 2.329 2.844 2.939 2.949 5.3 2.578 3.349 3.500 3.516 5.4 2.856 3.960 4.189 4.214 5.5 3.141 4.647 4.980 5.017 5.6 3,421 5.393 5.857 5.910 5.7 3.688 6.192 6 . 8 2 1 6.894 5.8 2.923 7.002 7 . 8 3 1 7.929 5.9 4.120 7 . 8 0 1 8 . 8 6 8 8.996 6.0 4.279 8.585 9 . 9 3 1 10.095

Intensity ofline I =

3.917(-16) a 9.269(-15) 6.187(-14) 1.559(-13) 1.862(-13) 1.029(-13) 1.992(-14) 1.624(-15) 1.403(-15) 1.481(-5)

4.782(-15) a 1.204(-13) 8.578(-13) 2.307(-12) 2.934(-12) 1.728(-12) 3.555(-12) 3.075(-14) 2.816(-15) 2.402(-6)

4.942(-14) ~ 4.960(-13)" 1.258(-12) 1.264(-ll) 9.075(-12) 9,130(-11) 2.472(-11) 2.490(-10) 3.187(-11) 3.216(-10) 1.904(-11) 1.923(-10) 3.978(-12) 4.027(-11) 3.496(-13) 3.546(-12) 3.256(-14) 3.310(-13) 2.588(-7) 2.595(-8)

a See note of Table 1.

296 S U R E S H C H A N D R A

TABLE V

Values of N2/N1, rE, and I for Mg viii

Log T N2/N1

Ne ~

10 v 108 109 101~ 107 10 s 109 101~

5.5 0.584 1.248 3.651 5.137 5.6 0.595 1.356 4.314 6.317 5.7 0.605 1.458 5,007 7.644 5.8 0.614 1.549 5.699 9,085 5.9 0.622 1 . 6 3 1 6.395 10.665 6.0 0.627 1 . 6 9 5 7.039 12.301 6.1 0.632 1 . 7 4 5 7.632 14.003 6.2 0.635 1 . 7 8 2 8.173 15.772 6.3 0.637 1 . 8 1 1 8.680 17.649

Intensity ofline I =

8.652(-16) a 1,849(-14) ~ 3.057(-14) 6.967(-13) 2,902(-13) 6.993(-12) 9.310(-13) 2.349(-11) 1.243(-12) 3,260(-11) 5.350(-13) 1.446(-11) 8.342(-14) 2.304(-12) 7.132(-15) 2.003(-13) 7.667(-16) 2.181(-14) 2.546(-4) 6.470(-5)

5.411(-13) a 7.612(-12)" 2.216(-11) 3.246(-10) 2.401(-10) 3.665(-9) 8.641(-10) 1.378(-8) 1.278(-9) 2.132(-8) 6.002(-10) 1.049(-8) 1.008(-10) 1.849(-9) 9.188(-12) 1.773(-10) 1.046(-12) 2.126(-11) 2.544(-5) 4.297(-6)

See note of Table I.

TABLE VI

Values of Nz/N1, Jt, and I for Six

Log T N2/ N~

Ne ~ 107 108

JL

109 101~ 107 108 109 101~

5.8 0.1463 0.2182 0.8442 3.3818 5.9 0.1466 0.2215 0.8830 3.7471 6.0 0.1469 0.2244 0.9183 4.1173 6.1 0.1471 0.2266 0.9459 4.4668 6.2 0.1473 0.2287 0.9726 4.8258 6.3 0.1474 0.2303 0.9947 5.1713 6.4 0.1475 0.2315 1.0129 5.5021 6.5 0.1476 0.2326 1.0291 5.8251 6.6 0.1477 0,2336 1.0445 6.1469

Intensity of the line I =

2.445(-14r 3.646(-13) ~ 1.411(-11) a 5.651(-10) a 4.888(-13) 7.386(-12) 2.944(-10) 1.249(-8) 2.754(-12) 4.208(-11) 1.722(-9) 7.720(-8) 6.173(-12) 9.510(-11) 3.971(-9) 1.875(-7) 4.582(-12) 7.115(-11) 3,026(-9) 1.502(-7) 1.126(-12) 1.758(-11) 7.598(-10) 3.950(-8) 1.324(-13) 2.078(-12) 9.090(-11) 4.938(-9) 1.453(-14) 2.288(-13) 1.013(-11) 5,731(-10) 2.200(-15) 3,480(-14) 1.556(-12) 9.155(-11) 2.760(-3) 4,196(-4) 1.861(-4) 8.677(-5)

a See note of Table I.

I t is obv ious f rom E q u a t i o n (3) tha t if A21 is negl ig ible in c ompa r i son to C21 and

AlE is negl ig ible in compar i son to e i ther C12, P12, C12c, or C12ci then N2/N1 b e c o m e s i n d e p e n d e n t of e lec t ron densi ty . H e n c e the va lues of N2/N1 o b t a i n e d for

C II, N m, O IV, and Si ii are i n d e p e n d e n t of the e l ec t ron dens i ty (Tables I, II , I I I ,

and VII) . The re la t ive p o p u l a t i o n increases with t e m p e r a t u r e for a pa r t i cu la r

e lec t ron densi ty . In Tab les I, I I , I II , and V I I the l ine emissivi t ies a re given for

Ne = 107. F o r o the r values Ne = 108, 109, 101~ the va lues can be o b t a i n e d by

mul t ip ly ing by 10, 102, and 103 respect ive ly .

EXCITATION EQUILIBRIUM FOR LOW LYING LEVELS 297

TABLE VII

Values of N2/N1 and JL for Si II

Log T N~/ NI IL

N e = 107, 108 107 109, 101~

3.8 1.87 2.518(-17) ~ 3.9 1.91 2.950(-16) 4.0 1.96 5.021(-16) 4.1 2.02 5.544(-16) 4.2 2.11 4.814(-16) 4.3 2.25 2.136(-16) 4.4 2.45 9.278(-17) 4.5 2.78 4.490(-17) 4.6 3.28 2.715(-17) 4.7 3.94 1.674(-17) 4.8 4.77 7.352(-18) 4.9 5.72 1.189(-18)

a See note of Table I.

Acknowledgements

I am grateful to Dr Udit Narain for his encouragements and suggestions. I am thankful to Dr K. C. Mittal (Principal) for providing facilities. I am also thankful to Mrs Purnima Sharma for her cooperation during the course of this work. Financial support by U.G.C. New Delhi is thankfully acknowledged. I would like to thank the learned referee for improving the manuscript.

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