Proceedings of the National Academy of Sciences Vol. 66, No. 2, pp. 282-288, June 1970 Excitation of Metastable Levels in Low Density Nebular Plasmas: [SIT] and [ArIV] S. J. Czyzak,* T. K. Krueger,t and L. H. Allert OHIO STATE AND OHIO WESLEYAN UNIVERSITIES; WRIGHT-PATTERSON AIR FORCE BASkE, OHIO; AND UNIVERSITY OF CALIFORNIA (LOS ANGELES) Communicated March 23, 1970 Abstract. Diagnostics of low density nebular plasma by means of its forbidden line spectrum require not only a knowledge of certain intensity ratios as a func- tion of its density and temperature but also a knowledge of the occupation num- bers of relevant ionic levels. We present the necessary data for important levels of ionized sulfur and triply ionized argon. As reliable atomic parameters become available for an increasing number of ionic species, such as [Sil], [C1iii], [ArIV], their relevant forbidden lines be- come correspondingly more useful for the diagnostics of nebular plasmas, i.e., for deducing the densities and temperatures of individual condensations or fila- ments in which these lines originate. The first step is the calculation of the occupation numbers of each level as a function of density NE (electrons per cm3) and electron temperature T,, ('K) or the convenient variables introduced by Seaton.' t = 1010m; x = 10- T.1/2- 1 We then express the population Nj of each level, j, in terms of the ground level population Nl,-by means of a Boltzmann-type equation: N1 Wj N,= - bj exp (xjlkT,) (2) where co and co, are the statistical weights of the jth level and ground level re- spectively, Xj is the height (in energy units) of the jth level above the ground level, k is Boltzmann constant, and bj(x,t) is the factor introduced by Menzel2 to express the deviation of the population of the jth level from that appropriate to thermodynamic equilibrium at temperature Te. Let the number of collisional excitations from a lower level i to a higher level j per cm3 per sec be designated by NiNeqlj and the corresponding number of de- excitations be denoted by NjNeqj. The analogous number of radiative de-exci- tations will be NjAji; where A i is the Einstein coefficient of spontaneous emis- sion. Of course there are no radiative excitations. 282 Downloaded by guest on September 25, 2021 VOL. 66, 1970 ASTRONOMY: CZYZAK, KRUEGER, AND ALLER 283 Consider a ground p3 configuration as is appropriate for [SH1], [ArIV]. There are five levels. We express all populations in terms of level 1, 4SS12. We set up the equations of statistical equilibrium for the five levels in the following form :3 4 5 t 5 Neqij + N. Niqij + a NjAij = Nj N i qji + EAj1f (3) i=20j i>j iij=1 i<j with j = 2, 3, 4, and 5. The equations of statistical equilibrium express the fact that the population of each level remains constant with time. The left side gives the rate at which ions enter the level j, and the right side gives the rate at which the ions leave this level. As a first illustration, let us write down the equations of statistical equilibrium for [Sil]. Explicit expressions for qjj and qji have already been given,3 as have the collision strengths and A values., Let us use the following abbreviations: a = N(2Ds) C = N(2P1) b2 = b(2Ds/2), b4 = b(2P1/2) b = d = (2P31) b3 = = (2D.')N,' N, b(2D5/2), b5 b(2P312). (4) Tables 1 and 2 list the values of the bj's for [SIH] and [ArIV], respectively. The equations of statistical equilibrium for [SIH] are: 2.222 X 10-(06074/t)a + 2.923 X 10-(0.6054/t) b + 1.612c - -[342.5 + 8.412]d + 10-(1.535/t) 0, 3.497 X 10-(°6074/i) a + 2.080 X 10(- 6024/t) b - . + 18.461 c + 1.611d + 10-(1.532/t) - 0 1.388a + [1 + 1.592 + 2.123 X 10 Ol6046/t) b + L1 + 1.6731c LX XJ + [538.3 + 2.348]d + 10-(0.9299/t) - 0, -[6917 + 3.081 + 3.190 X 10 (0 6o/t)]a + 1.387b + [744.9 + 2.811}c + [658.2 + 1.785]d + 10-(09280/t) = 0. (5) Downloaded by guest on September 25, 2021 284 ASTRONOMY: CZYZAK, KRUEGER, AND ALLER PROC. N. A. S. TABLE 1. bn values of [SII]. Te Ne x b2 N N b5 5000 71 0.01 1.492 X 10- 5.698 X 1O-3 5.203 X 10-6 2.996 X 10-6 223 0.0316 4.785 X 10-3 1.775 X 10-2 1.722 X 10- 1.001 X 10-5 707 0.10 1.569 X 10-2 5.153 X 10-2 6.181 X 10-5 3.673 X 10-5 2234 0.316 5.283 X 10-2 1.344 X 10-1 2.573 X 1O-4 1.510 X 1O-4 7071 1.0 1.632 X 10-1 2.904 X 10-1 1.254 X 10-3 7.664 X 10-4 22345 3.16 3.942 X 10-1 5.098 X 10-1 6.297 X 1O-3 3.761 X 1O-3 70711 10.0 6.698 X 10-1 7.240 X 10-1 2.726 X 10-2 1.614 X 10-2 7500 87 0.01 1.545 X 10-3 5.804 X 10-1 5.206 X 10-6 2.998 X 10-6 274 0.0316 4.955 X 10-2 1.784 X 10-3 1.724 X 10-5 1.003 X 10-6 866 0.10 1.626 X 10-1 5.203 X 10-2 6.199 X 10-5 3.683 X 10-5 2737 0.316 5.410 X 10-2 1.339 X 10-1 2.579 X 10-4 1.571 X 10-4 8660 1.0 1.659 X 10-1 2.835 X 10-1 1.248 X 10-3 7.594 X 10-4 27366 3.16 3.896 X 10-1 4.863 X 10-3 6.154 X 10-3 3.657 X 10-3 86603 10.0 6.387 X 10-1 6.760 X 10-1 2.608 X 10-2 1.537 X 10-2 10000 100 0.01 1.597 X 10-3 5.908 X 10-3 5.208 X 10-6 3.000 X 10-6 316 0.0316 5.124 X 10-3 1.811 X 10-2 1.727 X 10-5 1.004 X 10-5 1000 0.10 1.682 X 10-2 5.253 X 10-2 6.217 X 10-5 3.693 X 10-5 3160 0.316 5.573 X 10-2 1.335 X 10-1 2.587 X 10-4 1.572 X 10-4 10000 1.0 1.684 X 10-1 2.773 X 10-1 1.243 X 10-3 7.531 X 10-4 31600 3.16 3.854 X 10-1 4.661 X 10-1 6.031 X 10-3 3.568 X 10-3 100000 10.0 6.166 X 10-1 6.363 X 10-1 2.510 X 10-2 1.473 X 10-1 12500 112 0.01 1.642 X 10-3 5.998 X 10-3 5.211 X 10-6 3.001 X 10-6 353 0.316 5.269 X 10-1 1.835 X 10-2 1.729 X 10-5 1.005 X 10-5 1118 0.10 1.729 X 10-2 5.295 X 10-2 6.232 X 10-5 3.702 X 10-5 3533 0.316 5.713 X 10-2 1.331 X 10-1 2.593 X 10-4 1.574 X 10-4 11180 1.0 1.704 X 10-1 2.725 X 10-1 1.239 X 10-3 7.483 X 10-4 35330 3.16 3.820 X 10-1 4.506 X 10-1 5.936 X 10-3 3.499 X 10-8 111803 10.0 5.997 X 10-1 6.066 X 10-1 2.436 X 10-2 1.425 X 10-2 15000 122 0.01 1.679 X 10-3 6.073 X 10-3 5.213 X 10-6 3.002 X 106 387 0.0316 5.391 X 10-3 1.855 X 10-2 1.730 X 10-5 1.007 X 10-5 1225 0.10 1.769 X 10-2 5.333 X 10-2 6.244 X 10-5 3.708 X 1o-5 3870 0.316 5.828 X 10-2 1.328 X 10-1 2.597 X 10-4 1.575 X 10-4 12247 1.0 1.721 X 10-1 2.687 X 10-1 1.236 X 10-3 7.445 X 10-4 38702 3.16 3.794 X 10-1 4.388 X 10-1 5.863 X 10-2 3.446 X 10-3 122474 10.0 5.870 X 10-1 5.843 X 10-1 2.380 X 10-2 1.390 X 10-2 17500 132 0.01 1.711 X 10-3 6.135 X 10-3 5.214 X 10-6 3.003 X 10-6 418 0.0316 5.494 X 10-3 1.872 X 10-2 1.732 X 10-5 1.007 X 10-5 1323 0.10 1.803 X 10-2 5.359 X 10-2 6.255 X 10-5 3.715 X 10-5 4180 0.316 5.924 X 10-2 1.326 X 10-1 2.602 X 10-4 1.576 X 10-4 13229 1.0 1.734 X 10-1 2.657 X 10-1 1.234 X 10-3 7.416 X 10-4 41803 3.16 3.774 X 10-1 4.296 X 10-1 5.806 X 10-3 3.405 X 10-3 132288 10.0 5.770 X 10-1 5.674 X 10-1 2.337 X 10-2 1.362 X 10-2 20000 141 0.01 1.737 X 10-3 6.188 X 10-3 5.215 X 10-6 3.004 X 10-1 447 0.0316 5.580 X 10-3 1.886 X 10-2 1.733 X 10-5 1.008 X 10-5 1414 0.1 1.831 X 10-2 5.383 X 10-2 6.264 X 10-5 3.719 X 10-5 4469 0.316 6.004 X 10-2 1.324 X 10-1 2.606 X 10-4 1.577 X 10-4 14142 1.0 1.746 X 10-1 2.633 X 10-1 1.231 X 10-3 7.393 X 10-4 44689 3.16 3.757 X 10-1 4.223 X 10-1 5.761 X 10-8 3.373 X 10- 141421 10.0 5.692 X 10-1 5.542 X 10-2 2.304 X 10-2 1.341 X 10- Downloaded by guest on September 25, 2021 VOL.