REVIEWS OF MODERN PHYSICS VOLUME 16. NUMBERS 3 AND 4 JULY-OCTOBER, 1944

Recent Progress in the Interpretation of Stellar Spectra

OTTO STRUVE Yerkes Observatory, University of Chicago, Williams Bay, Wisconsin, and McDonald Observatory, University of Texas, Fort Davis, rexas

I. PECULIAR STELLAR SPECTRA Their spectra are unusual, and their atmospheres HE modern interpretation of stellar spectra do not resemble the reversing layer of the sun. dates from the appearance, in 1920, of The discovery that departures from thermo- ex- M. N. Saha's classical paper "Ionization in the dynamic equilibrium may be important in Solar Chromosphere. " ' Since that time the plaining the spectra of the "peculiar" has theory of ionization and excitation of stellar revived interest in the question of the mecha- atmospheres has been developed in considerable nisms which produce excitation and ionization. detail by H. N. Russell, E.'A. Milne, R. H. This is a field with which physicists —practical Fowler, and many others. This theory, which can and theoretical —are much more familiar than be designated as the "classical theory" of stellar are astronomers. Hence, I propose to discuss spectra, is dominated throughout b'y the concept several specific problems from this point of view, of thermodynamic equilibrium and the two in the hope that the information now lacking for fundamental equilibrium formulae based upon their complete solution may in time be supplied it: the Boltzmann formula which determines the by the physicists. ratio of the number of atoms in an excited state In order to understand the peculiar character to the number of atoms in the ground state, and of the spectra I shall discuss, it is necessary to the Saha ionization formula which determines describe briefly the appearance of a normal stellar the ratios of the number of ionized atoms to the spectrum. If we choose all stars included in a number of unionized atoms. The particular typical unit of volume of galactic space, we shall mechanisms of excitation and ionization —photo- encounter an enormous preponderance —perhaps electric ionization, collisions, etc.—play no con- of the order of ninety-nine percent —of stars, spicuous part in this theory and ar'e rarely whose spectra consist of absorption lines on the mentioned in that part of the astrophysical background of a continuous emission spectrum, literature of the past quarter of a century which whose distribution resembles that of a blackbody is devoted to stellar spectroscopy. The applica- having a temperature somewhere within the tion of the concept of thermodynamic equilibrium range of 3000'K and 100,000'K. The absorption with its corollary, the concept of detailed lines are of atomic, or molecular origin, and have, balancing, is, however, only an approximation. with few exceptions, been satisfactorily identi- The very fact that spectral lines are formed in a fied. All of these normal stellar spectra can be stellar atmosphere proves that the state of the classified in a two-dimensional scheme, the rela- atmosphere cannot be accurately described by tive intensities of the absorption lines changing means of these concepts. Hence, astrophysicists gradually as functions of two physical param- are led to ask the question how accurate is the eters: the temperature and the pressure. It is of "classical theory&" It has been shown that for fundamental importance in astrophysics that the ordinary stellar atmospheres of . stars which dependence upon temperature is much more resemble the sun, the departures from thermo- pronounced than the dependence upon pressure. dynamic equilibrium are usually insignificant, Hence, most empirical classification schemes are and the application of the Boltzmann and Saha essentially temperature sequences. The pressure formulae is therefore justified. But in recent dependence is introduced as a small correction , various phenomena have been found which to this principal sequence. For example, among cannot be reconciled with this simplifying idea. the stars of intermediate temperature, the in one reason Most of them occur stars which, for gradual increase in the intensity of the line Cal "peculiar. " or another, have been classified as 4226 corresponds to a sequence of decreasing ' M. N. Saba, Phil. Mag. 40, 472 (1920). temperature. But two stars having identical lines 86 I NTERPOLATION GF STELLAR SPECTRA

of CaI 4226 may show different intensities for mechanism with frequencies of transitions not SrII 4215. Because of the pressure dependence favored by the primary mechanism, Ruorescence of Saba's ionization equation, the of lower plays an important role. 8owen has called atmospheric pressure shows the stronger line of attention especially to the fact that certain SrII 4215. This results from the fact that the members of high level multiplets of OIII are ionization potential of Sr+ is higher than that of strong, while other members are absent. This Ca, Fe, and most of the other atoms represented he attributes to the fact that the line HeII 303.78 in the spectra of these stars. (1s'g —2p'P) is undoubtedly exceedingly strong An entirely diferent aspect is presented by the in all nebulae (although atmospheric absorption spectra of the nebulae (Fig. 1). Here we see a renders it unobservable) and agrees very closely series of strong emission lines superposed over a with the line OIII 303.80 (2P'P2 —3d'P2). The ' continuous spectrum which presents a fairly emission of HeII causes the OIII level 3d'P2 to conspicuous break at X3647, the limit of the be overpopulated, and all lines originating from . The continuum consists of a it are therefore greatly enhanced. superposition of a true recombination spectrum (3) Because high level transitions of certain of H, and what appears to be a blackbody con- ions, OIII, OII, XII, etc. , are weak in the tinuum produced by the non-selective scattering nebulae, Bowen has suggested that the excitation of star light by many small particles in the of low metastable levels occurs predominately by . the mechanism of collisions with free electrons. The emission lines in the nebulae are excited It can be shown that the forbidden lines origi- by three mechanisms, as was first clearly recog- nating from these levels are too strong to be nized by Bowen: attributed wholly to the mechanism of recom- (1) The continuous radiation of stars located bination. in, or near, the nebulae causes photoelectric There exist a number of stars whose spectra ionization of H, He, etc. , and also produces combine the normal features of a stellar spectrum excitation of atoms through line absorption. with features usually associated with gaseous (2) Because of certain chance coincidences in nebulae. These stars are usually designated as the frequencies of lines excited by the primary emission-line stars, and the spectroscopic symbols

"?,"';w~::"; ';"''; "»g', '??? ', '. ", ' ' ', j' '»&~:;;:, . .'~;;p',. .q~~'" -',",. ~;». ~', , '„;i.? . »,', , , ~ ~, '", . „""., ',»a., ~, , »a, N~A /pe? g, „' -. ,, , », ;. . .„.. . ; „. ~

&II%I I I II ~

.?'.. ~'/? ?:

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I $8RI» II 1»»= g~l I ~ sim 5 l Igy II I ' ~»» ss»»» ~ -- . — — . I

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Fro. 1. Nebulae: (a) Orion, (b) IC 418, (c) IC 2165. OTTO STRUVE

TABLE I. Physical characteristics of stars.

+Group Dwarf Giant Super-giant Nebula Property+ Example Sirius 8 Sun= 8 Capella Betelgeuse Orion Mass 18 18 58 158 Radius 0.018 18 =700 000 km 108 3008 Mean density 10' g/cm' 1 g/cm' 10 'g/cm' 10-6 g!cm3 Height of abs. atm. 100 km) 100 km 1000 km 100000 km 10"km Mean electron pressure of atm. 104—10' d/cm' 100 d/cm' 1—10 d/cm' 10 ' d/cm2 No. of electr. per cm' of atm. 10"—10'~ 1014 1013 1012 10'—104 T ~10,000' 3,000 to 50,000' same same 50,000'K which define their place in the classification bidden transitions of LFe] X, XI, XIII, XIV, scheme are followed by the letter e. These stars XV; LNi] XII, XIII, XV, XVI; LCa] XII, are quite rare, and most of them are faint. They XIII, XV; LA] X, XIV. The ionization poten- have been known for many years from the ob- tials of these ions are as high as 814 volts (for ' jective prism work of the Harvard Observatory, Ca XIV) and represent the highest stages of but in recent years they have been investigated ionization thus far observed in any astronomical mostly at Mount Wilson by P. W. Merrill, at source. The ionization level of the ordinary solar the University of Michigan by D. B.McLaughlin, reversing layer is, by contrast, only about 8 at the Victoria Observatory by C. S. Beals, and volts. The ionization equation shows that ordi- at the McDonald Observatory by P. Swings, and nary thermal ionization, with the solar tem- the writer. perature, cannot account for this high ionization To understand the significance of the emission- level in the corona. ' Hence, the mechanism of line stars, it may be useful to review the principal ionization must be something different. More- physical quantities which serve to describe dif- over, the existence of a layer showing strong ferent kinds of stars and nebulae. This has been forbidden lines in the vicinity of the sun shows done in Table I. The data given are enly rough that the concept of thermodynamic equilibrium approximations for each group and are not the can certainly not be used in describing its accurate values derived for the stars listed in the spectrum. first line. It is of interest to note that Adams and Joy The "classical theory" of stellar atmospheres' at Mount Wilson have found the strongest is concerned with the reversing layers whose coronal lings XX5303, 6375 of LFe XIV] and properties are described in the last four lines of LFe X] in the spectrum of the peculiar star RS Table I. But we know that even in a normal star Ophiuchi, while Swings and the writer found like the sun, the reversing layer is not sharply some evidence of the t Fe X] line in another limited at the top and at the bottom. At the top, star, AX Persei. ' The absence of these lines in it gradually merges into a very rarefied layer, the the integrated spectrum of the sun is not due to chromosphere, and this, in turn, gradually have other identifications in the sun and stars. The reader merges into the solar corona. The spectrum of is referred to Edlen's original papers and to a detailed the corona consists of a strong continuum in review by Swings (Ap. J. 98, 116 (1943). ' Saha's equation gives log (n„+1/n,)p. = —x,(5040/T) which the absorption features of the normal +5/2 log T+const. If we consider two such ratios, each solar spectrum can be distinguished, probably giving n, , 1/n, =1, the one corresponding to x,=s volts, the other to g, =800 volts, and if we adopt T=5040'K, as a result of non-selective scattering and of a then large number of emission lines. The latter have &Os (P./P') = &92, recently been identified' by B. Edlen as for- which would correspond to an impossibly low pressure in the corona —a pressure which would be much lower than that of the interstellar medium and would leave virtually ' In fairness to the reader not acquainted with the no gas to radiate! astronomical literature, it should. be stated that while "In April, 1945, Joy announced the discovery of the these identifications are distinctly probable, they have not coronal lines in the spectrum of another peculiar star, yet been established with the same degree of certainty as T Pyxidis. I NTE RPOLATI ON OF STELLA R 5 PE CTRA any important intrinsic causes; if the corona with the dilute continuous radiation of the rotat- were much larger than it actually is, the emission ing star. Usually, the ionization level of the shell lines might be observed in the integrated light, is lower than that of the normal reversing layers. and the sun would then be classified as a peculiar When lines of FeII are observed, they are almost star. It is evident that under normal conditions always those which correspond to permitted of development, single stars do not develop such transitions. Only in very few Be stars have for- extensive coronas, and the problem is to discover bidden LFeil j lines been observed. An example those conditions which render a corona suf- of this latter group is the star 3fWC 56 (Fig. 2). ficiently large in such stars as RS Ophiuchi and The diameters of the ring-like structures are AX Persei. estimated to be of the order of two to 6ve times The emission-line stars are, however, not all the diameters of their central stars. Particularly as spectacular as RS Ophiuchi and AX Persei. interesting and convincing information has been They can be roughly classi6ed into 6ve distinct obtained in the cases of several Be or Ae stars groups. which happen to be members of close binary A. Ordinary Be stars have normal spectra systems. In several such binaries, the lobes of the corresponding to temperatures of the order of rings are successively eclipsed by the other com- 20000'K with absorption lines of H, HeI, OII, ponents, with an eclipse of the central star itself MgII, etc. upon which are superposed emission taking place between. lines of H, FeI I, and occasionally, of other B. The Wolf-Rayet stars and P-Cygni type elements. It has been shown, mostly by the stars, for reasons which are not yet understood, writer, that these emission lines occur pre- are surrounded by rapidly expanding gaseous dominantly in normal stars whose axial rotation shells which produce very broad emission lines is very rapid —of the order of 300 km/sec. at the flanked on their violet sides by absorption lines equator —and the suggestion was made that of somewhat smaller widths. The velocities of rotational instability causes these stars to dis- expansion range from a few tens of km/sec. to sipate material in the- form of rings in their several thousands of km/sec. They are not the equatorial planes. When such rings are observed same for all lines, and definite indications of projected upon the star-disks (that is, when the stratification have been found in the expanding line of sight is in the equatorial plane), peculiar shells. The emission lines correspond to high absorption lines are formed; the H-lines are stages of ionization (NV, etc.) and are all of exceedingly sharp, being devoid of broadening permitted transitions. A surprising number of by Stark effect or by collisions, and those lines these stars are members of close binary systems, (SiII, MgII) whose lower levels are not meta- having periods of from 1.6 to more than 20 days. stable are greatly weakened, showing that the The velocities of the Wolf-Rayet stars in their mechanism of their excitation is to be identified are measured in hundreds of km/sec. and

Fir.. 2. MB'C 56. 290 OTTO STRUVE

FIG. 3. .

are much smaller than their velocities of ex- tion in overlying gases of CaII. There are other pansion. The emission and violet absorption lines similar cases of absorption lines which originate of I' Cygni (and of other related objects) show at higher levels than the emission lines and tend remarkable departures from the laboratory to weaken the latter. intensities, suggesting that the various levels are E. Finally, there are a number of peculiar populated by highly selective mechanisms and stars which cannot be classed in any of the pre- not by a process (such as recombination, or ceding four groups. The stars RS Ophiuchi and thermal excitation) which would permit the use AX Persei are examples. There is no evidence of the Boltzmann formula. that all these stars are physically related, and C. Novae are in many respects similar to stars several small sub-groups of closely similar objects of the preceding group, but while a Wolf-Rayet can already be distinguished. An attempt to star or a P-Cygni type star is a fairly stable isolate these sub-groups and describe them has object (their spectra remain the same over recently been made by Merrill. ' The problems l periods of many years), novae, supernovae, and want to discuss concern this group of peculiar recurrent novae represent cataclysmic phe- stars. nomena which can best be described by the word A particularly interesting representative of explosion. this group is the Z Andromedae. ' D. Certain variable stars of long period and low surface temperature develop periodically 4 Astrophys. J. 99, 22 (1944). ~ Non-astronomical readers are often confused by the emission lines of H, FeII, MgI, SiI, and other. bewildering names of individual stars. Greek letters and elements. These stars have been investigated proper names are used only for the brightest stars. Faint stars may be designated by the numbers which the stars mostly at the Mount Wilson Observatory. Of carry in some well-known catalogue. Variable stars are particular interest is the weakness of the line He designated by capital letters of the Latin alphabet, but occasionally, the same star may be designated in several which is undoubtedly caused by heavy absorp- different ways.

INTE RPOLATION OF STELLAR SPECTRA had developed a. theory by means of which it do not observe it directly. Perhaps the source of was possible to determine the temperature of excitation of the emission lines must be sought the exciting star from measurements of total in some other type of mechanism than blackbody energies contained in the emission lines. An ap- radiation. The disturbing aspect is the absence plication of this theory would give for Z An- of a continuous spectrum corresponding to a dromedae a temperature of perhaps 50,000'K. high temperature. This is, however, not neces- At the present time, the TiO absorption bands sarily fatal. We observe, for example, many are not seen in the spectrum of Z Andromedae. planetary nebulae with strong emission lines and But Fig. 6 shows the spectrum of a very similar with very faint, hot central stars. It requires object, CI Cygni, in which they can be easily only a slight eA'ort of the imagination to think distinguished. It is of considerable interest that of a central star so faint that it would not be in Z Andromedae we observe in the same observed at all. But are the circumstances spectrum lines of [FeII), [FeV), and [FeVII), really alike& The star Z Andromedae is roughly while [FeIII) is not seen. This may be caused by of the tenth visual magnitude. Most of this light the accidental absence in the object of a layer is, however, concentrated in the emission lines in which [FeIII) is favored. Another star of this and in the cool continuum. The photographic group, BF Cygni, shows [FeIII) conspicuously magnitude of the hypothetical hot companion (Fig. 7, taken from a recent paper by P. W. cannot be greater than about 11. On the other Merrill), so that its absence in Z Andromedae hand, the star cannot be very far from us, can probably not be attributed to any intrinsic because we fail to observe any interstellar lines weakness of the lines of [FeIII). The evidence of Ca II. From the known relation between inter- in regard to Z Andromedae suggests the existence stellar line intensity and distance, we infer that of four separate sources: a cool star producing probably the distance is less than 400 . Tio absorption, a very hot, but presumably At this distance, a star of exceedingly small, star whose existence is in- 11 would have an absolute magnitude of about ferred by the presence of lines requiring large +3. The known hot stars have absolute bright- excitation energies, a tenuous mass of gas- nesses of the order of 1000 times greater. The producing emission lines of relatively low hot companion, if it exists, must be an under- ionization ([Fell)), and another mass of gas luminous object. Such underluminous stars are producing lines of high ionization ([FeVII)). not unknown. But the problem of Z Andromedae In evaluating this picture, we are perhaps some- would then be even more complicated and what uncertain about the hot star, because we interesting. Since the temperature of the exciting

Fro. 7. Bt Cygni (a) August 31, 1941; (b) August 6, 1941; (c) September 15, 1942; (d) August 11, 1943. 0 CTO STRUVE

about two years ago. A few additional transitions

ss have been identified since then, but the picture, as shown, is essentially complete. We have already seen that in the spectra of j ~ Mg C 56 and Z Andromedae permitted and for- ~'e I ~ , I j&yrl' bidden lines occur simultaneously. In Z Andro- , 000 medae and probably in other stars, the relative 2$t intensities undergo large changes ~fbi g a5 Fell/PFeiij with time, but on all our spectrograms, the per- ~ a'S mitted lines are somewhat stronger than the forbidden lines. Figures 9 and 10, on the con- -?P,O+ trary, show two stars, Boss 1985 and S"I' Geminorum, in whose spectra the forbidden lines of [Fell( are strong while the permitted lines are either absent or exceedingly weak. The most .conspicuous forbidden lines of LFell j are XX4244, - }O,OOO 4277, 4287, and 4359, We are confronted here with a most remarkable problem, why are the permitted lines suppressed? To answer this question, let us examine the two spectra critically and list their principal characteristics. 1. Both stars have continuous spectra of low Frc. 8. Forbidden lines of FeII. Full-drawn lines: For- temperature and absorption features consisting bidden transitions observed in g Carinae; dashed lines: of Tio, Cal, and FeI which occur only in stars new observed lines; dotted lines: transitions probably low 3000' present. of temperature, of the order of to, 4000'K. 2. Both stars have Iong ultraviolet extensions star must be high, of the order of 50,000'K, the in the continuous spectra, with Stark-broadened only reason for the star to be underluminous higher members of the Balmer series in absorp- must be small size. Knowing the total luminosity tion. The spectra are composite and result from from the absolute magnitude and the surface the combination of a cool star and a hot star. brightness from the temperature, we find that The temperature of the latter may be of the the radius of the star is of the order of one- order of 15,000'K. third of that of the sun. This is abnormally 3. There are weak central emission com- small, since a normal star of the same tem- ponents of H in Boss 1985, - but not in 5'V perature has a radius of five to ten times larger Geminorum. The exciting mechanism is evidently than the sun. strong enough to excite the forbidden lines of PFelig in a tenuous mass of gas which must be II. THE PROBLEM OF FeII associated with the binary system, but is barely sufficient to excite H, despi'te the enormous A few months after Bowen identified the cosmic abundance of the latter. "nebulium" lines as forbidden transitions of After having ascertained these facts, Swings LOIIIj, Merrill announced that several strong and the writer obtained several spectrograms of emission lines in the spectrum of g Carinae are both stars in the ultraviolet region. ' The purpose caused by forbidden transitions of P'clif. Since of this work was to identify new forbidden lines. that time many new forbidden transitions of To our surprise, we found the spectra full of I Feiif have been identified in the spectra of permitted lines, in emission, of FelI, CrII, etc. several stars, mostly by P. Swings and the , writer. Figure 8 shows the metastable levels of ~ At ) 3000, the absorption of the atmosphere causes all Fe+ and gives the forbidden multiplets known astronomical spectra to be sharply cut off.

296 OTTO STRUVE

TABLE II. Estimated intensities of FeII lines. systems are unresolved on the slit of the spec- trograph. Lab. . aCyg Pec. stars Transition int. abs. emission Nature was kind in this instance and provided us with one relatively near-by star in which O'D — F 3~-42 3259 10 y 0—1 e,p. 3.9-7.7 v 2-,'—3-,' 3259 10 similar bright lines of fFel17 are observed. This star is n Scorpii (Antares). It is a visual double a4I' —z'F0 2-,'-3-,' 3196 10 e.p. 1.7—5.5 v star, whose principal component has a normal spectrum corresponding to a star of low tem- d'D- X4F0 1-',-2-', 3939 e.p. 5.9—9.0 v perature. The fainter component has a tem- perature of about 20,000'K. In the spectrum of a4P —S'D' 2-,'-2-,' 3938 e.p. 1.7—4.8 v this hot star, there appear weak, narrow, emis- sion lines of )Fell j. When the image of the star is held stationary on the slit, the emission lines together with all the expected forbidden lines. are seen to extend slightly on both sides of the Upon investigation it turned out that the per- normal continuous spectrum. We conclude: mitted lines of FeII were all low level transitions. (a) The emission of LFeII j occurs in the The observed stellar intensities were quite ab- vicinity of -the hot star and does not exist at normal. Those corresponding to low levels were other points located at a similar distance from greatly enhanced as compared with the usual the cool star; we do not, however, exclude the laboratory intensities or with the absorption possibility of weak emission in the immediate intensities of normal stellar spectra. This at once vicinity of the cool star, because the latter is so explained the great intensity of LFeIIj. These bright that the plate is burned out in a few lines were not favored by some exceptional seconds. mechanism, but were enhanced because their (b) The extensions of the emission lines excitation levels are lower than those of the per- suggest that the hot star is surrounded by a mitted FeII lines. A few examples will illustrate nebulous shell or ring whose radius is of ap- this point. (See Table II.) proximately the same size as the distance We can dehne an excitation temperature T' between the two stars. by making use of the Boltzmann formula for two (c) The absence of emission lines of LFeilj states s (e.p. Z, =2.5 volts) and t (e.p, 2~=5.5 in other single stars having temperatures of volts) and in two stars, for one of which (n Cygni) 20,000'K shows that the nebulosity owes its we know T=10,000'K. Then origin to the binary character of Antares. (d) The hot component of Antares is under- +s luminous,— thereby resembling the hypothetical log —+log —= 5040 (8,—E~) (I/'1' I/'1) . Ss / Sg hot component gf Z Andromedae. We next turn to the question of the source of The left-hand side is the observed ratio of the excitation. Two sources suggest themselves: (a) intensities. The result is continuous radiation from the hot star in a nebulosity whose origin may be somewhat T' =4500'K. similar to that discussed by Kuiper in the system of P Lyrae and (b) inelastic collisions This is too high a value for the cool star and too with free electrons. Let us consider the erst low a value for the hot star. We conclude that mechanism. the excitation is probably not produced by the We have essentially three levels of Fe+, the continuous radiation of either star. ground level, a low metastable level, and a We have as yet no information concerning the slightly higher normal level. Let the density of location of the tenuous gas which emits the lines the exciting radiation be of fFelig and FeII. In both, Boss 1985 and S'Y Geminorum, the components of their binary +ik P+Planck I N TE R POLAT ION OP' STELI.AR SPECTRA 297 where P ~&1 is the dilution factor. Then we find, where 2xkT " =0. —gi &a ;a2 when p, q —exp [ hv—,i,/kT], ga 2xkT '* 'l3/Ni P p13

'82 A 2y —= p» if p&)—;A»«A» Very little is known about the cross sections 0-'-'. R] A3g We shall assume 10 " cm'. We- next have approximately n2 A3g A2 —= — if p p« —;A»«A„. 2mkT ' m1 2A 2g 2 — =10', e 'I~~~=1, b12=10 ' The relative intensities of permitted and for- bidden lines are then given by the two limiting We shall have predominantly collisional excita- expressions' tion if

S1%g5120)S16 12 Int. (permitted) naAai piaA8i 128 =P or when Int. (forbidden) n2A 2i pi2A 2i n, )10"for P= i. Int. (permitted) naA ai =2. fhis is slightly in excess of the electron density Int. (forbidden) n~A 2i in the sun's reversing layer (Table I). If P&1, but n,/P = const, then we retain the same Let A3i/A2i 10'; pi3/p&2==10 '. We find that margin of safety. That is, for all shells in which (a) Int. (perm. )/Int. (forb. ) is never less than the density decreases at least as rapidly as the one, and (b) Int. (perm. )/Int. (forb. )))1 if dilution factor ( 1/r'), the radiative processes P) 10 6. But from geometrical considerations of excitation will probably predominate. For P =R'/4r' where R is the radius of the star and example, in an expanding atmosphere with r is the distance of the excited nebulous mass v,„~=const we have ' from the center of the star. The condition P )10 N 1/r' 1/r' N. = const. corresponds to r/R &500. In our example P /P (Antares) R 7 X 10" cm. The radius of the Hence, collisional processes should remain rela- emitting shell is about 3 seconds of arc, and the tively unimportant in such shells as those of distance of Antares is about 100 parsecs, or Pleione, 48 Librae, etc. But if the density 3X10"cm. Hence, r 5&10" cm and our con- decreases less rapidly than 1/r', then collisions dition for Int. (perm. )/Int. (forb. ) 1 is cer- 'may become more important. It is almost certain tainly obeyed. But it is not apparent why the that in the peculiar double star systems of forbidden lines .should be much stronger than Antares, CI Cygni, etc., we are concerned with the permitted lines, if the mechanism is that of a nebulous mass whose density is greater than radiative excitation from the hot star. It is true one produced by a uniformly expanding shell that we have neglected any possible departures like P Cygni. In fact, the state of ionization may from blackbody radiation in the exciting star, serve as a useful criterion to decide about the and that we have greatly simplified the problem density. If the normal reversing layer of the considering only three states. exciting star shows HeI, and other elements of We next consider the problem of collisional high ionization, and the nebulous shell shows excitation. The numbers of collisions from state LFeii), we can conclude that the latter has a 1—we again limit ourselves to three states —are lower level of ionization than the reversing layer. Now, it is probable that the ionization is of s]s 5y2 and sys, 5ys photoelectric origin. Hence it is reduced by the 298 STRUVE

owered ipniza tion should result Sing&ets Triplet& Volt 's. 3$ 3p frpm densities» ex 24 47

7S—— 7P 7P —— .-8 the excitation p d I js caused --7P i 7D 7S—— 7D peI 6S—— ——6Po r—-6D 6S——6P 6P ——69 6 24- 5S --&ran/ -5D -5D -5 by collisipns, tthenen the Peculiary1 lpwPw fjctltious 5S— 500'6- -4D -4D excitation temperaerature takes pn very different 4S- 10000- meaning. To make further Progrp ress we need 23 t-3D -33D reliable determinations of thee cocollisional PrPb- 3S t i5000- abilities b,I,.

22- 20000- III. THEE HeIe PROBLEM 25000- im' imilar ppro bl em to that of the "~ /, 2 ' , t/I es when we consi er 30000- ' 1 i Ii stellar spe ctra (Fig. 11). In tthee laboratory as in 35000- ' 20- al sources, the triplet '19 73 40000 sical" theory. . aaccounts for t is in

I I g ~ I factory mannner because of tthee largerar statistica I 1 tri let leve 1s. Inn normal ste a I I I y I I P ~ o '"' ' ~,' cocombination of turbulent broa d,en'ni i hb

d b radiation damping.am ing. But these e00000 -0744 ' phenomena a are now fair 1y we unn derstood a . 11.Level diagram of e ium. there is nothingno unexpecteected in the relative inte- ' sities. But wwhen we consi e n lines ' drae ig. arear- G Idber f eratu res of 50,50 000' and 000' y ~ o H'I ""'o 'h , and for d&lutionion factors w ic a r aseous ne b u Iae,' ' '" 't'"'k ~ 11 ~ t by the factt tthata the members o che ' s are relatively strong as indeed, all tnp e members of the 2' —n wiith respe t to th sin lets should be very m unced in the nebu ae a menon is of consi era 1 d'tis en mos h interest. Some years ago K. W"'u 'nd th dd tll t eres tre tdb St m uted the popuulationsa of the vel is about 8 s of HeI for two tempp ( ould be the case in th"e 'd an . . as shown thath in the case of diluu e ' blackbody ra aviationia the metastastabl e I 1' g ' o showed that, t e in population re lativea to t e non- levelse are overpopr o ulated by a factorctor oof about two dilution factor ecome as compared too the higher sing e . is the eve s triplet ga be in accordance wi s for 1 in d d g at examp e, a t fact that t e gaseous n ebulae, the triplets in b rved in h t 'P — n'D, and the lines i ht have thoughht inated the entire spec ' ccomputations were exten ed ""ntlrec b L 8 Astrophys. J. 93,3 249 (1941) I N TE R POLAT ION OF STELLAR SPECTRA

at first glance. In fact, it appears that very portant. Next, let us assume that high exciting temperatures, rendering the mech- — — — anisms of ionization and recombination more A24 A34, p, p. exp ( kv, i,/kT),

important than the mechanism of line absorp- A42 —A43, pi4= p&zp24& tion, would gradually tend to establish a balance A A between triplets and singlets at some such value 42 41~ p24= p34. as the factor two found by Goldberg. A2g —yA4g, Since the mechanism of radiative excitation Let the dilution factor P apply to transitions . which we have discussed continuously favors the — — triplets, it is extremely puzzling that in some 1 +4; 2~4; 3 +4; but let another dilution factor, peculiar stars the singlets appear distinctly apply to transition 1~2. The reason for stronger than the triplets. The presence in making this distinction is that in the nebulosity, the energy density corresponding to the fre- emission of HeI, HeII, OIII, t OIII7, t NeIII7, quencies of the strong ultimate emission lines etc. , all of which require high ionization energies, — and some of which, in addition, require high 1'S n'P must be very great and is not simply excitation energies, shows that the source of the that given by /Aped, „,i, . A similar problem, in the emission must be a tenuous layer of gas subjected case of hydrogen, leads to large energy densities to intense excitation, under conditions favoring in L, and this is the basis of all modern theories the production of forbidden lines, namely, very of hydrogen nebulae. We shall have low density and great departure from thermo- dynamic equilibrium. Then Let us, for convenience, simplify the problem and consider only four states' the ground level Singlets 2 yg+Pp24 = 712 IS3 = of HeI, a composite level containing all excited / Triplets p+Vp+Pp24 singlets, a composite level containing all excited triplets, and the continuum. Also, let us first The method is crude and only goes to show that suppose that radiative processes alone are im- we can enhance the singlets until they are ap-

Frr. 12. RS' Hydrae. 300 OTTO STRUUE proximately equal to the triplets by the assump- account for the strengthening of the HeI singlets. tion y))P. But it is not yet clear why this condi- But here, again, we are confronted by the lack tion should not also apply in the case of the of information —theoretical or experimental —of ordinary gaseous nebulae. If we have the collisional cross sections. It is probable that for collisions from the ground state to be im- n2/n3= =P. y=P((1, p(2+ p24) portant we must have This is the case we discussed before, which shows n.))10'8 when P=1 that uniform dilution tends to build up the excited triplets at the expense of the excited and that collisions between excited levels may singlets. become significant when If it were possible, somehow, to avoid ioniza- tion completely then we should in principle be n.))10"for P=1. able to build up the singlets without exciting the triplets at all (if collisions are negligible). But it There have, of course, been many laboratory is dificult to see how these conditions could be experiments to determine the collisional excita- realized when the exciting radiation comes from tion functions for HeI. Some of them have shown a star. As soon, however, as ionization sets in, a remarkable enhancement of the singlets over atoms begin to be diverted into the triplet the triplets. It is extremely tempting to attribute system where they remain, except through new the astronomical results to the same cause. But ionizations and 'recombinations. the theoretical interpretation of these excitation The question arises whether collisions from functions seems to be inadequate at the present the ground state, or between excited levels, can time for any direct application.