On the Origin of the Spectral Lines of Nebulae¹

V. Grotrian, Berlin–Potsdam.

Classification of Nebulae.

According to the system of classification now accepted, the cosmic formations known in astrophysics under the name of nebulae are divided, according to their position with respect to the Milky Way, into two groups: 1) galactic nebulae and 2) extra-galactic nebulae.

The second group includes, above all, the spiral nebulae. They probably represent accumulations of a large number of stars lying very far beyond the limits of our Milky Way system (the distance to the nebula in the constellation Andromeda is equal to 850,000 light-years), and they themselves are formations similar to it. Thus, strictly speaking, the spiral nebulae are called “nebulae” without justification, because by a nebula we always imagine some gaseous formation or a formation consisting of small particles. Spiral nebulae, however, like all other extra-galactic nebulae, consist of a large number of individual stars; even if there are true nebulae among them, to call this whole complex a nebula is just as incorrect as if we were to think of calling a nebula the entire complex of cosmic formations belonging to the Milky Way system. In the strict sense of the word, neb—

¹ Naturwissenschaften, 11, 177 and 12, 193, 1928.

properties are only cosmic formations belonging to group 1, and everything that follows concerns only nebulae of this group.

General Information on Galactic Nebulae

Galactic nebulae, which by their parallax and distribution in the sky belong to the system of the Milky Way, are either gaseous or consist of cosmic dust, i.e., of particles certainly exceeding atoms or molecules in size. By their outward appearance they are divided into 2 subgroups: diffuse, or irregular, nebulae and planetary nebulae. Diffuse nebulae, for which the Orion Nebula serves as the prototype, have a completely irregular form, indistinct outlines, and, as a general rule, very large dimensions. They may be either bright or dark; sometimes, as in the Orion Nebula, dark and bright regions alternate within them. Planetary nebulae owe their name to the exceptional circumstance that in the telescope they are resolved into a little disk and look like planets, although, of course, they have nothing in common with planets. Their form is circular or slightly elliptical, sometimes ring-shaped or still more complex, but almost always they have sharply bounded edges. The prototype of planetary nebulae may be the ring nebula in the constellation Lyra. Planetary nebulae are rather rare. In all, about 150 of them are known, whereas the number of spiral nebulae is estimated at approximately 1 million.

Characteristic of galactic nebulae is the circumstance that near them or within them themselves—in planetary nebulae sometimes even exactly at the center—there are stars which, by their spectroscopic classification, belong in approximately half of the observed cases to type B or to type O, i.e., to stars of the Wolf–Rayet type. These are the hottest stars known to us. The temperature of stars of type B is estimated at \(17000^\circ\), and that of stars of type O at from \(20000\) to \(30000^\circ\) and even higher. Stars of type B have a continuous spectrum in which clearly

noticeable first of all are the absorption lines of hydrogen. The spectra of type O stars differ somewhat depending on the subtype to which they belong. Sometimes they contain bright diffuse bands whose wavelengths cannot be determined exactly, but which in many cases agree approximately with the known lines of hydrogen (the Balmer lines) and with the lines of neutral and ionized helium [for example, \(\lambda = 4686\ \text{\AA}\), the first member of the Fowler series (Fowler), \(\nu = 4R\left(\dfrac{1}{3^2} - \dfrac{1}{m^2}\right)\)]. Other type O stars have a continuous spectrum, upon which either bright bands are superposed, or in which, on the contrary, there are dark absorption lines. The intensity of the continuous spectrum increases strongly toward the ultraviolet end and does not reach a maximum at those wavelengths which are still transmitted by the Earth’s atmosphere. It is impossible to say exactly where this maximum lies, but this increase in intensity makes it possible to estimate approximately the temperature of the star and leads to the values indicated above.

The radiation emitted by these type B or O stars is, as follows beyond doubt from the investigations of Hubble, the source that excites the glow in the surrounding nebula. Hubble found qualitative and quantitative relations between the brightness of these stars and the brightness of the nebulae surrounding them or located near them. In this he saw confirmation of the hypothesis, previously advanced by Russell, that the emission of light by nebulae is excited by radiation coming from these stars; this radiation may be either wave radiation of very short wavelength or corpuscular. Here there can be no question of a simple reflection or scattering, by the matter of the nebula, of the light emitted by the stars; this follows from the fact that the spectrum of the nebula is entirely different from the spectrum of the exciting star. Reflection or scattering can, perhaps, explain the continuous spectrum encountered in some nebulae and resembling, in its distribution of intensity, the spectrum of the exciting ...

stars. But it is impossible to explain in this way the origin of those parts of the spectrum which chiefly determine the brightness of the nebula.

The Spectrum of Galactic Nebulae and the Nebulium Hypothesis.

The spectra of nebulae differ from one another depending on the spectral type of the exciting star or, what is the same, on its temperature. If the star belongs to type \(B_1\), which corresponds to the lowest temperature that an exciting star can have, then, according to Slipher, the nebulae have a continuous spectrum with absorption lines. If the temperature of the star is somewhat higher, corresponding to type \(B_0\), then bright emission lines are superposed on the continuous spectrum. Finally, if the exciting star has the highest temperature, i.e. belongs to type O, then the continuous spectrum disappears, and only a spectrum with bright, sharp emission lines remains. This spectrum is of special interest to us. Its lines can in part be identified with known lines of terrestrial elements. Thus, in it we find fairly intense lines of the Balmer series of hydrogen; sometimes they can be traced to fairly high members of the series, and even the continuous spectrum adjoining the limit of the Balmer series can be observed. Further, in the spectrum we find lines of neutral and ionized helium; the former gives both the orthohelium lines and the parhelium lines, while the latter gives not only the well-known line

\[ \lambda = 4686 \]

from the Fowler series

\[ \nu = 4R\left(\frac{1}{3^2} - \frac{1}{m^2}\right), \]

but also lines from the Pickering series

\[ \nu = 4R\left(\frac{1}{4^2} - \frac{1}{m^2}\right). \]

Finally, the spectrum contains several weaker lines from the spark spectra of carbon, oxygen, and nitrogen; among them is the well-known line of the carbon spark spectrum (CII)

\[ \lambda = 4267,\ 14 \quad (\nu = 3d - 4f, \]

the first member of Bergman’s series). But besides these known lines, in the spectra of nebulae there are also

ON THE ORIGIN OF THE SPECTRAL LINES OF NEBULAE

a series of lines, in part very strong ones, which could not be detected in any of the spectra obtained from terrestrial light sources. The strongest of them are two green lines with wavelengths \(\lambda = 5006.84\) and \(4958.91\). The discovery of these entirely new lines, which stand out sharply

[Figure labels visible in the image: \(N. G. C. 7027\); 7662; 7009; 2392; 6572; 6543; 6896; Orion Nebula; \(I. C. 418\); \(B. D. +30^\circ 3639\). Spectral-line annotations include: 3726.16, 3728.91 Neb; 3868.74 Neb; 3869.86 Hζ; 3967.57 Neb; 3970.07 Hε; 4101.73 Hδ; 4340.47 Hγ; 4363.2 Neb; 4471 He; 4686 Heα; 4861.33 Hβ; 4958.91 N2; 5006.84 N1.]

Fig. 1. Spectra of some galactic nebulae according to Wright
(W. H. Wright, Publ. Lick. Observ. 13, plate 45, 1918).

in almost all nebulae with emission spectra led to the hypothesis according to which a new element, not found on Earth, must be present in the nebulae; it was named “nebulium.” Accordingly, for both strong green lines the designations \(N_1\) and \(N_2\) were introduced.

In Fig. 1 we reproduce the spectra of some nebulae that give emission lines. On the left is indicated the number

of the corresponding nebula according to the catalogue, or its designation1). At the top are given the wavelengths of the strongest lines and the element to which they belong is indicated: H, He, or nebulium ($N_1$, $N_2$, and Neb.). As we see, the lines $N_1$ and $N_2$ are very strong in the spectra of all nebulae; moreover, already from this figure it is clear that they cannot belong either to hydrogen or to helium, because the ratio of the intensities of the lines $H_\beta$ or $\lambda = 4686$, on the one hand, and of the lines $N_1$ and $N_2$, on the other, is entirely different for different nebulae. On the contrary, the intensity ratio $N_1 : N_2$ has approximately one and the same value for all nebulae. This was proved by Wright’s impeccable and careful measurements. We must, therefore, come to the conclusion that these lines have one and the same origin, i.e. that they belong to one and the same element. The same is true also for other lines of nebulium, for example for the ultraviolet lines $\lambda = 3728.91$ and $3726.16$, which are very strong in Fig. 1 in the spectrum of the Orion nebula. In the middle of the spectrograms of some planetary nebulae in Fig. 1, for example N. G. C. 2392, 6543, 6826, I. C. 418, a narrow strip is visible. This is the spectrum of the central star. We see that it is continuous and extends far into the ultraviolet region. Bright and dark bands in it are scarcely noticeable in the reproduction. However, we clearly see that the spectrum of the nucleus is not at all like the spectrum of the nebula. In some spectrograms, above all in the spectrum of the nebula N. G. C. 7662 and the Orion nebula, there is also noticeable the continuous spectrum of the nebula itself, with its distribution of intensity extending far into the ultraviolet.

Objections to the Hypothesis of Nebulium

The appearance in nebulae of lines which cannot be assigned to any of the spectra of the elements found on Earth has, until recently, constituted one of the most remarkable—

...the most remarkable and most difficult riddles of astrophysics. It must be borne in mind that cases in which it is not possible to explain the origin of lines occurring in stellar spectra are exceedingly rare. The number of lines of unknown origin is scarcely 1201, whereas thousands of lines can be identified with certainty with the lines of definite elements on the basis of the coincidence of the wavelengths of stellar lines with those lines which appear in the spectra of definite elements when artificial light sources are used. Since it has thereby turned out that the same elements as we find on the Earth are also present in the stars, and moreover in almost the same distribution, it becomes very improbable that in nebulae a new element could be present in such a large quantity that its spectrum dominates the spectrum of the nebula. To this is added the further circumstance that modern spectroscopy, together with atomic theory, has led us to the conclusion that each element has not one spectrum, but as many spectra as there are electrons contained in the corresponding atom. The difference between the arc and spark spectra had already been established long ago; the atomic-physical meaning of this difference is that the lines of the arc spectrum are emitted by a neutral atom, while spark lines are emitted by an ion with a single positive charge, i.e. by an atom which has already lost one electron in the process of ionization. New investigations, especially those of Millikan and his collaborators, have shown that sparks in a vacuum constitute a light source in which there appear the spectra not only of singly, but also of doubly, triply, etc. ionized atoms, up to, approximately, sevenfold ionization. Under these exceptionally severe initial conditions there appear lines which are absent from ordinary light sources. We thus see that, in general, one cannot assert that we already know all the lines of the elements occurring on Earth, and this compels one to suppose that the lines of nebulae also belong to well-

known to us, but that until now it has not yet been possible to obtain these lines in terrestrial sources of light. This supposition is further supported by the fact that in nebulae the temperatures are very high and the densities very low; both these conditions favor the appearance of highly ionized atoms.

Bowen’s Discovery

Guided, undoubtedly, by the considerations indicated above, one of Millikan’s well-known collaborators, J. S. Bowen, has very recently succeeded in solving the riddle of the nebulium lines, and the solution proved to lie precisely in the direction in which it was to be expected. Since in the spectra of nebulae there are only lines of the lightest elements H, He, C, O, and N, it was natural to raise the question whether the nebulium lines belong to the spectrum of one of these elements or to the spectrum of some other light element. Indeed, Bowen was able to show that nebulium is nothing other than a mixture of oxygen with nitrogen. Although it has not yet been possible to identify all the nebulium lines, Bowen nevertheless showed that of its eight strongest lines, six, including the lines \(N_1\) and \(N_2\), belong to oxygen, and two to nitrogen. Up to now Bowen has published only a short note in Nature (1 October 1927, p. 473)\(^1\), containing everything essential. The well-known English astrophysicist and spectroscopist A. Fowler soon afterward published in Nature two letters (22 October 1927, p. 582, and 29 October 1927, p. 617), in which he confirms Bowen’s discovery by certain calculations made on the basis of the most recent spectroscopic investigations. In what follows we shall present together the results of the work of Bowen and Fowler, without separating them.

\(^1\) At the present time Bowen’s work has been published in Astrophys. Journ. 1928.

Reasons for the failure of previous attempts to obtain nebular lines in terrestrial sources of light.

First of all it must be noted that Bowen by no means succeeded in obtaining the nebular lines under laboratory conditions, which would, of course, have been the surest proof that they belong to definite elements. Although, generally speaking, one cannot assert that it is completely impossible to obtain these lines under terrestrial conditions, nevertheless we can indicate in advance the reasons that make the success of such attempts very improbable. The spectra of oxygen and nitrogen have been obtained by the most varied methods, under the strongest possible conditions of excitation, and no traces whatever of the nebular lines have ever been detected in them. If, nevertheless, these lines belong to the indicated elements, then they can evidently arise only under special conditions existing in nebulae. To reproduce these conditions in the laboratory is almost impossible, since two conditions characteristic of nebulae and probably determining the emission of the lines are the utterly negligible density and the enormous extent of the luminous gas. Although modern technical means do make it possible to obtain very low densities, nevertheless, as we shall show below, they still considerably exceed the densities that occur in nebulae. Absolutely insurmountable difficulties also arise in attempting to reproduce the second condition. Nevertheless, one cannot regard as excluded the possibility that someday it will be possible to obtain nebular lines in a laboratory experiment as well. For, although it is impossible to reproduce in the laboratory the conditions that occur in nebulae, it may nevertheless be possible to find other laboratory-realizable conditions under which these lines will also appear. We have just such a case in the production of the well-known green line of the aurora. The latter was observed by McLennan (Mc. Lennan) in the laboratory, under conditions differing significantly from those that actually occur in the upper layers of the atmosphere. This example should inspire us

hope that, perhaps, someday it will be possible to obtain the lines of nebulae in the laboratory as well. So far, as has been said, this has not yet succeeded.

Method of identifying nebular lines.

How, then, did Bowen manage, without resorting to this experimental proof, to establish that the nebular lines belong to the spectra of oxygen and nitrogen? He was able to do this in the following way. According to Bohr’s theory, every spectral line arises when an atom passes from one quantum state with energy \(E_1\) into another with energy \(E_2\), and the frequency of the line emitted in this transition is

\[ \nu=\frac{E_1-E_2}{h} \]

(Bohr’s frequency condition), where \(h\) is Planck’s constant. This makes it possible, after the regular relations among the lines of a spectrum have been established, to calculate the energies of the possible quantum states of the atom. However, only those spectral lines which correspond to certain quite definite transitions between quantum states of the atom possess an intensity sufficient for them to be observed, i.e. those lines which are “allowed” by the so-called selection rules. But lines “forbidden” by the selection rules are conceivable, and under known initial conditions may be obtained with sufficient intensity; in any case, knowing the energy levels of the different quantum states, or, as spectroscopists say, knowing the “terms” of the atom, we can, by Bohr’s frequency condition, compute exactly the wavelengths or frequencies of these “forbidden” lines.

Fig. 2. Diagram of energy levels showing “allowed” and “forbidden” transitions.

In Fig. 2 we explain this important point by a simple example, since it is very important for understanding everything that follows. Suppose that analysis of the spectrum of some element has made it possible for us to establish for it three ener-

tic levels, denoted in Fig. 2 by the numbers 1, 2 and 3. Suppose further that only the transitions \(3 \to 2\) and \(3 \to 1\) are “allowed,” and therefore in the spectrum there exist only lines corresponding to these transitions; the frequencies of these lines in our diagram are proportional to the lengths of the segments \(a\) and \(b\). The transition \(2 \to 1\), marked in the figure by a dotted line, is “forbidden,” and accordingly there is no spectral line with frequency \(c\) in the spectrum. Nevertheless, from the difference of the energy levels 2 and 1 we can, of course, calculate the frequency and wavelength of this “forbidden” line \(c\) with almost the same accuracy with which the frequencies or wavelengths of the lines \(a\) and \(b\) are measured.

Bowen’s hypothesis: the nebular lines correspond to “forbidden” transitions from metastable initial states.

Bowen asked whether the nebular lines are precisely such lines which, although they cannot be obtained in the laboratory because they correspond to “forbidden” transitions, can nevertheless arise in nebulae under especially favorable conditions. In fact, there exists only one definite group of “forbidden” lines whose appearance may be expected in nebulae. These are lines whose initial states are the so-called metastable states of the atom. Metastable states are those states whose energy is greater than the energy of the normal state, but for which, according to the selection rules, there exist no “allowed” transitions to lower energy levels connected with the emission of light. Suppose that in our schematic Fig. 2 level 1 corresponds to the normal state of the atom, and that between levels 2 and 1 there are no other levels to which a transition from level 2 would be “allowed”; in this case level 2 would represent a metastable state.

V. GROTRIAN

THE DURATION OF THE EXISTENCE OF ATOMS IN A METASTABLE STATE

An atom that is in such a state and is not subjected to any external perturbations remains in it for a certain time. We as yet know little about the lifetime of such metastable atoms; we can only say that it is large in comparison with the duration of ordinary excited states, which are of the order of magnitude of \(10^{-8}\) sec. According to the most recent investigations, the duration of metastable states can undoubtedly reach from \(10^{-3}\) to \(10^{-2}\) sec.\(^1\) If, as a result of some process, excitation of atoms takes place for a long time, then metastable atoms, owing to the great duration of their existence, must accumulate until equilibrium is reached between the processes causing their production and their destruction. In laboratory experiments metastable atoms are destroyed either because they are again excited by light, or as a result of collisions with other atoms and with the walls of the vessel; in this case the excitation energy that they possess is transferred to the colliding atoms or to the walls of the vessel in the form of kinetic energy, without emission of light (collisions of the second kind; sometimes the excitation energy may be transferred to other atoms). What will happen if the metastable atom has no opportunity to collide with another atom or with a wall? Then, we assert, during the time corresponding to the duration of its existence, it will remain in this state, and then it will pass to one of the possible lower energy levels, emitting a “forbidden” line. In favor of this assumption speak both the numerous experimental observations of recent times and theoretical considerations. From these and others it follows: the selection rules should not be understood in the sense that transitions contradicting them can never occur at all; these transitions are merely very improbable. The probability

\(^1\) See, for example, H. V. Dorgelo, Zeitschr. f. Phys., 34, 766, 1925.

the transitions is inversely proportional to the lifetime of the atom in the given excited state. Therefore one should expect that, for metastable states, they are a hundred thousand times smaller than for normal excited states. If, during the interval of time in which the atom exists in a metastable state, it undergoes no collisions, then it will pass into a state of lower energy, emitting light just as a normally excited atom does. The “forbidden” lines corresponding to these transitions are therefore, even in the best cases, only very weakly noticeable in the discharge tubes of our laboratory experiments, because metastable atoms, while still in this state, undergo collisions that destroy them1. It is easy to see, however, that the extremely low density of nebulae is a circumstance favorable to the appearance of such lines.

V. TROTYAN

PHYSICAL CONDITIONS IN NEBULAE.

Let us recall what the physical conditions in nebulae are, using as an example the ring nebula in the constellation Lyra; two images of it are reproduced in Figs. 3a and 3b. Proceeding from the observed velocity of rotation of the nebula, Campbell and Moore calculated the approximate mass of the ring nebula in Lyra, contained within an angle of \(25''\)¹). Depending on which of the two parallax values obtained in different measurements was used in the calculation, they obtained for this mass the values, respectively, of 3.7 and 13.8 solar masses. As the basis for the following considerations, whose aim is only to determine the order of magnitude, we shall take the mean value, 8.7 solar masses.

3a.                3b.

Fig. 3a and 3b. The ring nebula in Lyra. On the left—a drawing from photographic plates with different exposures made by Curtis (H. D. Curtis, Publ. Lick Observ., 13. Table 17, 1918); on the right—a photograph.

Since the distance, as we have already noted, is approximately known, from the linear dimensions of the nebula one can calculate its volume and then its density. For the density an extremely small value is obtained, \(7 \cdot 10^{-17}\ \mathrm{g/cm^3}\). If we carry out the calculations with a mean atomic weight of 6, since, apparently, only the lightest elements are present in nebulae, then we shall find that in a cubic centimeter there are co-

¹) W. W. Campbell and J. H. Moore, Lick Observ. Bull., 13, 177, 1918.

contains approximately \(7\cdot 10^6\) atoms. If these atoms had room temperature, this would correspond to a pressure of about \(2\cdot 10^{-10}\) mm of mercury. We thus see that here we are dealing with rarefactions that are still \(10^4\) times smaller than those pressures which we can obtain with the aid of the best vacuum pumps.

Further, we can calculate the mean free path \(L\), if we make certain assumptions about the diameter of the atom. Taking it equal to \(2\cdot 10^{-8}\) cm, which in order of magnitude must be correct, we shall find that \(L = 1140\) km. If for the calculations we take the temperature, in round numbers, as \(20\,000^\circ\), then for the velocity of an atom of atomic weight 6 we obtain the value \(8.4\) km/sec., and hence for the mean interval between two collisions we find a value of approximately 2 minutes1. These numbers, of course, are very inaccurate, but the final result undoubtedly shows that the time between two collisions is large in comparison with the duration of existence of the metastable states. The distance between two minutes and \(10^{-2}\) sec. is so great that there can be almost no doubt about this. We may therefore expect that metastable atoms excited in nebulae do not undergo collisions before the end of their existence, and then emit the “forbidden” lines. With the enormous dimensions

of nebulae the intensity of these lines must be, despite the extreme rarefaction, sufficiently great for them to be accessible to observation.

The Structure of the Spark Spectra of Oxygen and Nitrogen

As we have already noted, one can speak only of nitrogen and oxygen atoms, and, moreover, not of lines emitted by neutral atoms and belonging to the arc spectrum, but of spark lines, whose carriers are ions. In spectroscopy it is customary to denote the arc spectrum of some atom by its chemical symbol with the numeral I, the first spark spectrum by the same symbol with the numeral II, the second spark spectrum by the numeral III, and so on. The nebular lines identified by Bowen belong to the spectra O II, O III, and N II. These spectra are very complex and rich in lines. Regular relations among these lines were found above all by Fowler1, and for the far ultraviolet part of the spectrum by Bowen2; they were interpreted in connection with Hund’s theory of atomic spectra. An attempt to set forth here the complex structure of these spectra would take us too far, and it is not necessary for understanding Bowen’s discovery. We may confine ourselves to a few indications concerning the lowest energy levels of these spectra.

The Ground States of the Spectra O III and N II

Let us first consider the spectra O III and N II, emitted by the doubly ionized oxygen atom and the singly

ON THE ORIGIN OF THE SPECTRAL LINES OF NEBULAE

by an ionized nitrogen atom. These ions contain the same number of electrons, namely 6, and in their structure they became similar, it came to be, to the neutral carbon atom. Both spectra therefore have one and the same structure, and we may consider them together. The six electrons of these ions are divided first of all into two groups: 2 and 4 electrons respectively. Both inner K-electrons have principal quantum number \(n=1\) and form a closed shell having no angular momentum, like the two electrons of helium in the normal state. The four electrons of the second group are L-electrons and have principal quantum number \(n=2\). They are again divided into two subgroups depending on the values of the second quantum number that we must assign to them. This second quantum number was formerly denoted, following Sommerfeld, as the azimuthal quantum number \(k\), and could take the values \(1, 2, 3,\ldots\), under the condition that \(k \leq n\). In modern quantum mechanics it is proved that instead of \(k\) one must introduce another quantum number, which is denoted by \(l\) and takes the values \(0, 1, 2,\ldots\), under the condition that \(l \leq n-1\). Of the four L-electrons, two belong to the subgroup with \(l=0\), the other two to the subgroup with \(l=1\). The former two L-electrons, like the K-electrons, form a closed shell and do not play an essential role in the occurrence of those quantum states with which we must concern ourselves; this also applies to the K-electrons. The other two L-electrons with \(l=1\), depending on how the angular momenta corresponding to the values of \(l\) combine (in the sense of the Bohr model, \(l\) is the angular momentum of the electron’s rotation in its orbit) with the spin angular momenta of the electrons \(s_i\), give rise to various states having essential significance for the occurrence of nebular lines. According to modern views each electron rotates about an axis passing through its center, so that the angular momentum of rotation is equal to

\[ \frac{1}{2}\cdot \frac{h}{2\pi}, \]

where \(h\) is Planck’s constant. For all electrons, consequently,

\[ s_i=\frac{1}{2}. \]

Depending on whether these spin momenta \(s_i=\frac{1}{2}\) for both electrons are directed in opposite directions \((\Sigma s_i=0)\) or have the same direction \((\Sigma s_i=1)\), there arise states (see Fig. 4) which in spectroscopy are called singlet or triplet states. In addition to the rotational momenta, the momenta \(l\) are also added geometrically; in this case, if for both electrons \(l=1\), then the resultant \(L\), obtained by their vector addition, can have the values 0, 1, or 2. In spectroscopic nomenclature it is customary to denote states for which \(L=0\) by the letter \(S\), states with \(L=1\) by the letter \(P\), and states with \(L=2\) by the letter \(D\). The multiplicity of these terms (in our case their singletness or tripletness) is indicated by the corresponding number placed to the left above the letter. Thus, for the spectra O III and N II we should expect states with the following spectroscopic designations:

Fig. 4. Vector addition of the momenta \(s\) and \(l\).

\[ {}^{1}S \qquad {}^{1}P \qquad {}^{1}D \]

\[ {}^{2}S \qquad {}^{2}P \qquad {}^{2}D \]

But a very deep principle, discovered by Pauli, shows that if both outer electrons have the same values of \(n\) and \(l\) (such electrons are called equivalent), then not all the states allowed according to our previous reasoning are possible; some of them drop out. It can be shown that only the states

\[ {}^{1}S \qquad {}^{3}P \qquad {}^{1}D. \]

remain. Of these, the middle one, \({}^{3}P\), is triplet, and the other two are singlets. The three states of the \({}^{3}P\) group differ from one another in the values of the quantum number \(j\) of the total angular momentum, which is the resultant of \(\Sigma s_i\) and \(L\). Introducing

in symbolic notation and the values of \(j\) and placing them at lower right, we obtain the following five states:

\[ {}^{1}S_{0}\qquad {}^{3}P_{0}\qquad {}^{3}P_{1}\qquad {}^{3}P_{2}\qquad {}^{1}D_{2}. \]

The energies of these states are different and, what is most important, for the spectra O III and N II they are known from the investigations of Fowler and Bowen. We can again represent them visually in a level diagram. Such a diagram for the O III spectrum is shown in Fig. 5, and for the N II spectrum in Fig. 6. On the left the spectroscopic designations are given; on the right are given the energy values of each level in the frequency units customarily used in spectroscopy \((\mathrm{cm}^{-1})\), and for the \({}^{3}P\) states the values of the differences of the energy states are also indicated.

Fig. 5. Level diagram of the principal states of the O III spectrum.

Fig. 6. Level diagram of the principal states of the N II spectrum.

We see that the \({}^{3}P\) states lie lowest of all; after them comes the \({}^{1}D\) state and, finally, the \({}^{1}S\) state. Of the \({}^{3}P\) states, the lowest is the one for which \(j=0\); it is, properly speaking, the normal state of the doubly ionized oxygen atom or the singly ionized nitrogen atom. All transitions between these five states are “forbidden,” since in an “allowed” transition \(l\) would have to change, at least for one electron, whereas for all these five states the values of \(l\) for both electrons have

value \(l=1\). Therefore all states, with the exception of the fundamental state \({}^{3}P_{0}\), are metastable. We have precisely the case which we have already considered above.

Nebular lines belonging to the spectra O III and N II.

What, then, does observation give us? In terrestrial light sources, up to now not a single line has been observed which could be interpreted as a transition between these five levels. In nebulae, however, some of these lines do appear. As was already indicated above, since the terms of these spectra are known to us, it is not difficult to calculate the frequencies or wavelengths of the lines corresponding to such transitions.

Considering first of all the O III spectrum, Bowen shows that the wavelengths of the lines corresponding to the transitions \({}^{1}D_{2}\to{}^{3}P_{2}\) and \({}^{1}D_{2}\to{}^{3}P_{1}\) coincide with the green nebular lines \(N_{1}\) and \(N_{2}\) with the accuracy to which we have a right to count here; moreover, in particular, the frequency difference of these two lines is exactly equal to the frequency difference known to us of the states \({}^{3}P_{2}\) and \({}^{3}P_{1}\). Likewise the wavelength of the line corresponding to the transition \({}^{1}S_{0}\to{}^{1}D_{2}\) agrees well with the wavelength of the strong nebular line \(\lambda=4363.21\). In Fig. 5 the transitions corresponding to these lines are marked by vertical arrows, beside which the wavelengths are indicated.

Analogous results are obtained also for the N II spectrum (Fig. 6). Here, for the wavelengths of the lines corresponding to the transitions \({}^{1}D_{2}\to{}^{3}P_{2}\) and \({}^{1}D_{2}\to{}^{3}P_{1}\), values are obtained which coincide with the wavelengths of two red nebular lines \(\lambda=6583.6\) and \(6548.1\) with an accuracy lying within the limits of observational error. As for the state \({}^{1}S_{0}\), according to Fowler its energy level is so high (if his analysis of the spectrum gives the correct result in this question1) that the line corresponding to the transition \({}^{1}S_{0}\to{}^{1}D_{2}\) lies in the

ON THE ORIGIN OF THE SPECTRAL LINES OF NEBULAE

the ultraviolet part of the spectrum, which is absorbed by the Earth’s atmosphere and is not accessible to observation.

We shall note here as well that, both for the O III spectrum and for the O II spectrum, the third possible transition, namely the transition $^{1}D_{2} \to {}^{3}P_{0}$, does not occur, since the lines that correspond to these transitions and whose wavelengths can be calculated exactly are not observed in the spectra of nebulae. The absence of these lines is, to a certain extent, understandable, since they are “forbidden” not only by the above-mentioned selection rule, but also by another selection rule relating to the values of $j$. This rule states that only such transitions may take place for which $\Delta j = 0$ or $\pm 1$. The transition $^{1}D_{2} \to {}^{3}P_{0}$, however, corresponds to $\Delta j = 2$. Thus this selection rule apparently remains valid. But, on the other hand, we have seen that the transition $^{1}S_{0} \to {}^{1}D_{2}$, for which $\Delta j = -2$, does take place, although it too is “forbidden” by the selection rules for $j$. It has not yet been possible to explain these contradictory results. One may suppose that, in the impossibility of the transition $^{1}D_{2} \to {}^{3}P_{0}$, the simultaneously occurring change of multiplicity plays a role, i.e. the transition from the singlet to the triplet system, but for the time being this remains only an unclear general supposition.

Transitions from the state $^{1}S_{0}$ to the states $^{3}P$ would also be conceivable, but, unfortunately, the lines corresponding to these transitions, both for the O III spectrum and for the N II spectrum, fall in the ultraviolet part of the spectrum that is not accessible to observation.

As for the intensities of the observed lines, here we have good agreement with what we are entitled to expect according to the intensity rules. Observation shows that the line $N_{1}$ $\lambda = 5006.84$ is stronger than the line $N_{2}$ $\lambda = 4958.91$; likewise the line $\lambda = 6583.6$ is stronger than the line $\lambda = 6548.1$. According to the qualitative rules of distribution

significantly lower. We obtain a term position analogous to the O III spectrum for $^{1}S_{0}$ if we assume that the nebular line $\lambda = 5754.8$ corresponds to the transition $^{1}S_{0} \to {}^{1}D_{2}$, whence for $^{1}S_{0}$ we obtain the value $\nu = 206159\ \mathrm{cm}^{-1}$. Unfortunately, the published material relating to wavelengths does not make it possible to verify this supposition.

intensities, which were established by Sommerfeld and then checked on a large body of experimental material, the strongest lines should be those for which \(\Delta l\) is equal to \(\Delta j\). But since for all the transitions with which we are concerned here \(\Delta l=0\), the lines for which \(\Delta j=0\) must be stronger than those lines for which \(\Delta j=1\). Indeed, as Figs. 5 and 6 clearly show, \(\Delta j=0\) for the lines \(N_1\), \(\lambda=5006.84\) and \(\lambda=6583.6\), and \(\Delta j=1\) for the lines \(N_2\), \(\lambda=4958.91\) and \(\lambda=6548.1\).

Nebular lines belonging to the O II spectrum.

We now turn to those nebular lines which, according to Bowen, belong to the O II spectrum. A singly ionized oxygen atom has 7 electrons. The seventh electron, joining the six electrons of the doubly ionized atom, is also an \(L\)-electron with \(n=2\) and \(l=1\). We now have, consequently, three such \(L\)-electrons. We shall not present calculations of what atomic states may arise as a result of the interaction of these three electrons; we shall give only the result. Doublet and quartet states are obtained, of which again five states with the lowest energy values in the whole spectrum correspond to the case when all three \(L\)-electrons are on “orbits” with \(n=2\) and \(l=1\). These atomic states have the following spectroscopic designations1:

\[ {}^{4}S_{2}\qquad {}^{2}D_{2}\qquad {}^{2}D_{3}\qquad {}^{2}P_{1}\qquad {}^{2}P_{2}. \]

The relative position of these states is explained by Fig. 7. The energy values are again shown on the right in units of frequency2. Lowest of all lies the level of the state \({}^{4}S_{2}\), followed by

follow the states \({}^{2}D\) and, finally, the states \({}^{2}P\). Knowing the energies of these states, we can again calculate the frequencies or wavelengths of the lines corresponding to the “forbidden” transitions between these fundamental states of the ion \(\mathrm{O}^+\). Thus, for the transitions \({}^{2}D_2 \to {}^{4}S_2\) and \({}^{2}D_3 \to {}^{4}S_2\), values are obtained which agree, within the errors of observation, with the strong ultraviolet lines of the Orion nebula \(\lambda = 3726.16\) and \(\lambda = 3728.91\). The distribution of intensity is again what one should expect. The line \(\lambda = 3726.16\), for which \(\Delta j = 0\), is stronger than the line \(\lambda = 3728.91\), corresponding to \(\Delta j = 1\). Bowen further assumes that the red line of nebulae \(\lambda = 7325\), lying at the boundary of the visible spectrum on the side of the long waves, corresponds to the transition \({}^{2}P \to {}^{2}D\). From the positions of the energy levels one can calculate the wavelengths corresponding to the transitions \({}^{2}P_2 \to {}^{2}D_2\) and \({}^{2}P_2 \to {}^{2}D_3\); for them the respective values obtained are \(\lambda = 7322\) and \(\lambda = 7330\). Besides these lines, there should also be a third line, corresponding to the transition \({}^{2}P_1 \to {}^{2}D_2\) (marked in Fig. 7 by a dashed line), but its wavelength cannot be calculated, since the position of the level \({}^{2}P_1\), marked in Fig. 7 by a dashed line, is unknown. The strongest of all should be the line corresponding to the transition \({}^{2}P_2 \to {}^{2}D_2\), and we must regard the agreement between \(\lambda_{\mathrm{calc.}} = 7322\) and \(\lambda_{\mathrm{obs.}} = 7325\) as satisfactory, if we take into account that the accuracy of the measurements in this part of the spectrum is very low.

Fig. 7. Level scheme for the fundamental states of the O II spectrum.

The remaining nebular lines.

We have shown in detail how, according to Bowen, eight strong lines of the spectrum of nebulae can be interpreted as lines of the spark spectra of oxygen and nitrogen. Of the remaining lines of nebulae, which until now have been attributed to the hypothetical

element, only three strong lines with wavelengths \(\lambda = 3967.51\), \(\lambda = 3868.74\), and \(\lambda = 3426.2\) Å, and a number of weak lines, remain unexplained1. Bowen’s success gives grounds to hope that in the near future it will be possible to uncover the origin of the remaining lines as well, and it can hardly be doubted that the solution of the problem lies in the same direction as for the lines already identified by Bowen. But even now it may be asserted that Bowen’s discovery makes the nebulium hypothesis entirely superfluous. The fact that in the distant worlds of the nebulae there are no new elements will be received by all with great satisfaction. Indeed, in the periodic system of the elements there is no place for such an element, which, if it exists at all, must have a low atomic weight.

Excitation of Light Radiation in Nebulae

Despite these results, so satisfactory on the whole, certain points still remain puzzling and remarkable. We shall note some of them. We see that the lines of the nebulae may be regarded as corresponding to “forbidden” transitions between the very lowest energy levels of ions. But in addition to these lines, the spectra of these ions contain a number of other lines which appear in terrestrial light sources; only the study of them made it possible to calculate the energy values of these basic states. Although the strongest of these lines, and precisely those of them which correspond to transitions from higher-lying levels to these basic states, fall in the extreme ultraviolet region, so that nothing can be said about their presence or absence in the spectrum, nevertheless it may definitely be said that a number of strong lines,

corresponding to “allowed” transitions between higher levels, is absent in the spectrum of nebulae1. On the contrary, in it we have perfectly normal lines of hydrogen and helium, with an intensity distribution quite similar to the spectra of terrestrial sources. The reason for this can lie only in those undoubtedly very remarkable conditions of excitation thanks to which light radiation arises in nebulae. What these conditions are cannot yet be said at the present time. As we have already noted at the beginning, the cause of the glow of nebulae must be the radiation emitted by the central star—either wave radiation of very small wavelength, or corpuscular radiation. Perhaps the following analogy speaks in favor of the supposition of corpuscular radiation, in particular of electronic radiation. We know that the aurora borealis is excited by electrons which are emitted by the sun and enter the upper, rarefied layers of the earth’s atmosphere. In the spectrum of the aurora borealis the green line \(\lambda = 5\,577.35\ \mathring{\mathrm A}\) stands out especially strongly. MacLennan has proved beyond doubt that this line belongs to the emission spectrum of the neutral oxygen atom, but until now it has not been possible to fit this line into the known scheme of levels of oxygen atoms. Bowen’s discovery makes natural the supposition that the green line of the aurora borealis too may be one of the “forbidden” lines2. This is confirmed by the circumstance that also in the spectrum

of the aurora there are no other well-known lines corresponding to “allowed” transitions and standing out strongly in discharge tubes. If we suppose that an analogy exists between these two phenomena, then we must come to the conclusion that the character of the excitation of the luminescence in nebulae must be the same as for the aurora, and this leads to the hypothesis of electronic radiation.

There is no reason to doubt that very hot central stars, in addition to wave radiation, also emit electrons. It is more difficult to imagine how these electrons penetrate to such enormous distances as, for example, in the ring nebula in Lyra, even with a very large initial velocity. To explain this, one must suppose that the density of the nebula has a much smaller value than we assumed in the preceding estimates. On the other hand, there is no doubt that the wave radiation emitted by the stars plays a very important role as a source exciting the luminescence of the nebula. In particular, H. Zanstra1 was able to show that the appearance of the Balmer lines with the intensity with which they are observed can be explained if one assumes that neutral, unexcited hydrogen atoms absorb, from the radiation of the exciting star, frequencies lying on the other side of the Lyman series and are thereby ionized. Upon recombination of the ions H$^{+}$ and electrons, among others the Balmer lines are emitted. It is also possible that secondary electrons, formed in the absorption of short-wave radiation, play a certain role in the excitation of spectral lines, especially, perhaps, of the “forbidden” lines.

Finally, we would like to note that in the solar corona we have entirely analogous circumstances. In the spectrum of the corona there also exist lines that cannot be identified. After the fiasco suffered by the nebular hypothesis, it can hardly be considered plausible

hypothesis of the existence of an unknown new element, “coronium.” The explanation of these lines should rather be sought in “forbidden” transitions. Most probably, these lines belong to the spectrum of calcium. It will therefore be necessary to look for “forbidden” lines in the spectrum of Ca II, or rather in the spectrum of Ca III. That corpuscular rays and, most probably, electrons play the decisive role in the excitation of the coronal lines follows quite clearly from the appearance of the corona.

Conclusion

Bowen’s discovery became possible only as a result of the interaction of methodological advances that had been achieved chiefly by American investigators in two entirely different fields. One of them was the study of nebulae with the aid of large reflecting instruments; the other was vacuum spectroscopy in the far ultraviolet. In an even broader sense, we may say that astrophysics and atomic physics had to unite their efforts in order to achieve this result. That this union benefits both disciplines is brilliantly confirmed by Bowen’s discovery. Both branches of science were enriched with valuable new material, which it would have been impossible to obtain without their mutual collaboration.

1. H. Zanstra, Astrophys. Journ., 65, 50, 1927. ↩↩↩↩↩↩↩↩↩↩

2. The supposition expressed by the author was justified in the shortest time. MacLennan has indeed shown that the green line of the polar aurora is a “forbidden” line of the oxygen spectrum and indicated the terms corresponding to this transition \(({}^{1}S_{0} \to {}^{1}D_{2})\). For details see the note “The Aurora and its Spectrum,” Nature, No. 3062, July 7, 1928. Translator. ↩↩↩