STELLAR ATMOSPHERES

THE most effective way of publishing the results of astronomical investigations is clearly dependent on the nature and scope of each particular research. The Harvard Observatory has used various forms. Nearly a hundred volumes of Annals contain, for the most part, tabular material presenting observational results on the positions, photometry, and spectroscopy of stars, nebulae, and planets. Shorter investigations have been reported in Circulars, Bulletins, and in current scientific journals from which Reprints are obtained and issued serially.

It now appears that a few extensive investigations of a somewhat monographic nature can be most conveniently presented as books, the first of which is the present special analysis of stellar spectra by Miss Payne. Other volumes in this series, it is hoped, will be issued during the next few years, each dealing with a subject in which a large amount of original investigation is being carried on at this observatory.

The Monographs will differ in another respect from all the publications previously issued from the Harvard Observatory—they cannot be distributed gratis to observatories and other interested scientific institutions. It is planned, however, to cover a part of the expenses of publication with special funds and to sell the volumes at less than the cost of production.

The varied problems of stellar atmospheres are particularly suited to the comprehensive treatment here given. They involve investigations of critical potentials, spectral classification, stellar temperatures, the abundance of elements, and the far-reaching theories of thermal ionization as developed in the last few years by Saha and by Fowler and Milne. Some problems of special interest to chemists and physicists are considered, and subjects intimately bound up with inquiries concerning stellar evolution come under discussion.

[Pg vi]

The work is believed to be fairly complete from the bibliographic standpoint, for Miss Payne has endeavored throughout to give a synopsis of the relevant contributions by various investigators. Her own contributions enter all chapters and form a considerable portion of Parts II and III.

It should be remembered that the interpretation of stellar spectra from the standpoint of thermal-ionization is new and the methods employed are as yet relatively primitive. We are only at the beginning of the astronomical application of the methods arising from the newer analyses of atoms. Hence we must expect (and endeavor to provide) that a study such as is presented here will promptly need revision and extension in many places. Nevertheless, as it stands, it shows the current state of the general problem, and will also serve, we hope, as a summary of past investigations and an indication of the direction to go in the immediate future.

In the course of her investigation of stellar atmospheres, Miss Payne has had the advantage of conferences with Professors Russell and Stewart of Princeton University and Professor Saunders of Harvard University, as well as with various members of the Harvard Observatory staff.

The book has been accepted as a thesis fulfilling the requirements for the degree of Doctor of Philosophy in Radcliffe College.

H. S.

MAY 1, 1925.

[Pg vii]

PART I
THE PHYSICAL GROUNDWORK
I. THE LABORATORY BASIS OF ASTROPHYSICS	3
Relation of physics to astrophysics. Properties of matter associated with nuclear structure. Arrangement of extra-nuclear electrons. Critical potentials. Duration of atomic states. Relative probabilities of atomic states. Effect on the spectrum of conditions at the source. (a) Temperature class. (b) Pressure effects. (c) Zeemann effect. (d) Stark effect.
II. THE STELLAR TEMPERATURE SCALE	27
Definitions. The mean temperature scale. Temperatures of individual stars. Differences in temperature between giants and dwarfs The temperature scale based on ionization.
III. PRESSURES IN STELLAR ATMOSPHERES	34
Range in stellar pressures. Measures of pressure in the reversing layer. (a) Pressure shifts of spectral lines. (b) Sharpness of lines. (c) Widths of lines. (d) Flash spectrum. (e) Equilibrium of outer layers of the sun. (f) Observed limit of the Balmer series. (g) Ionization phenomena.
IV. THE SOURCE AND COMPOSITION OF THE STELLAR SPECTRUM	46
General appearance of the stellar spectrum. Descriptive definitions. The continuous background. The reversing layer. Emission lines.
V. ELEMENTS AND COMPOUNDS IN STELLAR ATMOSPHERES	55
Identifications with laboratory spectra. Occurrence and behavior of known lines in stellar spectra. [Pg viii]
PART II
THEORY OF THERMAL IONIZATION
VI. THE HIGH-TEMPERATURE ABSORPTION SPECTRUM OF A GAS	91
The schematic reversing layer. The absorption of radiation. Low temperature conditions. Ultimate lines. Ionization. Production of subordinate lines. Lines of ionized atoms. Summary.
VII. CRITICAL DISCUSSION OF IONIZATION THEORY	105
Saha’s treatment—marginal appearance. Theoretical formulae. Physical constants required by the formulae. Assumptions necessary for the application. Laboratory evidence bearing on the theory. (a) Ultimate lines. (b) Temperature classes. (c) Furnace experiments. (d) Conductivity of flames. Solar intensities as a test of ionization theory.
VIII. OBSERVATIONAL MATERIAL FOR THE TEST OF IONIZATION THEORY	116
Measurement of line intensity. Method of standardization. Summary of results. Consistency of results.
IX. THE IONIZATION TEMPERATURE SCALE	133
Consistency of the preliminary scale. Effect of pressure. Levels of origin of ultimate and subordinate lines. Influence of relative abundance. Method of determining effective partial pressure. The corrected temperature scale. [Pg ix]
X. THE IONIZATION TEMPERATURE SCALE	133
PART III
ADDITIONAL DEDUCTIONS FROM IONIZATION THEORY
XI. THE ASTROPHYSICAL EVALUATION OF PHYSICAL CONSTANTS	155
Spectroscopic constants (Plaskett). Critical potentials (Payne). Duration of atomic states (Milne).
XII. SPECIAL PROBLEMS IN STELLAR ATMOSPHERES	161
Class stars. Class stars. The Balmer lines. Classification of stars. Silicon and Strontium stars. Peculiar Class stars. c-stars.
XIII. THE RELATIVE ABUNDANCE OF THE ELEMENTS	177
Terrestrial data. Astrophysical data. Uniformity of composition of stellar atmospheres. Marginal appearance. Comparison of stellar and terrestrial estimates.
XIV. THE MEANING OF STELLAR CLASSIFICATION	190
Principles of classification. Object of the Draper Classification. Method of classifying. Finer Subdivisions of the Draper Classes. Implications of the Draper system. Homogeneity of the classes. Spectral differences between giants and dwarfs.
XV. ON THE FUTURE OF THE PROBLEM	199
APPENDICES
I. INDEX TO DEFINITIONS	203
II. SERIES RELATIONS IN LINE SPECTRA	203
III. LIST OF STARS USED IN CHAPTER VIII	205
IV. INTENSITY CHANGES OF LINES WITH UNKNOWN SERIES RELATIONS	207
V. MATERIAL ON A STARS, QUOTED IN CHAPTER XII	208
SUBJECT INDEX	211
NAME INDEX	214

THE application of physics in the domain of astronomy constitutes a line of investigation that seems to possess almost unbounded possibilities. In the stars we examine matter in quantities and under conditions unattainable in the laboratory. The increase in scope is counterbalanced, however, by a serious limitation—the stars are not accessible to experiment, only to observation, and there is no very direct way to establish the validity of laws, deduced in the laboratory, when they are extrapolated to stellar conditions.

The verification of physical laws is not, however, the primary object of the application of physics to the stars. The astrophysicist is generally obliged to assume their validity in applying them to stellar conditions. Ultimately it may be that the consistency of the findings in different branches of astrophysics will form a basis for a more general verification of physical laws than can be attained in the laboratory; but at present, terrestrial physics must be the groundwork of the study of stellar conditions. Hence it is necessary for the astrophysicist to have ready for application the latest data in every relevant branch of physical science, realizing which parts of modern physical theory are still in a tentative stage, and exercising due caution in applying these to cosmical problems.

The recent advance of astrophysics has been greatly assisted by the development, during the last decade, of atomic and radiation theory. The claim that it would have been possible to predict the existence, masses, temperatures, and luminosities of the stars from the laws of radiation, without recourse to stellar observations, represents the triumph of the theory of radiation. It is equally true that the main features of the spectra of the stars could be predicted from a knowledge of atomic structure and the origin of spectra. The theory of [Pg 4] radiation has permitted an analysis of the central conditions of stars, while atomic theory enables us to analyze the only portion of the star that can be directly observed—the exceedingly tenuous atmosphere.

The present book is concerned with the second of these two problems, the analysis of the superficial layers, and it approaches the subject of the physical chemistry of stellar atmospheres by treating terrestrial physics as the basis of cosmical physics. From a brief working summary of useful physical data (Chapter I) and a synopsis of the conditions under which the application is to be made (Chapters II and Chapter III), we shall pass to an analysis of stellar atmospheres by means of modern spectrum theory. The standpoint adopted is primarily observational, and new data obtained by the writer in the course of the investigation will be presented as part of the discussion.

The first chapter contains a synopsis of the chief data which bear on atomic structure—the nuclear properties, and the disposition of the electrons around the nucleus. The origin of line spectra is discussed, and the ionization potentials corresponding to different atoms are tabulated. Lastly a brief summary is made of the effect of external conditions, such as temperature, pressure, and magnetic or electric fields, upon a line spectrum.

ATOMIC PROPERTIES ASSOCIATED WITH THE NUCLEUS

The properties determined by the atomic nucleus are the mass, and the isotopic and radioactive properties. The astrophysical study of these factors is as yet in an elementary stage, but it seems that all three have a bearing on the frequency of atomic species, and that future theory may also relate them to the problem of the source and fate of stellar energy. Moreover, up to the present no general formulation of the theory of the formation and stability of the elements has been possible, and it is well to keep in mind the data which are apparently most relevant to the problem—the observational facts relating to the nucleus. Probably the study of the nucleus involves the most fundamental[Pg 5] of all cosmical problems—a problem, moreover, which is largely in the hands of the laboratory physicist.

The chief nuclear data are summarized in Table I. Successive columns contain the atomic number, the element and its chemical symbol, the atomic weight[1] and the mass numbers of the known isotopes,[2] the percentage terrestrial abundance,[3] expressed in atoms, and the recorded stellar occurrence. Presence in the stars is indicated by an asterisk, absence by a dash.

TABLE I

ARRANGEMENT OF EXTRA-NUCLEAR ELECTRONS

Logically a description of the analysis of spectra should precede the discussion of electron arrangement, for our knowledge of the extra-nuclear electrons is very largely based on spectroscopic evidence. The established conceptions of atomic structure, however, are useful in classifying mentally the general outlines of the origin of line spectra, and therefore, for convenience of reference, Bohr’s table[4] of the arrangement of extra-nuclear electrons is here prefixed to our brief discussion of spectroscopic data. The chemical elements are given in order of atomic number, and successive columns contain, for the atom in its normal state, the numbers of electrons in the various quantum orbits.

In accordance with the notation of Bohr and Kramers,[5] the first figure in the orbit-designation that stands at the head of a column denotes the total quantum number, which determines the length of the major axis of the corresponding orbit. The subscript is the so-called azimuthal quantum number, which determines the ellipticity of the orbit; the orbits with the smallest azimuthal quantum numbers are the most eccentric, and those for which the azimuthal quantum number is [Pg 9] equal to the total quantum number are circular. The diagram (Figure 1) represents the normal arrangement of electrons around the nucleus of the sodium atom, which possesses eleven extra-nuclear electrons.

TABLE II

The table also gives the number of spectroscopic valency electrons, a quantity which is required by the theory of thermal ionization. The spectroscopic valency electrons are those in equivalent outer orbits (outer orbits of equal total quantum number which have the same azimuthal quantum number). The number is not necessarily the same as the number of chemical valencies (the number of orbits with the same total quantum number) although the two values coincide for the alkali metals and for the alkaline earths. For carbon,[6] on the other [Pg 11] hand, the number of spectroscopic valency electrons is two (the number of 22 orbits), while the chemical valency, corresponding to the total number of 2-quantum orbits, is four.

THE PRODUCTION OF LINE SPECTRA

It is not proposed to discuss the theory of the origin of line spectra here in any detail. What is important from the astrophysical point of view is the association of known lines in the spectrum with different levels of energy in the atom, these levels representing definite electron orbits. Absorption and emission of energy take place in an atom by the transfer of an electron from an orbit associated with low energy to an orbit associated with high energy, and vice versa. The frequency of the light which is thus absorbed or emitted is expressed by the familiar quantum relation:

where and are the initial and final energies, , and is the frequency of the light absorbed or given out.

The atom absorbs from its environment the quanta relevant to the particular electron transfers of which it is capable at the time. These transfers are, of course, governed by the number and arrangement of the spectroscopic valency electrons, or in other words, by the state of ionization or excitation of the atom.

The unionized (or neutral) atom in the unexcited state absorbs the ultimate lines by the removal of one electron from its normal stationary state to some other which can be reached from that state, and re-emits them by the return of the electron to that state. The electron may, of course, leave the state to which it was carried by the ultimate absorption and pass to some state other than the normal one. If this final state is a state of higher energy than the previous state, the line produced by the process will be an absorption line; if [Pg 12] it is of lower energy the result will be the production of an emission line. In either case the line produced by the transfer of an electron from a stationary state other than the normal state is known as a subordinate line. The distinction between series of ultimate and subordinate lines is of great importance in the astrophysical applications of the theory of ionization.

When the energy supply from the environment is great enough, the “outermost” (or most easily detachable) valency electron is entirely removed by the energy absorbed. In consequence the atom is superficially transformed, giving rise to a totally new spectrum, which strongly resembles the spectrum of the atom next preceding in the periodic system. Bohr’s table embodies the interpretation of [Pg 13] this resemblance—the so-called Displacement Rule of Kossell and Sommerfeld[7]—which has recently been strikingly confirmed by a very complete investigation of the arc and spark (neutral and ionized) spectra of the atoms in the first long period.[8] It may be seen at once, for instance, that the removal of the outermost (or ) electron from the atom of aluminum () produces an arrangement of external electrons identical with that for magnesium (). The ionized atom produced by the complete removal of one electron gives, like the neutral atom, two kinds of line spectrum—the ultimate lines and the subordinate lines.

[Pg 14]

Effectively, the ionized atom may be regarded as a new atom altogether. It reproduces the spectrum of the atom of preceding atomic number, in cases which have been fully investigated, with great fidelity, excepting that the Rydberg constant in the series formula is multiplied by four. For the twice and thrice ionized atoms the same is true, the Rydberg constant being multiplied by nine and by sixteen in the two cases. It is scarcely necessary to mention the beautiful confirmation of the theory that has been furnished by the analyses[9][10] of the spectra of Na, Mg, and Mg+, Al, Al+, and Al++, and Si, Si+, Si++, and Si+++. The attribution of the Pickering series (first observed in the spectrum of Puppis) to ionized helium was the first established example of the displacement rule, and constituted one of the earliest triumphs of the Bohr theory.[11] The detection and resolution of the alternate components of that series, which fall very near to the Balmer lines of hydrogen in the spectra of the hottest stars, and the consequent derivation of the Rydberg constant for helium,[12] represents an astrophysical contribution to pure physics which is of the highest importance.

IONIZATION AND EXCITATION

The ionization potential of an atom is the energy in volts that is required in order to remove the outermost electron to infinity. The excitation potential corresponding to any particular spectral series is the energy in volts that must be imparted to the atom in the normal state in order that there may be an electron in a suitable electron orbit for the absorption or emission of that series. Several different excitation potentials are usually associated with one atom. The ionization potential and the excitation potentials are collectively termed the critical potentials.

From the astrophysical point of view, ionization and excitation [Pg 15] potentials are important as forming the basic data for the Saha theory of thermal ionization, with which the greater part of this work is concerned. A list of the ionization potentials hitherto determined is therefore reproduced in the following table. The first two columns contain the values obtained by the physical and spectroscopic methods, respectively. The third column contains “astrophysical estimates,” which are inserted here to make the table more complete. The derivation of the astrophysical values will be discussed[13] in Chapter XI. Physical values result from the direct application of electrical potentials to the element in question, and spectroscopic values are derived from the values of the optical terms. (See Appendix.)

TABLE III

1 Horton and Davies, Proc. Roy. Soc., 97A, 1, 1920.

2 Mohler and Foote, J. Op. Soc. Am., 4, 49, 1920.

3 A. Fowler, Report on Series in Line Spectra, 1922.

4 Lyman, Phys. Rev., 21, 202, 1923.

5 Horton and Davies, Proc. Roy. Soc., 95A, 408, 1919.

6 Mohler, Science, 58, 468, 1923.

7 D. R. Hartree, unpub.

8 A. Fowler, Proc. Roy. Soc., 105A, 299, 1924.

9 Payne, H. C. 256, 1924.

10 Brandt, Zeit. f. Phys., 8, 32, 1921.

11 Hopfield, Nature, 112, 437, 1923.

12 R. H. Fowler and Milne, M. N. R. A. S., 84, 499, 1924.

13 Horton and Davies, Proc. Roy. Soc., 98A, 121, 1920.

14 Tate and Foote, Phil. Mag., 36, 64, 1918.

15 Foote, Meggers, and Mohler, Ap. J., 55, 145, 1922.

16 Foote and Mohler, Phil. Mag., 37, 33, 1919.

17 Paschen, An. d. Phys., 71, 151 and 537, 1923.

18 A. Fowler, Bakerian Lecture, 1924.

19 Menzel, H. C. 258, 1924.

20 Mohler and Foote, Phys. Rev., 15, 321, 1920.

21 Duffendack and Huthsteiner, Amer. Phys. Soc., 1924.

22 Horton and Davies, Proc. Roy. Soc., 102A, 131, 1922.

23 Shaver, Trans. Roy. Soc. Can., 16, 135, 1922.

24 Smyth and Compton, Amer. Phys. Soc., 1925.

25 Russell, Ap. J., 55, 119, 1922.

26 Kiess and Kiess, J. Op. Soc. Am., 8, 609, 1924.

27 Catalan, Phil. Trans., 223A, 1922.

28 Sommerfeld, Physica, 4, 115, 1924.

29 Gieseler and Grotrian, Zeit. f. Phys., 25, 165, 1924.

30 Ruark, Mohler, Foote, and Chenault, Nature, 112, 831, 1923.

31 Foote and Mohler, The Origin of Spectra, 67, 1922.

32 Udden, Phys. Rev., 18, 385, 1921.

33 Sponer, Zeit. f. Phys., 18, 249, 1923.

34 Foote, Rognley and Mohler, Phys. Rev., 13, 61, 1919.

35 Catalan, C. R., 176, 1063, 1923.

36 Kiess, Bur. Stan. Sci. Pap. 474, 113, 1923.

37 McLennan, Br. A. Rep., 25, 1923.

38 Foote and Mohler, The Origin of Spectra, 67, 1922.

39 Smyth and Compton, Phys. Rev., 16, 502, 1920.

40 Eldridge, Phys. Rev., 20, 456, 1922.

41 Mohler and Ruark, J. Op. Soc. Am., 7, 819, 1923.

42 Grotrian, Zeit. f. Phys., 18, 169, 1923.

[Pg 18]

By the use of one or other of the available methods, the data for neutral atoms are complete as far as atomic number 38, with the exception of carbon (6), fluorine (9) and germanium (32). The data for ionized atoms are also increasing, at the present time, in a very gratifying manner. The “hot spark” investigations of Millikan and Bowen,[14] which permit the estimation of the fifth and sixth ionization potentials of certain light atoms, are not included in the table. Under the conditions hitherto investigated in the stellar atmosphere, ionization corresponding to a potential of about fifty volts is the highest encountered, and accordingly ionization potentials that greatly exceed this value have no place in the present tabulation of astrophysically useful data. A knowledge of the higher critical potentials[15] is, however, of great interest in connection with the theoretical problems of the far interior of the star.

There are conspicuous gaps in the table, and it is to be feared that many of them are likely to remain unfilled. The spectra of the neutral atoms of carbon, phosphorus, and nitrogen have hitherto defied analysis, and our knowledge of the corresponding ionization potentials must therefore depend on physical methods. For carbon, silicon, and similar refractory materials, such methods are difficult of application; the same applies to the metals. It is therefore probable that the ionization potentials of the neutral atoms of several of the lighter elements, of the platinum metals, and of the rare earths, will remain unknown or uncertain for some time to come. None of the atoms thus omitted is of immediate astrophysical importance.

As shown in the table, the values for the ionized and doubly ionized light atoms O+, O++, C++, N++, S+, and S++ are deduced only astrophysically. It may be hoped that the spectra of these atoms will soon be arranged in series, so that an accurate value of the ionization potential may be available, in place of the approximate one deduced from the stellar evidence, for the corresponding absorption lines are of importance in the spectra of the hotter stars.

[Pg 19]

The spectroscopic ionization potentials have an advantage over the physical values, in that the corresponding state of the atom is known with certainty, whereas physical methods can in general only detect some critical potential, without assigning it definitely to a particular transition. For example, it seems likely that in some cases the first ionization, whether caused by incident radiation or by electron impacts, corresponds to the loss of an electron by the molecule: where represents the atom, and the electron. The effect of increased excitation would then be the decomposition The first reaction would produce the ionized molecule, and the second would produce the ionized and neutral atoms simultaneously. It might thus happen that the spectrum could appear without the previous appearance of the spectrum, since all of the element was present in the form before ionization.

The above is only a simple illustrative example of the possible complexity in the physical determination of ionization potentials. The interpretation of four successive critical potentials for hydrogen has been discussed by Franck, Knipping and Krüger,[16] while eight have been detected by Horton and Davies[17] for the same element. Similarly Smyth[18] discusses four critical voltages for nitrogen. No explicit attempt has yet been made to use these facts for the interpretation of astrophysical data, but they may account for the unexplained absence of some neutral elements from the cooler stars. The absence is generally to be attributed, as will be shown in Chapter V, to the non-occurrence of suitable lines in the part of the spectrum usually examined. But [Pg 20] it is possible that the persistence of the molecule has a definite significance in the case of nitrogen, where the ionization potential is as high as 16.9 volts.

The increasing completeness of the table of ionization potentials suggests a re-examination of the relation recently traced by the writer[19] between ionization potential and atomic number. The original diagram, in which columns of the periodic table are treated as abscissae, and the ordinates are ionization potentials on equal but shifted scales, so that analogous elements fall one below another, is here reproduced, with the addition of data more recently obtained.

[Pg 21]

The Displacement Rule of Kossell and Sommerfeld leads us to expect a pronounced similarity between the line drawn in the diagram from the point representing one element to that representing the next, and the corresponding line for the ionized atoms of the same elements, the latter being shifted one place to the left for each electron removed. The points for once and twice ionized atoms are inserted into the diagram on this principle, and the parallelism is found to exist. The regularities of the diagram and their possible significance (such, for example, as the pairing of the valency electrons, the second being harder to remove than the first) were discussed in the original paper. All the more recent data appear to confirm the conclusion there set forth, that the relation between ionization potential and atomic number is very closely the same in each period.

DURATION OF ATOMIC STATES

In addition to the critical potentials, which give a measure of the ease with which an atom is excited or ionized, astrophysical theory requires an estimate of the readiness with which an atom recovers after excitation or ionization. It appears probable that this factor, like the critical potentials, is independent of external conditions, and depends upon something that is intrinsic in the atomic structure. The “life” of the atom has been extensively investigated in the laboratory, and has been shown to be a small fraction of a second in duration. Probably this subject of “atomic lives” is still in an initial stage, and the accuracy of the results and the range of elements discussed will be greatly increased in the near future. A summary of the material obtained up to the present time is contained in the following table. Successive columns contain the atom discussed, the deduced atomic life in seconds, the authority, and the reference.

The data are practically confined to hydrogen and mercury, and for both these elements the atomic life appears to be of the order [Pg 22] .

Astrophysical estimates of the life of the excited calcium atom have been made by Milne,[20] who derives values of the order . This is so near to the values obtained in the laboratory that it seems permissible, in the absence of further precise data, to assume an atomic life of , as a working hypothesis, for all atoms. The same value is unlikely to obtain for all atoms; in particular it may be expected to differ for atoms in different states of ionization. But here astrophysics must be entirely dependent on further laboratory work for the determination of a quantity that is of fundamental importance.

TABLE IV

Atom	Life	Authority	Reference
		Wien	An. d. Phys., 60, 597, 1919
		Ibid.	Ibid.
		Ibid.	Ibid.
		Ibid.	Ibid.
		Dempster	Phys. Rev., 15, 138, 1920
		Wood	Proc. Roy. Soc., 99A, 362, 1921
g		Franck and Grotian	Zeit. f. Phys., 4, 89, 1921
,		Mie	An. d. Phys., 66, 237, 1921
,		Wien	An. d. Phys., 66, 232, 1921
bands		Ibid.	Ibid.
,		Ibid.	An. d. Phys., 73, 483, 1924
		Ibid.	Ibid.
		Ibid.	Ibid.
		Ibid.	Ibid.
		Turner	Phys. Rev., 23, 464, 1924
		Webb	Phys. Rev., 21, 464, 1923

RELATIVE PROBABILITIES OF ATOMIC STATES

The relative intensities of lines in a spectrum must depend fundamentally upon the relative tendencies of the atom to be in the corresponding states. To a subject which, like astrophysics, depends [Pg 23] for its data largely upon the relative intensities of spectral lines, the theory of the relative probabilities of atomic states is of extreme importance. The question is obviously destined to become an important branch of spectrum theory. It has been discussed, from various aspects, by Füchtbauer and Hoffmann,[21] Einstein,[22] Füchtbauer,[23] Kramers,[24] Coster,[25] Fermi,[26] and Sommerfeld.[27] The comparison with observation has been made, up to the present, only for a few elements. The relative intensities of the fine-structure components of the Balmer series of hydrogen were examined by Sommerfeld,[28] and exhaustive work with the calcium spectrum has recently been carried out by Dorgelo.[29] The astrophysical application of the data bearing on relative intensities of lines in the spectrum of one and the same atom, while an essential branch of the subject, is a refinement which belongs to the future rather than to the present.

EFFECT ON THE SPECTRUM OF CONDITIONS AT THE SOURCE

(a) Temperature Class.—It is found experimentally that the relative intensities of the lines in the spectrum of a substance are altered when the temperature is changed. Some lines, notably the ultimate lines mentioned in a previous paragraph, predominate at low temperature. Other lines, which are weak under these conditions, become stronger if the temperature is raised, and lines which are the characteristic feature of the spectrum at the highest temperatures that can be attained in the furnace are often imperceptible at the outset. The effects are more conspicuous, and have been most widely studied, in the spectra of the metals, which are rich in lines and are amenable to furnace conditions. The results of such experiments, which [Pg 24] are chiefly the work of A. S. King, are expressed by the assignment of a “temperature class,” ranging from I to V, to each line; Class I represents the lines characteristic of the lowest temperatures, and Class V denotes the lines that require the greatest stimulation.

The temperature class of a line is intimately connected with the amount of energy required to excite the line. It may, indeed, be used as a rough criterion of excitation potential, high temperature class indicating high excitation energy. The temperature class is therefore useful in assigning series relations to unclassified lines, and is of value to the astrophysicist chiefly in this capacity of a classification criterion. King’s work on silicon shows, for instance, that 3906 is of Class II, and is therefore not an ultimate line—a fact which has considerable significance in studying the astrophysical behavior of the line.

The correlation of temperature class with excitation potential receives an immediate explanation in terms of the theory of thermal ionization. It furnishes a useful laboratory corroboration of the theory by showing that the thermal excitation of successive lines, with rising excitation potential, takes place in qualitative agreement with prediction.

The appended list shows the atoms for which the spectra have been analyzed by King on the basis of temperature class:

(b) Pressure.—In the laboratory the observed effects of pressure[30] are a widening and shifting of the lines in the spectrum—effects which differ in magnitude and direction for different lines. The phenomena are well marked under pressures of several atmospheres.

[Pg 25]

Recent developments of astrophysics, such as are summarized in Chapter III and Chapter IX, have shown that the pressures in stellar atmospheres are normally of the order of a hundred dynes per square centimeter, or less. At such pressures no appreciable pressure shifts will occur, and indeed one of the most direct methods by which these exceedingly low pressures in reversing layers have been established[31] is based on the absence of appreciable pressure effects.

(c) Zeemann Effect.—The magnetic resolution of spectral lines into polarized components[32] has, as yet, for the astrophysicist, chiefly a value as a criterion for classifying spectra. In the field of solar physics proper, a direct study of the Zeemann effect has led to important results.[33] The present study is not, however, explicitly concerned with the sun, except in comparing solar features with similar features that can also be examined in the stars.

The investigations of Landé on term structure and Zeemann effect[34] for multiplets have shown how the Zeemann pattern formed by the components into which a line is magnetically resolved can be related to the series attribution of the line. This provides a method of classifying spectra which are rich in multiplets, and which have previously defied analysis. The indirect astrophysical value of the Zeemann effect is, therefore, very great.

(d) Stark Effect.—The effect of an electric field in resolving spectral lines into polarized components was first pointed out by Stark[35] for hydrogen and helium. Several other investigators have since studied the effect for these two elements,[36] and for [Pg 26] various metals.[37][38] Unlike the temperature and magnetic effects, the Stark effect has not been used as a criterion for the series relations of unclassified lines.

The Stark effect has not been detected in the solar spectrum, presumably because the concentration of free electrons prevents the formation of large electrostatic fields.

Several investigators, however, have contemplated in the Stark effect a possible factor influencing the stellar spectrum.[39][40] It does not seem unlikely that nuclear fields could operate as a sensible general electrostatic field at the photospheric level, thus producing a widening and winging of certain lines. The question has been numerically discussed by Hulburt,[41] and Russell and Stewart,[42] in an examination of Hulburt’s work, concluded that the Stark effect might possibly make some contribution (probably not a preponderant one) to the observed widths of lines in the solar spectrum. The question is not definitely settled, but it appears well to keep so important a possibility in mind.

IT is well to distinguish the different meanings that are to be associated with the term “stellar temperature.” The observed energy distribution in the spectrum, combined with the theory of black-body radiation, lead to a quantity known as the “effective temperature” of the star. This is the temperature of a hypothetical black body, the spectrum of which would have the observed energy distribution of the star in question. It has often been emphasized that the effective temperature is merely a label, for it is not the actual temperature of any specific portion of the star. Presumably the temperature of a star falls off, from the center outwards, according to the laws expressed by the theory of radiative equilibrium, and though it might thus be possible to specify, on certain assumptions, the depth in a star at which the effective temperature coincides with the actual temperature, no observational significance could attach to the information.

The theory of radiative equilibrium[43] enables us to specify the temperature gradient, and in particular to determine the central temperature, the effective temperature, and the boundary temperature, corresponding to a given energy output. These three quantities are essentially arbitrary, and the second is the only one susceptible of direct measurement, while none of them represents the actual temperature of any assignable region. In order to clarify ideas it is useful to regard the effective temperature as representing roughly the temperature of the photosphere, that is, of the region in the star that gives rise to the approximately black continuous background of the spectrum. It must, however, be remembered that “the theory provides a definite relation between temperature and optical depth, involving only one constant, the effective temperature. Suppose now ... [Pg 28] we arbitrarily select a certain temperature, and name it the photospheric temperature, and name the unknown depth at which it occurs the photospheric depth; this depth will be described by some unknown transmission coefficient, to be determined. If, taking account of absorption and emission, we proceed to calculate the transmission coefficient ... we shall simply recover the optical depth predicted by Schwarzschild’s theory.” (Milne.)[44] No method of measuring the effective temperatures of the stars by comparing their energy spectrum with that of a black body can remove the arbitrariness of the quantity thus measured.

The theory of thermal ionization permits estimates to be made of the temperatures in the reversing layers of stars. These temperatures refer to the average level at which are situated the absorbing atoms corresponding to the lines used. The differences of effective level[45] for different atoms render these “ionization temperatures” difficult to define consistently, but they represent actual temperatures of assignable regions in the star, and the extent of their agreement with the temperatures derived from the distribution of energy in the continuous spectrum is a matter of extreme interest. The material and theory from which the ionization temperatures are derived is the subject matter of Chapters VI to IX. The temperature scale used in calibration and in the discussion of the theory of thermal ionization is the scale derived from the measured effective temperatures.

The derivation of a definitive scale of effective temperatures from the numerous available observations is probably impossible at the present time. The methods employed differ widely, and the conditions for accurate intercomparison cannot be regarded as fully established. The material at present available, however, permits some general conclusions, and as the needs of astrophysics demand a working temperature scale, such conclusions are summarized in the present chapter.

[Pg 29]

In the discussion of the material a difficulty immediately arises. The scale to be derived must be based entirely, in the present stage of the observations, upon the apparently brighter stars, and it is notorious that they are not homogeneous in absolute magnitude. Theory predicts[46] that absolutely bright stars will have a lower effective temperature than stars of low luminosity belonging to the same spectral class, and this prediction is, on the whole, verified by observation. The material must therefore be selected on the basis of luminosity if a standard temperature scale is to be formed, and probably the temperature scale to be aimed at should refer to stars of some one absolute magnitude adopted as standard. Theoretically, standard mass might be preferable to standard luminosity, but, in the present state of the subject, so few masses are known that such a system would not be practicable. The ideal of referring to standard absolute magnitude was not attained by the earlier temperature scales, which were apparently based upon averages for all the available brighter stars.

The more comprehensive data for the study of the stellar temperature scale are the spectrophotometric measures of Wilsing and Scheiner,[47] of Wilsing,[48] of E. S. King,[49] and of Rosenberg.[50] The temperature scales derived by Wilsing and by Rosenberg differ by a linear factor; Rosenberg assigns higher temperatures to the hotter stars, and lower temperatures to the cooler stars. These temperature scales, and their intercomparison, have been very fully discussed by Brill,[51] who reduces all the measures to the scale given by Wilsing, and gives, for the principal Draper classes, the following comparative table for the corrected mean effective temperatures on the absolute centigrade scale.

In addition to the comprehensive data just quoted, there have been [Pg 30] numerous determinations of the temperatures of individual bright stars, chiefly by Abbot,[52] Coblentz,[53] Sampson,[54] and H. H. Plaskett.[55] In the main these values confirm the scale given in Table V, but sometimes considerable differences occur in the values given for individual stars by different investigators. At the same time, each observer is usually reasonably self-consistent, and the deviations must therefore be ascribed to differences of method. Some of the results are reproduced, for illustration, in Table VI.

TABLE V

Class	Wilsing	Rosenberg	E.S. King Color Temperature	E.S. King Total Radiation
	12300°	30000°	22700°	22700°
	11450	18000	15200	14900
	10250	1200	11600	11300
	9000	9000	8800	8600
	7950	7850	7900	7700
	6880	6930	7000	6800
	5980	6000	6040	5870
	5250	5200	5090	4950
	4570	4570	4570	4440
	3860	3840	3640	3550
	3550	3580	3430	3340

It is seen that the effective temperatures of individual hotter stars vary widely among themselves. This is largely a result of the difficulty of making the appropriate correction for atmospheric extinction. It must, then, be supposed that the temperatures derived by spectrophotometric methods are not trustworthy for stars hotter than Class . The values determined by the earlier observers for the and classes are almost certainly too low. Rosenberg’s value of 30,000° for is, however, most probably too high, as will be inferred later from the ionization temperature scale.

For the cooler stars small discrepancies also occur among the different observers. In the writer’s opinion, the lowest estimates for the [Pg 31] temperatures of the cooler stars are probably nearest to the truth.

TABLE VI

Star		Abott Radiometric	Coblentz Thermoelectric	Plaskett Wedge Method	Sampson Photoelectric
	Ori()		13000°		25000°
	Cas()			15000°	30000
	Per()			15000	14000
	Ori()	16000°	10000		14800
	Lyr()	14000	8000		11600
	()	11000			12800
(	Cyg()		9000	9000	10900
	Aql()		8000
	Cas()			9000	10700
	()		6000		8300
	Aur()	5800	6000	5500-6000	5500 *
	()		4000		4200
	Gem()		5500	5000-5500	4200
	Tau()	3000	3500		3400
	Ori()	2600	3000		3400
	Peg()	2850			3200

* Temperature assumed in calibration of scale.

It was mentioned at the outset that dwarf stars appear to be at a higher temperature than giants of the same spectral class. The following table summarizes the differences in temperature, as compiled by Seares.[56]

TABLE VII

Class	Effective Temperature
	Giant	Dwarf
	6080°	6080°
	5300	5770
	4610	5500
	3860	4880
	3270	4120
	3080	3330

[Pg 32]

A more detailed list of giant and dwarf temperatures was compiled in 1922 by Hertzsprung[57] from all the material then available. The tabulation that follows contains his values for (the “reciprocal temperature,” where is 14,600), and the corresponding absolute temperature, in degrees centigrade.

TABLE VIII

Mt. W. Class	Giant	Dwarf	Temperature Giant	Temperature Dwarf
		2.00		7300°
		2.16		6770
		2.08		6990
		2.26		6460
		2.30		6350
		2.11		6920
		2.30		6350
		2.29		6370
		2.34		6240
		2.36		6190
		2.48		5880
	2.30	2.51	6340°	5810
		2.45		5970
		2.71		5100
	2.83	2.62	5170	5580
	2.92	2.68	5020	5440
	2.92	2.64	5020	5530
	3.15		4730
	3.09		4820
	3.15		4730
	3.25	2.76	4480	5300
	3.20		4560
	3.29		4430
	3.39	3.03	4300	4840
	3.48	3.11	4180	4700
	3.50	3.05	4160	4790
	3.54		4130
	3.83		3810
	3.86		3870
	4.14		3530
	4.33		3370
	4.36		3350
	4.35		3360
	4.49		3250
	4.45		3280
	3.93		3720

[Pg 33]

The difference in temperature between giant and dwarf stars of the same spectral class is clearly shown in the foregoing tables. The relation of absolute magnitude to effective temperature within a given class must be regarded as definitely established by observation.

The temperatures for the cooler giant stars in both these lists are somewhat lower than those given for the corresponding classes in Table V. The temperature of , for instance, is placed nearer to 4000° than to 4500°. The fact that the sun, a typical dwarf, has an effective temperature of 5600° seems to favor these lower values.

TABLE IX

Class	Temperature	Class	Temperature
	3000°		9000°
	3000		10000
	3500		13500
	4000		15000
	5000		17000
	5600		18000
	7000		20000
	7500		25000
	8400		35000

In concluding the summary of stellar temperatures, the ionization temperature scale is given in the foregoing table. The discussion on which the table is based is contained in Chapters VI to IX, and it is merely placed here for comparison with the preceding tabulations.

THE theory of thermal ionization enables us to make an analysis of the spectrum of the stellar reversing layer by predicting the number of atoms of any given kind that will be effective in absorbing light from the interior of the star, under given conditions, and by comparing the predicted values with the observed intensities of the corresponding absorption lines. The results depend partly on definite physical constants associated with the atoms—the ionization and excitation potentials, and the arrangement of the electrons around the nucleus. The temperature and pressure of the region in which the atom is situated are also required before the theory can be applied. The scale of stellar temperatures was discussed in the preceding chapter, and the present chapter is devoted to a synopsis of the modern views as to pressures in the reversing layer.

Strictly speaking, we cannot refer to “the pressure in the reversing layer,” for, like the temperature, the pressure has a gradient throughout the star. This gradient, as derived from the theory of radiative equilibrium,[58] is steep in the far interior of the star, but towards the outside the rapid fall of pressure begins to decrease, and changes somewhat abruptly to a very small gradient in the photospheric region, where radiation pressure and gravitation are of the same order of magnitude. Outside this layer of transition between the region dominated by radiation pressure and the region dominated by gravitation, the pressure gradient is very shallow, and decreases until, in the tenuous outer regions of the star, there is no appreciable pressure gradient, and atoms are practically floating freely.

[Pg 35]

The outermost regions of the atmosphere, at these exceedingly low pressures, make little or no contribution to the ordinary stellar spectrum; they can only be studied in the high-level chromosphere by means of the flash spectrum obtained at a total eclipse of the sun. The spectra that are ordinarily examined are from a region that is at an appreciable depth within the star—the depth from which the light of each individual wave-length can penetrate. The “layer” of which we can obtain a spectrum is therefore not at the same depth for all frequencies; it is most deep-seated in regions of continuous background, and nearest to the surface of the star at the centers of strong absorption lines. The pressures from which the different parts of the spectrum originate differ in the same way, and the idea of “pressure in the reversing layer” is not an easy one to define significantly.

For theoretical purposes it is usual to deal with the pressure at a given “optical depth” (a measure of the amount of absorbing matter traversed by the radiation in coming from the level considered). The optical depth is connected with the density , the mass coefficient of absorption for unit density, , and the vertical depth, , in the star, by the relation[59]

The density gradient is thus eliminated. The optical depth is furthermore related to the pressure by the relations where is the value of gravity at the point in question, and whence

In considering the stellar atmosphere we are dealing with a layer so near the surface that the value of g involved is effectively the “surface gravity” for the star. If is constant, a condition [Pg 36] probably approximately fulfilled,[60] the pressure at constant optical depth is then directly proportional to the surface gravity, which varies as the product of the mean density and the radius of the star. Some idea of the range in pressure with which we shall be concerned in the stellar atmosphere can therefore be obtained from stars of known mean density and radius.

The data for eight such stars, all of the second type, are contained in Table X, which is adapted from tabulations given by Shapley.[61] Successive columns contain the name of the star, the spectral class, the mean densities of the two components in terms of the solar density, the hypothetical radii of the two components (on the assumption of solar mass) in terms of the sun’s radius, and the product of mean density and radius for each component.

TABLE X

Star		Class	Mean density		Radius		Product
SX	Cas		0.0004	0.0002	15.3	18.6	0.006	0.004
RX	Cas		0.0005	0.0004	14.3	14.3	0.007	0.006
RZ	Oph		0.001	0.00003	10.1	33.5	0.010	0.001
RT	Lac		0.0013	0.010	4.6	4.6	0.059	0.046
W	Cru		0.00002	0.000025	94	36	0.00019	0.0009
U	Peg		0.83	0.67	1.2	1.2	1.0	0.8
W		G	1.8	1.8	0.9	0.9	1.6	1.6
Sun			1.0		1.0		1.0

In mean density these stars display a range of , while the range in surface gravity is , illustrating the significant fact that the mean density varies far more widely than the surface gravity. The latter quantity is the important one in determining the pressure that may be assumed to exist in the reversing layer. If the masses of the very luminous stars of low mean density, such as W Crucis, exceed the solar mass, as they most probably do, the hypothetical radii are [Pg 37] increased, and the range in surface gravity becomes even smaller than before.

The data for stars of known mean density and radius permit the estimation of the range in surface gravity, and hence of the range in pressure, encountered in the reversing layer. In the absence of knowledge of the appropriate optical depth, however, the actual pressure cannot be deduced from such considerations, and recourse must be made to more indirect methods. The present view is based upon a number of considerations, none of which would alone be of great weight. All of the conclusions, taken together, however, indicate that the upper limit of the pressure for the region in which the Fraunhofer lines originate is of the order of .

Attention was first called to the probability of an extremely low pressure in the reversing layer by R. H. Fowler and Milne,[62] in advancing the form of ionization theory which is to be analyzed in later chapters. The conclusion that the pressure in the reversing layer is exceedingly low was a direct outcome of their discussion, and they mentioned that the results from other methods converged in the same direction.

Russell and Stewart,[63] in a specific discussion of the pressures at the surface of the sun, have established beyond question, and on quite other grounds, that the pressure for the solar reversing layer is indeed of the order suggested by Fowler and Milne. The value need then no longer be regarded as a result of the Fowler-Milne theory, and may be used without redundancy in deriving a stellar temperature scale from that theory.

METHODS OF ESTIMATING REVERSING LAYER PRESSURES

Russell and Stewart examined the evidence for reversing layer pressures derived from the following sources: (a) Shifts of spectral lines due to pressure, (b) Sharpness of lines, (c) Widths of lines, (d) Flash spectrum, (e) Equilibrium of outer layers, (g) Ionization and chemical equilibrium in the solar [Pg 38] atmosphere. In addition to these we have (f) the observed limit of the Balmer series in the hotter stars, where the hydrogen lines are at or near their maximum. These sources of evidence will now be briefly discussed.

(a) Shifts of Spectral Lines.—It was at one time supposed that displacements of spectral lines, corresponding to pressures of several atmospheres, could be found in stellar spectra. More recent work,[64] however, has shown conclusively that the pressure shifts that occur are so small that it is impossible to estimate a pressure from them with any approach to accuracy. The estimated pressures are of the same order as their probable errors. This being so, the most that can be expected of the method based upon pressure effects is a demonstration of whether or no the pressure exceeds 0.1 atmosphere, and this question has now been satisfactorily answered in the negative.

[Pg 39]

(b) Sharpness of lines.—The occurrence, as sharp distinct lines in the spectra of the stellar atmosphere, of lines that are diffuse in the laboratory at atmospheric pressure, and only become sharp when the pressure is very much reduced, indicates that the pressure in the reversing layer must be extremely low. The mere existence of distinct hydrogen lines points to a pressure of less than half an atmosphere, as was shown by Evershed,[65] and the lines 4111, 4097, 3912 of chromium,[66] 3421, 3183 of barium,[67] and 4355, 4108, 3972 of calcium,[68] which are sharp and distinct in the solar spectrum, but which only lose their diffuseness in the laboratory under vacuum conditions, indicates pressures probably far lower than 0.1 atmospheres. The lines of doubly ionized nitrogen, which are seen as sharp clear absorption lines in the early stars and the cooler stars,[69] are also somewhat hazy under even the finest laboratory conditions,[70] and probably arise in regions of very low pressure in the stellar atmosphere.

(c) Widths of lines.—The width of an absorption line, produced by “Rayleigh Scattering” close to resonance conditions, is given by Stewart[71] as where is the observed width of the line, the wave-length expressed in the same units, and the number of molecules per square centimeter column in the line of sight.

It is unfortunate that the widths of Fraunhofer lines are hard to measure and difficult to interpret. Results obtained from objective prism spectra will probably differ from those derived with the aid of a slit spectrograph, and moreover, in estimating a line with wings it is hard to judge what should be regarded as the “true” line width. Russell and Stewart[72] estimate for the lines in the solar spectrum. Then, on the assumption that the reversing layer has a thickness of a hundred kilometers, the partial pressure of neutral sodium in the reversing layer, as derived by Russell and Stewart from the formula just quoted, is of the order . At the solar temperature, 5600°, about 99 per cent of the sodium present is in the ionized condition,[73] and thus the total partial pressure of sodium atoms may be of the order . If it be assumed that sodium constitutes about 5 per cent of the total material present, the total pressure thus derived is of the order .

[Pg 40]

The lines are of course the ultimate lines of neutral sodium. It will be shown[74] in Chapter IX that the partial electron pressure in the region from which ultimate lines originate is probably between at maximum. When 99 per cent of the atoms are ionized, the pressure rises by a factor of about 100, and the corresponding partial electron pressure becomes between . As the total pressure is probably, at the solar temperature, about twice the partial electron pressure, the total pressure should be nearer to .

The total pressure derived in Chapter IX is the pressure corresponding to the median frequency of the sodium atoms that send out light to the exterior—it may be regarded as the average pressure for the visible sodium. The total pressure derived from the line width, on the other hand, is the pressure at the bottom of the layer of visible sodium, and might therefore be expected slightly to exceed the average pressure for the visible sodium atoms. The difference encountered, partial electron pressure, the total pressure should be nearer to for the average pressure, and partial electron pressure, the total pressure should be nearer to for the total absorption pressure, is in the direction that would be anticipated, although it is larger than might have been expected. Neither value is, however, of very high accuracy, and probably the agreement can be regarded as quite satisfactory.

If the same formula be applied to the hydrogen lines, which may have a width[75] of the order of 5Å, high values for the partial pressure of hydrogen are obtained. The behavior of hydrogen in the spectra of the cooler stars,[76] and the abnormally high abundance[77] derived for it in Chapter XIII, suggest that here, again, a definite abnormality of the behavior of hydrogen is involved.

(d) Flash Spectrum.—It was pointed out by Russell and Stewart[78] that the density in the region that gives the flash spectrum must be exceedingly low. If this were not the case, the intensity of the scattered sunlight would be great enough, as compared to the flash itself, to register on the plate as continuous background in the time required to photograph the flash. The pressure thus estimated, from the minimum amount of material required to give scattered sunlight strong enough to be registered, is less than .

(e) Radiative Equilibrium of the Outer Layers.—At the edge of a star, where radiation pressure and gravitation no longer balance, and in consequence the existence of temperature and pressure gradients, [Pg 41] such as we observe in the reversing layer, becomes possible, the equations given by Eddington[79] for the equilibrium of the interior no longer hold. The outer layers fall off more steeply than the equations predict, and in consequence it is not possible to use the equations in deriving values for the pressure or density corresponding to a layer near the boundary at a given temperature. It is certain, however, that the density deduced from the equations will be far too high, and so the predicted density at a given temperature may be used to indicate that the pressures at the boundary of a giant star are indeed very low.

The following table is adapted from the one given by Eddington for the relation between distance, , from the center, density , and temperature , for a typical giant star of Class , effective temperature 6500°. The distance from the center is expressed in terms of the solar radius, the density in grams per cubic centimeter, and the temperature in absolute units. The last entry in the first column represents the total radius of the star.

0	0.1085	6,590,000°	4	0.0010	1,380,000°
1	0.0678	5,640,000	5	0.00015	730,000
2	0.0215	3,840,000	6	0.0000093	290,000
3	0.0050	2,370,000	6.9	0.000000	......

At a depth where the temperature is 290,000°, ten times the temperature in the reversing layer of any known star, the density given is about . An atmosphere a hundred kilometers in thickness (the supposed approximate depth of the reversing layer) and of this density would contain only a hundred grams per square centimeter of surface. In order to bring the density into harmony with the densities derived for the reversing layer it is necessary to suppose that the value[80] of falls to 0.4 per cent of its value at 290,000° as the temperature falls, from [Pg 42] 290,000° to 29,000°, to 10 per cent of its value. The fall of density displayed in the table appears to be rapid enough to warrant this supposition; and in any case, as was pointed out earlier, the actual fall is probably greater than the formula predicts. The general theory of stellar equilibrium is, then, consistent with very low pressures in the reversing layer. More than this cannot be said, as the formulae are not directly applicable.

(f) Observed Limit of the Balmer Series.—The earlier members of the Balmer series of hydrogen are produced by the transfer of electrons from 2-quantum orbits to 3-quantum orbits (), 4-quantum orbits (), and so forth. The later members of the series are associated with orbits of higher and higher quantum numbers. The major axis of the orbit varies as the square of the quantum number, and therefore a hydrogen atom which is producing, say, , is effectively much larger than one which is giving rise to . As was early suggested by Bohr,[81] the production of the higher members of the series must depend upon the possibility of existence of the corresponding outer orbits. As a preliminary assumption it appears probable that the existence of the larger orbits will depend on the proximity of neighboring atoms, and hence on the pressure.

The theoretical questions involved are very complex, and the present discussion is merely tentative. When the idea that the maximum number of lines that could be produced was a function of the pressure was first set forth, the available laboratory evidence appeared all to be in its favor. The maximum number of Balmer lines that had been produced in the vacuum tube was five, while it was well known that over twenty could be traced in absorption in some stellar atmospheres. Since that time, however, the work of R. W. Wood[82] has produced forty-seven lines of the Balmer absorption series of sodium in the laboratory at considerable pressures, and evidently the simple theory, relying on the mutual distances of the atoms to determine the number of lines that [Pg 43] can be produced, cannot be applied in this case. The matter has been discussed by Franck,[83] who points out that the outermost effective orbit in the sodium atom that gives the forty-seventh line must embrace large numbers of other atoms. He suggests that collisions are chiefly responsible for the production of the absorption lines.

Even though the simple theory is inapplicable to the laboratory conditions, it is not necessarily invalid in the stellar atmosphere, where conditions are far more simple, and where, in particular, the effects of collisions are negligible. There appears, moreover, to be a distinct observational correlation between the pressure and the number of observable hydrogen lines. The importance of the wave-length of the beginning of the continuous absorption, which lies just to the red of the last Balmer line observed, and extends toward the violet, was first indicated by Wright,[84] who recorded that the absorption head was farther to the red in Lyrae than in Cygni. This fact is obviously reflated to the difference in pressure in the atmospheres of the two stars, one of which is a normal star, while the other is a super-giant. The observational and theoretical importance of the question has also been discussed by Saha,[85] and by Nicholson.[86]

The observational data in the hands of the writers just quoted were very meagre, and the present writer and Miss Howe[87] have recently attempted to obtain information on the number of observed Balmer lines in a large number of stars, and to examine the correlation with absolute magnitude. A distinct correlation is found between the number of lines observed and the reduced proper motion, which is chosen as the best available criterion of absolute magnitude for the numerous stars involved (Class brighter than the fifth magnitude). It therefore appears that the pressure, and hence the proximity of the atoms, has some influence upon the possibility of the production of a line. The [Pg 44] application of Bohr’s original suggestion is hence of considerable interest, and the resulting pressures may profitably be compared with the pressures otherwise derived for the reversing layer.

The maximum number of lines seen, while quite consistent for plates made with the same dispersion, is somewhat increased when the dispersion is made much greater. The number of lines seen in the spectra of various stars with strong hydrogen lines, made with a dispersion of about 40 mm. between and , varies between thirteen and twenty. The corresponding pressures, derived from Bohr’s estimate that a pressure of about 0.02 mm. would be required for the production of thirty-three Balmer lines, and on the assumption that the pressure varies as the sixth power of the quantum number, lie between and . These pressures are of course to be regarded as upper limits, for it is possible to miss several lines at the violet end of the series, and Wright, with larger dispersion, does indeed record twenty-four Balmer lines in Cygni; on the other hand it is not likely that the estimated number will exceed the actual number of lines.

The pressures in the reversing layer, as derived from the observed limit of the Balmer series, are then of the same order as the pressures derived by the other methods outlined above. This is of especial interest because the method, if applicable, is a direct one, and gives results for individual stars, whereas all the other methods, excepting the one based on pressure shifts, are essentially indirect.

(g) Ionization and Chemical Equilibrium.—The evidence adduced by Russell and Stewart[88] has been greatly amplified by Fowler and Milne,[89] and by the data bearing on their theory which were subsequently published by the writer[90] and by Menzel.[91] It is not intended to present the evidence from ionization theory here in support of the low pressures inferred by the other methods for [Pg 45] the reversing layer. The pressure derived in the present chapter, and considered as independently established, will be used in Chapters VII ff. to derive a stellar temperature scale, for the reversing layer, from the line-intensity data presented.

SUMMARY

The following tabulation contains a synopsis of the reversing layer pressures derived by the methods that have been outlined.

The extreme tenuity of the stellar atmosphere appears to be unquestionably established by the data set forth above, and a maximum effective pressure of may therefore be assumed in a discussion of the spectra of reversing layers.

Pressure Shifts	less than
Line Sharpness	less than
Line Width
Flash Spectrum
Radiative Equilibrium	order of
Limit of Balmer Series	to (upper limit)
(Ionization	to )

THE spectrum of a laboratory source offers a somewhat inadequate comparison with the spectrum of a star. Matter can be studied terrestrially in small quantities only, and when a laboratory source is used in obtaining a spectrum, all the contributing material is collected into a very small region. With the stellar source it is quite otherwise. An enormous mass of matter, spread over a very large region, gives rise to the spectrum, and probably widely different physical conditions prevail at the origin of light of different wave-lengths. The present chapter contains a brief survey of the chief components which go to make up the stellar spectrum.

The spectrum of a star nearly always consists of a continuous background, in which the energy distribution corresponds more or less to that of a black body, and of absorption and emission lines and bands. The observed stellar spectrum is the integrated contribution from all parts of the disc, the unlined portion representing radiation that passes undisturbed from the photosphere through the reversing layer, and the light within any individual absorption line coming from the greatest depth in the reversing layer that can be penetrated by light of the corresponding frequency. This depth, which is a function of the monochromatic coefficient of absorption for the wave-length considered, is negligible when compared with the radius of the star.

DESCRIPTIVE DEFINITIONS

The solar atmosphere is probably qualitatively representative of all normal stellar atmospheres. It has been satisfactorily described [Pg 47] by Russell and Stewart:[92] “At the top is a deep layer, the chromosphere, in which the gases are held up by radiation pressure, acting on individual atoms. The pressure and density in this layer increase slowly downwards (as gravity somewhat overbalances radiation pressure) and the pressure at its base may be of the order of , or 0.0001 mm. of mercury. Below this level, gravity is predominant in the equilibrium, and the pressure increases rapidly with depth—the temperature remaining nearly constant, and not far from 5000°, so long as the gases are transparent. This region is the reversing layer. When the pressure reaches 0.01 atmosphere, the general absorption by electron collisions begins to render the gas hazy. This opacity increases greatly with the pressure, and the reversing layer passes, by a fairly rapid transition, into the photosphere, which on the scale on which we have to study it resembles an opaque mass. As soon as the opacity becomes important the temperature rises in accordance with the theory of radiative equilibrium developed by Schwarzschild and Eddington. The observed effective photospheric temperature is a mean value for the layers from which radiation escapes to us.”

[Pg 48]

The photosphere, as has been stated, is at an extremely small depth compared with the radius of the star. Taking the sun as an example, it is estimated by Russell and Stewart[93] that the reversing layer, which, with the chromosphere, is responsible for all the solar phenomena that can be spectroscopically studied, consists of about four tenths of a gram of matter per square centimeter of surface, and is only a few hundred kilometers in thickness. As this embraces only about of the mass and of the volume of the sun, it is clear that the features that can be studied spectroscopically are purely superficial, and that the larger aspects of stellar composition and constitution are left essentially untouched.

THE CONTINUOUS BACKGROUND

The continuous background of the spectrum represents the photosphere—the deepest layers from which we receive light. The energy that produces it is practically the total energy output of the star. While the actual distribution of energy in the spectrum probably conforms, in general, to that of a black body, the observed distribution naturally deviates considerably. But when corrections have been applied for atmospheric absorption, the resulting energy curves so far obtained do not appear to furnish certain evidence of serious deviation from blackness, although several investigators have suggested that their measures lead to this conclusion.[94][95][96]

If it is admitted that the energy distribution in the continuous background is sensibly black, the application of the Planck and Wien formulae furnishes methods of deriving the effective temperatures of stars from the energy distribution and the position of maximum intensity, respectively. The energy curve has therefore been extensively studied, both photographically and photometrically, and our present knowledge of stellar temperatures rests primarily upon work of this nature. The solar spectrum has been the subject of exhaustive photometric researches by Abbot[97] and Wilsing,[98] and the theory of the energy distribution, and its relation to the law of darkening, have been discussed by Lindblad,[99] and by Milne.[100] In a discussion of the solar energy curve, Milne[101] shows that the continuous spectrum can be regarded as that of a black body displaced to the violet, and that the displacement can be ascribed to the distortion of a normal black body curve by the presence of strong absorption.

H. H. Plaskett,[102] in applying the wedge method of spectrophotometry [Pg 49] to the same problem, took care to measure continuous background intensities in spectral regions free from absorption lines stronger than 0 per Angstrom, as measured on Rowland’s scale of intensities. In this way he obtained a series of measures which should give a distribution sensibly free from distortion. His result for the solar temperature agrees more nearly with that derived from the solar constant than do the results of previous observers, and therefore the idea that the continuous background approximates to blackness is borne out by observations made with the proper precautions. R. H. Fowler[103] has remarked that “there is no longer any large discrepancy between the solar constant and the color temperatures, and one may hope that further more accurate work will leave them in full agreement.”

[Pg 50]

The position of maximum intensity governs the color of the star, which is quite unrelated to the colors absorbed and radiated by the atoms in the reversing layer. In some of the Wolf-Rayet stars, apparently at very high temperatures and with atmospheres under special conditions of excitation, the continuous spectrum appears extremely faint, although there seems to be no reason for supposing that this is not merely an effect of contrast with the powerful emission “bands.” The writer believes that long exposures would demonstrate the presence of continuous background for all such stars.[104] In the spectra of some gaseous nebulae, however, no continuous background has as yet been observed,[105] nor would any be expected, if our conception of the tenuity of these bodies is correct, unless they shine partly by pure reflection. (For example, the presence of some reflected starlight is inferred from the existence of a continuous background for the Orion nebula.) The transparency of gaseous nebulae to the light of stars indicates that their general opacity is extremely low, and it is this general opacity that is operative in producing the continuous background of a photosphere.

THE REVERSING LAYER

The reversing layer, comprising the layers above the photosphere, where the general opacity has greatly decreased and selective opacity begins to be appreciable, is responsible for the lines in the spectrum, which form the major part of the material of stellar spectroscopy. When the energy flowing out through the reversing layer in any specified wave-length is less than the energy in the neighboring continuous background, an absorption line is produced in the spectrum.

Roughly speaking, if an atom absorbs the whole of the light of any given frequency that reaches it from below, it will re-emit all the energy so absorbed, and will in general do so in a random direction.[106] The intensity of the absorption line so formed will then be about 50 per cent of the intensity in the neighboring continuous background. This argument is merely illustrative; it must suffice to point out that if pure selective absorption is operative the spectrum will be crossed by lines that are considerably less intense than the background. If, on the other hand, the energy leaving the atmosphere with any wave-length is greater than the energy in the neighboring continuous background, a bright line or “emission” line appears in the spectrum. Actually, of course, it is no more an emission line than is an ordinary Fraunhofer line, for the difference between stellar absorption and emission is merely a matter of contrast with the continuous background. Both kinds of line are “full of light.”

ABSORPTION LINES

The absorption lines vary greatly among themselves and from star to star, both in intensity and in general appearance. The metallic lines, more particularly those of ionized atoms, are often extremely narrow and sharp—a feature difficult to reproduce in the laboratory, and referable to the very low pressures in the stellar atmosphere.[107] Other lines, such as those of the Balmer series of hydrogen, may be [Pg 51] of considerable width, and spread out into wings that extend as much as thirty Angstrom units on each side of the center of the line. Many other lines are probably winged, but are not of sufficient strength for the feature to be seen. The form of the wings and the general shape of the line are of high significance, and should ultimately give much information bearing on the structure of the stellar atmosphere.

Although the absorption lines are commonly regarded as “dark,” the foregoing section indicates that they should always have an appreciable intensity even at their centers. Measures of the central intensities of strong absorption lines have been published by various investigators, and the results are not all in agreement. Schwarzschild[108] gives from a single measurement of the and lines in the solar spectrum (center of disc) with the Hartmann microphotometer, wings ten Angstrom units in width on either side of the line center, and a weakening of the intensity of the light, from the continuous background to the center of the line, of about two and a half magnitudes. Bottlinger’s curves[109] appear to lead to considerable intensities at the centers of the hydrogen lines in the stars. Others have suggested that the central intensities are considerably lower. Abbot[110] quotes estimates ranging from one fifth to one tenth of the continuous background for solar lines, and H. H. Plaskett[111] states that the faintest stellar lines have about one tenth the intensity of the continuous background, as measured by his wedge method.[112]

Determinations of central intensity by means of precise photometry have been made by Kohlschütter[113] and by Shapley,[114] objective prism spectra being used in both cases. Kohlschütter gives the results of the analysis of the spectra of twenty-one stars of Classes and [Pg 52] by means of the Hartmann microphotometer. The darkening from the continuous background to the center of the line is tabulated in his paper for , , , , and ; it ranges for from 1.14 magnitudes for a Lyrae to 0.42 magnitudes for Cygni. The corresponding central intensities are 35 and 68 per cent of the intensity of the continuous background. The method used by Shapley employed a special set of apertures to obtain a graded series of images for a comparison of the central intensity with that of the adjacent background. Although it is not certain that all the very complex photographic and photometric difficulties involved were overcome by this method, its results are presumably entitled to greater weight than any other determinations of central intensity hitherto made. The intensity in the hydrogen absorption lines of Vega was ascertained to be about 25 per cent of that of the background.

SATURATION OF ABSORPTION LINES

The discussion outlined above presupposes that the substance producing the absorption line in the reversing layer is present in quantities great enough to absorb all the light of the appropriate wave-length, subsequently re-emitting it and giving rise to an absorption line with considerable central intensity. If the atom in question is present in quantities too small for complete absorption to take place, the central intensity of the line produced will of course be higher still. Such atoms are designated “unsaturated.” Saturation has been described by Russell[115] as follows:—“For the strong lines ... the absorption in the reversing layer is so great that a large increase in the number of absorbing atoms present alters the strength of the line very little. For the weak components ... absorption under ordinary conditions is incomplete, and the strengthening (in the spectra of sunspots) is noteworthy”—an increase in the amount of available material produces an increase in the strength of the line. The strong components are [Pg 53] saturated, the weak ones are not. It should be noted that here there is an excess of atoms for the radiation. “Saturation” is used in another sense when the word is applied to the conditions at the center of a star,[116] where there is an excess of radiation for the atoms present.

EMISSION LINES

The emission lines observed in stellar spectra differ more widely among themselves than do the absorption lines, and theory has so far been less successful in suggesting the physical conditions under which they may arise.[117] The appearance of the bright-line flash spectrum of the sun, from a region that gives no appreciable continuous spectrum, is of interest in comparing emission and absorption lines. It is fairly obvious that if the source of the flash spectrum had the photosphere behind it, the bright line would appear as absorption lines—which is indeed the case when the sun is ordinarily observed. Russell assigns both the Fraunhofer lines and part of the flash spectrum to the same region, namely the upper reversing layer. The high-level flash is, of course, assigned to the lower chromosphere. The difference between absorption and narrow emission is, as was pointed out in an earlier paragraph, purely a matter of contrast. There has, however, been no satisfactory explanation of how the phenomenon displayed by an ordinary emission line can be produced—an atom that re-emits in some wave-length more light than it receives in that wave-length. Some form of “fluorescent” emission would seem to be involved, and the question is evidently an important one for spectrum theory.

The chief types of emission are found in (a) the long period variables at maximum, (b) the emission stars, (c) the stars, including the Wolf-Rayet stars. All these stars are apparently very luminous.[118] Emission is also found in some late dwarfs—for example the and lines are reversed in the spectrum of [Pg 54] 61 Cygni,[119] and doubly reversed in the solar spectrum. Furthermore the spectra of gaseous nebulae are almost entirely composed of emission lines; and completely abnormal types of stars, with spectra partly or wholly composed of emission lines, might also be mentioned, notably the novae,[120] Carinae,[121] Merrill’s “iron star,”[122] Z Andromedae,[123] and[124] B. D.+11°4673. The conditions under which bright lines appear vary so widely that a single theory is manifestly inadequate to account for the phenomenon in every case.

THE identification of stellar lines and bands with those observed in the laboratory has furnished a rich source of data for astrophysics. About 25 per cent of the observed solar lines are assigned to elements in Rowland’s Table of Solar Spectrum Wave-lengths. The majority of the solar lines which are still unidentified are faint. Notwithstanding practical difficulties of identification caused by blending, and the consequent uncertainty of wave-length, most of the observed lines, at least in the cooler stars, have been satisfactorily accounted for. There remain some important strong lines and bands of unknown origin, which have been usefully summarized by Baxandall.[125]

The present chapter contains a summary of the stellar occurrence and astrophysical behavior of the chief spectrum lines which are of known origin and series relations. A few other lines, such as those of C++, N++, and O+ are included, as their series relations will probably be forthcoming in the near future. The observed chemical elements are arranged in order of atomic number. At the conclusion of the chapter the elements which have not been detected in stellar spectra are enumerated. The series notation employed follows the system advocated by Russell and Saunders,[126] which appears to meet, more fully than any other, the practical needs of modern spectroscopy.

HYDROGEN (1)

Hydrogen is represented in stellar spectra by the Balmer series (); the ultimate lines are those of the Lyman series () in the far ultra-violet, and cannot therefore be [Pg 56] traced in the stellar spectrum. The occurrence of the secondary spectrum of hydrogen, ascribed to the hydrogen molecule H₂, has been suspected,[127] but not definitely established. Only one of the lines has been recorded, and this should almost certainly be attributed[128] to N++. The familiar Balmer series appear as emission lines in the Wolf-Rayet stars, but normally they are absorption lines in all succeeding classes.

The intensity of the hydrogen lines is at a maximum[129] in the neighborhood of Class . They vary greatly in width, however, within a given spectral class,[130] and it is difficult to find a method of photometry applicable to the comparison of lines of very different widths. The maximum of the Balmer lines has been placed by Menzel[131] at . The writer is inclined to believe that no significant maximum can in fact be derived for the Balmer lines; beyond , however, their intensity falls off rapidly.

It is peculiar to the Balmer series to appear in every class of the normal stellar sequence, and its lines at maximum exceed in strength the lines of every other element which appears in stellar spectra, excepting those of ionized calcium.

Although hydrogen is presumably unable to give rise to an “enhanced” spectrum, as the atom only possesses one extra-nuclear electron, the lines of the Balmer series share with those of neutral helium the peculiarity of behaving like the lines of an ionized atom.[132] They are weakened in dwarf stars, and greatly strengthened in the cooler super-giants, such as Orionis. The peculiarity of the astrophysical behavior of the hydrogen atom also appears in the impossibly high value that is assigned by ionization theory to the relative abundance of this element.[133] An explanation, in terms of metastability, has been suggested by Russell and Compton,[134] but although the hypothesis appears very satisfactory in the case [Pg 57] of hydrogen, it is not applicable to the similar problem of helium. Russell[135] has remarked that “there seems to be a real tendency for lines, for which both the ionization and excitation potentials are large, to be much stronger than the elementary theory would indicate.”

The hydrogen lines are often conspicuously winged. Measures of the width and intensity-distribution of the wings are discussed elsewhere.[136] Wings are probably not peculiar to the hydrogen lines, but the hydrogen wings can be studied because of their strength. The feature is also seen in helium, calcium and iron lines, and wings of greater or less strength are probably universal.

The width of the hydrogen lines in stars has been correlated with absolute magnitude, and used for the estimation of luminosities.[137] It appears, however, that the line width may not furnish an accurate measure of absolute magnitude, although it serves to discriminate stars having the c-character from those of smaller luminosity.[138] The occurrence of wings seems, moreover, to be independent of line width and of absolute magnitude.[139] These questions are connected with the problem of classifying the stars, and are discussed in a later chapter.[140]

The continuous spectrum of hydrogen, beyond the limit of the Balmer series, corresponding to the continuous radiation observed in the laboratory for sodium by Wood,[141] and for helium by Lyman,[142] was first noted in stellar spectra by Sir William Huggins.[143] The beginning of the band appears just to the red of the last Balmer line observed.[144] It appears, from work in progress at the Harvard Observatory,[145] that the limit is nearer to the violet, the higher the luminosity, and in a nebular spectrum quoted by Hubble,[146] it almost coincides with the theoretical limit of the series.

[Pg 58]

The largest number of hydrogen lines recorded is thirty-five, measured by Mitchell[147] in the flash spectrum. Thirty-three were observed in emission by Evershed[148] in the solar chromosphere, and Deslandres[149] traced twenty-nine in the spectrum of a bright solar prominence. Twenty-seven Balmer lines have been observed by Curtiss[150] in the spectrum of Tauri—the greatest number recorded for the spectrum of a star. The number of Balmer lines observed is related in Chapter III to the pressure in the reversing layer.

HELIUM (2)

Helium is represented in stellar spectra by the , , , , and possibly the series. Lines associated with these series appear almost simultaneously as we progress through the star sequence, attain a maximum[151] at , and have disappeared[152] in normal stars. The ultimate lines are the series,[153] in the far ultra-violet, and cannot be traced in the stars.

The helium lines vary much in width and definition and are often winged. Their intensity does not certainly appear to vary with absolute magnitude within a given spectral class, and they cannot therefore be used in the estimation of spectroscopic parallaxes.[154] The question of absolute magnitude effects cannot be usefully pursued in the absence of more reliable parallaxes, for the stars, than are at present available.

[Pg 59]

Although the lines of helium do not appear in the normal star, they are observed in the spectrum of the super-giant Cygni, where the pressure is presumably exceedingly low. The lines also appear in the flash spectrum.[155]

IONIZED HELIUM

The lines of ionized helium appear only in the hottest stars, being peculiar to the sequence. The lines (the “Pickering,” or “ Puppis” series) are well marked in the hotter stars, although all the lines usually available are probably blended.[156] The alternate Pickering lines are practically superposed on the Balmer lines, and the components were separated for several stars of Class by H. H. Plaskett.[157] The “4686” series () appears in absorption in all the so-called “absorption stars,” and is even faintly seen in some stars. The line at 4686 appears very readily as an emission line, and the wide bright “band” at this wave-length, which is a conspicuous feature of the Wolf-Rayet stars, of gaseous nebulae, and of certain stages of a nova, is also presumably due to ionized helium.

LITHIUM (3)

The element lithium is represented in the sunspot spectrum by the (ultimate) doublet at 6707, which is not, however, strong enough to be detected in stellar spectra. Russell[158] has called attention to the fact that this line is fainter, in the sun, than would be anticipated from the terrestrial abundance of the element. Compton[159] has suggested that the faintness may be ascribed to low atomic weight, and the consequent blurring of the line by a Doppler effect, owing to the high velocity of thermal agitation.

CARBON (6)

There is no evidence of the presence of neutral carbon in stellar atmospheres. The apparent absence of the element is partly due to the fact that the ultimate[160] line is at 2478, too far in the ultra-violet to be detected. The spectrum of neutral carbon is as yet unclassified, and other lines cannot, therefore, be sought for in the stellar spectrum. The temperature at which the element vaporizes is [Pg 60] given by Kohn and Guckel[161] as 4000°, and by Violle[162] as 3800°. The heat of vaporization has been evaluated by de Forcrand.[163] At stellar temperatures, the carbon present is probably vaporized, but possibly it is largely in combination as cyanogen or as an oxide, since spectra associated with these compounds appear in low-temperature stars.

IONIZED CARBON

Ionized carbon[164] is represented in the stellar spectrum by the fundamental doublet (), at 4267, and by the principal doublet () at 6580. The occurrence of these lines is of great interest. The line at 4267 is found in the stars,[165] reaches a maximum at , and is last seen[166] at . It also occurs in the spectra of some gaseous nebulae.[167] In the stellar spectra in which it occurs, the line is sharp and clear, and, apart from appearing as an emission line in certain stars of Class , it has no abnormal stellar behavior.

The principal doublet at 6580 has been said to occur in the Wolf-Rayet spectrum,[168][169][170] and to be much stronger than the fundamental doublet. The identification has been discussed by Wright,[171] and does not appear to be very probable. A knowledge of the behavior of the line at 6580 in the late and early stars is greatly to be desired.

DOUBLY IONIZED CARBON

Merton[172] has described a spectrum, produced under conditions of high excitation, which shows several correspondences with the emission bands of the Wolf-Rayet stars. His spectrum contains the [Pg 61] fundamental and principal doublets of C+, as well as a number of other lines, which have not as yet been assigned to series. Some of these lines are probably to be referred[173] to the atom of C++, and the writer[174] considers it unnecessary to assume the occurrence of a higher degree of excitation for the Wolf-Rayet spectrum. Some of the lines which are bright in the spectra of emission-line stars have been attributed to C+++ on astrophysical grounds,[175] and also from a discussion of frequency differences.[176] The four strongest groups in Merton’s spectrum, however, consist of triplets, and this points more probably to C++, as does also the ionization potential deduced astrophysically[177] from the behavior of the only group accessible in ordinary stellar spectra. When the doublets due to C+, and the triplets already mentioned, are accounted for in Merton’s spectrum, there remain only two lines at 5696 and 5592. A line[178] with the latter wave-length is attributed by Fowler and Brooksbank[179] to O++. The evidence for stellar C+++ appears, therefore, to be inconclusive.

COMPOUNDS OF CARBON

Cyanogen. The bands headed at 3885, 4215, have been attributed [180] to the CN or the C₂N₂ radical, or to the molecule of nitrogen. The assignment to a particular atom is essentially a question for the terrestrial physicist, and to discuss it here would be out of place.[181] The bands are universally known as the “cyanogen bands,” and this designation will therefore be adopted.

The 3885 and 4215 bands are conspicuous in and stars of low density,[182] and furnish a valuable method for the measurement [Pg 62] of absolute magnitude—a method which has been used both at Mount Wilson[183] and at Harvard.[184] The band at 3885 is largely responsible for cutting off the ultra-violet light of the cooler stars.[185]

Cyanogen absorption has been reported as early[186] as , and according to Lindblad[187] it reaches a maximum at . The cyanogen bands reach great intensity in the stars, and are indeed the most conspicuous feature of these spectra. Shane[188] places the maximum in Class , and is doubtless correct in so doing. The maximum given by Lindblad refers to the series , and the stars are notoriously not members of that sequence.[189] Cyanogen is also a typical constituent of the comet-head spectrum.[190][191][192]

Carbon Oxides. The band spectrum attributed to the CO molecule,[193][194] is a strong feature of the spectra of and stars.[195][196] It is also the chief component of the spectrum of the comet tail, which has been reproduced in the laboratory, at very low pressures, by A. Fowler.[197]

Swan Spectrum. The bands of the Swan spectrum are clearly to be assigned to some compound of carbon,[198][199] but the source is not as yet certainly established. They are characteristic of the comet head.[200] Another band, presumably to be associated with the Swan spectrum, was identified in the heads of nine comets by Baldet.[201] [Pg 63] The ordinary Swan bands are also identified in the comet tail.[202]

Hydrocarbon. The identity of the “” band with the 4314 hydrocarbon group was pointed out by Newall, Baxandall and Butler.[203] The strength of the band is increased, in the stellar spectrum, by the superposition of the lines of calcium, and by the lines of titanium, as well as other metallic lines, but the presence of the hydrocarbon band is certain, and is of the highest interest. The “” band is first seen in some spectra[204] of Class , and it attains a maximum at or .

The number of carbon compounds which occur lends plausibility to the suggestion that much of the stellar carbon is in combination at temperatures below 5000°.

NITROGEN (7)

The spectrum of neutral nitrogen has not as yet been satisfactorily analyzed into series.[205] It is quite possible that the first ionization that takes place is the ionization of the molecule,[206] which is accompanied by the production of the well known band spectrum. This spectrum has not been observed in the stars; presumably it would appear at lower temperatures than those involved in the coolest spectral classes. It is, however, stated to be a conspicuous feature of the spectrum of the aurora,[207][208] and it is found in the spectrum of the comet head.[209] These occurrences seem to point to very low temperature and pressure at the source. It is possible that much of the nitrogen present in cooler stars is in combination with carbon.[210]

The green Aurora line was thought by Vegard[211] to coincide [Pg 64] with a line emitted in the laboratory by solid nitrogen. The conclusion was questioned by McLennan and Shrum,[212] who failed to produce the line under similar conditions, and subsequently found a line, of the same wave-length as the aurora line, in the spectrum of a mixture of oxygen and helium.[213] Various previous attempts to identify the aurora line with a line produced in the laboratory had failed conspicuously.[214]

IONIZED NITROGEN

The spectrum of ionized nitrogen has recently been analyzed by A. Fowler.[215] The line which is most conspicuous in stellar spectra is the one at 3995 (), which appears[216] at or earlier, reaches maximum at , and is last seen at . Many of the fainter lines[217] are not observed.

DOUBLY IONIZED NITROGEN

The lines of doubly ionized nitrogen were singled out by Lockyer[218] as showing “abnormal behavior”—they do not appear in the same classes as the N+ line. The early work on the subject is discussed by Baxandall.[219] The most conspicuous lines are those at 4097, 4103, and they attain great intensity in the stars;[220] they are, for example, very conspicuous in 29 Canis Majoris. H. H. Plaskett[221] places the maximum of the N++ lines in the Victoria class . They are last seen in some stars.

[Pg 65]

The occurrence and behavior of the N+ and more especially the N++ lines in the Nova spectrum has been the subject of numerous investigations.[222][223][224][225][226][227]

OXYGEN (8)

The ultimate lines of neutral oxygen occur[228] at a wave-length of about 1300, and accordingly cannot be observed in the spectra of stars. It was long supposed that neutral oxygen was entirely absent, but the triplet at 7700 is observed in the solar spectrum,[229] is strengthened in sunspots, and is strong in the high level chromosphere.[230] The ionization and excitation potentials corresponding to the production of these lines are of the same order as those for the Balmer series of hydrogen, and the astrophysical behavior of the triplet should therefore be similar to that of the hydrogen lines, with a maximum at or near . Special work in the red is, however, required to trace the behavior of the series. The second member, the triplet at 3947, is not certainly present in the solar spectrum, and is not recorded for any star of Class . In the laboratory, the second triplet is about as powerful as the first,[231] and its apparent weakness at the theoretical maximum is difficult to explain.

IONIZED OXYGEN

The spectrum of ionized oxygen should consist of pairs, and numerous lines have been tabulated as belonging to this atom.[232] The lines are found in stars, as seems first to have been noticed by Lunt.[233] According to the present writer,[234] they are first seen at , although H. H. Plaskett, working with slit spectra, records[235] some O+ lines in Class . The maximum of the O+ lines falls between and , and their disappearance is mentioned[236] as a criterion of Class .

[Pg 66]

The lines at 4069, 4072, 4076, appear to form a triplet, but are more probably two pairs with two of the lines coalesced. Some stronger lines (page 207) persist in Class .

DOUBLY IONIZED OXYGEN

The spectrum of O++ has been tabulated by A. Fowler and Brooksbank,[237] but not analyzed into series. The lines of this atom are certainly present[238][239] in the stars of Class . The astrophysical behavior of the lines of doubly ionized oxygen has led to the estimation of an ionization potential,[240][241] of 45 volts for the corresponding atom.

COMPOUNDS OF OXYGEN

Oxides.—Numerous oxides, such as carbon monoxide CO, titanium oxide TiO₂, zirconium oxide ZrO₂, and water H₂O, are present in the cooler stars. The metallic oxides are discussed under the corresponding metallic element. The occurrence of steam in the spectrum of the sunspot was announced by Cortie,[242] who supported his argument, originally based upon the widening, over sunspots, of telluric water vapor bands, by the observation that the presence of water vapor is essential, in the laboratory, to the production of the spectrum of magnesium hydride, which also occurs in the sunspot spectrum.[243] It is possible that the formation of oxides may account for the weakness of the spectrum of neutral oxygen in the cooler stars, but this explanation can hardly account for the absence of the second member of the series from the spectra of the stars, where the lines should have their maximum intensity.

[Pg 67]

Ozone.—The ozone bands which appear in solar and stellar spectra have been shown by Fowler and Strutt[244] to be of telluric origin. The maximum thermal formation of ozone occurs [245] at and 3500°, and thus its presence in giant and stars might possibly be anticipated.

SODIUM (11)

The ultimate lines () of the neutral atom of sodium are the lines, which lie at 5889, 5895. These are the only sodium lines which are certainly identified in stellar spectra.[246] They are first seen in the later classes, and appear to be strengthened in cool stars, in accordance with theory.

Stationary sodium lines are observed[247] in Scorpii, Orionis, and other Class stars.[248]

The lines are said to show an absolute magnitude effect, being strengthened in giant stars.[249]

No lines of ionized sodium are found in stellar spectra, presumably because they all lie in the far ultra-violet.

MAGNESIUM (12)

The neutral atom of magnesium is represented in the solar spectrum by the , the , and the series, and the first triplet of the latter series constitutes the conspicuous “b” group in the green. The “b” group and the second member of the series, the triplet near 3800, are first seen[250] at , have a maximum near or , and are still strong in the coolest stars examined. The series, represented in the solar spectrum by a line at 4571, are faint ultimate lines; the strong ultimate lines[251] are the lines beginning at 2852, and are therefore outside the range of observed solar and stellar spectra.

IONIZED MAGNESIUM

The ionized magnesium atom gives rise to the important combination doublet at 4481 (). These lines appear in the sequence,[252] reach maximum[253] at (not at , as stated by several investigators), and are lost in the increasing strength of [Pg 68] the iron line at the same wave-length, at about . The doublet varies with absolute magnitude, and may be found to furnish a useful criterion of that quantity. It has been used by H. H. Plaskett[254] in the estimation of the temperatures of some of the stars of Class .

COMPOUNDS OF MAGNESIUM

Magnesium hydride.—The compound magnesium hydride, MgH₂, which has been studied in the laboratory by Brooks[255] and Fowler,[256] was detected by the latter in the sunspot spectrum.[257] It is perhaps significant that the only other hydride reported in celestial spectra is that of calcium, the next heavier alkaline earth after magnesium.

ALUMINUM (13)

Neutral aluminum is represented in the solar spectrum by the lines, the series that constitutes the ultimate lines in the third column elements of the periodic table.[258] The two conspicuous lines of the series in aluminum are those at 3944, 3957, and they are strengthened in cool stars,[259] in accordance with theory. They are especially mentioned as being strong in the spectrum[260] of 61 Cygni, as might be expected for a dwarf star. The series is also traced in the solar spectrum, but is too far in the ultra-violet to be studied effectively in the stars.

The series lines[261] of Al+ and Al++, although they might be expected in the stars, apparently have not yet been traced in stellar spectra.

SILICON (14)

Four stages of the silicon atom are observed in stellar spectra. The line at 3905 is found in the coolest stars, has an observed [Pg 69] maximum[262] at , and disappears at about . This line is regarded by A. Fowler[263] as the ultimate line of the neutral atom, and on this basis an ionization potential of 10.6 volts was assigned to silicon. In view of the fact that the line appears to have a maximum within the stellar sequence, and is of temperature class II, according to King,[264] while the true ultimate line[265] of silicon is at 2881, it seems possible that 3905 is actually a subordinate line.

IONIZED SILICON

Ionized silicon is represented by the lines 4128, 4131, which appear at , attain maximum[266] at , and disappear at . These lines are of especial interest, as they form the characteristic feature of the “silicon stars” which occur in the early classes. The silicon stars are specially discussed[267] in Chapter XII.

DOUBLY IONIZED SILICON

The lines associated with the atom Si++ which appear in stellar spectra are the three at the wave-lengths 4552, 4568, 4574. These lines are first seen at , have a maximum[268] between and , and disappear at . Fowler[269] regards these lines as constituting a principal triplet; it might be expected, however, that principal lines would show a more persistent maximum.

TRIPLY IONIZED SILICON

[Pg 70]

The atom of silicon which has lost three electrons is the most highly ionized atom of which we have certain evidence in stellar spectra. The lines at 4089, 4096, and 4116 are strong[270] among the cooler stars, and are last seen at Class . The hotter stars, such as H.D. 165052, do not display the lines of Si+++, and probably the intensity of the lines has fallen, owing to the temperature, which is above that required for the maximum of these lines.

SULPHUR (16)

The spectrum of neutral sulphur which has hitherto been analyzed is chiefly in the far ultra-violet,[271] and is therefore not traceable in the sun or stars.

Two sets of sulphur lines, differing in astrophysical behavior, were noted by Lockyer[272] at 4163, 4174, 4815, and at 4253, 4285, 4295. These lines have been attributed by the writer,[273] and by Fowler and Milne,[274] to S+ and S++ respectively. The S+ lines appear to be in pairs, and the S++ lines suggest a triplet, although one of the three lines is extremely faint in stellar spectra, and it would be expected that the once and twice ionized spectra of sulphur would display even and odd multiplicities respectively. The two series have maxima at and at , but the stellar intensities of the lines are small. An amplification of our knowledge of stellar sulphur is greatly to be desired.

POTASSIUM (19)

The ultimate lines[275] of potassium () are at 7664 and 7699, and have been traced in the solar spectrum, although they are very faint. They appear to be absent from the flash spectrum.[276] Russell[277] expresses the opinion that they persist, with rising temperature, as far as in the stellar sequence.

CALCIUM (20)

The element calcium is extensively represented in stellar spectra. The ultimate line of the neutral atom is at 4227 () and appears at . The line increases in strength in all cooler stars, in accordance with theory, and has a distinct variation with [Pg 71] absolute magnitude. The , and multiplets[278] are satisfactorily identified in the solar spectrum and can be traced with certainty in the spectra of stars cooler than . The , , , and lines appear to be present with the appropriate intensities in the sun, but are too faint to be seen with small dispersion. Thus all the classified lines of calcium which are strong in laboratory spectra have been traced in the spectra of the sun and stars.

IONIZED CALCIUM

The and lines of ionized calcium are seen throughout the stellar sequence, and reach a maximum within the type,[279] where their intensity is greater than that attained by any other line in any class. They vary with absolute magnitude.[280] In the sun the lines are doubly reversed, and they are probably singly reversed[281] in 61 Cygni.

Stationary calcium lines have long been known to occur in the spectra of certain spectroscopic binaries, having first been noticed by Hartmann[282] for Orionis. Various “calcium cloud” hypotheses have been advanced to account for the phenomenon. It appears, from several considerations, notably the apparent small oscillation of the calcium lines with the same period as the star, that there is some physical connection between the two. Lee[283] discussed the idea that the system of 9 Camelopardalis was surrounded by a cloud of calcium vapor, which, as he showed, could be made to account for the behavior of the lines of ionized calcium. The same idea was discussed by J. S. Plaskett, who suggested that we might “assume that the absorbing material is near to or envelopes the stars, which is probable from its wide distribution, and in this form it combines the two original hypotheses of interstellar and surrounding clouds.”[284] The lines of sodium[285] [Pg 72] and possibly the hydrogen lines[286] have been added to the list of stationary lines, and Plaskett[287] has suggested that the ultimate lines of the ionized atoms of strontium and barium should also show the effect, which has not yet, however, been observed.

SCANDIUM (21)

The element scandium[288] is represented in the solar spectrum by faint lines corresponding to the multiplets , , . The multiplet may possibly be present, but the lines are very weak. The element is not recorded in the spectra of stars; most of the lines are unsuitably placed in the green.

IONIZED SCANDIUM

Six multiplets of ionized scandium, out of the eight tabulated by Meggers, Kiess, and Walters[289] appear in the solar spectrum, and all the corresponding lines have been traced in Rowland’s tables. The intensity of two of the lines is great enough for their behavior to be traced through the stellar sequence, and they are greatly enhanced in the spectra of the c-stars. The ultimate lines are near 3600, but in the solar spectrum they are less powerful than the lines near 3500.

Table XI on page 73 contains, in successive columns, the series relations, the wave-length as determined in the laboratory, the intensity, the temperature class, and the attribution, solar intensity, and wave-length given by Rowland, for the six multiplets which lie within the observed range of the solar spectrum. Ultimate lines are designated by an asterisk.

TITANIUM (22)

[Pg 73]

The spectrum of titanium is so rich in lines, and is so largely represented in stellar spectra, that a tabulation would occupy an undue amount of space.

TABLE XI

Series	Wave-Lenght	Int.	Cl.	Attribution	Int.	Wave-Lenght
	3613.84	60	II	-, Sc	4	3613.947
	3645.31	30	III	Sc?, -	3	3645.475
	3630.76	50	II		4	3630.876
	3666.54	3	III		1	3666.676
	3651.81	25	III	-, Sc	4	3651.940
	3642.79	40	II	Sc	2	3642.912
	3572.53	50	II	-, Sc	6	3572.71
	3558.55	20	II	(Fe	8	3558.672)
	3590.48	20	II		2	3590.609
	3576.35	35	II	-, Sc?	3	3576.527
	3567.70	20	II		4	3567.835
	3589.64	20	II		5	3589.773
	3580.94	30	II		5	3581.067
	5657.89	25	V E	Y, -	2	5658.09
	5684.21	12	V E		1	5684.415
	5640.99	15	V E		2	5641.206
	5667.16	9	V E		0	5667.368
	5658.35	8	V E		0	5658.561
	5669.05	10	V E		1	5669.258
	4374.46	40	III E	Sc, Fe?	3	3374.628
	4420.66	2			00	4420.832
	4354.60	5	V E		1	4354.776
	4400.38	30	III E	Sc	3	4400.555
	4431.35	3	V E		0	4431.525
	4384.80	6	IV E		0	4384.986
	4415.55	20	III E		2	4415.722
	4314.09	60	III E	Sc	3	4314.248
	4294.77	8	IV E	Zr	2	4294.932
	4320.73	50	III E	Sc	3	4320.90
	4279.95	1	-		-	----
	4305.70	10	IV E		2	4305.871
	4325.00	40	III E	Sc	4	4325.152

From an examination of Rowland’s tables of the solar spectrum, it appears that the fainter components of the multiplets invariably accompany the stronger ones, thus making the identifications certain. [Pg 74] Only the stronger components are, however, powerful enough to appear in stellar spectra, with the dispersions ordinarily used.

The following multiplets, as analyzed by Russell[290] and Kiess,[291] are definitely present: , , , , , , , , , , . Doubtfully present are: , .

The maximum of these lines is difficult to determine; they are not well placed for measurement, many of the most important are seriously blended, and all are rather faint, even at maximum. They are first seen[292] at Class , and their maximum appears to be[293] at or .

The solar intensities of the lines of both neutral and ionized titanium fall off regularly with increasing excitation potential. The subject is discussed in Chapter VII, as part of the evidence for the validity of the Saha theory.[294]

IONIZED TITANIUM

The lines of ionized titanium are about as strong in the solar spectrum as those of the neutral atom. Many of them appear, with the lines of the ionized iron atom, with abnormal strength in the spectra of the c-stars.[295] The following multiplets[296] are present in the solar spectrum: , , , , , , , , , , , , , , , , , , , , , . Doubtfully present are , , , . The lines which are especially enhanced in the c-stars are: , , , , , , , .

The lines of ionized titanium come to a maximum at about Class , but a significant maximum is difficult to determine, for the lines are [Pg 75] extremely sensitive to absolute magnitude. Menzel,[297] using Cassiopeiae (classed by him as ) for his typical star, found a maximum development of lines in that star. The present writer,[298] using the wider selection of stars enumerated in the appendix, obtains as the maximum for Ti+. A glance at the measures[299] will indicate that the position of the maximum is in any case very uncertain, as the intensity does not change smoothly in going from class to class.

COMPOUNDS OF TITANIUM

The absorption bands of titanium oxide, TiO₂, are the characteristic flutings[300][301] of the stars of Class , and the strength of these bands has been proposed[302] as a criterion of class for the stars in which they are found. It is perhaps noteworthy that titanium, zirconium, and carbon, the only elements which give oxides in stellar spectra (hydrogen excepted) belong to the fourth group of the periodic system.

VANADIUM (23)

The vanadium lines are best identified by intensity from Rowland’s table. The following multiplets[303] are present in the solar spectrum: , , , , , , . The multiplet is well seen in stellar spectra from onwards, and increases in strength as cooler stars are approached.[304] Slipher[305] called attention to the strength in Ceti of the vanadium group near 4400, presumably the two multiplets , , with excitation potential 0.28 volts.

[Pg 76]

IONIZED VANADIUM

Three multiplets, all far in the ultra-violet, are tabulated for ionized vanadium by Meggers, Kiess, and Walters,[306] and two of them are within the range of Rowland’s table. All the lines of these, the and multiplets, have been satisfactorily identified with solar lines. The strength of the ultimate lines of ionized vanadium, which occur in the multiplet last named, is a little greater, in the solar spectrum, than that of the strongest lines of the neutral atom, at 4379, which are also ultimate lines.

The following tabulation contains, in the same form as Table XI, the data respecting the two multiplets which are identified in the solar spectrum.

TABLE XII

Series	Wave-Lenght	Int.	Cl.	Attribution	Int.	Wave-Lenght
	3727.348	20	-		1	3727.488
	3760.230	5	-		1	3760.364
	3718.163	3	-			3718.291
	3750.873	15	-		2	3751.015
	3778.359	3	-	(Fe	3	3778.463)
	3743.63	3	-	(Cr	1	37243.726)
	3770.976	10			2	3771.116
*	3093.10	40	III Er			3093.229
	3121.144	20	IV E	V	4	3121.270
*	3102.301	40	III Er	V	3	3102.404
	3145.35	-	-		3	3145.484
	3126.221	25	IV E	V, Fe	5	3126.319
*	3110.710	30	III Er	Ti, V	?	3110.810
	3145.979	5	V Er	Zr	1	3146.091
	3130.270	25	III E	V	3	3130.380
*	3118.382	30	III Er	V	3	3118.498
	3145.344	10	IV E		3	3145.484
	3133.336	20	III E	V	2	3133.449
*	3125.286	40	III Er		5	3125.399

[Pg 77]

CHROMIUM (24)

The lines of chromium were classified by Catalan,[307] and those which occur in the sun are comprised in the following multiplets:[308] , , , , , , , , , , , .

The ultimate lines , at 4254, 4274, 4289 increase with advancing type.[309] The maximum for subordinate lines[310] is at .

IONIZED CHROMIUM

Of the six multiplets of ionized chromium tabulated by Meggers, Kiess, and Walters,[311] only two are within the measured range of the solar spectrum, but every line in these two multiplets accords satisfactorily in wave-length and intensity with a line in Rowland’s table. The ultimate lines are in the neighborhood of 2800, and are therefore unattainable. The lines, and the solar intensities, are contained in the appended table.

TABLE XIII

Series	Wave-Lenght	Int.	Attribution	Int.	Wave-Lenght
	3328.34	3		1	3328.487
	3336.33	5	Cr	2	3336.477
	3324.06	3			3324.19
	3339.80	10	Co, Cr	3	3339.932
	3347.83	6	Cr	3	3347.970
	3342.58	10	Cr	3	3342.717
	3358.50	10	Ti, Cr	4	3358.649
	3368.04	20	Cr, -	?	3368.193
	3132.04	20	-, Cr	4	3132.169
	3124.97	20	Cr	4	3125.109
	3147.22	5	Cr	3	3147.350
	3120.36	15	Cr, -	3	3120.481
	3136.69	5	Cr, Co	3	3136.822
	3159.10	1		0	3159.225
	3118.65	10	Cr, -	2	3118.764
	3128.68	5	Cr, -	2	3128.819
	3145.07	2		2	3145.251

[Pg 78]

MANGANESE (25)

The lines of manganese are conspicuous in stellar spectra, and all the classified lines[312] within the range of Rowland’s table are found in the solar spectrum, namely the multiplets , , , , , , , , , . The ultimate lines are at 4030, and constitute a conspicuous group in the solar spectrum. They are well seen in the cooler stars, and are progressively strengthened with advancing type.[313] They first appear at . The multiplet, at 4018, 4041, 4055, 4084, etc., has a maximum, according to Menzel,[314] at .

IONIZED MANGANESE

Meggers, Kiess, and Walters[315] give one multiplet of ionized manganese, and this is within the range of Rowland’s table. The multiplet was previously picked out by Catalan[316] as being analogous to the arc multiplet . All the lines can be satisfactorily identified with lines in the solar spectrum, as in the following table.

TABLE XIV

Series	Wave-Lenght	Int.	Cl.	Attribution	Int.	Wave-Lenght
	3441.999	9	V	Mn	6	3442.118
	3474.050	7	V	Mn	2	3474.197
	3460.332	8	V	Mn, -	?	3460.460
	3496.815	4	V	Co, Mn	3	3496.952
	3482.918	7	V	Mn, -		3483.047
	3474.13	6	V	Mn	2	3474.287
	3497.540	6	V	Mn	3	3497.668
	3488.618	8	V	Mn	4	3488.817
	3495.810	8	V	Mn	2	3495.974

[Pg 79]

IRON (26)

The extensive occurrence of the arc lines of iron in the stellar spectrum is well known. The following multiplets[317] have been traced in the solar spectrum, and the corresponding lines are also to be traced in the spectra of the cooler stars: , , , , , , , , , , , , , , , . The iron lines have, in general,[318] a maximum at , but the only ultimate lines which are well shown in stellar spectra, the lines near 4480, increase with advancing type to the end of the sequence.[319]

The following lines are used as criteria of absolute magnitude by Harper and Young:[320] 4202, 4250, 4272 (), 4072 (), 4482 ().

IONIZED IRON

[Pg 80]

The lines of ionized iron are strong in F stars of high luminosity, and are especially conspicuous in the stars which have the c-character. Menzel[321] places the maximum at , and the writer[322] finds it at . The following multiplets, as classified by Russell,[323] occur in the solar spectrum: , , , , , , , , , , , , , , , , , , , , . Doubtfully present are: , , . The ionized iron lines are strengthened, as are other enhanced lines, over sunspots, and many of the fainter components of multiplets are observed only in the spot spectrum.

COBALT (27)

The series relations for the arc spectrum of cobalt[324] have been published by Walters. Cobalt lines are frequent in the solar spectrum, but as the strongest of them lie near 3500, they cannot be traced in the spectra of stars. The following multiplets are certainly identified in the spectrum of the sun: , , , , , , , , , , and . The incompletely observed multiplet is apparently absent from the solar spectrum.

NICKEL (28)

The series relations for nickel are as yet unpublished. The lines appear in great numbers in the solar spectrum, but they are not strong enough to be conspicuous in the spectra of the stars. The line 5476 appears to have a maximum at , indicating either that it is an enhanced line of nickel, or that it is blended with the enhanced line of some other element. The lines 5081, 4714 are strengthened in low temperature stars, and are probably due to neutral nickel. From the solar behavior of the lines of this element,[325] the ionization potential seems to be of the same order as that for cobalt, probably about 8 volts.

COPPER (29)

Copper is represented in the solar spectrum by the ultimate doublet 3273, 3247 (), which is strong. The pair 5700, 5782 () is probably also present. The former lines are too far in the ultra-violet to have been studied in the stars, and the latter are too faint.

ZINC (30)

The principal singlet is at 2138, and has therefore not been observed in stellar spectra. The lines at 4722, 4810, are seen in the stellar sequence, where they appear at , and have a maximum[326] at .

[Pg 81]

Two unclassified lines of ionized zinc are mentioned in Fowler’s Report as lying at 5894, 6214. Neither of these lines can be traced in solar or stellar spectra.

GALLIUM (31)

The occurrence of gallium in stellar spectra is confined to the identification of two solar lines by Hartley and Ramage.[327] The lines in question are at 4033, 4172, and are the ultimate lines of the element (). They are too faint to be studied in the stars.

RUBIDIUM (37)

The ultimate lines of rubidium have been detected in the sunspot spectrum,[328] but they are not found in the spectra of the sun or stars.

STRONTIUM (38)

The element strontium is of great astrophysical importance, owing to the use of its enhanced lines in the estimation of absolute magnitudes. The neutral atom is represented in the sun and stars by the ultimate line () 4607, which is first clearly seen[329] at , and increases progressively in strength with advancing type. It varies with absolute magnitude, being weakened in stars of high luminosity later than . Estimates for the intensity of this line are difficult with small dispersions, as it is blended in cool stars.

IONIZED STRONTIUM

Ionized strontium is represented in stellar spectra by the and the series. The former contains the important absolute magnitude lines 4215, 4077, which are first seen at about , and reach a maximum[330] near . They appear to have “abnormal” intensities in certain stars,[331] and in the stars are often the finest and sharpest lines in the spectrum. This behavior suggests a high-level origin, but “stationary Strontium,” [Pg 82] although suggested by Plaskett[332] as likely to occur, has not yet been observed.

YTTRIUM (39)

Numerous lines of yttrium[333] are found in the solar spectrum. The lines of the ionized atom are somewhat stronger than the lines of the neutral atom. The lines of the neutral element which can be identified in the solar spectrum are contained in the following table.

TABLE XV

Series	Wave-Lenght	Int.	Attribution	Int.	Wave-Lenght
	3620.94	20	Y?	00	3621.110
	3592.91	10	Y	0	3593.040
	3552.69	3		-	-
	4128.32	30		00	4128.46
	4039.83	5	Y	00	4040.013
	4047.65	8	Y		4047.823
	4102.38	20	Y	0	4102.541
	4167.52	10		00	4167.737
	4077.39	20	La, Y	?	4077.498

The multiplets at 4174, etc., and at 4674, etc., and the multiplets, do not appear in the solar spectrum. None of the above lines is strong enough to be seen in the spectra of the stars.

IONIZED YTTRIUM

[Pg 83]

Four of the multiplets attributed to ionized yttrium[334] are satisfactorily identified in the solar spectrum. The wave-lengths and identifications are contained in Table XVI, p. 83. The arrangement is as in Table XI.

TABLE XVI

Series	Wave-Lenght	Int.	Attribution	Int.	Wave-Lenght
*	3710.30	100	Y	3	3710.431
	3832.87	20			3833.026
*	3774.33	50	Y	3	3774.473
	3878.27	4		1	3878.334
	3818.37	10	Y	1	3818.487
*	3788.69	30		2	3788.839
	3600.72	50	Y	3	3600.880
	3548.99	20	Y?	2	3549.151
	3664.59	20	Y	2	3664.760
	3611.05	30	Y, Mg?	2	3611.189
	3584.51	10	Y	2	3584.660
	3628.70	10	Y, Mg?	2	3628.847
	3601.91	20	Y	1	3602.060
	4309.61	20		1	4309.792
	4235.71	6		0	4235.894
	4199.283	3		00	4199.434
	4398.03	15	In zircon *	1	4398.178
	4358.72	8	Y-Zr	0	4358.879
	4422.60	10	Fe, Y	3	4422.741
	5087.42	10	Y?	1	5087.601
	4982.12	3		000	4982.319
	5320.77	1		-	-
	5205.71	10	Y	0	5205.897
	5119.10	3		00	5119.292
	5289.81	2		000	5289.988
	5200.41	8	V	0	5200.590

* But not Zr.

ZIRCONIUM (40)

The ultimate lines of the zirconium atom[335] are all found in the solar spectrum, far into the ultra-violet.

The bands in the spectra of stars of Class are found to correspond with those of ZrO₂, zirconium oxide.[336] A comparison [Pg 84] of the furnace spectrum of zirconium oxide with that of titanium oxide, which produces the characteristic flutings in Class , indicates that titanium oxide persists to lower temperatures.[337] It is of interest to note that the only oxides, other than water, which have been detected in stellar spectra, are those of elements in the fourth column of the periodic table, namely carbon, titanium and zirconium. Probably this has a chemical interpretation. The presence of silicon dioxide SiO₂ has not been detected, although it might be anticipated.

NIOBIUM (41)

Rowland identifies some of the lines associated with niobium in the solar spectrum. The series relations are unknown, and the lines are too faint to be detected in stellar spectra.

MOLYBDENUM (42)

All the ultimate lines of molybdenum are present in the solar spectrum. They are too faint to be detected in the stars. The spectrum has been analyzed into series by Kiess,[338] and by Catalan.[339]

RUTHENIUM (44) RHODIUM (45) PALLADIUM (46)

The strongest lines in the spectra of the three lighter platinum metals are all present in the solar spectrum,[340] but are too faint to be traced in the spectra of stars. Series relations are as yet unknown. The heavier platinum metals, osmium (76), iridium (77), and platinum (78), are not certainly found in the solar spectrum.

SILVER (47)

[Pg 85]

The ultimate () lines of silver are at 3281 and 3383. They are both faintly present in the solar spectrum. The doublet at 4669, 4476 () is also probably present in the spectrum of the sun. The lines cannot be traced in stellar spectra.

TIN (50)

A line of neutral tin was reported by Lunt[341] in the spectrum of Scorpii. Series relations are as yet unknown. In view of the absence of identifications of related lines, the attribution cannot be regarded as very certain. The strongest line in the spectrum of ionized tin is stated by the same investigator to lie at 4585.80. This line is either absent from or exceedingly weak in the solar spectrum.

BARIUM (56)

Neutral barium is not certainly present in stellar spectra. The first two ultimate lines () fall in the red and the ultra-violet respectively, and would therefore escape notice in the stars. No lines of corresponding wave-length appear in Rowland’s table, but they are found in sunspots.[342] The groups are also absent from the solar spectrum.

The strength of the barium lines in the sun has been thought by Russell to be abnormal, and the question has been considered by several investigators.[343][344][345]

IONIZED BARIUM

Ionized barium is represented by the lines which are present, though weak, in the sun, and by the lines, which appear[346] at , and increase in intensity for all cooler stars. The line is at 4555, and its behavior is difficult to trace, as it is much blended.

THE RARE EARTHS (57-71)

The spectra of the rare earths are so rich in lines that spurious identifications with lines in stellar spectra are often likely to occur. Numerous attributions to lanthanum (57), cerium (58), and [Pg 86] neodymium (60) are given in Rowland’s table. The occurrence of some of these elements has also been definitely established in the spectra of certain stars. Kiess[347] has demonstrated the presence of europium (63) and of terbium (65) in Canum Venaticorum. Numerous lines, identified with those of rare earth elements, are reported by Mitchell[348]in the chromospheric spectrum.

If the lines in the chromosphere and the star are indeed derived from the rare earths, the atoms concerned must be at least singly ionized. No series relations have as yet been published for any rare earth element, excepting a short list of relative term values for lanthanum.[349] From analogy with the previous long period it would seem unlikely that the first ionization potential of these atoms can be as great as 13 volts, the value which would be required if the lines have a maximum intensity at .

LEAD (82)

A single line is attributed to lead in Rowland’s table.

RADIUM (88)

Giebeler and Küstner[350] suggested the occurrence of radium lines in the chromosphere. The identification was discussed by Dyson[351] and by Mitchell.[352] In the light of later knowledge it appears improbable that an element so heavy, and terrestrially so rare,[353] would be present in the sun at sufficient heights and in great enough quantity to appear in the flash spectrum. The identification is probably to be regarded as spurious.

ELEMENTS NOT DETECTED IN STELLAR SPECTRA

The table which follows contains a list of elements which are absent, or of doubtful occurrence. The rare earths are omitted from the list.

[Pg 87]

The elements marked “doubtful” in the list are those for which coincidences with very faint solar lines occur.[354] Twelve out of the twenty-nine elements enumerated are halogens, inert gases, or metalloids, and it is significant that all the elements of these groups are absent, with the sole exception of helium.