Part 1

Proceedings of the American Academy of Arts and Sciences.

VOL. 61. NO. 10—JULY, 1926.

ON THE DISTRIBUTION OF INTENSITY IN STELLAR ABSORPTION LINES

BY CECILIA H. PAYNE AND HARLOW SHAPLEY

ON THE DISTRIBUTION OF INTENSITY IN STELLAR ABSORPTION LINES[1]

Footnote 1:

The cost of publication of this research has been met with the help of a grant from the Rumford Fund.

BY CECILIA H. PAYNE[2] AND HARLOW SHAPLEY

Footnote 2:

National Research Fellow.

1. It is unnecessary to emphasize the significance of the form of absorption lines in the study of problems of atomic structure and the physical constitution of stellar atmospheres. There has been an abundance of theoretical work on line contour, but a remarkable scarcity of quantitative observation. The present preliminary study is aimed to meet, in part, the need for measurements on the broad and strong lines in the spectra of stars of various types.

In general the investigation has been based on objective prism spectra, analyzed with a photographically recording microphotometer. The ease with which a photometric scale can be set up on these plates, available throughout the whole length of the spectrum, and essentially independent of the variability of plates and development, is a decided factor in favor of using objective prism spectra. Other advantages include the efficiency of the objective prism spectrograph and its simple operation. The possible disadvantage of lack of purity is not important, at least in the case of the lines discussed in this communication; the extent to which scattered light affects the true contours of the absorption lines is considered below.

That the results from slit spectrographs are in essential agreement with these slitless spectrograms is shown in Figure 1, where microphotometer tracings of spectra from the two sources are shown. Through the courtesy of Professor W. J. Hussey and Professor R. H. Curtiss, of Ann Arbor, some excellent spectrograms made with the single prism spectroscope at the Detroit Observatory have been sent to Harvard for this comparison. The dispersion is practically the same on the Michigan and Harvard plates. The microphotometer records were made under identical conditions for the two sets of spectra, though the presence of comparison lines on the Michigan plates and the narrowness of the spectra made their analysis more difficult.

[Illustration: Figure 1.—Microphotometer tracings made from the spectra of four stars. The names of the stars, and the sources of the analyzed spectra, are as follows: (1) α Canis Majoris (Sirius), Harvard objective prism spectrum, (2) α Lyrae (Vega), slit spectrogram, Detroit Observatory, (3) α Aquilae, slit spectrogram, Detroit Observatory, (4) β Pegasi, slit spectrogram, Detroit Observatory. The violet ends of the spectra are to the left.]

2. The work on the Harvard spectrograms has been carried out by the method that was described in the preliminary report (H.B. 805, 1924). The plates were all made with the sixteen-inch refractor, using two prisms and a special set of apertures. The different apertures provide relative objective areas of 16, 8, 4, 2, and 1, respectively. The apertures are rectangular, and the successive reducing strips are placed perpendicular to the refracting edge of the prism. It is assumed in the discussion that the amounts of light admitted by the apertures are in the same ratio as their areas.

A standard procedure has been adopted in securing the spectrograms. A series of spectra with the several apertures was obtained upon each plate. Focus, clock rate, and exposure time were kept constant over any one series. In general the apertures were used in the order 16, 8, 4, 2, 16. Aperture 1 was omitted in nearly every case, and for a few stars other apertures were also omitted, or found to be useless owing to faintness of the image. Omission of apertures is indicated by notes to Table I.

TABLE I LIST OF PLATES USED ┌────────┬───────────────┬────────┬─────────────────┬─────────────────┐ │ Plate │ Star │Spectral│ Apertures │ Remarks │ │ Number │ │ Class │ │ │ ├────────┼───────────────┼────────┼─────────────────┼─────────────────┤ │MC 20790│α Lyrae │ A0│1, 16a, 8, 4, 2 │Ap. 2 not used │ │ 20797│α Bootis │ K0│1, 16a, 8, 4, 2, │Ap. 1 and 2 not │ │ │ │ │ 16b │ used │ │ 20800│α Aquilae │ A5│1, 16a, 8, 4, 2, │Ap. 1 and 2 not │ │ │ │ │ 16b │ used │ │ 21640│α Cygni │ cA2│16a, 8, 4, 2, 16b│ │ │ 21645│δ Cassiopeiae │ A5│16a, 8, 4, 2, 16b│ │ │ 21646│α Cassiopeiae │ K0│16a, 4, 2, 16b │Ap. 16b not used │ │ 21721│α Aurigae │ G0│16a, 8, 4, 2, 16b│ │ │ 21722│δ Canis Majoris│ cF8│16a, 8, 4, 2, 16b│Ap. 16b not used │ │ 21788│β Orionis │ cB8│16a, 8, 4, 2, 16b│Ap. 16b not used │ │ 21789│ε Orionis │ B0│16a, 8, 4, 2, 16b│Ap. 16b not used │ │ 21802│α Canis Majoris│ A0│8, 16, 4, 2 │ │ └────────┴───────────────┴────────┴─────────────────┴─────────────────┘

The apertured spectra were examined, and any that showed irregularities were rejected. In cases of interference by clouds, whether or not the spectra were visibly impaired, the plates were not measured. Spectra which appeared from experience to be too strong or too weak for satisfactory analysis were also rejected.

3. The present report deals with the spectra of the eleven stars enumerated in Table I. Successive columns contain the plate number, the name of the star, its spectral class, the apertures employed, and remarks.

In addition to the plates enumerated in Table I, the following focus plates were obtained.

┌─────┬───────────────┬────────────────────────┬──────────────────────┐ │Plate│ Star │ Apertures │ Remarks │ ├─────┼───────────────┼────────────────────────┼──────────────────────┤ │21648│α Canis Majoris│16, 4, 4, 4, 4, 4, 4, 4,│Various focus settings│ │ │ │ 4, 4, 16 │ │ │21803│α Canis Majoris│16, 16, 4, 2, 8, 8, 8, │ „ │ │ │ │ 8, 8, 16 │ │ └─────┴───────────────┴────────────────────────┴──────────────────────┘

4. All the plates have been analyzed by means of the Moll thermoelectric microphotometer of Harvard Observatory,[3] which furnishes a photographic record of the plate density. The adjustments of this instrument were made with several ends in view. The analyzing beam of light was kept as narrow as possible, so that no integrating effect should enter into the final result. At the same time it was desired that the total galvanometer deflection—the quantity on which the measures depend—should be of reasonable size; otherwise the errors of measurement would become proportionately too great. Some of the analyzed spectra, especially those of fainter stars, were so narrow that the slit admitting the analyzing beam had to be considerably shortened. This cut down the total light transmitted in the same proportion, and to keep the deflections of the galvanometer of reasonable size, a wider slit, and therefore a wider analyzing beam, had to be used. A compromise was worked out, for each plate, between a narrow analyzing beam and a reasonable galvanometer deflection.

Footnote 3:

This instrument was purchased with the aid of the Rumford Fund of the American Academy of Arts and Sciences and the Bache Fund of the National Academy of Sciences.

Special precautions were taken to secure the greatest uniformity of conditions possible throughout the analysis of each series of spectra of any one star. At first it was hoped that the whole series of plates could be analyzed under exactly uniform conditions. Owing to the narrowness of some of the spectra, however, it was necessary to introduce the modifications indicated in the preceding paragraph. Even if all the spectra had been analyzed under precisely the same conditions, experience showed that direct intercomparison between different stars would have been impossible, owing to varying amounts of fog on different plates.

The instrumental settings were made and recorded at the beginning of the analysis of each series of spectra, and when possible were kept untouched throughout the process. The voltage supplying the analyzing beam, and the temperature of the room, were recorded at the beginning and end of each analysis, since both these factors may affect the galvanometer deflection.

TABLE II ┌─────────────┬─────────────┬─────────────┬─────────────┬─────────────┐ │Plate Number │ Star │ Slit Width │ Slit Length │ Total │ │ │ │ mm. │ mm. │ Deflection │ │ │ │ │ │ scale div. │ ├─────────────┼─────────────┼─────────────┼─────────────┼─────────────┤ │ MC 20790│ α Lyr │ .25 │ 6.0 │ 77 │ │ 20797│ α Boo │ .10 │ 7.0 │ 35 │ │ 20800│ α Aql │ .10 │ 7.0 │ 42 │ │ 21640│ α Cyg │ .10 │ 5.5 │ 30 │ │ 21645│ δ Cas │ .10 │ 4.0 │ 35 │ │ 21646│ α Cas │ .40 │ 3.0 │ 45 │ │ 21648│ α CMa │ .25 │ 4.0 │ 67 │ │ 21721│ α Aur │ .25 │ 5.0 │ 62 │ │ 21722│ δ CMa │ .25 │ 5.0 │ 74 │ │ 21788│ β Ori │ .25 │ 6.5 │ 91 │ │ 21789│ ε Ori │ .25 │ 6.0 │ 69 │ │ 21802│ α CMa │ .25 │ 6.0 │ 90 │ │ 21803│ α CMa │ .25 │ 6.0 │ 85 │ └─────────────┴─────────────┴─────────────┴─────────────┴─────────────┘

The instrumental settings for the different plates analyzed are summarized in Table II. Successive columns contain the plate number, the name of the star, the width in millimeters of the slit producing the analyzing beam, and the total length of that slit. The effective width of the slit producing the analyzing beam differs somewhat from the quantity recorded in the third column. For the three entries .10, .25 and .40, the corresponding effective slit widths are .101, .262, and .385 mm., respectively. The corresponding widths in millimeters of the analyzing beam are 0.010, 0.026, and 0.038, respectively, which are approximately equivalent to .02, .05, and .08 angstroms at Hδ for the dispersion used in this series of plates.

5. _Measurement of microphotometer tracings._—In addition to the line representing the density of the image at different points along the spectrum, reference marks were inserted by registering a line for “darkness,” by interposing an opaque screen in the path of the analyzing beam, and a line for “clear film,” by passing the beam through the plate background close to the spectrum, though not close enough to bring it within range of disturbing photographic effects due to the image.

The microphotometer tracings on paper prints were measured with respect to the reference marks. Lines, representing “darkness” and “clear film,” were ruled from end to end of the tracing, and across the absorption lines a curve was drawn, completing the curve of the neighboring continuous background. For early type stars this background curve can be drawn without ambiguity; but when the spectrum is rich in lines, the course of the unlined continuous background is largely a matter of judgment.

[Illustration: Figure 2.—Diagram of an absorption line, as registered by the microphotometer, showing the method of measuring the tracings. The quantities n (“darkness” to “background curve”), _m_ (“background curve” to “line”), and _l_ (“line” to “clear film”) were measured at intervals of five scale divisions, indicated by the vertical lines.]

The quantities measured on the microphotometer tracings are best described by a diagram. Figure 2 represents a wide absorption line, and the various distances that were measured in analyzing such a line. The measures were all made with a half-millimeter réseau scale photographed upon glass, which was laid directly upon the tracing.

6. _Method of reduction._—The spectra obtained with various apertures provide, as was pointed out in Harvard Bulletin 805, several measures of the intensity at any point of an absorption line. The intensity is compared, in the present paper, with the intensity that the continuous background would have at the same point if the line were not present, which is assumed to be represented by the “background curve” drawn across the absorption line.

The method has the advantage of making a determination separately for each wave length. The difficulties introduced by the varying color sensitivity of the photographic plate are thus avoided. It has, however, the disadvantage that the measured quantity depends to some extent upon the individual judgment of the investigator in drawing the “background curve”—a matter that is simple for Classes B and A, but may prove serious for second-type stars.

The intensity differences, background _minus_ line, were determined for several points by direct measurement. The distances, _n_ and _m_ + _n_ for the same wave length in all the spectra of any one series, were obtained from the microphotometer tracings, and were separately plotted against the logarithms of the corresponding apertures. Smooth curves were drawn, joining the plotted points for any one wave length, as in Figure 3. The drawing of the curves is somewhat simplified by considering together several for the same star, remembering that the sections lying between the same abscissae should be roughly parallel. These various curves represent different sections of the familiar characteristic curve for photographic blackening, the logarithm of the aperture being here substituted for the more usual logarithm of the intensity. Differences of intensity between line and background are then readily obtained by interpolating values of n on the curve connecting _m_ + _n_ and aperture, and similarly by interpolating values of _m_ + _n_ on the curve connecting aperture with measured values of _n_. Each spectrum thus furnished at least one, and sometimes two, values for the intensity difference at any point.

It will be seen from Table IX that for several stars two mean values of line intensity are given, one being the mean of all the measures, and the other the “selected mean.” The selected means are obtained by using only points from the more linear portions of the characteristic curve, and by rejecting values derived from microphotometer tracings of exceptional total deflection.

[Illustration: Figure 3.—Relation between galvanometer deflection (representing plate density) and aperture (representing light intensity), from measures of the microphotometer tracings made from the apertured spectra of α Lyrae, MC 20790. Ordinates are galvanometer deflections in scale divisions, abscissae are (above) apertures, (below) logarithms of apertures. Smooth curves are drawn joining the points corresponding to the same wave length, for the three apertures represented.]

The intensity drop from background to line is thus obtained in the form log. intensity of background _minus_ log. intensity of line. The change in intensity may readily be converted into stellar magnitudes by dividing the difference of the logarithms by 0.4.

7. The results embodied in the present paper differ so materially from those of some previous workers, that it is of especial interest to examine the accuracy that may be claimed for each stage of the work, and the weight that may be assigned to the results, (Cf. Harvard Monograph No. 1, p. 51). Three stages of the investigation should be considered separately; the plates, (a and b), the microphotometer records (c), and the measures (d).

a. _Accuracy of plates._—A qualitative test of the reliability of the spectra used is made by examining the reproduction of line detail throughout the whole series made for one star. Figure 4 shows the microphotometer tracings for a portion of the spectrum of δ Canis Majoris, made with apertures 16, 8, and 4. Figure 5 shows a similar series of tracings made from spectra of α Persei, taken with apertures 16, 8, 4, and 2. It may be seen that the reproduction of line detail is satisfactorily faithful, although a few spurious details can be detected.

[Illustration: Figure 4.—Microphotometer tracings made from a portion of the Harvard apertured objective prism spectra of δ Canis Majoris, MC 21722. The different apertures used are indicated on the left margin. A few of the more important lines are marked on the lower edge of the diagram.]

[Illustration: Figure 5.—Microphotometer tracings made from a portion of Harvard apertured objective prism spectra of α Persei. The different apertures used are indicated on the left margin. A few of the more important lines are marked on the lower edge of the diagram.]

The best quantitative test of the reliability of the spectra used in this work is the consistency of the numerical results obtained from the different members of a series. From Table IX it may be seen that the residuals very seldom exceed 0.2 m., while the majority are less than 0.05 m.

In specific criticism of the use of the objective prism in line photometry, it has been claimed that the intensity at the line center is affected, and measurably increased, by stray light, and that such an effect is inappreciable for slit spectra. The results of the present work, which deals with lines of various depths, widths, and qualities, are relevant to a discussion of the question, so far as it concerns objective prism spectra.

Presumably the effects of stray light must be greatest in the immediate neighborhood of the stronger portions of the spectrum, and fall off at greater distances from the more heavily exposed parts of the plate. Skylight contributes mainly to plate fog, is uniform over the spectrum and its vicinity, and is eliminated by the use of the line representing “clear film” as a reference base in measuring the tracings.

If the effects of stray light are of importance in the immediate vicinity of the continuous spectrum, they will presumably affect all absorption lines to some extent, and will in particular be greatest for narrow lines. The effects should also be greater for heavily exposed spectra than for the more lightly exposed spectra of the same star. Further, the effects of stray light should appear not only within absorption lines, but also alongside of the spectrum on either edge.

A comparison of the results for δ Cassiopeiae and α Aquilae, both stars of Class A5 (see Table X) shows that the observed line depth is not, in this case at least, a function of line width. The lines of δ Cassiopeiae are both narrower and deeper (that is, they show greater contrast with the background) than those of α Aquilae. The same is true of δ Canis Majoris and Capella; the lines of the former are both narrower and deeper.

The results for apertures 16, 8, 4, and 2 have been compared for all the stars discussed, and the intensity differences between line and background are not appreciably smaller for the larger apertures, which would be the case if stray light were an important factor. Indeed, for α Cygni and β Orionis an opposite effect is shown.

[Illustration: Figure 6.—Microphotometer tracing taken across the spectra of Sirius (MC 21647) made with the different apertures indicated along the upper margin.]

To examine the distribution of light at the edges of the spectrum, a microphotometer tracing was made by running MC 21803 (Sirius) through the instrument in a direction perpendicular to the length of the spectra. The resulting tracing is reproduced in Figure 6. Effects of stray light are not to be found, except for the strongest spectrum. Evidently such effects depend on the heaviness of the exposure, but are not simply proportional to it; they may indicate mainly the “creep” of the overexposed image rather than stray incident light. The point of exposure beyond which stray light begins to be a disturbing factor would have to be determined separately for each plate. In no case is it likely to involve any but the strongest spectrum, and spectra that are strong enough to exhibit the effect are for other reasons not usable. Such measures, in fact, are omitted in deriving the “selected mean,” and it would seem that effects of stray light are thus eliminated, while an upper limit may be assigned to their magnitude by comparing the mean derived from all the measures with the selected mean in Table IX. Stray light, although certainly present to some degree, is therefore probably not an important factor in affecting the results of line photometry with the present objective prism spectra.

[Illustration: Figure 7.—Microphotometer tracing taken across the spectrum of Vega made with the single prism spectrograph of the Detroit Observatory.]

Figure 7 represents the result of a similar test made by taking a microphotometer tracing across an excellent slit spectrogram of Vega that was made with the spectrograph at Ann Arbor. There are no traceable effects of stray light outside the edges of the spectrum, but on the contrary there is a distinct drop in intensity, which may partly be due to an Eberhard Effect. The objective prism spectrum therefore appears to have a slight advantage in this regard, judging from a comparison of Figures 6 and 7.

b. _Effect of focus._—The effect of poor focus in blurring absorption lines suggests that this factor may enter into the accuracy of the results. It is not possible, in a stellar spectrograph, when working with flat plates, to keep all parts of the spectrum in focus at the same time. Two plates of Sirius were taken for the purpose of examining the magnitude of the effect. The apertures used, and the focus settings, were as follows.

PLATE MC 21648 Spectrum 1a 3a 3b 3c 3d 3e 3f 3g 3h 3i 1b Aperture 16 8 8 8 8 8 8 8 8 8 16 Setting 17.2 17.2 17.4 17.6 17.8 18.0 17.0 16.8 16.6 17.2 17.2

PLATE MC 21803 Spectrum 1a 1b 2e 3 4 2c 2d 2b 2a Aperture 16 16 8 4 2 8 8 8 8 Setting 16.6 16.6 16.6 16.6 16.6 16.2 16.4 16.8 17.0

From MC 21648 it is possible to obtain a qualitative estimate of focus effects; MC 21803, including spectra taken with all four apertures, furnishes a quantitative estimate of the magnitude of the focus errors. Microphotometer tracings were made, under uniform conditions, of the spectra of each of the focus plates, and measures were made at the centers of the lines only.

For the plate MC 21648, the observing record book contains the entry: “Frost in center of prism at close.” Apparently the frosting resulted in a gradual decrease in the intensity of successive spectra, which is shown, when the spectra are arranged in the order in which they were photographed, by a gradual decrease in _n_, a quantity that should remain constant for the same aperture, since the edges of the spectrum, the portion where focus would affect the intensity, are not crossed by the analyzing beam of the microphotometer. The progressive change in _n_ is shown in Table III.

TABLE III Spectrum 3a 3b 3c 3d 3e 3f 3g 3h 3i _n_ at Hβ 13 (12) 13 15 16 16 17 18 17 Hγ 8 8 8 11 9 10 11 10 11 Hδ 11 9 10 12 12 14 12 13 15 Hε 16 14 17 15 18 19 19 19 20 K 19 17 19 18 20 22 21 22 23 Hζ 27 25 28 29 29 31 31 31 33

That the change in _n_ is progressive and not due to change of focus is shown by arranging the columns in the order of focus setting, 3h, 3g, 3f, 3i, 3a, 3b, 3c, 3d, 3e. No regular change in _n_ is then evident.

The total deflection of the galvanometer is satisfactorily constant for all the microphotometer records of the spectra on MC 21648, excepting 3i, which is rejected for a large voltage drop (0.2 volts), producing a reduction of four scale units in total deflection. Spectrum 3i is omitted from further discussion. The quantity _l_ must be corrected for change in _n_, and this may be done by adding to _l_ a quantity equal to the increase in _n_, since the observed change in _n_, which should be constant, corresponds to a shift of the whole spectrum, tending to decrease _l_. The change in _l_, the distance from “clear film” to line center, as measured on the microphotometer tracings, with changing focus, is shown in Table IV. Values of _l_ are corrected.