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Title: On the distribution of intensity in stellar absorption lines
Author: Cecilia Payne-Gaposchkin
Harlow Shapley
Release date: April 20, 2025 [eBook #75914]
Language: English
Original publication: Cambridge: Harvard, 1926
Credits: Richard Tonsing and the Online Distributed Proofreading Team at https://www.pgdp.net (This book was produced from images made available by the HathiTrust Digital Library.)
*** START OF THE PROJECT GUTENBERG EBOOK ON THE DISTRIBUTION OF INTENSITY IN STELLAR ABSORPTION LINES ***
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.
TABLE IV
Spectrum 3h 3g 3f 3a 3b 3c 3d 3e
Focus 16.6 16.8 17.0 17.2 17.4 17.6 17.8 18.0
_l_ at Hβ 33 36 40 47 49 49 48 43
Hγ 37 38 39 47 47 50 46 47
Hδ 32 35 31 40 41 45 43 40
Hε 24 26 27 33 33 35 37 31
K 42 44 42 50 50 52 54 47
Hζ 12 14 13 19 18 22 24 20
The line depth is the greatest, and the focus presumably the best, where
_l_ is smallest. It appears that spectrum 3h is at best focus.
Table V contains the values of _m_ for different focus settings, in the
same form as Tables III and IV. The quantity _m_ requires no correction
for change of _n_. For all the spectra on this plate the K line appears
double. The last line of Table V contains the distance, in scale
divisions, between the two maxima of the K line on the microphotometer
tracing. One scale division corresponds approximately to one Angstrom.
TABLE V
Spectrum 3h 3g 3f 3a 3b 3c 3d 3e
Setting 16.6 16.8 17.0 17.2 17.4 17.6 17.8 18.0
_m_ at Hβ 16 16 14 13 13 12 9 11
Hγ 19 18 18 16 15 14 12 13
Hδ 22 20 20 19 18 17 15 16
Hε 24 22 20 21 22 21 21 19
K 3 3 2 2 2 2 2 2
Hζ 24 23 23 24 25 23 29 28
Width of K 4 4 5 5 7 6.5 9 9
The data of Table V, and the changing width of the K line (thus shown to
be an effect of focus) indicate 3h as being the best focussed of the
nine spectra. This can also be seen visually from the plate.
The focus plate MC 21803 was similarly analyzed and measured. No
progressive weakening of the spectra is shown by this plate, and the
measures are therefore uncorrected. For the same plate Table VI shows
the change of _l_ with focus setting, in the same form as Table IV.
TABLE VI
Spectrum 2c 2d 2e 2b 2a
Setting 16.2 16.4 16.6 16.8 17.0
_l_ at Hβ 51 52 51 54 53
4481 77 78 79 79 81
Hγ 54 55 56 55 56
Hδ 47 48 51 50 50
Hε 39 39 42 43 41
K 62 64 65 65 64
Hζ 22 26 28 28 26
Hη 8 10 12 12 8
Hθ 4 5 4 6 2
Table VII is in the same form as Table V, and represents the change of
_m_ with changing focus. Evidently Spectrum 2c is at best focus.
TABLE VII
Spectrum 2c 2d 2e 2b 2a
Setting 16.2 16.4 16.6 16.8 17.0
_m_ at Hβ 22 22 21 20 19
4481 3 3 2 2 2
Hγ 24 24 23 23 25
Hδ 28 27 26 27 26
Hε 31 31 30 28 30
K 6 5 5 4 4
Hζ 36 33 34 33 34
Hη 32 31 30 30 31
Hθ 20 19 20 19 19
By the use of the four apertured spectra that occur on MC 21803 it is
possible to evaluate the differences of intensity, produced by the
change of focus, directly in stellar magnitudes. The method used in
deriving the intensities is the one employed in compiling Table IX. The
intensities at the centers of the lines of the various spectra are
summarized in Table VIII. It appears that Spectrum 2c is at best focus
for lines at either end of the spectrum, and that the curve of best
focus moves towards 2b for intermediate lines. The effect is what would
have been anticipated on general grounds. The magnitude of the effect is
satisfactorily small, as may be seen by comparing the differences in
Table VIII with the residuals in Table IX. Errors arising from bad
focus, while they are of appreciable size, do not exceed the errors due
to other causes. If the spectra to be analyzed appear upon visual
examination to be in good focus, they will probably not give results
impaired by serious focus error.
[Illustration: Figure 8.—Microphotometer tracings made from Harvard
objective prism spectra of Sirius, MC 21648, to illustrate the effects
of focus. Analyses are shown of the five lines indicated on the left
margin, for the focus settings given above. The best focus is at 16.8;
the short lines below the absorption minima indicate the change in line
depth with changing focus. The doubling of the K line, and the
increasing distance between the components, is a noticeable effect of
focus.]
Figure 8 shows, for MC 21648, the lines Hβ, Hγ, Hδ, Hε, and K, for four
out of the nine focus settings. The change in line depth, and the
blunting of the intensity curve, are at once apparent.
TABLE VIII
Spectrum 2c 2d 2e 2b 2a
Setting 16.2 16.4 16.6 16.8 17.0
Hβ .53 .53 .51 .49 .47
4481 .13 .13 .09 .09 .09
Hγ .60 .59 .60 .60 .63
Hδ .63 .65 .65 .66 .62
Hε .62 .62 .66 .62 .65
K .15 .14 .13 .12 .10
c. _Accuracy of microphotometer records._—As was pointed out in Harvard
Bulletin 805, the width of the analyzing beam, which is not in any case
greater than one-tenth of an Angstrom, is such that no smoothing effect
need be considered at the line center.
In a few cases the same line of the same spectrum was registered twice.
The measures made upon the two tracings were always satisfactorily
accordant.
[Illustration: Figure 9.—Test of the consistency of spectra taken with
different apertures.]
Ordinates are distance from “clear film” to “line center” taken from
microphotometer tracings of spectra of α Aquilae, MC 20800. Abscissae
are the ratio (_l_ + _m_ for one aperture)/(_l_ + _m_ for twice the
aperture). The fact that the points lie on a smooth curve indicates that
the results are satisfactorily consistent.
The consistency of the results given by the tracings of several spectra
of the same star, when photographed with different apertures, may be
examined by means of the plot shown in Figure 9. Ordinates are values of
_l_ + _m_. Abscissas are values of the ratio
((_l_ + _m_) for one aperture)/((_l_ + _m_) for twice the aperture).
It is evident that if the points thus derived fall on a smooth curve,
the results derived from different tracings of the same spectrum will be
mutually consistent. The method of interpolation described in Section 6
may therefore be used in deriving the differences of intensity between
line and background.
If the method of Section 6 is to be successfully applied, it is
essential that the total range (“darkness” to “clear film”) shall be
uniform for a single series of tracings. In general the variations in
total range do not exceed three or four scale units, but, for some
spectra, occasional changes of eight or ten units have occurred,
generally owing to changes of voltage or room temperature.
Under these circumstances, it has been thought best not to attempt to
apply any correction for variations in total range, but to reject from
the “selected mean” readings from spectra that gave very discordant
total ranges.
d. _Accuracy of measures._ In comparison with the errors of the plates
and of the microphotometer tracings, the errors in the measurement of
the records are of relative unimportance. The chief difficulty, as
mentioned above, is that of drawing from fiducial points the reference
lines representing the continuous background and the “clear film.” The
error thus introduced may occasionally amount to one millimeter, or two
divisions of the scale.
It is sometimes difficult to decide upon the position of the center of a
line, especially when it is wide, without a sharp maximum. This may lead
to large residuals for measures on the wings, especially for such lines
as Hε and Hζ.
8. The results of the investigation are given in Table IX, which
contains, in successive columns, the name of the line, the wave length,
expressed to the nearest Angstrom, the mean value of the difference of
intensity, background _minus_ line, expressed in stellar magnitudes, the
residuals, the “selected mean” value of the same intensity difference
(see Section 6) and its residuals. The stars are mentioned at the
beginnings of their respective records, and are arranged in order of
plate number. In the case of stars for which no “selected mean” is
quoted, all the values used for the mean conform to the criterion for
“selected mean.”
TABLE IX
DIFFERENCES OF INTENSITY, BACKGROUND _minus_ LINE
┌───────────┬──────┬──────────┬────────────────────┬──────────┬───────────────┐
│ Plate and │ Wave │ Mean │ Residuals │ Selected │ Residuals │
│ Star │Length│Intensity │ │ Mean │ │
│ │ │Difference│ │Difference│ │
├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤
│MC 20790 │4877 │ .11│1, _4_, 4 │ .11│_4_, 4 │
│α Lyrae │4872 │ .23│2, _3_, 2 │ .23│_3_, 2 │
│ │4866 │ .49│_2_, 1, 1 │ .50│ │
│ │4861 │ .95│_10_, 0, 7, 5 │ .95│ │
│ │Hβ │ │ │ │ │
│ │4856 │ .73│2, _3_, 2, _3_ │ .73│_3_, 2 │
│ │4851 │ .35│_5_, 5, 2, _3_ │ .38│2, _1_ │
│ │4846 │ .17│_5_, 3, 3, 0 │ .19│1, 1, _2_ │
│ │4840 │ .07│_2_, 0, 3, _2_ │ .07│0, 3, _2_ │
│ │4358 │ .11│_6_, _9_, 6, 6, 1 │ .10│_8_, 7 │
│ │4354 │ .23│_11_, _1_, 9, 4 │ .27│_5_, 5 │
│ │4349 │ .45│_15_, 0, 15, 2 │ .52│_7_, 8 │
│ │4345 │ .83│8, _3_, 19, _8_ │ .86│_6_, 16, _11_ │
│ │4340 │ 1.43│_6_, 19, _6_, _3_, │ 1.62│ │
│ │Hγ │ │_3_ │ │ │
│ │4336 │ .92│8, _17_, 5, 3 │ .92│8, _17_, 5, 3 │
│ │4331 │ .51│_19_, 4, _11_, 14, │ .55│0, _15_, 10, 7 │
│ │ │ │11 │ │ │
│ │4327 │ .25│_8_, _5_, _5_, 15, │ .29│_9_, _9_, 11, 8│
│ │ │ │12, _10_ │ │ │
│ │4322 │ .14│2, _4_, _4_, 11, 8, │ .17│_7_, _7_, 8, 5 │
│ │ │ │_7_ │ │ │
│ │ │ │ │ │ │
│ │4116 │ .13│_3_, 4, 9, _8_ │ .19│_2_, 3 │
│ │4112 │ .32│_10_, 3, 8 │ .37│_2_, 3 │
│ │4109 │ .60│_15_, 2, 12 │ .67│_5_, 5 │
│ │4105 │ .92│_17_, 18, _17_, 13, │ .92│18, _17_ │
│ │ │ │5 │ │ │
│ │4102 │ 1.60│0, 22, _15_, _5_ │ 1.82│ │
│ │Hδ │ │ │ │ │
│ │4098 │ 1.11│ │ 1.11│ │
│ │4095 │ .72│_17_, 8, 8 │ .80│0, 0 │
│ │4091 │ .33│_1_, 7, _1_, _3_ │ .36│4, _4_ │
│ │4088 │ .21│_6_, _1_, _4_, 9 │ .22│_2_, _5_, 8 │
│ │4084 │ .13│_6_, _3_, _3_, 12 │ .15│_5_, _5_, 10 │
│ │ │ │ │ │ │
│ │3986 │ .11│_1_, 1 │ .11│_1_, 1 │
│ │3983 │ .21│_4_, 1, _6_, 9, 6 │ .23│_1_, _8_, 7, 4 │
│ │3980 │ .45│_10_, 0, _5_, 7, 10 │ .48│_3_, _8_, 4, 7 │
│ │3976 │ .73│_26_, 7, 14, 4 │ .80│ │
│ │3973 │ 1.08│_6_, 5, _3_, 2 │ 1.17│ │
│ │3970 │ 1.68│_8_, 7 │ 1.60│ │
│ │Hε │ │ │ │ │
│ │3967 │ 1.17│ │ │ │
│ │3964 │ .70│_13_, _8_, 20 │ .62│ │
│ │3960 │ .56│_21_, 4, 14, 4 │ .65│_5_, 5 │
│ │3957 │ .28│_11_, 2, _3_, 12 │ .32│_2_, 7, 8 │
│ │3954 │ .13│_3_, _3_, _1_, 7 │ .13│_3_, _3_, _1_, │
│ │ │ │ │ │7 │
│ │ │ │ │ │ │
│ │3936 │ .05│0, 0 │ .05│0, 0 │
│ │3933 K│ .23│_1_, _3_, _3_, 7 │ .23│1, _3_, _3_, 7 │
│ │3930 │ .11│1, _4_, _4_, 4, 4 │ .11│1, _4_, _4_, 4,│
│ │ │ │ │ │4 │
│ │ │ │ │ │ │
│ │3899 │ .55│5, 5, 2, 0 │ .50│ │
│ │3895 │ .76│1, _1_, 1, _1_ │ .77│ │
│ │3892 │ 1.03│4, _3_ │ 1.07│ │
│ │3889 │ 1.42│ │ │ │
│ │Hζ │ │ │ │ │
│ │3887 │ 1.10│ │ 1.10│ │
│ │3884 │ .78│_3_, 2, _3_, 2 │ .75│ │
│ │3880 │ .43│_1_, _1_, _1_, 2 │ .42│ │
│ │ │ │ │ │ │
│ │3845 │ .62│ │ │ │
│ │3842 │ > .75│ │ │ │
│ │3839 │ > .75│ │ │ │
│ │3835 │ > .75│ │ │ │
│ │Hη │ │ │ │ │
│ │3832 │ .75│ │ │ │
│ │3829 │ .25│ │ │ │
│ │3826 │ .16│ │ │ │
├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤
│MC 20797 │4340 │ .54│_2_, 1, 1 │ │ │
│ │Hγ │ │ │ │ │
│α Bootis │4227 │ 1.34│2, 2, _3_ │ │ │
│ │Ca │ │ │ │ │
│ │4215 │ .50│_7_, 8 │ │ │
│ │Sr+ │ │ │ │ │
│ │4101 │ .74│_2_, 3, _2_ │ │ │
│ │Hδ │ │ │ │ │
├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤
│MC 20800 │4877 │ .00│0, 0 │ .00│0, 0 │
│α Aquilae │4872 │ .12│_5_, 5 │ .12│_5_, 5 │
│ │4866 │ .36│_6_, 6 │ .30│ │
│ │4861 │ .71│_1_, 1 │ .70│ │
│ │Hβ │ │ │ │ │
│ │4856 │ .45│_5_, 5 │ .45│_5_, 5 │
│ │4851 │ .20│_5_, 5 │ .20│_5_, 5 │
│ │4846 │ .15│_3_, 2 │ .15│_3_, 2 │
│ │4840 │ .09│_7_, 8 │ .09│_7_, 8 │
│ │ │ │ │ │ │
│ │4363 │ .06│_1_, 1 │ .06│_1_, 1 │
│ │4358 │ .11│_4_, 4 │ .11│_4_, 4 │
│ │4354 │ .16│_4_, 4 │ .16│_4_, 4 │
│ │4349 │ .21│_4_, 4 │ .21│_4_, 4 │
│ │4345 │ .39│10, _9_ │ .49│ │
│ │4340 │ .81│1, _1_ │ .82│ │
│ │Hγ │ │ │ │ │
│ │4336 │ .39│10, _9_ │ .49│ │
│ │4331 │ .21│_4_, 4 │ .21│_4_, 4 │
│ │4327 │ .16│_4_, 4 │ .16│_4_, 4 │
│ │4322 │ .07│0, 0 │ .07│0, 0 │
│ │4318 │ .01│1, _1_ │ .01│1, _1_ │
│ │ │ │ │ │ │
│ │4116 │ .03│4, _3_ │ .03│4, _3_ │
│ │4112 │ .10│5, _5_ │ .10│5, _5_ │
│ │4109 │ .23│_7_, 8 │ .23│_7_, 8 │
│ │4105 │ .46│6, _6_ │ .40│ │
│ │4102 │ .71│1, _1_ │ .70│ │
│ │Hδ │ │ │ │ │
│ │4098 │ .50│5, _5_ │ .50│5, _5_ │
│ │4095 │ .23│7, _6_ │ .17│ │
│ │4091 │ .10│5, _5_ │ .10│5, _5_ │
│ │4088 │ .01│1, _1_ │ .01│1, _1_ │
│ │ │ │ │ │ │
│ │3986 │ .20│ │ .20│ │
│ │3983 │ .25│0, 0 │ .25│ │
│ │3980 │ .32│_2_, 3 │ .30│ │
│ │3976 │ .43│_3_, 4 │ .40│ │
│ │3973 │ .81│1, _1_ │ .82│ │
│ │3970 │ > 1.50│ │ > 1.50│ │
│ │Hε │ │ │ │ │
│ │3967 │ .79│_1_, 1 │ .78│ │
│ │3964 │ .48│_13_, 14 │ .35│ │
│ │3960 │ .25│_12_, 13 │ .17│ │
│ │3957 │ .12│_2_, 3 │ .10│ │
│ │3954 │ .02│ │ .02│ │
│ │ │ │ │ │ │
│ │3942 │ .15│ │ .15│ │
│ │3939 │ .22│_2_, 3 │ .20│ │
│ │3936 │ .53│_3_, 4 │ .50│ │
│ │3933 K│ .79│_3_, 2 │ .82│ │
│ │3930 │ .51│_1_, 1 │ .50│ │
│ │3927 │ .07│5, _5_ │ .12│ │
│ │3924 │ .05│ │ .05│ │
├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤
│MC 21640 │4866 │ .07│_7_, _5_, 0, _7_, │ .07│0, 0, 0 │
│ │ │ │10, 0, 0 │ │ │
│α Cygni │4861 │ .33│2, 4, _3_, _1_, _3_,│ .32│0, 0 │
│ │Hβ │ │_1_, 2 │ │ │
│ │4856 │ .18│4, _3_, _1_, 2, _3_,│ .16│1, _1_, 1 │
│ │ │ │_1_ │ │ │
│ │ │ │ │ │ │
│ │4345 │ .11│1, 1, 1, _1_, _1_ │ .10│0, 0 │
│ │4340 │ .63│_1_, 2, _16_, 4, 17,│ .67│_2_, 3 │
│ │Hγ │ │_16_, 2, 7 │ │ │
│ │4336 │ .21│1, _1_, 1, _1_ │ .21│1, _1_ │
│ │ │ │ │ │ │
│ │4105 │ .16│9, 1, _6_, 4, _4_, │ .11│_1_, 1, _1_ │
│ │ │ │_6_ │ │ │
│ │4101 │ .63│17, _3_, _16_, 2, 2 │ .56│_8_, 9 │
│ │Hδ │ │ │ │ │
│ │4098 │ .37│13, _2_, _7_, 0, _5_│ .31│_1_, 1 │
│ │ │ │ │ │ │
│ │3973 │ .25│_5_, 5, 5, 0, _5_, │ │ │
│ │ │ │0, 7, 2, _5_, 0, _5_│ │ │
│ │3970 │ .70│15, 5, _5_, _5_, 22,│ .66│_1_, 1, _1_, 1 │
│ │Hε │ │_8_, _5_, _3_, _5_, │ │ │
│ │ │ │_3_ │ │ │
│ │3967 │ .46│24, _4_, _19_, 14, │ .34│_7_, _2_, 8 │
│ │ │ │_1_, _4_, 16, _14_, │ │ │
│ │ │ │_16_, 4, 1 │ │ │
│ │3936 │ .10│20, 0, _3_, _5_, │ .06│_1_, 1 │
│ │ │ │_5_, 0, 2, _3_, _3_ │ │ │
│ │3933 K│ .54│13, 1, _7_, 1, _10_ │ .52│3, _5_, 3 │
│ │3933 │ .37│8, _7_, _7_, _5_, 8,│ .35│_3_, 2 │
│ │ │ │8, 0, _10_ │ │ │
├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤
│MC 21645 │4877 │ .32│_15_, 15 │ .47│ │
│δ │4872 │ .42│ │ .42│ │
│Cassiopeiae│ │ │ │ │ │
│ │4866 │ .72│_2_, 3 │ │ │
│ │4861 │ 1.49│_7_, _7_, 23, _7_ │ │ │
│ │Hβ │ │ │ │ │
│ │4856 │ .72│_17_, 18 │ .90│ │
│ │4851 │ .34│_9_, _7_, 16 │ .50│ │
│ │4846 │ .13│_1_, _3_, 4 │ .17│ │
│ │ │ │ │ │ │
│ │4354 │ .31│4, _14_, _16_, 6, 6,│ .31│_16_, 6, 9 │
│ │ │ │9, 9, _4_ │ │ │
│ │4349 │ .45│5, _13_, 12, 7, 5, │ .45│_13_, 7, 5 │
│ │ │ │5, _23_ │ │ │
│ │4345 │ .81│1, _1_, 24, _6_, │ .75│5, 0, _5_ │
│ │ │ │_11_, 16, _21_ │ │ │
│ │4340 │ 1.46│4, 9, _4_, 9, _16_ │ │ │
│ │Hγ │ │ │ │ │
│ │4336 │ .84│33, 18, _9_, _14_, │ .86│16, _16_ │
│ │ │ │_9_, _19_ │ │ │
│ │4331 │ .55│20, _18_, _5_, 7, │ .50│_13_, 12, 0 │
│ │ │ │_5_, 5, _3_ │ │ │
│ │4327 │ .32│20, _15_, _2_, 13, │ .32│_15_, 13, 3 │
│ │ │ │3, 0, _17_ │ │ │
│ │ │ │ │ │ │
│ │4112 │ .34│_2_, _4_, _14_, 8, │ .30│0, _10_, 5, 5 │
│ │ │ │1, 1, 6, 1 │ │ │
│ │4109 │ .54│_4_, _12_, _22_, 21,│ .47│_5_, _15_, 3, │
│ │ │ │_4_, 11, 13 │ │18 │
│ │4105 │ .88│2, _8_, _18_, _13_, │ .75│5, _5_, 0 │
│ │ │ │34, 17, _13_, _3_ │ │ │
│ │4102 │ 1.54│1, 6, _4_, 1, _4_ │ │ │
│ │Hδ │ │ │ │ │
│ │4098 │ .86│_4_, _6_, _11_, 29, │ .74│6, 1, 1, _7_ │
│ │ │ │_11_, _19_, 26 │ │ │
│ │4095 │ .53│_13_, _8_, _8_, 22, │ .47│_2_, _2_, 3, 3 │
│ │ │ │_3_, _3_, 14 │ │ │
│ │4091 │ .33│_11_, _8_, _8_, 17, │ .29│_4_, _4_, 13, │
│ │ │ │9, _8_, 9 │ │_4_ │
│ │ │ │ │ │ │
│ │3976 │ .84│_9_, _4_, _29_, _7_,│ │ │
│ │ │ │56, _17_, _9_, │ │ │
│ │ │ │21 │ .68│_13_, 9, _1_, 7│
│ │3973 │ 1.37│_7_, 23, _32_, 13, 1│ 1.27│_22_, 23 │
│ │3970 │ 2.15│_5_, 15, _5_, _10_, │ │ │
│ │Hε │ │12 │ │ │
│ │ │ │ │ │ │
│ │3933 K│ 1.48│_23_, _3_, 2, 22, 2 │ │ │
├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤
│MC 21646 │4861 │ .25│ │ .25│ │
│ │Hβ │ │ │ │ │
│α │4444 │ .31│_6_, 6 │ .31│_6_, 6 │
│Cassiopeiae│Ti+ │ │ │ │ │
│ │4340 │ .42│_5_, 5 │ .42│_5_, 5 │
│ │Hγ │ │ │ │ │
│ │4227 │ .83│2, _1_ │ .83│2, _1_ │
│ │Ca │ │ │ │ │
│ │4215 │ .71│1, _1_ │ .71│1, _1_ │
│ │Sr+ │ │ │ │ │
│ │4101 │ .56│11, _11_ │ .56│11, _11_ │
│ │Hδ │ │ │ │ │
│ │3970 │ 2.50│5, _5_ │ 2.50│5, _5_ │
│ │Hε │ │ │ │ │
│ │3933 K│ 2.47│ │ 2.47│ │
├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤
│MC 21721 │4861 │ .43│_16_, _11_, 4, 32, │ │ │
│ │Hβ │ │_11_, 4 │ │ │
│ │ │ │ │ │ │
│α Aurigae │4444 │ .21│_9_, _14_, _1_, 11, │ │ │
│ │Ti+ │ │4, 11, 1 │ │ │
│ │ │ │ │ │ │
│ │4340 │ .74│21, 11, 1, _7_, _9_,│ │ │
│ │Hγ │ │_4_, _12_ │ │ │
│ │ │ │ │ │ │
│ │4326 │ .62│13, 5, _10_, 13, 5, │ │ │
│ │Fe │ │_17_ │ │ │
│ │ │ │ │ │ │
│ │4227 │ .57│30, _37_, 5, _7_, 8 │ │ │
│ │Ca │ │ │ │ │
│ │ │ │ │ │ │
│ │4215 │ .36│14, _11_, 1, 4, _6_ │ │ │
│ │Sr+ │ │ │ │ │
│ │ │ │ │ │ │
│ │4101 │ .57│0, _12_, 10, 13, │ │ │
│ │Hδ │ │_2_, 5, _17_ │ │ │
│ │ │ │ │ │ │
│ │3976 │ .53│2, _1_ │ │ │
│ │3973 │ 1.14│8, _7_ │ │ │
│ │3970 │ 1.62│13, 5, _17_, 23, │ │ │
│ │Hε │ │_22_ │ │ │
│ │3967 │ 1.13│17, _16_ │ │ │
│ │3964 │ .62│ │ │ │
│ │3939 │ .80│0, _5_, _5_ │ │ │
│ │3936 │ 1.27│10, _10_ │ │ │
│ │3933 K│ 1.67│5, 3, _10_, 0, 5 │ │ │
│ │3930 │ 1.27│10, _10_ │ │ │
│ │3927 │ .76│4, _6_, 1 │ │ │
├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤
│MC 21722 │4866 │ .32│5, 0, _10_, 5 │ │ │
│δ Canis │4861 │ .61│1, 4, _4_ │ │ │
│ │Hβ │ │ │ │ │
│Majoris │4856 │ .28│4, _1_, _6_, 2 │ │ │
│ │ │ │ │ │ │
│ │4444 │ .76│4, 4, _6_ │ │ │
│ │Ti+ │ │ │ │ │
│ │ │ │ │ │ │
│ │4345 │ 1.12│_7_, 8 │ │ │
│ │4340 │ 1.12│ │ │ │
│ │Hγ │ │ │ │ │
│ │4336 │ 1.21│_9_, 9 │ │ │
│ │ │ │ │ │ │
│ │4326 │ .78│_7_, _8_, 2 │ │ │
│ │Fe │ │ │ │ │
│ │ │ │ │ │ │
│ │4227 │ .70│_10_, 10 │ │ │
│ │Ca │ │ │ │ │
│ │ │ │ │ │ │
│ │4215 │ .51│_1_, 1 │ │ │
│ │Sr+ │ │ │ │ │
│ │ │ │ │ │ │
│ │4105 │ .31│1, _1_ │ │ │
│ │4101 │ .86│_1_, _1_, 1 │ │ │
│ │Hδ │ │ │ │ │
│ │4098 │ .21│6, _6_ │ │ │
│ │ │ │ │ │ │
│ │3970 │ > 2.25│ │ │ │
│ │Hε │ │ │ │ │
│ │ │ │ │ │ │
│ │3933 K│ > 2.25│ │ │ │
├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤
│MC 21788 │4861 │ .22│0, 3, 3, 3, 3, _10_ │ .25│0, 0, 0, 0 │
│ │Hβ │ │ │ │ │
│ß Orionis │4481 │ .22│3, 3, 0, 8, 0, _12_ │ .22│3, 0, 8, 0, │
│ │Mg+ │ │ │ │_12_ │
│ │4471 │ .21│4, 4, 1, 9, 1, _11_ │ .16│1, 6, _6_ │
│ │He │ │ │ │ │
│ │4340 │ .45│20, _5_, _5_, 15, │ .36│4, 4, _9_ │
│ │Hγ │ │_5_, _18_ │ │ │
│ │4101 │ .43│12, _3_, _3_, 12, │ .40│0, 0 │
│ │Hδ │ │_3_, _13_ │ │ │
│ │4026 │ .14│3, 1, _2_, 8, _2_, │ .12│0, 0 │
│ │He │ │_5_ │ │ │
│ │3970 │ .45│10, 5, 0, 7, _5_, │ .46│4, _1_, 6, _6_ │
│ │Hε │ │_18_ │ │ │
│ │3933 K│ .17│_2_, 3, 3, 0, _2_, │ .18│2, 2, _1_, _3_ │
│ │ │ │_2_ │ │ │
│ │3889 │ .43│12, 12, _8_, 11, │ .54│1, 1, _2_ │
│ │Hζ │ │_8_, _18_ │ │ │
├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤
│MC 21789 │4861 │ .23│7, _3_, _1_, _3_ │ .23│7, _3_, _1_, │
│ │Hβ │ │ │ │_3_ │
│ε Orionis │4471 │ .31│16, _6_, 1, _11_ │ .20│ │
│ │He │ │ │ │ │
│ │4387 │ .24│_2_, _4_, 8, _2_ │ .20│ │
│ │He │ │ │ │ │
│ │4340 │ .40│12, _8_, 2, _5_ │ .35│ │
│ │Hγ │ │ │ │ │
│ │4116 │ .17│5, _2_, _5_, _2_, 3 │ .17│_2_, _2_, 3 │
│ │He │ │ │ │ │
│ │4101 │ .37│5, _5_, 3, _2_ │ .36│_4_, 4, _1_ │
│ │Hδ │ │ │ │ │
│ │4097 │ .17│5, _2_, _2_, _2_ │ .15│0, 0, 0 │
│ │4026 │ .19│1, 1, 1, _4_ │ .17│3, _2_ │
│ │He │ │ │ │ │
│ │3970 │ .32│8, _2_, 5, _10_ │ .30│7, _8_ │
│ │Hε │ │ │ │ │
│ │3889 │ .33│2, 14, _6_, _11_ │ .33│2, 14, _6_, │
│ │Hζ │ │ │ │_11_ │
├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤
│MC 21803 │4877 │ .12│3, _2_, _2_, 0, _2_,│ .11│_1_, _1_, 1, │
│ │ │ │0 │ │_1_, 1 │
│α Canis │4872 │ .30│25, _8_, _5_, 0, │ .25│_3_, 0, 5, _5_,│
│ │ │ │_10_, _5_ │ │0 │
│Majoris │4866 │ .56│11, _4_, _4_, 9, │ .55│_3_, _3_, 10, │
│ │ │ │_6_, 4 │ │_5_ │
│ │4861 │ 1.02│18, _7_, _2_, _10_ │ .96│_1_, 4, _4_ │
│ │Hβ │ │ │ │ │
│ │4856 │ .67│13, _12_, 0, 13, │ .65│_10_, 2, 15, │
│ │ │ │_12_, 0 │ │_10_, 12 │
│ │4851 │ .31│11, _4_, _4_, 1, │ .29│_2_, _2_, 3, │
│ │ │ │_4_, 1 │ │_2_, 3 │
│ │4846 │ .13│9, _1_, _3_, _3_, 2,│ .12│0, _2_, _2_, 3,│
│ │ │ │_1_, _3_ │ │0, _2_ │
│ │ │ │ │ │ │
│ │4481 │ .20│5, 0, 0, 0, 0, _8_ │ .18│2, 2, 2, 2, _6_│
│ │Mg+ │ │ │ │ │
│ │ │ │ │ │ │
│ │4354 │ .28│2, _6_, 7, _6_, _1_,│ .31│4, _4_, 1 │
│ │ │ │4 │ │ │
│ │4349 │ .45│5, _3_, 2, _3_, _3_,│ .45│2, _3_, 2 │
│ │ │ │2 │ │ │
│ │4345 │ .80│10, _5_, 0, _5_, 2 │ .79│1, _4_, 3 │
│ │4340 │ 1.38│7, _8_, 7, _6_ │ 1.39│6, _7_ │
│ │Hγ │ │ │ │ │
│ │4336 │ .83│_1_, 4, _6_, _3_, 2,│ .82│_5_, 3, 3 │
│ │ │ │2 │ │ │
│ │4331 │ .43│_3_, _1_, 4, _8_, 4,│ .46│1, 1, _1_ │
│ │ │ │2 │ │ │
│ │4327 │ .27│3, _5_, 3, 0, 0, 0 │ .28│2, _1_, _1_ │
│ │ │ │ │ │ │
│ │4125 │ .12│10, _7_, _5_, _2_, │ .11│_4_, _1_, 4 │
│ │ │ │_2_, 3 │ │ │
│ │4121 │ .20│15, _5_, _5_, _3_, │ .17│_2_, _2_, 4 │
│ │ │ │_5_, 2 │ │ │
│ │4116 │ .42│15, _7_, _10_, 0, │ .39│_7_, _7_, 13 │
│ │ │ │_10_, 10 │ │ │
│ │4112 │ .60│15, _5_, _8_, 15, │ .52│0, 0, 0 │
│ │ │ │_8_, _8_ │ │ │
│ │4109 │ .98│17, _16_, 4, _6_ │ .97│5, _5_ │
│ │4102 │ 1.45│12, _13_, 17, _15_ │ 1.46│16, _16_ │
│ │Hδ │ │ │ │ │
│ │4098 │ 1.04│21, _9_, 2, _12_ │ .97│5, _5_ │
│ │4095 │ .61│29, _6_, _9_, _9_, │ .53│_1_, _1_, 2 │
│ │ │ │_6_ │ │ │
│ │4091 │ .43│14, _3_, _16_, 4, │ .37│_10_, _5_, 15 │
│ │ │ │_11_, 9 │ │ │
│ │4088 │ .24│11, _2_, _7_, 1, │ .20│_3_, 0, 2 │
│ │ │ │_4_, _2_ │ │ │
│ │4084 │ .12│10, 0, _7_, 0, _7_, │ .08│_3_, _3_, 7 │
│ │ │ │3 │ │ │
│ │ │ │ │ │ │
│ │3986 │ .12│7, 0, _12_, _5_, 10,│ .12│0, _12_, _5_, │
│ │ │ │2, 0 │ │10, 2, 0 │
│ │ │ │ │ │ │
│ │3983 │ .25│7, _2_, _7_, 7, 0, 2│ .25│_2_, _7_, 7, 0,│
│ │ │ │ │ │2 │
│ │3980 │ .42│15, _2_, _10_, 12, │ .42│_2_, _10_, 12, │
│ │ │ │0, _7_ │ │0 │
│ │3976 │ .66│22, _2_, _5_, 0, │ .58│5, 2, 7, _10_ │
│ │ │ │_18_ │ │ │
│ │3973 │ .86│_22_, 13, 8 │ .97│3, _2_ │
│ │3970 │ 1.47│11, _11_, 18, _11_ │ 1.45│_11_, 20, _9_ │
│ │Hε │ │ │ │ │
│ │3967 │ 1.10│20, _8_, 2, _15_ │ 1.02│0, 10, _7_ │
│ │3964 │ .70│27, _3_, _10_, _5_, │ .64│_5_, _2_, 3, │
│ │ │ │_15_ │ │_7_ │
│ │3960 │ .47│23, _2_, _5_, 3, │ .43│2, _1_, 7, _3_,│
│ │ │ │_7_, _10_ │ │_6_ │
│ │3957 │ .33│24, 0, _6_, 0, _8_, │ .28│5, _1_, 5, _3_,│
│ │ │ │_8_ │ │_3_ │
│ │3954 │ .23│19, 4, _6_, _13_, │ .16│11, 1, _6_, _4_│
│ │ │ │_11_ │ │ │
│ │ │ │ │ │ │
│ │3933 K│ .18│12, 2, _6_, 4, _3_, │ .17│3, _5_, 5, _2_ │
│ │ │ │_6_ │ │ │
│ │ │ │ │ │ │
│ │3889 │ 1.48│7, _9_, 17, _16_ │ 1.55│ │
│ │Hζ │ │ │ │ │
└───────────┴──────┴──────────┴────────────────────┴──────────┴───────────────┘
9. Table X contains a summary of the results, for line centers only.
Successive columns give the name of the star, the spectral class, the
absolute magnitude, and the drop in magnitudes from background to line
center, for the spectrum lines mentioned at the heads of the columns.
The greater line depth for absolutely brighter stars, at least among
those of the second type, is especially to be noted.
TABLE X
DROP IN INTENSITY, FROM BACKGROUND TO LINE CENTER, FOR ELEVEN STARS,
EXPRESSED IN STELLAR MAGNITUDES
┌──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┐
│ Star │Class │ M │ Hβ │ Hγ │ Hδ │ Hε │ K │ 4227 │ 4215 │
├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
│ε Ori │ B0│ │ .23│ .40│ .37│ .32│ │ │ │
│ß Ori │ cB8│ 5:│ .22│ .45│ .43│ .46│ .17│ │ │
│α Lyr │ A0│ 0.6│ .95│ 1.43│ 1.60│ 1.68│ .23│ │ │
│α CMa │ A0│ 1.2│ .96│ 1.39│ 1.46│ 1.47│ │ │ │
│α Cyg │ cA2│ 4:│ .33│ .63│ .63│ .70│ .54│ │ │
│α Aql │ A5│ 2.4│ .71│ .81│ .71│ 1.50│ .79│ │ │
│δ Cas │ A5│ 1.6│ 1.49│ 1.46│ 1.54│ 2.15│ 1.48│ │ │
│δ CMa │ cF8│ 3:│ .61│ 1.12│ .86│ >2.25│ >2.25│ .70│ .51│
│α Aur │ G0│ 0.0│ .43│ .76│ .57│ 1.62│ 1.67│ .57│ .36│
│α Boo │ K0│ 0.3│ │ .54│ .74│ │ │ 1.34│ .70│
│α Cas │ K0│ 0.0│ .25│ .42│ .56│ 2.50│ 2.47│ .83│ .71│
└──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘
10. The material contained in Table X is reproduced in Table XI, where
the intensity at the line center is expressed in terms of percentage of
the background intensity, instead of in stellar magnitudes. The
“background intensity,” as defined in Section 6, is the intensity that
the background would have if the line were not present. It is noteworthy
that, for the great majority of the lines, the residual intensity at the
line center is greater than 30 per cent of the background intensity.
11. The material presented above constitutes the first systematic study
of the contours of strong absorption lines. In view of the preliminary
nature of the work the discussion has been devoted for the most part to
presentation of method. Extended discussion seems at present to be
premature, and only a few points need be mentioned.
Probably the chief interest of Table X lies in the result that the
maximum intensity drop from background to line recorded for any of these
stars is 2.50 magnitudes, corresponding to a light loss of ninety per
cent. Except for the supergiant cF8 star and the Ca+ absorption for α
Cassiopeiae and Hε for δ Cassiopeiae, the light remaining at the center
of the line is at least fifteen per cent of the background intensity. On
the average for all these strong absorption lines there is something
like twenty-five per cent of the background light remaining at the
center of the lines. The significance of these residual intensities will
be discussed in a later publication, when the forms of the lines as
shown by the data of Table IX will also be considered.
TABLE XI
RESIDUAL INTENSITIES AT LINE CENTERS, EXPRESSED AS PERCENTAGES OF
BACKGROUND INTENSITY
┌───────┬───────┬───────┬───────┬───────┬───────┬───────┬──────┬──────┐
│ Star │ Class │ Hβ │ Hγ │ Hδ │ Hε │ K │ 4227 │ 4215 │
├───────┼───────┼───────┼───────┼───────┼───────┼───────┼──────┼──────┤
│ε Ori │ B0│ 81│ 69│ 71│ 74│ │ │ │
│β Ori │ cB8│ 82│ 66│ 67│ 65│ 86│ │ │
│α Lyr │ A0│ 42│ 27│ 23│ 21│ 81│ │ │
│α CMa │ A0│ 41│ 28│ 26│ 26│ │ │ │
│α Cyg │ cA2│ 74│ 56│ 56│ 52│ 61│ │ │
│α Aql │ A5│ 51│ 47│ 51│ 25│ 48│ │ │
│δ Cas │ A5│ 25│ 26│ 24│ 14│ 26│ │ │
│δ CMa │ cF8│ 57│ 36│ 45│ <13│ <13│ 52│ 63│
│α Aur │ G0│ 67│ 50│ 59│ 22│ 21│ 59│ 72│
│α Boo │ K0│ │ 61│ 51│ │ │ 29│ 52│
│α Cas │ K0│ 79│ 68│ 60│ 10│ 10│ 47│ 52│
└───────┴───────┴───────┴───────┴───────┴───────┴───────┴──────┴──────┘
For the wider lines, especially those that are strong and heavily
winged, the intensities derived in this paper are probably of the right
order. Probably, however, the dispersion used is too small to reproduce
satisfactorily the detail at the centers of lines as narrow as those of
such stars as α Cygni and β Orionis. The difficulty introduced does not
involve inaccuracy of plates, microphotometer, or process of
measurement; it is concerned solely with the fact that the spectral
region examined is so narrow that, with the dispersion used, the grain
of the plate is not fine enough to reproduce the spectral detail. The
same difficulty would prevent any recognition of the double reversal of
the solar H and K lines, if they were studied with the present
dispersion.
Whatever the dispersion used, the same qualification must be made in
discussing the results; probably the dispersion would have to be greatly
increased before the measured effective line depth becomes much greater
for narrow line stars.
Relative effective line depth, derived from numerous spectra made with
the same dispersion, is still, however, of considerable significance. It
permits us to recognize differences of surface gravity, and to form an
idea of relative chromospheric depths for different classes of stars.
SUMMARY
1. The investigation deals with the determination of the depth and
contour of prominent absorption lines in the spectra of stars of various
classes.
2. The spectra used were made with the 16-inch refractor of the Harvard
Observatory, using two prisms and a special set of apertures.
3. Results are presented for eleven stars, of spectral class ranging
from B0 to K0.
4. The spectra were analyzed under uniform conditions by means of the
Moll thermoelectric microphotometer. The resolving power of this
instrument is such that no integrating effect need be considered in
discussing the results.
5. The microphotometer tracings were measured with reference to fiducial
lines representing “darkness” and “clear film,” and to a line,
representing the continuous background, drawn across the absorption
lines.
6. The intensity drop from continuous background to line was deduced
graphically from the measures.
7. The accuracy of the results is discussed in detail.
a. The reliability of the plates, as judged from qualitative
reproduction of detail, and from the consistency of the numerical
results, is satisfactory. Effects of stray light are of negligible
magnitude, and in this respect slit spectra appear to have no advantage
over objective prism spectra.
b. Effects of poor focus are measurable, but small. Spectra that are in
such poor focus as to cause appreciable inaccuracy would be rejected
from visual inspection.
c. The accuracy of the microphotometer tracings is in general
satisfactory. Tracings showing abnormal deflections from “darkness” to
“clear film” are not susceptible of correction, and are omitted in
deriving results.
d. The measures upon the tracings are also of satisfactory accuracy.
8. The differences in intensity between the continuous background and
various points along the line contour are tabulated for the eleven stars
under discussion.
9. The general results for the intensities at the centers of lines show
an interesting relation to absolute brightness; the brighter stars have,
in general, lines that cut more deeply into the background. A result of
considerable interest is that the average residual intensity in the
strong wide absorption lines is more than 30 per cent of the background
intensity.
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