An introduction to the study of variable stars online

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ELIZABETHAN TRANSLATIONS FROM THE ITAL-
IAN. By MARY AUGUSTA SCOTT, Ph.D. (A.B. Vas-
sar, 1876), Professor of English Literature in Smith
College.

SOCIAL STUDIES IN ENGLISH LITERATURE.
By LAURA J. WVLIE, Ph.D. (A.B. Vassar, 1877), Pro-
fessor of English in Vassar College.

THE LEARNED LADY IN THE EIGHTEENTH
CENTURY. By MVRA REYNOLDS, Ph.D. (A.B. Vas-
sar, 1880), Professor of English Literature in Chicago
University. [/ preparation]

THE CUSTOM OF DRAMATIC ENTERTAINMENT IN
SHAKESPEARE'S PLAYS. By ORIH J. HATCHER,
Ph.D. (A.B. Vassar, 1888), Formerly Associate Pro-
fessor of Comparative Literature in Bryn Mawr Col-
lege. {In preparation.]

INTRODUCTION TO THE STUDY OF VARIABLE
STARS. By CAROLINE E. FURNBSS, Ph.D. (A.B. Vas-
sar, 1891), Professor of Astronomy in Vassar College.

MOVEMENT AND MENTAL IMAGERY. By MAR-
GARET FLOY WASHBURN, Ph.D. (A.B. Vassar, 1891),
' Professor of Psychology in Vassar College. [/ prep-
aration^

BRISSOT DE WARVILLE: A STUDY IN THE HIS-
TORY OF THE FRENCH REVOLUTION. By ELOISE
ELLERY, Ph.D. (A.B. Vassar, 1897), Associate Profes-
sor of History in Vassar College.

HOUGHTON MIFFLIN COMPANY
BOSTON AND NEW YORK



AN INTRODUCTION TO THE STUDY
OF VARIABLE STARS




Plate I

ATLAS WITH THE GLOBE. NAPLES MUSEUM



&emi-entenmai



AN INTRODUCTION TO

THE STUDY
OF VARIABLE STARS



BY

CAKOLINE E. FUKNESS, PH.D.

Director of the Vassar College Observatory



With Illustrations




BOSTON AND NEW YORK
HOUGHTON MIFFLIN COMPANY

re?s Cambridge
1915



COPYRIGHT, 1915, BY CAROLINE E. FURNESS
ALL RIGHTS RESERVED

Published October 1315



PUBLISHED IN HONOR OF THE
FIFTIETH ANNIVERSARY

OF THE

FOUNDING OF VASSAR COLLEGE
1865-1915



DEDICATED TO

MARY W. WHITNEY

IN MEMORY OF MANY HAPPY HOURS

SPENT TOGETHER IN THE PURSUIT OF

OUR LOVED SCIENCE



PREFACE

DURING the past few years the subject of variable stars
has become increasingly interesting to the amateur who is the
owner of a telescope, as well as to the average college student
who has some knowledge of astronomy, while to the research
worker it offers many lines of investigation which are full of
promise. However, so complex is the subject, and so diverse
the principles involved in a complete understanding of it, that
extensive reading in several different directions is required as
a foundation.

It is with the purpose of supplying this need as well as of
making an important and attractive branch of astronomy
accessible to the student that the present volume has been
prepared. It is the outcome of several years of teaching the
subject in Vassar College, for which the material was prima-
rily collected. This material is scattered throughout various
periodicals in the form either of research papers or quite popu-
lar articles, intended to give directions for observation to
owners of small telescopes. A large amount of historical matter
is also included, which is taken from sources not within easy
reach of the general reader. Mention may be made of some of
the subjects treated, which are introductory to the study of
stellar variation, such as the study of the Durchmusterung
charts, photometry in all its branches, spectroscopy, and star
color. The purpose of the present volume is to consider all of
these points, and in particular to give in as simple and clear a
form as possible a full presentation of the physical principles
upon which many of the instruments and methods of investi-
gation are based, principles such as those of polarized light,
spectrum analysis, the formation of the photographic image,
and photo-electricity. Textbooks on astronomy rarely include



x PREFACE

such preliminary matters, even though they are not subjects
which the student is necessarily expected to know.

Thus far no general book on variable stars has been pre-
sented to the public in English. In German a comprehensive
treatise is being prepared by Father Hagen, and issued a sec-
tion at a time. Two parts have already appeared, and in the
introduction to the first, which is called the historical techni-
cal part, Hagen states that it is primarily a collection of sources,
and that brief handbooks in different languages can easily be
formed from the material included. The author, in a personal
interview with this distinguished astronomer at Rome, in 1914,
received encouragement from him to proceed with her project,
and permission to use any of the material in his treatise. The
present volume, however, is an introduction rather than a hand-
book, and as such devotes more space to explanatory mate-
rial than to an extensive treatment of the results of research.
Much of the material had already been collected before 1914,
but frequent reference to Hagen's work will be found in the
footnotes.

[ The writer wishes now to express her indebtedness to her
many friends who have assisted her at various points in this
undertaking; first to her astronomical colleagues, who looked
over the outline and made valuable suggestions as to the points
which should be included in it; to Professors Schlesinger and
Jordan, of the Allegheny Observatory; to Professors Frost and
Parkhurst, of Yerkes; and to Professor Pickering, of the Har-
vard Observatory. It is owing to suggestions from these as-
tronomers that the chapter on photo-electric cells was included,
and that so much space was given to photographic photome-
try and star colors. They also freely offered the use of any
material from their publications which might be desired.

Whatever clearness of presentation there may be in the dis-
cussion of the photo-electric cell the writer owes to her col-
league at Vassar, Professor Saunders, of the Physics Depart-
ment, who gave generously of his time to the discussion of that
difficult and unfamiliar subject, as well as of several other



PREFACE xi

technical points. Miss Ernestine Fuller, of the Astronomical
Department, assisted by looking up references at several
points and criticized the presentation of some of the physical
principles. Professor Treadwell has given useful suggestions
in regard to the drawings.

At the suggestion of Miss Helen Swartz several items were
included which were thought to be useful to the non-profes-
sional observer. She also read a large part of the manuscript
and made valuable criticisms of the form.

The writer wishes to express her thanks also to her students
in the course on variable stars during the present year, Miss
Vera Ringwood and Miss Evelyn Wickham, with whom she
has held many discussions as to the form of presentation, and
who, by their interest and candid criticism, have aided greatly
in maintaining the standard of clearness which she has striven
to reach.

Mr. Olcott, secretary of the American Variable Star Section,
made suggestions as to what points the amateur observer
would be especially interested in, and sent several items which
have been incorporated in the chapter on "Hints to Observ-
ers." Mr. David Blencoe, also a member of the Association,
has kindly sent his work on a statistical study of variable stars,
which had been prepared for private circulation.

The author's greatest debt, however, is to Miss Helen Van
Kleeck, who at several times in the past has assisted in prepar-
ing the publications of Vassar College for the press. To her
faithful and intelligent work in transcription the writer owes
the completion of the volume in the required time, and to her
careful criticism is due much of the clearness of style. Miss
Van Kleeck also prepared the drawings for the illustrations,
which are provided for by the publication fund of the Observa-
tory.

The observation of variable stars was introduced into the
program of the Vassar Observatory by Professor Mary W.
Whitney in 1901, and when later the subject was made a regu-
lar course of study in the astronomical department, the writer



xii PREFACE

co-operated with her for the first few years in giving the in-
struction. The writer cannot adequately express her constant
indebtedness to Professor Whitney for the opportunity and
encouragement afforded her during all her years of work at
Vassar.

CAROLINE E. FUBNESS.

VASSAB COLLEGE OBSERVATORY,
March 26, 1915.



CONTENTS

I. INTRODUCTORY

General description of stellar variation. Elements of
variation. Julian Day. Classification of variables. Prin-
ciples of spectrum analysis. Classification of stellar spec-
tra. Connection between spectral type and type of varia-
tion 3

H. STAR CHARTS FOR GENERAL USE

Argelander, Uranometria Nova. Heis, Atlas Coelestis.
Schurig, Himmels Atlas. Upton, Klein, etc. Argelander,
Banner Durchrmisterung, detailed account, with sugges-
tions for its use. Palisa and Wolf, photographic maps.
Ecliptic charts. Charts of Carte du del. Precession . 38

HI. STAR CHARTS FOR VARIABLES

Hagen, Atlas Stellarum Variabilium, very detailed ac-
count, with directions for its use. Parkhurst, enlarge-
ments. Harvard photographic maps. Miscellaneous . 52

IV. CATALOGUES OF VARIABLES

Naming of variables. Harvard, Hartwig, Chandler.
Methods of discovery; visual, photographic, spectro-
scopic. Illustrations. Systematic search .... 68

V. STELLAR MAGNITUDE

Early history. Ptolemy, Bayer, and others, before the
invention of the telescope. Herschel. Argelander, mag-
nitudes in the Durchmusterung. Gould. Pogson's rule.
Fechner 81

VI. VISUAL PHOTOMETRY

Methods of observing variable stars visually. Arge-
lander's step method. Harvard method of relative bright-
ness. Use of direct magnitude. Precautions in observing.



xiv CONTENTS

Purkinje phenomenon. Dove's phenomenon. Polarized
light. Zb'llner photometer. Harvard meridian photome-
ter. Pickering's wedge photometer 103

VH. PHOTOGRAPHIC PHOTOMETRY

The formation of star images. Chromatic aberration
and color curve. Visual and photographic telescopes.
Effect of color on size of image. Formulas for deriving
magnitudes from measurements of photographic images.
Stained plates. Connection with spectral type. Extra-
focal images. Comparisons by Argelander's method.
Work at Harvard 130

VHI. PHOTO-ELECTRIC PHOTOMETRY

Work of Stebbins with selenium cell. Principles of
photo-electric action. Electrometer. Work at Berlin-
Babelsberg. Description of instrument and the results.
General conclusions . . . . . . . . .154

IX. FORMATION OF LIGHT SCALE

Combination of observations made by the Argelander
method. Formation of light scale for comparison stars
without weights. Light scale for variables. Light step
converted into magnitude. Plotting of light curve by
light step or magnitude. Determination of maximum or
minimum from single light curve. Use of weights in
forming scale 170

X. MEAN LIGHT CURVE

Use of Heis's observations of 8 Cephei. Determina-
tion of period and epoch from light curve. Correction of
approximate elements by later observations. Mean
light curve. Use of mean light curve in determining min-
imum of Algol type. Harvard method for long period
variables . ... . .186

XI. PREDICTION OF MAXIMA AND MINIMA FROM
THE ELEMENTS

Explanation of Julian Day. Simple formula. Addi-
tion of periodic term. Secular term. Reduction to sun
for short period variables 204



CONTENTS xv

XII. ECLIPSING BINARIES

Doppler's principle. Spectrographic apparatus. Ap-
plication to variable stars. Explanation of Algol type.
Evidence from light curve. Spectroscopic evidence.
General relations, ft Lyrae type. Cepheid variable
type. Cluster type 216

XHI. LONG PERIOD VARIABLES

Irregular variables. Temporary stars. Collections of
observations: Argelander, Schb'nfeld, Heis, Krueger,
Schmidt, Pogson, Knott, Goodricke and Pigott, Gould,
Chandler 248

XIV. STATISTICAL STUDY

Correlation of number, length of period, color, range
of brightness, and spectral type for long and short period
variables. Galactic distribution. Miscellaneous facts . 273

XV. HINTS FOR OBSERVERS

Circulars issued by Harvard College Observatory in-
viting co-operation. American Association of Variable
Star Observers. British Association. Hints for observ-
ers: (1) Use of telescope; (2) Time; (3) Identification of
variable; (4) Methods of recording ; (5) Precautions.
Stars suitable for observers with telescopes of different
aperture, mounted or unmounted. Brief bibliography. . 289

APPENDIX

Table I. Julian Days 311

Table II. Fractions of a day . . . . . . .312

Explanation of Tables 313

/ Description of plates of stellar spectra 315

INDEX . 319



PLATES

I. Atlas with the Globe. Naples Museum . . . Frontispiece
H. Typical Stellar Spectra . . r . . .... .33

III. Frontispiece from Bayer's Uranometria, 1639 ... 83

IV. The Constellation Gemini from Bayer's Uranometria . . 85

V. Double-slide plate-carrier on the 40-inch Telescope. Yerkes

Observatory 139

VI. The two-foot Reflector. Yerkes Observatory . . .141
VII. The Bruce Photographic Telescope. Yerkes Observatory . 145

VIII. The Bruce Spectrograph of the Yerkes Observatory, at-
tached to the Telescope 219

IX. The Bruce Spectrograph of the Yerkes Observatory, ul-
terior structure 223

X. Spectra of Ursae Majoris, showing lines single and

double 235

XI. Spectra of //, Orionis, showing different amounts of radial

velocity 237

XII. Spectra of Sun and Type A 318

XIII. Typical Spectra 318

XIV. Peculiar Spectra. 318



,



FIGURES IN THE TEXT

1. Single Light Curve of S Ursae Majoris . .... 4

2. Light Curve of Nova Persei . . . . . . . . 7

3. Mean Light Curve of T Cassiopeiae . .,*..&

4. Mean Light Curve of R Ursae Majoris ... , .

5. Light Changes of SS Cygni . . . ..... 10

6. Mean Light Curve of 8 Cephei 11

7. Mean Light Curve of S Arae 12

8. Mean Light Curve of /? Lyrae 13

9. Light Curve of Geminorum 14

10. Light Curve of Algol 15

11. Mean Light Curve of U Cephei . . . . . . .16

12. Prism Spectroscope . . . .18

13. Diagram of a Complete Wave 20

14. The Solar Spectrum 28

15. Square from Durchmusterung Chart 47

16. Magnitude Curve for RV Hydrae 59

17. The Nicol's Prism . . 115

18. The Zollner Photometer 117

19. Pickering's Meridian Photometer 123

20. Wedge Photometer, Yerkes Observatory 127

21. Color Curve of the 40-inch Objective. Yerkes Observatory . 143

22. Spectral Type and Color Intensity 150

23. Diagram of the Photo- Electric Apparatus. Berlin-Babels-

berg 161

24. Single Light Curves of 8 Cephei 175

25. Light Curve of o Ceti 178

26. Magnitude Curve for o Ceti 180



xx FIGURES IN THE TEXT

27. Mean Light Curve of 3 Cephei 199

28. Diagram for obtaining the Reduction to the Sun . . . 214

29. Diagram I. The Light Curve of an Eclipsing Binary . . 231

30. Diagram II. The Relative Orbit 232

31. Diagram HI. The Real Orbits 233

32. Diagram IV. Spectroscopic Evidence 234

33. Diagram V. The Velocity Curve 234

34. The System of /? Lyrae 242

35. Theoretical System of 8 Cephei 247

36. Relation between Color and decreasing Brightness . . . 277



AN INTRODUCTION TO THE STUDY
OF VARIABLE STARS



ABBREVIATIONS

Annals, H.C.O., Annals of the Harvard College Observatory.

A. G., Astronomische Gesellschaft.

A. N., Astronomische Nachrichten.

Ast. Jour., Astronomical Journal.

Ap. J., Astrophysical Journal.

H.C.O. Circ., Harvard College Observatory Circulars.

L.O.B., Lick Observatory Bulletins.

Mem. R.A.S., Memoirs of the Royal Astronomical Society.

Phil. Trans., Philosophical Transactions of the Royal So-

ciety, London.

Physik. Zeits., Physikalische Zeitschrift.

Pop. Ast., Popular Astronomy.

Potsdam Phot. DM., Potsdam Photometric Durchmusterung.
Rad. Obs., Radcliffe Observatory Publications.

Uran. Arg., Uranometria Argentina.

Ver. St., I Veranderliche Sterne, by Hagen.

V.J.S., VVierteljahrsschrift der Astronomischen Gesell-

v schaft.



AN INTRODUCTION TO THE STUDY OF
VARIABLE STARS

CHAPTER I

INTRODUCTORY

WE shall take it for granted that the reader is already ac-
quainted with the main facts of Astronomy, but since this
does not necessarily include a knowledge of the points which
bear directly upon the study of variable stars, a brief resume
of them will be given in this introductory chapter. However,
the statements made here are to be considered as preliminary
only, and each will be more fully discussed in some later chap-
ter. The topics presented will be a general description of stel-
lar variation, the elements of variation, classes of variables,
the general principles underlying spectrum analysis, the classi-
fication of stellar spectra, and the connection between the
spectral type and the type of variation.

GENERAL DESCRIPTION OF STELLAR VARIATION

A variable star is one that undergoes a change in brightness.
With some stars the change is as great as four or even six mag-
nitudes, while with others it may be only one magnitude, and
in some cases as small as half a magnitude. This change in
brightness is observed by comparing the light of the variable
with the light of some standard star which is assumed to be
constant in brightness, the comparison being made either
directly, or through the medium of some sort of artificial star.
The different methods of making the comparisons will be dis-
cussed at length in the chapters on photometry. It is sufficient
here to state that the result of the observations is to furnish
the magnitudes of the variables at certain recorded instants



STITDY OF VARIABLE STARS

of time. In order to represent the variation to the eye, the
data are plotted on co-ordinate paper, using the time as the
horizontal co-ordinate, or abscissa, and the observed magni-
tude as the vertical co-ordinate or ordinate. A smooth curve
is then drawn through the points which is called the single
light curve of the variable. This is illustrated in the following
diagram.



7.0
8.0
9.0
10.0
11.0

JLD
14
















































STc


/yto


K














\\J










c


A


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\




















f










\




















1












V
















i























<i


\^ ^


3




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5




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c


12,900 3000 3100 32.00



Figure 1

SINGLE LIGHT CURVE OF S URSAE MAJORIS
ELEMENTS OF VARIATION

When a long series of observations has been made and the
results plotted as just described, a study of the curves will
show that the same form recurs with more or less regularity,
and that certain quantities can be determined which will de-
scribe it. They are the magnitude at maximum, the magnitude
at minimum, and the length of the period, i.e., the time from
one maximum or minimum to the one next following. These
are known as elements of variation and to them is added the



INTRODUCTORY 5

epoch, that is, the date of some very well-determined maxi-
mum or minimum, its selection depending upon the nature
of the curve. This date is usually changed from the calendar
date into the corresponding day of the Julian period, and is
known as Julian Day. The Julian period, as the name implies,
is a continuation of that introduced at the time of Julius Csesar,
according to which the days are numbered consecutively, be-
ginning at 4713 B.C. It has been adopted into variable star
work, in order to facilitate the combination of observations
scattered over a long period of time. The Julian Day for Janu-
ary 1, 1915, is 2,420,499. For a fuller explanation see Chapter
XI.

The observations as described above are finally combined
into one curve called the mean light curve, which represents the
average course of variation of the star, smoothing out the small
irregularities. It is upon the study of the mean light curves of
great numbers of variables that the classification is based.
The method of forming it will be treated in Chapter X.

CLASSES OF VARIABLES

From the study of their curves, it has been found that vari-
able stars may be divided into distinct groups, each one hav-
ing its own particular light curve. Several different groupings
have been made by different astronomers. The one which is
best known and most widely used is due to Professor E. C.
Pickering, of the Harvard College Observatory. It was first
proposed by him in 1880 in the Proceedings of the American
Academy of Arts and Sciences, vol. xvi, pp. 17, 257. It is
later repeated in the Provisional Catalogue of Variable Stars,
which forms No. in of vol. 48 of the Annals of the Harvard
College Observatory, from which source the present statement
is taken.

Class I represents new or temporary stars; Class II, vari-
ables of long period; Class III, variables of small range, or
irregular variation according to laws as yet unknown; Class
IV, variables of short period; and Class V, variables of the



6 THE STUDY OF VARIABLE STARS

Algol type. Class II may be subdivided into Class Ha, which
contains the ordinary variables of long period, and Class lib,
to which U Geminorum and SS Cygni belong. The latter are
usually faint and of nearly uniform brightness, with occasional
sudden and irregular outbursts of light which diminish gradu-
ally. Class IV can similarly be divided into Class IVa, which
contains ordinary variable stars of short period, and Class IVb,
of which ft Lyrae is the typical star.

CLASS I. New or Temporary Stars. A new star is one which
grows bright very suddenly, often in a few hours, and then
fades away, more or less gradually, becoming either a faint
star, or a planetary nebula. An excellent discussion of these
stars may be found in Miss Clerke's interesting and valuable
volumes, The System of the Stars and Problems in Astrophysics.
The two brightest novae of recent years were discovered by
Thomas Anderson of Edinburgh. They are Nova Aurigae and
Nova Persei. A portion of the curve of the latter star is given
below. Though it appears for a time to have somewhat regu-
lar fluctuations, it is in reality a variable having but one maxi-
mum, which is followed by a prolonged minimum.

One might inquire whether it is possible to obtain any in-
formation regarding the history of a new star before the time
of the first observation, and also whether any such stars have
been observed before their maximum brightness was attained.
The answer to both questions is an affirmative one. By means
of the great store of photographic plates at the Harvard Ob-
servatory and elsewhere, it is always possible to trace back the
history of each new star, until we reach a time when it is fainter
than any star recorded on the photograph. Just what magni-
tude is thus represented depends upon the length of the photo-
graphic exposure, being sometimes the eleventh magnitude,
and sometimes even fainter.

For example, Nova Aurigae, when discovered by Anderson,
was a yellowish star of the fifth magnitude. From October 21
to December 1, 1891, photographs of the same region had been
taken at the Harvard Observatory, thirteen in number, from



8



THE STUDY OF VARIABLE STARS



all of which it was absent. On December 8 it is also lacking on
a photograph taken by Wolf, of Heidelberg, which shows stars
of the ninth magnitude. On December 10, a plate taken at
Harvard shows it to be of the 5.4 magnitude, and following
photographs at the same Observatory show that it reached a
maximum of 4.4 on December 20, hence it was already on the
downward slope of its light curve when discovered. Its sudden
increase in brightness from below the ninth magnitude to 5.4
must have taken place in about twenty-four hours. The case
of Nova Persei is equally striking. When discovered on Feb-
ruary 22, 1901, it was brighter than the second magnitude and
had not then attained its greatest brightness. On a plate taken
twenty-eight hours previously, containing stars of the twelfth
magnitude, it did not appear, hence it must have increased ten
magnitudes during that time.

A very extensive series of observations covering the recent
history of some of these stars has been made by Professor
Barnard at the Yerkes Observatory, and published in the



M



s



8.0
9.0

100
1 1.0




Days 100 00 300 400 500



Figure 3

MEAN LIGHT CURVE OF T CASSIOPEIAE



INTRODUCTORY



9



Astronomische Nachrichten, No. 4655. They include eleven
stars and cover a period of twenty years. Briefly stated the
result is that some of the novae are now merely ordinary faint
stars, while others, from their hazy, ill-defined appearance,
are regarded as probably nebulous stars. Some are no longer
visible.

CLASS II. Variable Stars of Long Period. As the name im-
plies, the variation of these stars is periodic in character, that