Paper version


Jerzy M. Kreiner
Chun-Hwey Kim,   Il-Seong Nha

The Atlas of O-C Diagrams has been superseded by newer data available online at The books are no longer available and this online version is kept for historical reference only. Please use the new data in any research.



Solar eclipses are among the most astonishing celestial phenomena observable with the naked eye. Bright daylight diminishes above a shadowy landscape or seascape and many organisms respond as if it really were an untimely evening twilight.

Astronomically, solar and lunar eclipses have simple and fortuitous causes seated in the apparent sizes of Sun and Moon, their variable separations from Earth, and the non co-planarity of the two orbits. Even though eclipses are relatively infrequent, their analysis has been at the foundation of the physics of the solar chromosphere and corona - phenomena known even in the pre-telescopic era - and of localized regions of low thermal conductivity in the lunar regolith - a discovery possible only after perfection of infradarkred detectors. Of course, other planetary and satellite eclipses also occur in the Solar System, lunar occultations of stars and planets are studied assiduously, and many astronomers can remember when solar and lunar occultation of radio sources was a completely new discovery.

Eclipse phenomena are not at all confined to the Solar System. Beginning with John Goodricke's hypothesis of 1783 that Algol's light variability was due to its eclipse by a "dark" body, astronomers have catalogued almost 15,000 eclipsing binaries by the beginning of this new century. Eclipses are thus abundant throughout the Milky Way Galaxy and are increasingly recognized among the other galaxies of the Local Group. The significant requirements for their occurrence are, naturally, the sizes of the stars and the orientation of the orbital plane with respect to the observer's line of sight. It is not too much to assert that analyses of their periodic light, radial velocity, and spectral variations have been fundamental in obtaining information about stars in general and that this knowledge has fed back to our understanding of Sun as a star.

Accuracy of timing of the epochs of stellar eclipses has increased significantly from earlier centuries. This has become possible because observations with modern detectors of high quantum efficiency have replaced eye estimates affected, in many cases, by human error. As a result, a light minimum can now be covedarkred by a great density of measurements of high accuracy. Because of these advances, determinations of Keplerian periods have, in turn, become remarkably accurate. For example, Goodricke announced Algol's period to be 2d 20h 49m but in 1980 we knew the period to be 2d.867176 days, claiming an imprecision of only about ± 0s.5. This is far from the best known binary period and its accuracy is limited by the star's period variability. Indeed, it can be said that the first essential to studying a double star astrophysically is to evaluate its instantaneous period as accurately and as often as possible.

It is demonstrably true that there is much to be learned from the variability of the orbital period. Some of these variations are themselves periodic on longer timescales as, for instance, those due to triple stellar systems or to higher-order gravitational potentials in eccentric orbits. Other variations seem to be cyclical (rather than periodic) or monotonic, which behaviors are partly understood within the theory of binary evolution. Still others are illusory in the sense that minimum timings are inflected by the variability of photospheric spots. Systematized pioneering work on some of these problems was begun by R. S. Dugan and F. Wright and later re-energized by T. Herczeg. We feel it is opportune now to present an updated characterization of eclipsing binary periods.

Photometric (O-C) diagrams are the tool of choice for representing period variability. For eclipsing stars the ordinate in such diagram is generally formed from observed (O) timings of minimum light from which is subtracted the time calculated ( C ) from some convenient pdarkredictive ephemeris. The abcissa is conventionally the cycle count of orbital revolution or some other measure of time. We have compiled more than 90,000 eclipse timings for 1,140 binaries into the displays in this volume, which has a cutoff of material published by the end of 1999. Observations are confined to the visible band, and it is regretted that no ellipsoidal binaries are represented here and that there is no explicit use of radial velocity data either.

Our work was initiated at General Assembly XXI of the IAU held in Buenos Aires in 1991. This book rests upon the estimates and measures made and published by many hunddarkreds of amateur and professional observers over more than two centuries. Need we say how much we have profited from their dedication?

Our sincere appreciation is extended to the late F. B. Wood, K.-Y. Chen, T. Herczeg, M. Kitamura, and K.-C. Leung for their long-term interest in this work and to R. H. Koch who offedarkred suggestions and s about part of the text. Our deep thanks go to Prof. Liu Xuefu of the BAO for sending the numerous minima appearing only in local Chinese publications. We also express our gratitude to Cracow Pedagogical University, Poland which provided a grant of support to JMK., and to the Chungbuk National University in Cheongju, Korea and the Yonsei University in Seoul, Korea for providing the facilities that permitted completion of the contributions by the two other authors. We also acknowledge our debt to the staff of the CDS for their maintenance and continued availability of the SIMBAD database.


The Authors

July 2000



As mentioned briefly in the preface, the idea of the Atlas was first discussed when the authors gathedarkred for Symposium 151 in Cordoba, Argentina in August, 1991. After several subsequent meetings in Korea and Poland, we agreed to apportion the task in the following way: (1) JMK to collect timings of minimum light and develop the database for the entries and (2) CHK and ISN to compose the general information of the document and the (O-C) diagrams for the individual stars.

The sources of the collected timings were the usual international journals, local journals, observatory publications, and unpublished minima. Among this source material there is a considerable representation by amateur astronomers. To make the collection as complete as possible, we searched in the libraries of Kraków, Warszawa, Poznań, Toruń, Chorzów, St. Petersburg, Tatranská Lomnica, Budapest, Heraklion, Chongju, and Seoul. Some timings were found in the card-index catalogue of the Astronomical Observatory of the Jagiellonian University.

All timings were collected into a database for which code was written by Dr. Krzysztof Koczur of the Institute of Computer Science of the Jagiellonian University and by JMK. The authors are planning to provide Internet access to the database in the near future. When this is ready, we will offer wide notice of the capability in a timely manner.At the moment of printing (2001), the database contains 134,349 timings for 3,851 eclipsing binaries and is as complete as possible through 1999.

Stars were included in the Atlas provided they satisfied 3 criteria: (1) at least 20 minima had been timed; (2) these minima spanned at least 2,500 cycles; and (3) the 2,500 cycles represented no fewer than 40 years. Inevitably, some relaxation of these demands was necessary in order to avoid suppressing useful information. For example, a star was included if it showed apsidal rotation or even just displaced secondary minima but failed to satisfy criterion (1); if it showed unambiguous evidence of a period change but satisfied neither of criteria (2) or (3); if it has a very long period but fewer than 20 minimum timings were observed; if many timings of an object of very short period had been accumulated over an interval shorter than 40 years. The remarks for each star are necessary for interpreting its (O-C) diagram.

In the end, a total of 1,140 binaries corresponding to about 30% of the objects in the database was chosen for the Atlas. These stars are represented by 91,798 timings, i.e., about 70% of the entries that have been collected. The stars are arranged in alphabetical order by constellation into 6 separate volumes. (And-Cnc: 186 stars), (CVn-Cir: 188 stars), (Com-Eri: 200 stars), (Gem-Lyr: 185 stars), (Men-PsA: 187 stars), and (Pup-Vul: 194 stars).


General characteristics

General information pertaining to each star and its (O-C) diagram appear on facing pages. The general information contains 7 items: binary characteristics; assorted catalogue numbers; the statistics of the collected minimum timings; the light ephemeris; scaling information; comments; and literature references. Explanations of these items are given below. Five stars (AP Aur, 44i Boo, SV Cen, U Cep, and β Lyr) show long-term parabolic period variations. These are represented by two (O-C) diagrams which show, first, the effect of only linear light ephemerides and, second, the effect of quadratic light elements.

Successive columns list the J2000 equatorial coordinates, the V magnitude at maximum light, the depth of each eclipse, the spectral types of the component stars if known, the (B-V)-index at maximum light, and the binary type. All these entries we took preferentially from the SIMBAD data base maintained by the CDS at Strasbourg, France; the 1980 version of A Finding List for Observers of Interacting Binary Stars by Wood, et al.; and the 4th edition of the GCVS. The entry under Type preserves the notation from the GCVS editors and the reader is referdarkred to that volume for complete descriptions of all types. If information was not to be found in any of these references, it was extracted from a useful primary paper.

Catalogue numbers

The codes for the various catalogues used for star designations follow:

BD Bonner Durchmusterung number
HD Henry Draper Catalogue number
SAO Smithsonian Astrophysical Observatory Catalogue number
CoD Cordoba Durchmusterung number
CPD Cape Photographic Durchmusterung number
HV Harvard Variable number
BV Bamberg Variable number
HR Harvard Revised Catalogue number
ADS Aitken's Double Star Catalogue number
FL Number in A Finding List For Observers of Interacting Binary Stars (5th ed.)

Other Other Catalogue number. Only one other catalogue designation for each star, if any, is listed. The reader may find the full understanding of an entry under "Others" by consulting SIMBAD, the GCVS, or the Finding List.

Statistics of collected times of minima

Assorted statistics for the times of minimum light of each star appear next. Column 1 shows the total number of the timings; columns 2 and 3 indicate the numbers of primary (Pri) and secondary (Sec) minima; column 4 summarizes the numbers of minima by observational method which is described more amply below; and column 5 gives the initial and ending years of observation.

Vi Visual, the time of minimum light from a series of visual estimates or observations
P Plate, the time of the mid-exposure of a photographic plate, taken accidentally ` when the star was near minimum
Pg Photographic, the time of minimum light from a series of photographic observations
Pe Photoelectric, the time of minimum light from a series of photoelectric observations
Ccd Charge-Coupled Device, the time of minimum light from a series of CCD observations
Other The time of minimum light obtained from methods other than the above (e.g., spectroscopic observations, it etc.)

Light ephemerides

The linear ephemeris used for constructing the star's (O-C) diagram refers to its entire observational history. It is not necessarily useful for pdarkredicting future minima. Each ephemeris has been generated by the authors as were also the non-linear ephemerides for the 5 binaries already cited.


An activity scale

We calculated the quantities ΔT and Δ(O-C)/P for each star in the Atlas. ΔT (hereafter X) indicates the interval in years between the first and last timings. Δ(O-C)/P (hereafter Y) represents the difference between the maximum and minimum values of (O-C) in units of P. Because of the way in which the (O-C)-values are generated from the ephemerides, Y is always positive.

Figure 1 shows the representation of Y against X for all stars in the Atlas segmented by the authors into 9 sub-groups which are based on the authors' arbitrary judgments and not on any physical criteria. Table 1 indicates the character of each of the sub-groups and provides the basis for the segmenting seen in Figure 1. The reader will note a gap in the distribution in time of the history of minimum timings. The gap can be ascribed convincingly to the incidence of World War I.

Table 1. Divisions of X and Y scales.






50y -100y



<0.p 03

0.p 03-0.p 2

>0.p 2


Interpretive remarks appear next if they seemed useful for clarifying the (O-C) diagram. These comments typically explain some detail about the selection of data for composing the diagram or indicate a known physical cause (e.g., apsidal motion, eccentric orbit causing non-equal minima spacings, light time effect due to a gravitationally-bound third star) for the diagram itself.


A complete set of literature references to a star is not given. Rather, one or more reference is cited if it contained a list of minimum timings, a period discussion, or an (O-C)-curve itself. The full list of references may appear in SIMBAD. Abbreviations for the literature references were composed as follows:

A&A Astronomy & Astrophysics
A&AS Astronomy & Astrophysics Supplement Series
AcA Acta Astronomica
AcASn Acta Astronomica Sinica
AJ Astronomical Journal
AN Astronomische Nachrichten
ApJ Astrophysical Journal
ApJS Astrophysical Journal Supplement Series
Ap&SS Astrophysics & Space Science
Azh Astronomicheskij Zhurnal
BAC Bulletin of the Astronomical Institutes of Czechoslovakia
BAVSC Circulars of the Variable Stars Section of the British Astronomical Association
BAN Bulletin of the Astronomical Institutes of the Netherlands
BAVM Mitteilungen der Berliner Arbeitgemeinschaft für Veränderliche Sterne
BAVR Rundbrief der Berliner Arbeitgemeinschaft für Veränderliche Sterne
BBSAG Bulletin der Bedeckungsveränderlichen-Beobachter der Schweizerischen Astronomischen Gesellschaft
ChA&A Chinese Astronomy & Astrophysics
CoSka Contribution of the Astronomical Observatory Skalnaté Pleso
IBVS Information Bulletin of Variable Stars
IAPPP The International Amateur-Professional Photoelectric Photometry Communications
JApA Journal of Astrophysics and Astronomy
JAVSO Journal of the American Association of Variable Star Observers
JRASC Journal of the Royal Astronomical Society of Canada
MitVS Mitteilungen über Veränderliche Sterne, Sonneberg
MNRAS Monthly Notices of the Royal Astronomical Society
MmSAI Memorie della Societa Astronomica Italiana
Obs The Observatory
PASAu Proceedings of the Astronomical Society of Australia
PASJ Publications of the Astronomical Society of Japan
PASP Publications of the Astronomical Society of the Pacific
PAZh Pis'ma v Astronomicheskij Zhurnal
PZ Peremennye Zvezdy (Variable Stars)
RmxAA Revista Mexicana de Astronomia y Astrofisica
VA Vistas in Astronomy
ZfA Zeitschrift für Astrophysik

The (O-C) diagrams themselves

In constructing the diagrams for the ensemble of stars we tried to consider a small number of matters which may be useful and important for the reader.

The first matter has to do with diagram scales. The left and right ordinates are in units of days and period length, respectively. The bottom abscissa counts cycles while the upper, external one is in calendar year and the upper, internal scale shows Julian Day Number. The termination of the abscissa is set for the year 2010 so naturally there are no entries over the interval 2000-2010. Instead a grid covers this extent so that an observer can insert future residuals from the given ephemeris. The scaling of the grid is in days versus years.

Secondly, assorted symbols, differing in size and shape, indicate the different observational techniques. Primary and secondary minima are shown by filled and open symbols, respectively. A legend expressing these symbols appears at the bottom of each diagram.

If there were sufficient photoelectric or CCD timings over a specific interval, concurrent timings by other methods are not shown in the diagram. Information about this choice appears in the comments on the facing page.

The major significance of this Atlas consists in it being the first large, systematic collating of eclipsing minimum timings scattedarkred through the literature. In addition, we foresee that the collection can be used by workers examining period behavior by evolutionary class and binary configuration and other stellar characteristics. Should this lead to more informed choices in composing observing programs, we will be amply rewarded.

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