The Nature of Variable Stars*

Transactions of the Royal Society of New Zealand : General, Volume 1, Issue 21, 30 November 1966, Page 233

The Nature of Variable Stars*

Frank M. Bateson

By

It is probably fitting that the theme of this Donovan Memorial Lecture should deal with Variable Stars, since it is almost 31 years to the day that the Donovan Trustees made their second award to me. Whereas their first award had been for the observations of meteors, the second was given “ for work on variable stars and in the organisation of the Variable Star Section of the New Zealand Astronomical Society This award directly led to a life-long interest in fostering the observation of variable stars.

A variable star can be defined simply as one that changes in apparent brightness. If you look out over the lights of Wellington at night you will at once notice that the majority appear to shine steadily. But you will also see that some flash on and off at regular intervals; others suddenly blaze forth and then gradually die away, whilst still others shine with a fluctuating intensity. So it is in the heavens. There, the vast majority of stars shine steadily. Those that do not are the variable stars.

Historical

Novae were undoubtedly the first variable stars recorded. Records of their outbursts date back thousands of years. Almost one hundred are recorded in the Chinese annals. It is probable that some of the brighter ordinary variable stars were also known in ancient times. But if this is true then no records of their behaviour have been passed down to us. Most likely nobody considered them very important.

The first definite record of a variable star was made in 1596 when Fabricius discovered Mira Ceti. The history of variable stars can, however, be dated from 1639. It was in that year that Holwarda and Fallenius first showed that Mira appeared and disappeared from naked eye visibility at regular intervals. Progress in discovery was at first slow since this depended entirely on chance. The first catalogue of these stars was published by Pigott in 1786 and contained 12 entries. Systematic charting of the sky, combined with the establishment of a proper magnitude system, resulted in more discoveries. This in turn lead to the regular observation of these stars, mainly through the efforts of E. C. Pickering and Hagen.

With the application of the photographic plate to astronomy both the rate of discovery and studies of known variables were greatly accelerated. This was especially true at Harvard under Pickering. The advances thus made possible resulted in many important discoveries, such as the period-luminosity relation for Cepheids in the Magellanic Clouds and the recognition of a new class of variables—the cluster or RR Lyrae type. Photographic photometry was born and has been of enormous importance ever since. Spectrum analysis also has played a large part in interpreting the physical nature of variable stars.

The much more recent development of photo-electric photometry has permitted the discovery of stars of very small range. It has also made possible detailed studies that have provided much of our knowledge of the masses, sizes, atmospheric conditions, surface temperatures and densities of stars. It has permitted the precise study of stars in several different colours.

The last edition of the General Catalogue of Variable Stars, published by Kukarkin and his colleagues in 1958, contains data on 14,708 stars. Even since then the number known has increased by several thousand, whilst, in addition, there are something like ten thousand others, whose suspected variations await confirmation.

Methods of Observation

The attempt to learn new facts about these thirty thousand stars has brought about a high degree of international co-operation that embraces both amateur and professional alike. The observation of variable stars is one field in which observations by amateurs play a most important part. Much of the basic data has been built up entirely through the efforts of the members of the great national organisations that direct the work of the amateurs. It is essential to our understanding that records be secured visually as well as by all other means.

In visual work simple eye estimates are made of the variable star under observation. This is done by comparison with stars whose brightness is not only constant but well determined. Normally due to the consistent observations available it is possible to take the mean magnitude derived from such observations in an interval that may be ten days for the long-period stars, but only a day or less for the short-period or rapidly-changing stars. Such means are quite accurate and permit the form and nature of the light curve to be determined as well as fixing the times of maxima and minima. After a star has been followed through a large number of cycles it is possible to establish its mean light curve and to find the amount by which the star varies from such mean curve. It leads to the first basis of classification.

In order to take full advantage of the efforts of the thousands of individual amateurs, several national variable star organisations correlate the records of their members and publish the results in a form that makes the observations readily available to those wishing to make detailed studies of stellar variability. Examples of analysis of the light curves are to be found in the classic discussion of the AAVSO results by Campbell (1955) and in our own discussions of the New Zealand results.

The Variable Star Section of the Royal Astronomical Society of New Zealand is one of the main centres for the collection and publication of results. One can truthfully say that the original encouragement from the Donovan Trustees has led directly to this work, which embraces not only New Zealand but also Australia and observers elsewhere. Since the establishment of the New Zealand Section in 1927, almost half a million observations have been made by its members. These have resulted in a major contribution to our knowledge of southern variables. The

true behaviour of many of these stars was entirely unknown before we commenced observing them. It is not inappropriate to mention just what one person can do. We are very proud of the fact that among our members we have the world’s most prolific observer—Albert Jones of Nelson. In 21 years of observing he has made just over 150,000 separate records. That represents a monumental effort, notably not only for its number but also for the accuracy of his devoted application.

Far from the day of the visual observer being past, such records are more essential than ever. In the Southern Hemisphere there is a vast number of stars yet to be investigated as well as the most interesting of all stars in such objects as Eta Garinae, the large groups of RW Aurigae stars and classic examples of every known type of variable.

Allied with visual estimates are various types of photometers, that permit the more accurate measurement of small variations in light intensity . However, these have now been largely superseded by the photoelectric photometer. Some of our members, notably Harries-Harris and Waters, in South Australia, have applied simple photometry to short-period variables with marked success.

Photographic observations have the great advantage that the plates can be stored and their records are available for studies at all times. From these plates direct estimates can be made of the brightness of any star recorded. Such estimates have the same degree of accuracy as visual estimates. For the average amateur, photographic recording has to be limited in extent due to the cost. But we number among our members some, notably Menzel in Western Australia, who are providing regular photographic observations. These enable light curves to be constructed separately for comparison with visual records, an aspect of research that is normally left to the professional.

Photographic results are particularly valuable in patrol or survey work. For instance at Mount John we shall have a programme, in conjunction with other observatories, whereby plates are taken at frequent intervals of certain selected areas. This has a twofold purpose. It enables all variables within such fields to be studied and at the same time permits the detection and study of variables as yet unknown. This method has been applied with some success in the discovery of supernovae. Another example of the value of the photographic method is the detailed study of variables made by the Harvard Milton Bureau survey, under Sergei Gaposchkin, resulting in well-determined elements for all the stars studied. We have made a similar study of the extensive plates being taken by Stranson in Queensland of all variable star fields south of declination South 30°. These form the basis of charts that are prepared under a grant from the International Astronomical Union. To date 44 charts have been published, and 100 more will be ready in about two months’ time, covering some 200 variables.

Because of the precise nature of photo-electric photometry, and its advantage of being able to observe in several colours, it is specially suited to the study of shortperiod variables. There is a wide open field here, especially in the Southern Hemisphere, for amateurs willing to undertake photo-electric observing. In this regard, size of the instrument is not the limitation that many people think. A telescope of around 16 inches aperture, equipped with a modem photo-electric photometer, has the same relative value in the study of variable stars as the 200-inch at Palomar has in securing slit spectral plates.

Glassification of Variables

As the number of known variables grew, attempts were made to classify them into different groups or classes- At first such classification was entirely dependent

on the more obvious features of the light variations, such as period, range and form of the light curve. The first classifications that attempted to reveal deeper relations among variable stars were due to Ludendorff (1928) and the Gaposchkins (1938), based on interpretative models. Amendments are still being made, and will continue to be made as our knowledge of the stars grows and new groups are discovered.

The three main groups of variables are:

ERUPTIVE, PULSATING, ECLIPSING.

Each main class can be divided into a large number of types, each of which represents stars of a distinctive kind. Smaller differences among the objects within a type are taken care of by several sub-types within each class.

Before we consider these divisions we need to refer to what is known as the Hertzsprung-Russell diagram, or more simply as the H-R diagram, in which we plot spectral types (or temperatures, or colour indices) against absolute magnitudes. In effect these plots show the relation between temperatures and the intrinsic brightness of the stars, since absolute magnitudes are defined as the magnitudes that stars would have if they were at the standard distance of 10 parsecs (about 32.6 light years).

The name eruptive suggests stars whose light variations are due to some form of explosion. It would appear that they represent non-stable objects, whose changes in brightness are due to some deep-seated internal cause within the star.

The most spectacular variables are the supernovae. These appear to have a preference for appearing in spiral nebulae, especially in those with open resolved arms. At maxima they shine with a brilliance that is between 100 million and 100,000 million times that of the Sun. Perhaps you can appreciate this better if I mention that the absolute magnitude of the Sun is +5. Thus, at the standard distance of 10 parsecs, the Sun would shine as a star just visible to the naked eye. At the same distance the average supernova would appear four times brighter than the Full Moon appears to us. These objects have a very sudden and large increase in brightness that amounts to 20 magnitudes or more. They remain at maximum briefly before commencing to decline and after several months they return to their original brightness.

We do not know what precedes a supernova. What remains after an outburst is probably an expanding shell of gas. For instance, the Crab Nebula is the remnant of the supernova of 1054. It is at the present time a strong cosmic radio source. Systematic searches are now made for supernovae in various extra-galactic nebulae in the hope that a better knowledge of their distribution in space can be obtained. It is also desired to understand more fully how they behave. Zwicky (1958) has estimated that within the volume of space accessible to the 200-inch telescope there exists at any given time, about 200 million supemovae at stages near maxima.

If we regard supemovae as the ultimate in explosions then ordinary novae, whilst certainly spectacular, are just small ones. These stars suddenly increase in brightness, usually in a matter of hours, by some 10 to 12 magnitudes. In general the rapid rise is followed by a slight pre-maximum halt, before a final slower and slight rise to maximum brightness. Then follows a decline of a magnitude or two and the nova fluctuates as if passing through a transition stage. Then comes the more or less smooth decline until the star returns to its original magnitude. The time taken for this decline is a few years for a fast nova to perhaps a 100 years for a very slow one.

Many of you, no doubt, remember the brilliant nova of 1925 in the constellation Pictor. This star reached first magnitude and for a few brief days was one of the brightest stars in the southern sky. Now 41 years after its outburst it is still very, very slowly fading and has not quite reached 12th magnitude. It is still observed by many of our members. It is a typical slow nova.

Again many more of you will remember the brilliant nova that flashed forth in 1942 in Puppis. This was even brighter than Nova Pictoris and is a typical fast nova. By 1958, it had faded below the fourteenth magnitude.

Many interesting facts have been found about these stars. Not the least of these is that a number are close binaries. Nova Herculis 1934, for instance, is an Algol type variable with an extremely short period around a fifth of a day and a range of one and a-half magnitudes. Prior to its outburst this star had a slightly shorter period. Kukarkin and Parenago (1963) have suggested that the increase in period, since the outburst, indicates that less than half percent of its mass was lost. That means essentially that a nova outburst does not change the character of a close pair. Nova Pictoris 1925 is even more interesting. Three years after its outburst Van den Bos and Finsen saw, surrounding the star, what appeared to be three satellites of unequal brightness. It is certain that these were merely irregular patches of ejected matter that travelled away from the star.

It is estimated that about 50 galactic novae appear every year, of which we observe one or two. Since they are concentrated towards the galactic centre, a search in the Scorpio-Sagittarius region would repay anybody willing to make a regular photographic patrol of them from this country. For instance many have been found clustered around the well-known variables SX and SV Scorpii and appear on our chart of that region.

Allied with ordinary novae are what are termed recurrent novae. Compared to the explosion of an ordinary nova these represent rather small sneezes. They have a smaller range, usually of around eight magnitudes, and differ from the novae proper in having had more than one outburst. Only a limited number are known and for these there is a rough average cycle of 35 years between outbursts. Of course, quite a number of people have suggested that all novae are recurrent but we are unable to observe more than one outburst simply because ordinary novae might have a cycle that is measured in millions of years. These are frustrating stars to observe since year in and year out they remain dormant with little variation. Then suddenly one is rewarded by an outburst. Such has been the case with RS Ophiuchi, whose last outburst was discovered by myself.

Included in the eruptive type stars are several groups in which flares are frequent but small in amplitude. The best known type are the U Geminorum variables. Like so many of the eruptive class these are dwarf stars that normally have slight fluctuations during the intervals between flares. The extent of the flares range from two to six magnitudes, reached in a period of hours or one or two days. They return to their normal brightness in a period that may be from a few days to several weeks. The intervals between flares for any one star changes within wide limits, but each star has some mean cycle, usually between 20 and 600 days.

One of the best known examples in the southern sky is VW Hydri, about which little was known until our studies commenced. It deserves to rank as one of the most important and interesting stars of this group. Whilst the intervals in its outbursts may vary between 11 and 59 days it has a mean cycle of 28.72 days. There are two types of maxima, which I have termed “ flat ” and “ normal ”. Flat maxima, when the variable remains bright for longer periods but with some fluctuations, are separated by five “normal” maxima. Flat maxima occur roughly every 179 days. Following such a maximum the star is very active and normal maxima follow each other in rapid succession, but with the intervals between them gradually lengthening.

It almost suggests that the source of the activity is growing weaker. Then preceding the next “ flat ” maximum is a long quiet period. It has been found that several of the stars of this class are double and it appears likely that all will eventually be found to have companions.

By contrast, the R Coronae Borealis variables have rather slow non-periodic drops in brightness ranging from one to nine magnitudes. Such drops may last from around 10 days to several hundred days. Stars of this type are of high luminosity and belong to classes F, G, K and R. It has been suggested that their variations are due to a veiling effect. Among stars of this type studied by us are S Apodis and RY Sagittarii. It has been found that for these two stars there is a periodic fluctuation during the time they are bright.

We find another type of dwarf star in the UV Ceti variables. These have infrequent and very short flares with a range of from one to six magnitudes. The increase takes place in a matter of a few seconds, after which they fade away in a period of a few minutes. As some of you know efforts are made to obtain observations both visually, photo-electrically and by radio techniques at the same time for such flares.

We now come to the RW Aurigae and T Tauri stars, which are associated with dark nebulae. One of the best examples of such an association is that in Corona Australis. Here too we have surrounding R Coronae Australis a typical example of the fan-shaped nebula that often exists in association with such stars. The nebula itself is variable, and appears together with similar nebulae attached to two other T Tauri type stars. The R Coronae Australis nebula does not fluctuate in step with the star with which it is associated. Rather it appears as if waves of light spread outwards from the star across the nebula, successively illuminating different portions of it.

RW Aurigae variables are usually considered to be irregular. Their spectra can range from B to M, both with and without emission lines. In brightness they can change by a fraction of a magnitude to as much as four magnitudes. They are among the most interesting stars to observe, since, at times, they are extremely active and changes can take place from one hour to the next or even within a matter of minutes. At other times they shine almost steadily for weeks. Our organisation has paid particular attention to the RW Aurigae class and has taken part in several international programmes of intensive study of them. One result of this is the discovery that a number do actually have a basic period, around two and a-half days, although their actual variation can be quite different at different times. However, this period appears stable no matter how the stars are changing. It lead Hoffmeister, at the Hamburg I.A.U. meeting, to suggest that the cause of variation is something akin to sunspots causing alternate bright and dark areas on the outer surface of the star. It is more probable that being very young stars the cause of the variations is due to instability within the star.

Within the Orion nebula and surrounding regions there lie a large number of these objects. Another of these associations is to be found in the southern sky in Chamaeleon. The star T Chamaeleontis is notable for its almost continuous changes.

So far I have told you something of the nature of some rather wonderful and perhaps weird stars. But it remains to tell you about the most striking of them all. Again it is a star that can only be seen from the southern hemisphere and is one that has been most consistently studied by our members. This is Eta Carinae, a star so complex that it is simply unique. At present this star is almost constant just below naked eye visibility at magnitude 6.4. It was known at the end of the 17th century as a star of third or fourth magnitude. By the middle of the 18th century it was second or third magnitude. It then faded slightly but in 1835 it increased to

reach first magnitude. Its greatest glory was yet to come. In 1843 it outshone every star in the sky except Sirius, the brightest of all stars. For 15 years it remained a first magnitude star after which it took seven years to fade below naked eye visibility. After remaining around eighth magnitude for many years, Eta Garinae commenced to brighten around 1936. It has increased very slowly ever since. It is probable that this brightening has not been due to any increase from the star itself, but has resulted from a brightening of the halo that surrounds the star. No observer can watch this region without failing to be impressed by the wonder and beauty of both stars and nebulae. Just what Eta Garinae will do next I cannot predict. We all hope that eventually it will shine forth as it did in 1843.

The pulsating type of variable, whilst lacking in the spectacular appeal of the eruptive class, pose their own problems and number among their members the largest group of variables studied by us.

Many giants and supergiants, mainly of the late spectral types, belong to the large class of semi-regular variables. On the whole these stars do show some kind of period but these are subject to considerable variations. Their light curves are often different from period to period. This is often the result of different periods and amplitudes for the same star superimposed on each other. It is rather natural that since they include a wide diversification, they are sub-divided into several groups. Most do not have a range in excess of one or two magnitudes, whilst their periods range from around 30 days to 1,000 days or more. Alpha Orionis is a typical red semi-regular variable, whilst RV Tauri is representative of a distinctive class of supergiants with periodically varying mean brightness.

By far the most numerous and best known class of variables is the long period type, like Mira Ceti. These are giant stars with emission spectra of the late spectral types, M, N, S and R. Their periods can range from 80 to 1,000 days and their visual amplitudes from two and a-half to seven or eight magnitudes. In general the light curves remain in form much the same from one period to the next, but there is a certain amount of irregularity in individual periods. This can amount to up to 15 per cent of the mean period.

Two main groups of Cepheids are included among pulsating variables. First are the long-period, or classical Cepheids of which Beta Doradus is a typical example. The group is sub-divided into three sub-groups dependent upon their position in space. The periods of these stars, between one and a-half days and 80 days, show very little departure from the means. All such stars are supergiants of spectral types F, G and K. Cepheids happen to be very useful stars. If you observe one long enough to determine its period, and knowing also its apparent brightness, you can determine its distance.

Like the long-period Cepheids, those of short periods have spectra and temperatures that vary in phase with the brightness. In this group we have stars whose periods range from one and a-half hours to one and a-half days. More often these stars are referred to as RR Lyrae or cluster-type variables. Their amplitudes do not exceed one or two magnitudes. The name, cluster variable, was given because so many of them were found in globular clusters. Then Mrs Fleming found one, RR Lyrae, that was not a member of a cluster. It was thought it represented a star that had escaped from a cluster. But as the number discovered outside clusters rapidly increased it could not be held that they were all stars escaped from clusters.

Finally among the pulsating variables we come to stars of spectral types B 1 to 83. These have periods that lie between 0.1 and 0.3 days. Their range is extremely small and generally amounts to a mere tenth of a magnitude.

Eclipsing stars are not intrinsic variables; their variations are due to the eclipse of one component of a close double by the second component during their revolution around a common centre of gravity for the system. They have proved extremely important in unravelling many of the problems of stellar structure. They are best studied by photo-electric methods, which enables precise determination of their changes. In turn these data provide information on the complex processes that take place in stellar atmospheres and the envelopes around them.

Their light between minima is almost, but not quite constant. This can be caused by physical effects in the atmospheres of the components. Periods for this type range from four and a-half hours to many years. This wide difference appears to depend on the nature of the components, which may be any kind from subdwarfs to supergiants. The components have the form of slightly flattened spheroids.

Beta Lyrae eclipsing stars have curves showing that the light variations are continuous between minima. Their periods are from half a day to about 200 days. It is probable that their components have complicated figures so that their projected surfaces as seen by us change continuously as the components revolve around the common centre.

With very short periods of from six-hundredths of a day to one day, the W Ursae Majoris variables also have a continuous light variation. These stars have figures very much the same for both components and are also in direct contact with each other.

Variable Stars and Stellar Evolution

Naturally there are a host of questions that can be asked concerning variable stars once we have determined their nature. Is their instability due to passing through some stage of transition in the life history of a star? How do they indicate the stage reached in their life history?

Modern theories of stellar evolution suggest that stars originate in a cloud of dust and gas which condenses into a group of stars. They spend a short time, comparatively speaking, at a phase when they are subject to gravitational contraction. This phase is terminated when sufficient heat has been built up within the star to produce pressure that will withstand gravitational contraction. The star then enters on a long life as a star of the main sequence. The actual mass of the star determines its position on the main sequence.

In young galactic clusters, the fainter stars of O and B types are already on the main sequence. Within the cluster other still fainter stars may be found not yet on the main sequence. Such clusters are associated with interstellar clouds. The RW Aurigae and T Tauri type stars exist in these associations and are above the main sequence. That means that such stars are extremely young and are still contracting.

When a star is on the main sequence, its intrinsic brightness (or mass) controls how rapidly it burns up its hydrogen. The stage at which stars leave the main sequence is dependent on the luminosity of the star, so that we may find supergiants, giants and subgiants off the main sequence. Variability is a distinguishing mark of instability in the life of a star.

A useful method of discussing points about stellar evolution is by use of what is known as the H-R diagram as I have already pointed out. Naturally such diagrams show marked differences between various parts of the Universe. That is due to the age and composition and type of stellar population that makes up the parts of the various clusters and nebulae.

With this background in mind it is possible to see exactly where the various classes of variables are placed in such diagrams. That in turn enables us to obtain some idea of whether they do in fact mark stages of transition.

It has been impossible to deal more than superficially with variable stars. But I have attempted to tell you something of their nature and to indicate their importance. I hope I have also conveyed to you something too of the reasons that make them such a fascinating study to amateur and professional alike. Locked within them are the secrets of stellar evolution for they are the fossils of the heavens from which we can extract information that will cast light on a star’s history if we can but read the clues aright.

Acknowledgment

I wish to thank Mr M. S. Bessell, Mount Stromlo Observatory, for supplying the slides with which this lecture was illustrated.

References

Campbell, L., 1955. Studies of Long Period Variables. Wakefield, Mass: Murray Printing. Gaposghkin, G. P. and S., 1938. Variable Stars. Harvard Observatory Monograph No. 5. Kukarkin, B. V., and Parenago, P. P., 1963. Basic Astronomical Data. Edited by K. Aa. Strand. Chicago: Univ. Press. Page 341. Ludendorff, H., 1928. Die veranderlichen Sterne. Hdb. d. Ap. Vol. 6. Berlin: Springer. Zwicky, F., 1958. Handbuch Der Physik. Vol. LI, Berlin. Springer. Pages 773-775.

F. M. Bateson, Mount John University Observatory, Lake Tekapo.

* The text of the Donovan Lecture for 1965.