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Intrinsic Variable Stars
Pulsating variables account for more than half of the known variable stars. They are characterized by slight instabilities that cause the star alternately to expand and contract. This pulsation is accompanied by changes in absolute luminosity and temperature. The pulsating variables can be further divided into the following subclasses: short-term, long-term, semiregular, and irregular. Short-term variables have well-defined periods ranging from less than one day to more than 50 days.
Relatively rare among this subclass are the Cepheid variables; these yellow supergiant stars are historically important because, having periods roughly proportional to their absolute brightness, they provide a means of measuring galactic and extragalactic distances. A key research program of the Hubble Space Telescope is the measurement of Cepheid variables in distant galaxies in order to refine our concept of the size and age of the universe. Cepheid variables are classed as either population I Cepheids, which are found in the spiral arms of galaxies, or population II Cepheids, also known as W Virginis stars, which are found in star clusters (see also stellar populations). About 700 Cepheids of both types have been found in our galaxy.
A more common short-term variable is of the RR Lyrae group; about 6,000 of this type are known in our galaxy and are concentrated in globular clusters. They have periods of less than one day, and all have roughly the same intrinsic brightness. The latter feature, along with their wide distribution throughout the galaxy, makes them another useful distance indicator.
The long-term variables are the most numerous of all pulsating stars. They are red giant and supergiant stars with periods ranging from a few months to more than a year. The best known of these stars is Omicron Ceti, also known as Mira. Over a period of about 11 months, it brightens by about 7 magnitudes and then gradually fades. Semiregular variables are stars whose periodic variations are occasionally interrupted by sudden bursts of light. The best-known example is the red supergiant Betelgeuse, in Orion. Irregular variables show no periodicity in their variations in brightness. The amplitude of their fluctuations in brightness is in general smaller than the fluctuations of the long-term regular variables.
Extrinsic Variable Stars
See D. Levy, Observing Variable Stars (1989).
variable starA star whose physical properties, such as brightness, radial velocity, and spectral type, vary with time: about 30 000 have been cataloged so far. The variation in brightness is the easiest to detect, occurring in almost all variables. It can be seen on the light curve of the star and may be regular – with a period given by one complete cycle in brightness on the light curve – or may be irregular or semiregular. The periods range from minutes to years. The range between maximum and minimum brightness – the amplitude – is also very wide.
There are three major groups of variables: eclipsing, pulsating, and cataclysmic variables. The eclipsing or geometric variables are systems of two or more stars whose light varies as one star is periodically eclipsed by a companion star. These eclipsing binaries can be subdivided into Algol variables, W Serpentis stars, and W Ursae Majoris stars. Pulsating variables, such as the Cepheid variables, periodically brighten and fade as their surface layers expand and contract. Cataclysmic variables are close binary stars where one component is a white dwarf to which mass is being transferred from the other component. This group includes novae, recurrent novae, and dwarf novae. Minor groups of variables include flare stars, rotating variables, spectrum variables, and R Coronae Borealis stars.
These many types also fall into three other main categories: with extrinsic variables the brightness variation results from some process external to the star, as with some eclipsing binaries; with intrinsic variables the variation results from some change in the star itself, as with the pulsating variables; in other cases, such as W Ursae Majoris stars, the variation can result from a combination of intrinsic and extrinsic agencies.
Different types of variable can be distinguished by period and also by light-curve shape: by amplitude of the variation, depth of the minima, size and shape of the maxima, characteristic irregularities, and by the continuous or steplike changes involved. Spectroscopic and photometric measurements can be used to differentiate between borderline cases and to investigate changes in temperature, radial velocity, and spectral type. See also stellar nomenclature.
a star whose visual brightness is subject to variation. Many variable stars are unstable, and the brightness variation in such stars is associated with changes in temperature and radius, ejection of matter, convective motion, and other phenomena. In certain types of stars these changes are regular and repeat with a strict periodicity. However, the instability of stars does not always cause their variability; there are stars in which the ejection of matter, revealed by spectral emission lines, is not accompanied by any noticeable change in brightness. On the other hand, some stable stars are variables: in binary stars, periodic decreases in brightness are caused by one component eclipsing the other. However, in close binary systems physical instability also arises, and streams of gas appear, complicating the apparent picture of the system’s changing brightness. The rotation of stars with an inhomogeneous surface luminosity also leads to variations in brightness.
Variable stars are highly valuable sources of information on physical characteristics of stars. In addition, the properties of variables permit them to be used to estimate the distance to the stellar systems to which they belong; variables also serve as indicators of the stellar population type in these systems. Since variable stars can be easily detected—often at very great distances—they have deservedly received special attention from astronomers. By 1975 the number of variables and suspected variables in our galaxy that had been included in catalogs totaled about 40,000; each year the number of known variables increases on the average by 500 to 1,000. Approximately 5,000 variables in other galaxies are known, and more than 2,000 are known in the globular clusters of our own galaxy. Within each constellation, variables are denoted by Latin letters—a single letter from R to Z or a combination of two letters—or by numerals preceded by the letter V.
Of stars that change in brightness, the easiest to detect are novae. The appearance and subsequent disappearance of novae were noticed in remote antiquity. Bright novae—more accurately, supernovae—were observed in 1572 by Tycho Brahe and in 1604 by J. Kepler. But the first variable whose brightness changed more or less regularly—and not “temporarily,” as in novae—was the star o Ceti (Mira), discovered by the German astronomer D. Fabricius in 1596; in 1667 the French astronomer I. Boulliau determined that o Ceti had an 11-month period. In 1669 the Italian scientist G. Montonari discovered the variability of β Persei (Algol). The British astronomer J. Goodricke (1764–86) discovered a strict periodicity in the decreases of brightness of Algol and discovered and studied the brightness variations in δ Cephei. The British astronomer E. Pigott discovered and studied the brightness variations in η Aquilae. However, the systematic study of variables originated with F. Argelander, who in the 1840’s introduced a method for visually estimating the brightness of variables. By 1866 there were already 119 known variable stars. By the end of the 19th century, it had been demonstrated that the variability of Algol was caused by eclipses of a brighter component by a darker one, and thus the existence of eclipsing variables was discovered. At the same time, the German astronomer A. Ritter advanced a hypothesis according to which the observed variations in stars’ brightness could be explained by pulsations.
The introduction of astrophotography into the study of variable stars led to the discovery of a large number of new variables. In 1915 there were already 1,687 known variables, and in 1940, 8,254. The relation between period and luminosity discovered in 1912 by the American astronomer H. Leavitt allowed H. Shapley to determine the distance to the center of the Milky Way Galaxy and permitted E. Hubble to demonstrate in 1924 that nebulae such as the one in Andromeda are independent stellar systems, that is, other galaxies.
In Russia the systematic photographing and study of variable stars was begun by V. K. Tseraskii and S. N. Blazhko in Moscow in 1895. A new era in the study of variables was inaugurated with the introduction of color photoelectric photometry in the early 1950’s. Under good viewing conditions, modern light detectors permit the study of brightness variations of the order of thousands of 1 stellar magnitude, and a time resolution of thousandths of a second. Careful study is revealing that more and more stars previously considered not to be variables actually do vary but on a very small scale.
In 1946 the International Astronomical Union entrusted the naming of new variables, the publication of catalogs, and the development of a classification system to the Astronomical Council of the Academy of Sciences of the USSR and the P. K. Shternberg State Astronomical Institute (B. V. Kukarkin, P. P. Parenago, P. N. Kholopov). The collection Peremennye zvezdy (Variable Stars) has been published since 1928. In the USSR the study of variable stars is being actively pursued at astronomical institutes in Moscow, Odessa, the Crimea, Biurakan, Leningrad, Abastumani, Dushanbe, Tashkent, Kazan, and Shemakha. Outside the USSR, the most intensive studies of variable stars are being conducted in the USA at the Mount Wilson, Mount Palomar, Kitt Peak, Lick, and Harvard College observatories.
Variable stars are divided into two large classes: eclipsing variables and physical variables.
Eclipsing variables. An eclipsing variable is a system of two stars revolving around a common center of mass, where the orbital plane of the stars is so close to the line of sight of a terrestrial observer that the eclipse of one star by the other is observed every revolution, accompanied by a decrease in the total brightness of the system. The distance between the components is usually comparable to their dimensions. In our galaxy, more than 4,000 stars of this type have been detected. For some of them, namely, β Persei stars, the brightness is practically constant when the stars are not eclipsed, while for others, such as β Lyrae and W Ursae Majoris stars, the brightness changes continuously. This is explained by the fact that because of the relatively small distance between the components, the stars are not quite spherical; they are extended due to tidal forces. The change in brightness in these systems is caused not only by eclipses but also by the star’s continuously changing surface area facing the observer; in certain cases, the eclipse is absent altogether. The periods of brightness variation in eclipsing variables, which coincide with the orbital periods, are diverse. In W Ursae Majoris stars with almost contiguous components (dwarfs), the periods are less than a day; in β Persei stars, of the order of hundreds of days; and in certain systems that include supergiants, for example, VV Cephei and ε Aurigae, of the order of tens of years.
Eclipsing variables provide a unique opportunity for determining a number of very important stellar characteristics, especially when the distance to the system and the radial velocity curves of the components are known. Interest in eclipsing binaries grew dramatically when a number of them were identified as cosmic X-ray sources. In some cases—including HZ Herculis or Hercules X-l, and Centaurus X-3—eclipses are also observed in the X-ray region. Moreover, by means of the Doppler shift in the period of the X-ray pulses it is possible to determine the orbital elements of the components. As in the case of radio emission from pulsars, these periods are of the order of a few seconds and provide evidence of the rapid rotation of an X-ray-emitting white dwarf, or neutron star, belonging to the binary system. In a number of close binary systems the optically visible component is a class-B supergiant; in these cases, eclipses are not observed in the X-ray region and sometimes not even in the optical region. The mass of the invisible component in these systems apparently exceeds three solar masses, and such stars, especially Cygnus X-l or V1357 Cygni, should evidently be regarded as black holes. The cause of the X-radiation in close binary systems is, from all appearances, the accretion by the dense component of stellar wind or gas streams from the visible component.
Physical variables. Physical variables change in brightness as a result of physical processes occurring within them. They are subdivided into pulsating variables and eruptive variables.
PULSATING VARIABLES. Pulsating variables are characterized by smooth and continuous changes in brightness; in the majority of cases these can be explained by pulsations in the outer layers of the star. When a star contracts, its radius decreases, and the star gets hotter and its luminosity increases. When a star expands, its luminosity decreases. The periods of pulsating variables range from fractions of a day (RR Lyrae, δ Scuti, and β Canis Majoris variables) to tens of days (cepheids, RV Tauri stars) and hundreds of days (Mira-type variables, irregular variables). The period of the brightness variation is maintained in some variables with clockwork precision (certain cepheids and RR Lyrae stars), but in others it is almost entirely lacking (red irregular variables). About 14,000 pulsating stars are known.
Long-period cepheids are supergiants with periods of 1 to 50–200 days and brightness-variation amplitudes of 0.1 to 2 photographic magnitudes. The period and shape of the light curve is, as a rule, constant. The radial velocity curve is almost a mirror image of the light curve: its maximum practically coincides with the minimum of the light curve, and its minimum with the light curve’s maximum. Long-period cepheids fall in the spectral classes F5-F8 at maximum brightness and F7–KO at minimum. The later the cepheid’s spectral class, the longer the period, and the longer the period, the greater the luminosity.
Mira-type stars are long-period giants with amplitudes of more than 2.5 stellar magnitudes—up to 5–7 magnitudes and more—well-defined periodicity, with periods ranging from approximately 80 to 1,000 days, and emission spectra characteristic of the late spectral classes (Me, Ce, Se).
Irregular variables are stars of late spectral classes (F, G, K, M, C, S), which are subgiants, giants, or supergiants and which have a marked periodicity accompanied by various irregularities in brightness variation. The periods of irregular variables vary widely, approximately 20 to 1,000 days or longer. The light curves are very diverse in shape, and the amplitude usually does not exceed 1 to 2 magnitudes.
RR Lyrae stars, which are short-period cepheids, or globular cluster variables, are pulsating giants with the characteristics of cepheids. Their periods range from 0.05 to 1.2 days. They fall in spectral classes A and F and have amplitudes of up to 1 or 2 magnitudes. Cases are known in which both the shape of the light curve and the period change. Sometimes these changes are periodic (the Blazhko effect).
δ Scuti stars are subgiants of spectral classes A and F that pulsate with a period of a few hours and an amplitude of several hundredths or tenths of a magnitude.
RV Tauri stars are supergiants with a relatively stable periodicity and an overall amplitude of up to 3 magnitudes. The light curve consists of double waves with alternating principal and secondary minima. The period ranges from 30 to 150 days, and the spectral class ranges from G to late K, although occasionally titanium oxide bands appear, which are characteristic of stars of spectral class M.
β Cephei stars, or, as they are often called, β Canis Majoris stars, are a homogeneous group of pulsating giants with an amplitude of no more than 0.1 magnitude. Their periods range from 0.1 to 0.6 days, and they fall in spectral classes B0 to B3. In contrast to cepheids, their maximum brightness occurs when their radii are at their minimum.
ERUPTIVE VARIABLES. Eruptive variables are characterized by irregular, often rapid and pronounced, changes in brightness brought about by processes of an explosive (eruptive) nature. These stars are divided into two groups: (1) young, recently-formed stars—such as fast irregular variables (Orion stars) — irregular T Tauri stars, flare stars of the UV Ceti type, and related objects that are numerous in very young star clusters and are often associated with diffuse matter; and (2) stars that are usually more or less always stable but from time to time exhibit rapid and pronounced increases in brightness: novae, super-novae, recurrent novae, U Geminorum stars, nova-like stars, and symbiotic variables; the last are characterized by the presence of spectral lines typical both of hot and of cool stars. In many, if not all, cases, stars of this group turn out to be binaries. More than 1,600 eruptive stars are known.
Orion stars are irregular variables associated with diffuse nebulae or observed in regions of such nebulae. This group also includes some fast irregular variables that are apparently not associated with diffuse nebulae and that vary in brightness by 0.5–1.0 magnitude over the course of several hours or days. These stars are sometimes assigned to the special class of RW Aurigae variables; however, there is no sharp dividing line between RW Aurigae and Orion stars.
T Tauri stars are irregular variables whose spectra have the following attributes: the spectral class ranges from F to M; a typical spectrum resembles the spectrum of the solar chromosphere; and the spectrum contains abnormally intense fluorescent emission lines of FI, with wavelengths of 4,046 Ǻ and 4, 132 Ǻ. These stars are usually observed only in diffuse nebulae.
UV Ceti stars are stars that sometimes flare up with amplitudes of 1 to 6 magnitudes. Maximum brightness is achieved a few seconds or tens of seconds after the outburst begins, and the star returns to its normal brightness in several minutes or tens of minutes. UV Ceti stars are encountered in star clusters as well as in the neighborhood of the sun.
Novae are hot dwarfs that increase in brightness by 7 to 15 magnitudes in a few days and then return to their former brightness over the course of several months or years. Spectral data show that the star ejects an expanding shell, which gradually dissipates in space. In recurrent novae the outbursts repeat themselves with a period of several tens of years; it is possible that even ordinary novae, whose brightness variation is much greater, repeat their outbursts every few hundred or thousand years.
U Geminorum stars are stars that usually exhibit small, rapid fluctuations in brightness. During an average cycle of several tens or hundreds of days, increases in brightness of 2 to 6 magnitudes are observed; moreover, the larger the outbursts, the more rarely they occur. Like novae, stars of this type are close binary systems; their outbursts are somehow connected to an exchange of material between the components, which are at different stages of evolution.
In a separate group are stars whose brightness variation is caused by an inhomogeneous surface brightness, which causes the apparent brightness to change as the star rotates. To this group belong first of all BV Draconis stars, which, like UV Ceti stars, exhibit sudden, rapid outbursts but also undergo small, periodic brightness variations. Apparently this group also includes magnetic variables and α Canum Venaticorum stars. These are stars of spectral class A, whose spectra contain abnormally intense lines of silicon, strontium, chromium, and rare-earth elements, which change in intensity with the same period as the brightness and the magnetic field, which is always observed in stars of this type. The variation usually does not exceed 0.1 magnitude, and the period varies from 1 to 25 days. The variability can apparently be explained by the symmetric surface disposition of regions of different temperatures and chemical composition relative to the magnetic axis, which is inclined with respect to the axis of rotation (the “oblique rotator” hypothesis).
Supernovae have not been observed in our galaxy since the time of Tycho Brahe and Kepler, but up to 20 are discovered in other galaxies every year; in all, more than 400 had been discovered by 1975. A supernova explosion is the mightiest phenomenon in the stellar world. At maximum brightness, a supernova sometimes attains a brightness equal to the combined brightness of all the remaining stars in its galaxy. Supernova explosions are related to the onset of a star’s collapse after its sources of nuclear energy have been exhausted. After the explosion, the supernova is transformed into a pulsar—a neutron star rotating with a period of a few seconds or fractions of a second. The observed pulses of radiation from a pulsar are a result of a narrow cone of electromagnetic radiation emerging from the magnetic poles of the pulsar, which do not coincide with the pulsar’s poles of rotation. At present, only one pulsar has been identified with a visible celestial object—CM Tauri. It is the result of a supernova explosion in 1054, which also led to the formation of the Crab Nebula.
The reasons for brightness variations in physical variables and the place occupied by these variables in stellar evolution form a closely related set of problems. Evidently, variability is characteristic of stars at certain stages in their evolution. The study of variables in star clusters is particularly important for an understanding of the nature of variability, since for stars belonging to clusters it is possible to determine both the age and stage of evolution. Also important for understanding variability is the analysis of the position of variable stars of different types on a spectrum-luminosity diagram—the Hertzsprung-Russell diagram.
Clusters that contain fast irregular variables are very young (106–107 years). In these clusters, only the most massive stars, with high luminosities, have reached the main sequence on the Hertzsprung-Russell diagram, occupying its upper part and appearing as ordinary stable stars. In stars with smaller mass and lower luminosity, gravitational contraction is not yet complete, and a broad convective zone still exists in which irregular, violent motions of gas occur; apparently, both brightness and spectral variations in young stars are related to this.
A number of types of pulsating variables are situated on the Hertzsprung-Russell diagram within a band of instability, which cuts across the diagram from the red supergiants of class K to the white dwarfs of class A. These include cepheids, RV Tauri stars, RR Lyrae stars, and δ Scuti stars. In all these stars there is apparently a single variability mechanism at work that causes a pulsation in the stars’ outer layers. Neighboring stars on the Hertzsprung-Russell diagram, for example, cepheids of types I and II, have similar variation characteristics, but their evolutionary history, masses, and internal structures can differ sharply.
The study of the spatial and kinematic characteristics of variable stars have one of the principal factors leading in the 1940’s to the development of an understanding of the components of our galaxy and of stellar populations.
REFERENCESObshchii katalog peremennykh zvezd. 3rd ed., vols. 1–3. Moscow, 1969-71.
Pul’siruiushchie zvezdy. Moscow, 1970.
Eruptimy zvezdy. Moscow, 1970.
Zatmennye peremennye zvezdy. Moscow, 1971.
Metody issledovaniia peremennykh zvezd. Moscow, 1971.
IU. N. EFREMOV