A star is classified as variable if its apparent magnitude as seen from Earth changes over time, whether the changes are due to variations in the star's actual luminosity, or to variations in the amount of the star's light that is blocked from reaching Earth. Many, possibly most, stars have at least some variation in luminosity: the energy output of our Sun, for example, varies by about 0.1% over an 11 year solar cycle,[1] equivalent to a change of one thousandth of its magnitude.
It is convenient to classify variable stars as belonging to one of two types:
The first variable star was identified in 1638 when Johannes Holwarda noticed that Omicron Ceti (later named Mira) pulsated in a cycle taking 11 months; the star had previously been described as a nova by David Fabricius in 1596. This discovery, combined with supernovae observed in 1572 and 1604, proved that the starry sky was not eternally invariable as Aristotle and other ancient philosophers had taught. In this way, the discovery of variable stars contributed to the astronomical revolution of the sixteenth and early seventeenth centuries.
The second variable star to be described was the eclipsing variable Algol, by Geminiano Montanari in 1669; John Goodricke gave the correct explanation of its variability in 1784. Chi Cygni was identified in 1686 by G. Kirch, then R Hydrae in 1704 by G. D. Maraldi. By 1786 ten variable stars were known. John Goodricke himself discovered Delta Cephei and Beta Lyrae. Since 1850 the number of known variable stars has increased rapidly, especially after 1890 when it became possible to identify variable stars by means of photography.
The latest edition of the General Catalogue of Variable Stars[2] (2008) lists more than 46,000 variable stars in our own galaxy, as well as 10,000 in other galaxies, and over 10,000 'suspected' variables.
The most common kinds of variability involve changes in brightness, but other types of variability also occur, in particular changes in the spectrum. By combining light curve data with observed spectral changes, astronomers are often able to explain why a particular star is variable.
Variable stars are generally analysed using photometry, spectrophotometry and spectroscopy. Measurements of their changes in brightness can be plotted to produce light curves. For regular variables, the period of variation and its amplitude can be very well established; for many variable stars, though, these quantities may vary slowly over time, or even from one period to the next. Peak brightnesses in the light curve are known as maxima, while troughs are known as minima.
Amateur astronomers can do useful scientific study of variable stars by visually comparing the star with other stars within the same telescopic field of view of which the magnitudes are known and constant. By estimating the variable's magnitude and noting the time of observation a visual lightcurve can be constructed. The American Association of Variable Star Observers collects such observations from participants around the world and shares the data with the scientific community.
From the light curve the following data are derived:
From the spectrum the following data are derived:
In very few cases it is possible to make pictures of a stellar disk. These may show darker spots on its surface.
Combining light curves with spectral data often gives a clue as to the changes that occur in a variable star. For example, a pulsating star betrays itself in its spectrum because its surface periodically moves to and from us, in the same tempo as its brightness varies.
About two-thirds of all variable stars appear to be pulsating. In the 1930s astronomer Arthur Stanley Eddington showed that the mathematical equations that describe the interior of a star may lead to instabilities that cause a star to pulsate. The most common type of instability is related to oscillations in the degree of ionization in outer, convective layers of the star.
Suppose the star is in the swelling phase. Its outer layers expand, causing them to cool. Because of the decreasing temperature the degree of ionization also decreases. This makes the gas more transparent, and thus makes it easier for the star to radiate its energy. This in turn will make the star start to contract. As the gas is thereby compressed, it is heated and the degree of ionization again increases. This makes the gas more opaque, and radiation temporarily becomes captured in the gas. This heats the gas further, leading it to expand once again. Thus a cycle of expansion and compression (swelling and shrinking) is maintained.
The pulsation of cepheids is known to be driven by oscillations in the ionization of helium (from He++ to He+ and back to He++).
In a given constellation, the first variable stars discovered were designated with letters R through Z, e.g. R Andromedae. This system of nomenclature was developed by Friedrich W. Argelander, who gave the first previously unnamed variable in a constellation the letter R, the first letter not used by Bayer. Letters RR through RZ, SS through SZ, up to ZZ are used for the next discoveries, e.g. RR Lyrae. Later discoveries used letters AA through AZ, BB through BZ, and up to QQ through QZ (with J omitted). Once those 334 combinations are exhausted, variables are numbered in order of discovery, starting with the prefixed V335 onwards.
Variable stars may be either intrinsic or extrinsic.
These subgroups themselves are further divided into specific types of variable stars that are usually named after their prototype. For example, dwarf novae are designated U Geminorum stars after the first recognized star in the class, U Geminorum.
Examples of types within these divisions are given below.
The pulsating stars[3] swell and shrink regularly by stellar radius, magnitude and spectrum, most often with a defined period, sometimes semiregularly with an average period and amplitude, or a pseudoperiod. The two most important types are:
This group consists of several kinds of pulsating stars that swell and shrink very regularly by the star's own mass resonance, generally by the fundamental frequency. Generally the Eddington valve mechanism for pulsating variables is believed to account for cepheid-like pulsations: a certain helium layer of the star has variable opacity depending on the ionization degree, greater opacity for the greater level of ionization. At minimum the star is contracted so that the layer has the higher ionization and opacity, and therefore absorbs fusion energy for the star to expand. When the star swells up to a certain size, the ionization suddenly switches from higher to lower, switching the opacity to lower too. The inner fusion energy now radiates more easily through this star layer, so the star shrinks to the original contracted state, and the cycle begins anew.
Classical Cepheids, Type II Cepheids, RR Lyrae variables and Delta Scutis belong to the instability strip which is believed to be driven by Eddington pulsations in helium, while for the Beta Cepheids the pulsation mechanism is unknown. The instability strip stars are spectral type late A through M stars (from "white" to "red" by convention). Beta cepheids belongs to type B or sometimes late O ("blue" and deeper "blue").
Generally in each subgroup a fixed relation holds between period and absolute magnitude, as well as a relation between period and mean density of the star. This period-luminosity relationship was first established for Delta Cepheids by Henrietta Swan Leavitt.
Classical Cepheids (or Delta Cephei variables) are population I yellow supergiants which undergo pulsations with very regular periods on the order of days to months. On September 10, 1784 Edward Pigott detected the variability of Eta Aquilae, the first known representative of the class of Cepheid variables. However, the namesake for classical Cepheids is the star Delta Cephei, discovered to be variable by John Goodricke a few months later.
Cepheids are important because they are a type of standard candle. Their luminosity is directly related to their period of variation, with a slight dependence on metallicity as well. The longer the pulsation period, the more luminous the star. Once this period-luminosity relationship is calibrated, the luminosity of a given Cepheid whose period is known can be established. Their distance is then easily found from their apparent brightness. Observations of Cepheid variables are very important for determining distances to galaxies within the Local Group and beyond. A relationship between the period and luminosity for classical Cepheids was discovered in 1908 by Henrietta Swan Leavitt in an investigation of thousands of variable stars. Edwin Hubble used this method to prove that the so-called spiral nebulae are in fact distant galaxies.
Of the brighter stars in the sky, Polaris is a Cepheid, although a somewhat unusual one.
Type II Cepheids (historically termed W Virginis stars) have clock regular light pulsations and a luminosity relation much like the δ Cephei variables, so initially they were confused with the latter category. Comparing the light curve, the amplitude and the radial velocity variations as compared to the light curve, Type II Cepheids constitute a different class of star with a luminosity relation offset from that of the δ Cepheids. Type II Cepheids stars also belong to Population II, compared to Population I of δ Cepheids, and so have a lower metallicity.
These stars are somewhat similar to Cepheids, but are not as luminous. They are older than cepheids, belonging to Population II. Due to their common occurrence in globular clusters, they are occasionally referred to as cluster Cepheids. They also have a well established period-luminosity relationship, and so are also useful distance indicators. These spectral type A stars vary by about 0.2 - 2 magnitudes (20% to over 500% change in luminosity) over a period of several hours to a day or more. Their brightness is greatest when their radii are at their maximum.
Delta Scuti (δ Sct) variables are similar to Cepheids but rather fainter, and with shorter periods. They were once known as Dwarf Cepheids. They often show many superimposed periods, which combine to form an extremely complex light curve. The typical δ Scuti star has an amplitude of 0.003 - 0.9 magnitudes (0.3% to about 130% change in luminosity) and a period of 0.01 - 0.2 days. Their spectral type is usually between A0 and F5.
These stars of spectral type A2 to F5, similar to δ Scuti variables, are found mainly in globular clusters. They exhibit fluctuations in their brightness in the order of 0.7 magnitude (about 100% change in luminosity) or so every 1 to 2 hours.
Bluewhite stars, often giants, with small brightness variations and short periods.
Beta Cephei (β Cep) variables, or Beta Canis Majoris variables, as these stars are sometimes called, especially in Europe)[4] undergo short period pulsations in the order of 0.1 - 0.6 days with an amplitude of 0.01 - 0.3 magnitudes (1% to 30% change in luminosity). They are at their brightest during minimum contraction. Many stars of this kind exhibits multiple pulsation periods.
Stars in this class are type Bp supergiants with a period of 0.1 - 1 day and an amplitude of 0.1 magnitude on average. Their spectra are peculiar by having weak hydrogen while on the other hand carbon and helium lines are extra strong.
Various groups of red giant stars that pulsate with periods in the range of weeks to several years. The period is not always constant but changes from cycle to cycle.
Mira variables are very cool red supergiants, which are undergoing very large pulsations. The mechanism is believed to be Eddington pulsations, like for the yellow Cepheids (see above), but with molecular hydrogen as the variable opacity layer of the star instead of helium. Since hydrogen is the most abundant element almost everywhere in Universe and in stars, the pulsations generally have a great amplitude. Over periods of usually many months, they may brighten by between 2.5 and up to 11 magnitudes (sixfold to 30 thousandfold change in luminosity) before fading again. Mira itself, also known as Omicron Ceti (ο Cet), varies in brightness from almost 2nd magnitude to as faint as 10th magnitude with a period of roughly 332 days.
These are usually red giants or supergiants. Semiregular variables may show a definite period on occasion, but also go through periods of irregular variation. A well-known example of a semiregular variable is Betelgeuse, which varies from about magnitudes +0.2 to +1.2 (a factor 2.5 change in luminosity).
These are usually red supergiants with little or no periodicity. They are often poorly studied semiregular variables that, upon closer scrutiny, should be reclassified.
These are yellow supergiant stars which have alternating deep and shallow minima. This double-peaked variation typically has periods of 30–100 days and amplitudes of 3 - 4 magnitudes. Superimposed on this variation, there may be long-term variations over periods of several years. Their spectra are of type F or G at maximum light and type K or M at minimum brightness.
Alpha Cygni (α Cyg) variables are nonradially pulsating supergiants of spectral classes Bep to AepIa. Their periods range from several days to several weeks, and their amplitudes of variation are typically of the order of 0.1 magnitudes (10% change in luminosity). The light changes, which often seem irregular, are caused by the superposition of many oscillations with close periods. Deneb, in the constellation of Cygnus is the prototype of this class.
These non-radially pulsating stars have short periods of hundreds to thousands of seconds with tiny fluctuations of 0.001 to 0.2 magnitudes. Known types of pulsating white dwarf (or pre-white dwarf) include the DAV, or ZZ Ceti, stars, with hydrogen-dominated atmospheres and the spectral type DA;[5] DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB;[6] and GW Vir stars, with atmospheres dominated by helium, carbon, and oxygen. GW Vir stars may be subdivided into DOV and PNNV stars.[7][8]
The Sun oscillates with very low amplitude in a large number of modes having periods around 5 minutes. The study of these oscillations is known as helioseismology. Oscillations in the Sun are driven stochastically by convection in its outer layers. The term solar-like oscillations is used to describe oscillations in other stars that are excited in the same way and the study of these oscillations is one of the main areas of active research in the field of asteroseismology.
Protostars are young objects that have not yet completed the process of contraction from a gas nebula to a veritable star. Most protostars exhibit irregular brightness variations.
Variability of more massive (2-8 solar mass) Herbig Ae/Be stars is thought to be due to gas-dust clumps, orbiting in the circumstellar disks.
Orion variables are young, hot pre–main sequence stars usually embedded in nebulosity. They have irregular periods with amplitudes of several magnitudes. A well known subtype of Orion variables are the T Tauri variables. Variability of T Tauri stars is due to spots on the stellar surface and gas-dust clumps, orbiting in the circumstellar disks.
These stars reside in reflection nebulae and show gradual increases in their luminosity in the order of 6 magnitudes followed by a lengthy phase of constant brightness. They then dim by 2 magnitudes (six times dimmer) or so over a period of many years. V1057 Cygni for example dimmed by 2.5 magnitude (ten times dimmer) during an eleven year period. FU Orionis variables are of spectral type A through G and are possibly an evolutionary phase in the life of T Tauri stars.
In Main Sequence stars major eruptive variability is exceptional; it is common only among the heaviest (Wolf-Rayet) and the lightest (UV Ceti) stars.
Wolf-Rayet stars are massive hot stars that undergo periodic mass ejections causing them to brighten by 0.1 magnitude on average. They exhibit broad emission line spectra with helium, nitrogen, carbon and oxygen lines.
Flare stars, also known as the UV Ceti stars, are very faint main sequence stars, which undergo regular flares. They increase in brightness by up to two magnitudes (six times brighter) in just a few seconds, and then fade back to normal brightness in half an hour or less. Several nearby red dwarf stars are flare stars, including Proxima Centauri and Wolf 359.
Large stars lose their matter relatively easily. For this reason eruptivity is fairly common among giants and supergiants.
Also known as the S Doradus variables, the most luminous stars known belong to this class. Examples include the hypergiants η Carinae and P Cygni.
Gamma Cassiopeiae (γ Cas) variables are BIII-IVe type stars that fluctuate irregularly by up to 1.5 magnitudes (fourfold change in luminosity) due to the ejection of matter at their equatorial regions caused by a fast rotational speed.
While classed as eruptive variables, these stars do not undergo periodic increases in brightness; instead, they spend most of their time at maximum brightness. At irregular intervals, however, they suddenly fade by 1 - 9 magnitudes (2.5 to 4000 times dimmer), slowly recovering to their maximum brightness over months to years. This variation is thought to be caused by episodes of dust formation in the atmosphere of the star. As dust is formed and moves away from the star, it eventually cools to below the dust condensation temperature, at which point a cloud becomes opaque, causing the star's observed brightness to drop. The dissipating dust results in a gradual increase of brightness.
R Coronae Borealis (R CrB) is the prototype star. Other examples include Z Ursae Minoris (Z UMi) and SU Tauri (SU Tau). DY Persei variables are a subclass of R CrB variables that have a periodic variability in addition to their eruptions.
These are close binary systems with a longer period chromospheric activity, including flares, that typically last 1–4 years. This activity cycle is comparable to the solar cycle of the Sun. The type is often abbreviated RS CVn. The prototype of this class is also an eclipsing binary.
Supernovae are the most dramatic type of cataclysmic variable, being some of the most energetic events in the universe. A supernova can briefly emit as much energy as an entire galaxy, brightening by more than 20 magnitudes (over one hundred million times brighter). The supernova explosion is caused by a white dwarf or a star core reaching a certain mass/density limit, the Chandrasekhar limit, causing the object to collapse in a fraction of a second. This collapse "bounces" and causes the star to explode and emit this enormous energy quantity. The outer layers of these stars are blown away at speeds of many thousands of kilometers an hour. The expelled matter may form nebulae called supernova remnants. A well known example of such a nebula is the Crab Nebula, left over from a supernova that was observed in China and North America in 1054. The core of the star or the white dwarf may either become a neutron star (generally a pulsar) or disintegrate completely in the explosion.
Supernovae can result from the death of an extremely massive star, many times heavier than the Sun. At the end of the life of this massive star, a non-fusible iron core is formed from fusion ashes. This iron core is pushed towards the Chandrasekhar limit till it surpasses it and therefore collapses.
A supernova may also result from mass transfer onto a white dwarf from a star companion in a double star system. The Chandrasekhar limit is surpassed from the infalling matter. The absolute luminosity of this latter type is related to properties of its light curve, so that these supernovae can be used to establish the distance to other galaxies. One of the most studied supernovae is SN 1987A in the Large Magellanic Cloud.
Novae are also the result of dramatic explosions, but unlike supernovae do not result in the destruction of the progenitor star. Also unlike supernovae, novae ignite from the sudden onset of thermonuclear fusion, which under certain high pressure conditions (degenerate matter) accelerates explosively. They form in close binary systems, one component being a white dwarf accreting matter from the other ordinary star component, and may recur over periods of decades to centuries or millennia. Novae are categorised as fast, slow or very slow, depending on the behaviour of their light curve. Several naked eye novae have been recorded, Nova Cygni 1975 being the brightest in the recent history, reaching 2nd magnitude.
Dwarf novae are double stars involving a white dwarf star in which matter transfer between the component gives rise to regular outbursts. There are three types of dwarf nova:
These symbiotic binary systems are composed of a red giant and a hot blue star enveloped in a cloud of gas and dust. They undergo nova-like outbursts with amplitudes of some 4 magnitudes.
There are two main groups of extrinsic variables: rotating stars and eclipsing stars.
Stars with sizable sunspots may show significant variations in brightness as they rotate, and brighter areas of the surface are brought into view. Bright spots also occur at the magnetic poles of magnetic stars. Stars with ellipsoidal shapes may also show changes in brightness as they present varying areas of their surfaces to the observer.
These are very close binaries, the components of which are non-spherical due to their mutual gravitation. As the stars rotate the area of their surface presented towards the observer changes and this in turn affects their brightness as seen from Earth.
The surface of the star is not uniformly bright, but has darker and brighter areas (like the sun's solar spots). The star's chromosphere too may vary in brightness. As the star rotates we observe brightness variations of a few tenths of magnitudes.
These stars rotate extremely fast (~100 km/s at the equator); hence they are ellipsoidal in shape. They are (apparently) single giant stars with spectral types G and K and show strong chromospheric emission lines. Examples are FK Com, HD 199178 and UZ Lib. A possible explanation for the rapid rotation of FK Comae stars is that they are the result of the merger of a (contact) binary.
BY Draconis stars are of spectral class K or M and vary by less than 0.5 magnitudes (70% change in luminosity).
Alpha-2 Canum Venaticorum (α2 CVn) variables are main sequence stars of spectral class B8 - A7 that show fluctuations of 0.01 to 0.1 magnitudes (1% to 10%) due to changes in their magnetic fields.
Stars in this class exhibit brightness fluctuations of some 0.1 magnitude caused by changes in their magnetic fields due to high rotation speeds.
Few pulsars have been detected in visible light. These neutron stars change in brightness as they rotate. Because of the rapid rotation, brightness variations are extremely fast, from milliseconds to a few seconds. The first and the best known example is the Crab Pulsar.
Extrinsic variables have variations in their brightness, as seen by terrestrial observers, due to some external source. One of the most common reasons for this is the presence of a binary companion star, so that the two together form a binary star. When seen from certain angles, one star may eclipse the other, causing a reduction in brightness. One of the most famous eclipsing binaries is Algol, or Beta Persei (β Per).
Algol variables undergo eclipses with one or two minima separated by periods of nearly constant light. The prototype of this class is Algol in the constellation Perseus.
Beta Lyrae (β Lyr) variables are extremely close binaries, named after the star Sheliak. The light curves of this class of eclipsing variables are constantly changing, making it almost impossible to determine the exact onset and end of each eclipse.
The stars in this group show periods of less than a day. The stars are so closely situated to each other that their surfaces are almost in contact with each other.
Stars with planets may also show brightness variations if their planets pass between the earth and the star. These variations are much smaller than those seen with stellar companions and are only detectable with extremely accurate observations. Examples include HD 209458 and GSC 02652-01324.
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