variable star

A star is classified as variable if its apparent brightness 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 a magnitude. Astronomers use the term millimagnitude, abbreviated as mmag, for one thousandth of a magnitude.

It is convenient to classify variable stars as belonging to one of two types:

• Intrinsic variables, whose luminosity actually changes; for example, because the star periodically swells and shrinks.
• Extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth; for example, because the star has an orbiting companion that sometimes eclipses it.

Discovery

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 to be described variable star was the eclipsing variable Algol by Geminiano Montanari in 1669; John Goodricke in 1784 gave the correct explanation of its variability. In order of discovery Chi Cygni was next, 1686 by G. Kirch, then R Hydrae in 1704 by G. D. Maraldi, and so on. 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.

Types of variability

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 star observations

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:

• are the brightness variations periodical, semiperiodical, irregular, or unique?
• what is the period of the brightness fluctuations?
• what is the shape of the light curve (symmetrical or not, angular or smoothly varying, does each cycle have only one or more than one minima, etcetera)?

From the spectrum the following data are derived:

• what kind of star is it: what is its temperature, its luminosity class (dwarf star, giant star, supergiant, etc.)?
• is it a single star, or a binary? (the combined spectrum of a binary star may show elements from the spectra of each of the member stars)
• does the spectrum change with time? (for example, the star may turn hotter and cooler periodically)
• changes in brightness may depend strongly on the part of the spectrum that is observed (for example, large variations in visible light but hardly any changes in the infrared)
• if the wavelengths of spectral lines are shifted this points to movements (for example, a periodical swelling and shrinking of the star, or its rotation, or an expanding gas shell) (Doppler effect)
• strong magnetic fields on the star betray themselves in the spectrum
• abnormal emission or absorption lines may be indication of a hot stellar atmosphere, or gas clouds surrounding the star.

In very few cases it is possible to make pictures of a stellar disk. These may show darker spots on its surface.

Interpretation of observations

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⁺⁺).

Variable star nomenclature

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.

Classification

Variable stars may be either intrinsic or extrinsic.

• Intrinsic variable stars: stars where the variability is being caused by changes in the physical properties of the stars themselves. This category can be divided into three subgroups.
  • Pulsating variables, stars whose radius alternately expands and contracts as part of their natural evolutionary aging processes.
  • Eruptive variables, stars who experience eruptions on their surfaces like flares or mass ejections.
  • Cataclysmic or explosive variables, stars that undergo a cataclysmic change in their properties like novae and supernovae.

• Extrinsic variable stars: stars where the variability is caused by external properties like rotation or eclipses. There are two main subgroups.
  • Eclipsing binaries, double stars where, as seen from Earth's vantage point the stars occasionally eclipse one another as they orbit.
  • Rotating variables, stars whose variability is caused by phenomena related to their rotation. Examples are stars with extreme "sunspots" which affect the apparent brightness or stars that have fast rotation speeds causing them to become ellipsoidal in shape.

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.

Intrinsic variable stars

Intrinsic variable types in the Hertzsprung-Russell diagram

Examples of types within these divisions are given below.

Pulsating variable stars

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:

• Cepheids and cepheid-like stars. They have short periods (days to months) and their luminosity cycle is very regular;
• Long Period Variables. Their period is longer, on the order of a year, and much less regular.

Cepheids and cepheid-like variables

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 easier through this star layer, so the star shrinks to the original contracted state, and the cycle begins anew.

Delta Cepheid, W Virginids, RR Lyrae variables and Delta Scutids 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.

Delta Cepheid variables

One of the most important types of variables star are Delta Cephei variables, yellow giant stars which undergo pulsations with very regular periods. Usually referred to simply as Cepheid variables, they are named after Delta Cephei (δ Cep), the first of the class to be discovered, and have periods ranging from about a day to several weeks.

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.

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.

W Virginis variables

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, W Virginis constitute a different class of star with a luminosity relation offset from that of the δ Cepheids. W Virginis stars also belong to Population II, compared to Population I of δ Cepheids, and so have a lower metallicity.

RR Lyrae variables

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 variables

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.

SX Phoenicis variables

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 variables with early spectra (O and B)

Bluewhite stars, often giants, with small brightness variations and short periods.

Beta Cephei variables

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.

PV Telescopii variables

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.

Long Period and Semiregular variables

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

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 (six-fold to 30 thousand-fold 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.

Semiregular variables

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 (20% to 200% change in luminosity).

Slow irregular variables

These are usually red supergiants with little or no periodicity. They are often poorly studied semiregular variables that, upon closer scrutiny, should be reclassified.

RV Tauri variables

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 variables

Alpha Cygni (α Cyg) variables are nonradially pulsating supergiants of spectral classes B_ep to A_epIa. 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.

Pulsating white dwarfs

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]

Solar-like oscillations

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 known as asteroseismology.

Eruptive variable stars

Protostars

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.

Herbig Ae/Be stars

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

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.

FU Orionis variables

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.

Main Sequence variables

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 variables

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

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.

Giants and supergiants

Large stars lose their matter relatively easily. For this reason eruptivity is fairly common among giants and supergiants.

Luminous blue variables

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 variables

Gamma Cassiopeiae (γ Cas) variables are BIII-IVe type stars that fluctuate irregularly by up to 1.5 magnitudes (four-fold change in luminosity) due to the ejection of matter at their equatorial regions caused by a fast rotational speed.

R Coronae Borealis variables

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.

Eruptive binary stars

RS Canum Venaticorum variables

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.

Cataclysmic or explosive variable stars

Supernovae

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

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

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:

• U Geminorum stars, which have outbursts lasting roughly 5-20 days followed by quiet periods of typically a few hundred days. During an outburst they brighten typically by 2 - 6 magnitudes. These stars are also known as SS Cygni variables after the variable in Cygnus which produces among the brightest and most frequent displays of this variable type.
• Z Camelopardalis stars, in which occasional plateaux of brightness called standstills are seen, part way between maximum and minimum brightness.
• SU Ursae Majoris stars, which undergo both frequent small outbursts, and rarer but larger superoutbursts. These binary systems usually have orbital periods of under 2.5 hours.

Z Andromedae variables

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.

Extrinsic variable stars

There are two main groups of extrinsic variables: rotating stars and eclipsing stars.

Rotating variable 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.

Non-spherical stars

Ellipsoidal variables

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.

Stellar spots

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.

FK Comae Berenices variables

These stars rotate extremely fast; hence they are ellipsoidal in shape.

BY Draconis variable stars

BY Draconis stars are of spectral class K or M and vary by less than 0.5 magnitudes (70% change in luminosity).

Magnetic fields

Alpha-2 Canum Venaticorum variables

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.

SX Arietis variables

Stars in this class exhibit brightness fluctuations of some 0.1 magnitude caused by changes in their magnetic fields due to high rotation speeds.

Optically variable pulsars

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.

Eclipsing binaries

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

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 variables

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.

W Ursae Majoris variables

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.

Planetary transits

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.

References

See also

• List of variable stars
• Guest star (astronomy)
• W. Strohmeier, Variable Stars, Pergamon (1972)

External links

• The American Association of Variable Star Observers
• WWW.SEMIREGULAR.COM WEB-service where variable star observers can manage and report their observations
• GCVS Variability Types
• Society for Popular Astronomy - Variable Star Section