Pulsar

From Wikipedia, the free encyclopedia

A slow-motion videoclip of the Crab Pulsar taken at 800 nm wavelength using a Lucky Imaging camera from Cambridge University, showing the bright pulse and fainter interpulse.

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Video of the Vela pulsar in X-ray light

A pulsar (portmanteau of pulsating star) is a highly magnetized, rotating neutron star that emits a beam of electromagnetic radiation. This radiation can only be observed when the beam of emission is pointing toward the Earth, much the way a lighthouse can only be seen when the light is pointed in the direction of an observer, and is responsible for the pulsed appearance of emission. Neutron stars are very dense, and have short, regular rotational periods. This produces a very precise interval between pulses that range from roughly milliseconds to seconds for an individual pulsar.

The precise periods of pulsars make them useful tools. Observations of a pulsar in a binary neutron star system were used to indirectly confirm the existence of gravitational radiation. The first extrasolar planets were discovered around a pulsar, PSR B1257+12. Certain types of pulsars rival atomic clocks in their accuracy in keeping time.

History of observation

Discovery

Composite Optical/X-ray image of the Crab Nebula, showing synchrotron emission in the surrounding pulsar wind nebula, powered by injection of magnetic fields and particles from the central pulsar.

The first pulsar was observed on November 28, 1967, by Jocelyn Bell Burnell and Antony Hewish.^[1][2][3] They observed pulses separated by 1.33 seconds that originated from the same location on the sky, and kept to sidereal time. In looking for explanations for the pulses, the short period of the pulses eliminated most astrophysical sources of radiation, such as stars, and since the pulses followed sidereal time, it could not be man-made radio frequency interference. When observations with another telescope confirmed the emission, it eliminated any sort of instrumental effects. At this point, Burnell notes of herself and Hewish that "we did not really believe that we had picked up signals from another civilization, but obviously the idea had crossed our minds and we had no proof that it was an entirely natural radio emission. It is an interesting problem—if one thinks one may have detected life elsewhere in the universe, how does one announce the results responsibly?"^[4] Even so, they nicknamed the signal LGM-1, for "little green men" (a playful name for intelligent beings of extraterrestrial origin). It was not until a second pulsating source was discovered in a different part of the sky that the "LGM hypothesis" was entirely abandoned.^[5] Their pulsar was later dubbed CP 1919, and is now known by a number of designators including PSR 1919+21, PSR B1919+21 and PSR J1921+2153. Although CP 1919 emits in radio wavelengths, pulsars have, subsequently, been found to emit in visible light, X-ray, and/or gamma ray wavelengths.^[6]

The word "pulsar" is a contraction of "pulsating star",^[7] and first appeared in print in 1968:

An entirely novel kind of star came to light on Aug. 6 last year and was referred to, by astronomers, as LGM (Little Green Men). Now it is thought to be a novel type between a white dwarf and a neutron [sic]. The name Pulsar is likely to be given to it. Dr. A. Hewish told me yesterday: "… I am sure that today every radio telescope is looking at the Pulsars."^[8]

The existence of neutron stars was first proposed by Walter Baade and Fritz Zwicky in 1934, when they argued that a small, dense star consisting primarily of neutrons would result from a supernova.^[9] In 1967, shortly before the discovery of pulsars, Franco Pacini suggested that a rotating neutron star with a magnetic field would emit radiation, and even noted that such energy could be pumped into a supernova remnant around a neutron star, such as the Crab Nebula.^[10] After the discovery of the first pulsar, Thomas Gold independently suggested a rotating neutron star model similar to that of Pacini, and explicitly argued that this model could explain the pulsed radiation observed by Bell Burnell and Hewish.^[11] The discovery of the Crab pulsar later in 1968 seemed to provide confirmation of the rotating neutron star model of pulsars. The Crab pulsar has a 33-millisecond pulse period, which was too short to be consistent with other proposed models for pulsar emission. A rotation speed of 1,980 revolutions per minute was considered perfectly acceptable. Moreover, the Crab pulsar is so named because it is located at the center of the Crab Nebula, consistent with the 1933 prediction of Baade and Zwicky.^[12]

In 1974, Antony Hewish and Martin Ryle became the first astronomers to be awarded the Nobel Prize in physics, with the Royal Swedish Academy of Sciences noting that Hewish played a "decisive role in the discovery of pulsars".^[13] Considerable controversy is associated with the fact that Professor Hewish was awarded the prize while Bell, who made the initial discovery while she was his Ph.D student, was not. Bell claims no bitterness upon this point, supporting the decision of the Nobel prize committee.^[14]

Milestones

The Vela Pulsar and its surrounding pulsar wind nebula.

In 1974, Joseph Hooton Taylor, Jr. and Russell Hulse discovered for the first time a pulsar in a binary system, PSR B1913+16. This pulsar orbits another neutron star with an orbital period of just eight hours. Einstein's theory of general relativity predicts that this system should emit strong gravitational radiation, causing the orbit to continually contract as it loses orbital energy. Observations of the pulsar soon confirmed this prediction, providing the first ever evidence of the existence of gravitational waves. As of 2010, observations of this pulsar continue to agree with general relativity.^[15] In 1993, the Nobel Prize in Physics was awarded to Taylor and Hulse for the discovery of this pulsar.^[16]

In 1982, Don Backer led a group which discovered PSR B1937+21, a pulsar with a rotation period of just 1.6 milliseconds (38,500 rpm).^[17] Observations soon revealed that its magnetic field was much weaker than ordinary pulsars, while further discoveries cemented the idea that a new class of object, the "millisecond pulsars" (MSPs) had been found. MSPs are believed to be the end product of X-ray binaries. Owing to their extraordinarily rapid and stable rotation, MSPs can be used by astronomers as clocks rivaling the stability of the best atomic clocks on Earth. Factors affecting the arrival time of pulses at the Earth by more than a few hundred nanoseconds can be easily detected and used to make precise measurements. Physical parameters accessible through pulsar timing include the 3D position of the pulsar its proper motion, the electron content of the interstellar medium along the propagation path, the orbital parameters of any binary companion, the pulsar rotation period and its evolution with time. (These are computed from the raw timing data by Tempo, a computer program specialized for this task.) After these factors have been taken into account, deviations between the observed arrival times and predictions made using these parameters can be found and attributed to one of three possibilities: intrinsic variations in the spin period of the pulsar, errors in the realization of Terrestrial Time against which arrival times were measured, or the presence of background gravitational waves. Scientists are currently attempting to resolve these possibilities by comparing the deviations seen between several different pulsars, forming what is known as a Pulsar timing array. The goal of these efforts is to develop a pulsar-based time standard precise enough to make the first ever direct detection of gravitational waves. In June 2006, the astronomer John Middleditch and his team at LANL announced the first prediction of pulsar glitches with observational data from the Rossi X-ray Timing Explorer. They used observations of the pulsar PSR J0537-6910.

In 1992, Aleksander Wolszczan discovered the first extrasolar planets around PSR B1257+12. This discovery presented important evidence concerning the widespread existence of planets outside the solar system, although it is very unlikely that any life form could survive in the environment of intense radiation near a pulsar.

Nomenclature

Initially pulsars were named with letters of the discovering observatory followed by their right ascension (e.g. CP 1919). As more pulsars were discovered, the letter code became unwieldy, and so the convention then arose of using the letters PSR (Pulsating Source of Radio) followed by the pulsar's right ascension and degrees of declination (e.g. PSR 0531+21) and sometimes declination to a tenth of a degree (e.g. PSR 1913+167). Pulsars appearing very close together sometimes have letters appended (e.g. PSR 0021-72C and PSR 0021-72D).

The modern convention prefixes the older numbers with a B (e.g. PSR B1919+21), with the B meaning the coordinates are for the 1950.0 epoch. All new pulsars have a J indicating 2000.0 coordinates and also have declination including minutes (e.g. PSR J1921+2153). Pulsars that were discovered before 1993 tend to retain their B names rather than use their J names (e.g. PSR J1921+2153 is more commonly known as PSR B1919+21). Recently discovered pulsars only have a J name (e.g. PSR J0437-4715). All pulsars have a J name that provides more precise coordinates of its location in the sky.^[18]

Formation

Schematic view of a pulsar. The sphere in the middle represents the neutron star, the curves indicate the magnetic field lines, the protruding cones represent the emission beams and the green line represents the axis on which the star rotates.

The events leading to the formation of a pulsar begin when the core of a massive star is compressed during a supernova, which collapses into a neutron star. The neutron star retains most of its angular momentum, and since it has only a tiny fraction of its progenitor's radius (and therefore its moment of inertia is sharply reduced), it is formed with very high rotation speed. A beam of radiation is emitted along the magnetic axis of the pulsar, which spins along with the rotation of the neutron star. The magnetic axis of the pulsar determines the direction of the electromagnetic beam, with the magnetic axis not necessarily being the same as its rotational axis. This misalignment causes the beam to be seen once for every rotation of the neutron star, which leads to the "pulsed" nature of its appearance. The beam originates from the rotational energy of the neutron star, which generates an electrical field from the movement of the very strong magnetic field, resulting in the acceleration of protons and electrons on the star surface and the creation of an electromagnetic beam emanating from the poles of the magnetic field.^[19][20] This rotation slows down over time as electromagnetic power is emitted. When a pulsar's spin period slows down sufficiently, the radio pulsar mechanism is believed to turn off (the so-called "death line"). This turn-off seems to take place after about 10–100 million years, which means of all the neutron stars in the 13.6 billion year age of the universe, around 99% no longer pulsate.^[21] The longest known pulsar period is 8.51 seconds.^[22]

Though the general picture of pulsars as rapidly rotating neutron stars is widely accepted, Werner Becker of the Max Planck Institute for Extraterrestrial Physics said in 2006, "The theory of how pulsars emit their radiation is still in its infancy, even after nearly forty years of work."^[23]

Categories

Three distinct classes of pulsars are currently known to astronomers, according to the source of the power of the electromagnetic radiation:

• Rotation-powered pulsars, where the loss of rotational energy of the star provides the power.
• Accretion-powered pulsars (accounting for most but not all X-ray pulsars), where the gravitational potential energy of accreted matter is the power source (producing X-rays that are observable from the Earth).
• Magnetars, where the decay of an extremely strong magnetic field provides the electromagnetic power.

The Fermi Space Telescope has uncovered a subclass of rotationally-powered pulsars that emit only gamma rays.^[24] There have been only about one hundred gamma-ray pulsars identified out of about 1800 known pulsars.^[25][26]

Although all three classes of objects are neutron stars, their observable behavior and the underlying physics are quite different. There are, however, connections. For example, X-ray pulsars are probably old rotationally-powered pulsars that have already lost most of their power, and have only become visible again after their binary companions had expanded and began transferring matter on to the neutron star. The process of accretion can in turn transfer enough angular momentum to the neutron star to "recycle" it as a rotation-powered millisecond pulsar. As this matter lands on the neutron star, it is thought to "bury" the magnetic field of the neutron star (although the details are unclear), leaving millisecond pulsars with magnetic fields 1000-10,000 times weaker than average pulsars. This low magnetic field is less effective at slowing the pulsar's rotation, so millisecond pulsars live for billions of years, making them the oldest known pulsars. Millisecond pulsars are seen in globular clusters, which stopped forming neutron stars billions of years ago.^[21]

Of interest to the study of the state of the matter in a neutron stars are the glitches observed in the rotation velocity of the neutron star. This velocity is decreasing slowly but steadily, except by sudden variations. One model put forward to explain these glitches is that they are the result of "starquakes" that adjust the crust of the neutron star. Models where the glitch is due to a decoupling of the possibly superconducting interior of the star have also been advanced. In both cases, the star's moment of inertia changes, but its angular momentum does not, resulting in a change in rotation rate.

Disrupted recycled pulsar

When two massive stars are born close together from the same cloud of gas, they can form a binary system and orbit each other from birth. If those two stars are at least a few times as massive as our sun, their lives will both end in supernova explosions. The more massive star explodes first, leaving behind a neutron star. If the explosion does not kick the second star away, the binary system survives. The neutron star can now be visible as a radio pulsar, and it slowly loses energy and spins down. Later, the second star can swell up, allowing the neutron star to suck up its matter. The matter falling onto the neutron star spins it up and reduces its magnetic field. This is called “recycling” because it returns the neutron star to a quickly-spinning state. Finally, the second star also explodes in a supernova, producing another neutron star. If this second explosion also fails to disrupt the binary, a double neutron star binary is formed. Otherwise, the spun-up neutron star is left with no companion and becomes a “disrupted recycled pulsar”, spinning between a few and 50 times per second.^[27]

Applications

The discovery of pulsars allowed astronomers to study an object never observed before, the neutron star. This kind of object is the only place where the behavior of matter at nuclear density can be observed (though not directly). Also, millisecond pulsars have allowed a test of general relativity in conditions of an intense gravitational field.

Maps

Relative position of the Sun to the center of the Galaxy and 14 pulsars with their periods denoted

Pulsar maps have been included on the two Pioneer Plaques as well as the Voyager Golden Record. They show the position of the Sun, relative to 14 pulsars, which are identified by the unique timing of their electromagnetic pulses, so that our position both in space and in time can be calculated by potential extraterrestrial intelligences.^[28] Because pulsars are emitting very regular pulses of radio waves, its radio transmissions do not require daily corrections. Moreover, pulsar positioning could create a spacecraft navigation system independently, or be an auxiliary device to GPS instruments.^[29][30]

Precise clocks

For some millisecond pulsars, the regularity of pulsation is more precise than an atomic clock.^[31] This stability allows millisecond pulsars to be used in establishing ephemeris time^[32] or building pulsar clocks.^[33]

Timing noise is the name for rotational irregularities observed in all pulsars. This timing noise is observable as random wandering in the pulse frequency or phase.^[34] It is unknown whether timing noise is related to pulsar glitches.

Probes of the interstellar medium

The radiation from pulsars passes through the interstellar medium (ISM) before reaching Earth. Free electrons in the warm (8000 K), ionized component of the ISM and H II regions affect the radiation in two primary ways. The resulting changes to the pulsar's radiation provide an important probe of the ISM itself.^[35]

Because of the dispersive nature of the interstellar plasma, lower-frequency radio waves travel through the medium slower than higher-frequency radio waves. The resulting delay in the arrival of pulses at a range of frequencies is directly measurable as the dispersion measure of the pulsar. The dispersion measure is the total column density of free electrons between the observer and the pulsar,

where is the distance from the pulsar to the observer and is the electron density of the ISM.
The dispersion measure is used to construct models of the free electron distribution in the Milky Way Galaxy.^[36]

Additionally, turbulence in the interstellar gas causes density inhomogeneities in the ISM which cause scattering of the radio waves from the pulsar. The resulting scintillation of the radio waves—the same effect as the twinkling of a star in visible light due to density variations in the Earth's atmosphere—can be used to reconstruct information about the small scale variations in the ISM.^[37] Due to the high velocity (up to several hundred km/s) of many pulsars, a single pulsar scans the ISM rapidly, which results in changing scintillation patterns over timescales of a few minutes.^[38]

Probes of space-time

Pulsars orbiting within the curved space-time around Sgr A*, the supermassive black hole at the center of the Milky Way galaxy, could serve as probes of gravity in the strong-field regime.^[39]
Arrival times of the pulses would be affected by special- and general-relativistic Doppler shifts and by the complicated paths that the radio waves would travel through the strongly curved space-time around the black hole. In order for the effects of general relativity to be measurable with current instruments, pulsars with orbital periods less than about 10 years would need to be discovered;^[39] such pulsars would orbit at distances inside 0.01 pc from Sgr A*. Searches are currently underway; at present, five pulsars are known to lie within 100 pc from Sgr A*.^[40]

Gravitational waves detectors

There are 3 consortia around the world which use pulsars to search for gravitational waves. In Europe, there is the European Pulsar Timing Array (EPTA); there is the Parkes Pulsar Timing Array (PPTA) in Australia; and there is the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) in Canada and the US. Together, the consortia form the International Pulsar Timing Array (IPTA). The pulses from Millisecond Pulsars (MSPs) are used as a system of Galactic clocks.
Disturbances in the clocks will be measurable at Earth. A disturbance from a passing gravitational wave will have a particular signature across the ensemble of pulsars, and will be thus detected.

Significant pulsars

Pulsars within 300 pc^[41]

PSRJ	Distance (pc)	Age (Myr)
J0030+0451	244	7,580
0108−1431	238	166
0437−4715	156	1,590
0633+1746	156	0.342
0659+1414	290	0.111
0835−4510	290	0.0113
0453+0755	260	17.5
1045−4509	300	6,710
1741−2054	250	0.387
1856−3754	161	3.76
2144−3933	165	272

Gamma-ray pulsars detected by the Fermi Gamma-ray Space Telescope.

The pulsars listed here were either the first discovered of its type, or represent an extreme of some type among the known pulsar population, such as having the shortest measured period.

• The first radio pulsar CP 1919 (now known as PSR 1919+21), with a pulse period of 1.337 seconds and a pulse width of 0.04 second, was discovered in 1967.^[42]
• The first binary pulsar, PSR 1913+16, whose orbit is decaying at the exact rate predicted due to the emission of gravitational radiation by general relativity
• The first millisecond pulsar, PSR B1937+21
• The brightest millisecond pulsar, PSR J0437-4715
• The first X-ray pulsar, Cen X-3
• The first accreting millisecond X-ray pulsar, SAX J1808.4-3658
• The first pulsar with planets, PSR B1257+12
• The first pulsar observed to have been affected by asteroids: PSR J0738-4042
• The first double pulsar binary system, PSR J0737−3039
• The longest period pulsar, PSR J2144-3933
• The most stable pulsar in period, PSR J0437-4715
• The first millisecond pulsar with 2 stellar mass companions, PSR J0337+1715
• PSR B1931+24 "... appears as a normal pulsar for about a week and then 'switches off' for about one month before emitting pulses again. [..] this pulsar slows down more rapidly when the pulsar is on than when it is off. [.. the] braking mechanism must be related to the radio emission and the processes creating it and the additional slow-down can be explained by the pulsar wind leaving the pulsar's magnetosphere and carrying away rotational energy."^[43]
• PSR J1748-2446ad, at 716 Hz, the pulsar with the highest rotation speed.
• PSR J1903+0327, a ~2.15 ms pulsar discovered to be in a highly eccentric binary star system with a sun-like star.^[44]
• A pulsar in the CTA 1 supernova remnant (4U 0000+72, in Cassiopeia) was found by the Fermi Gamma-ray Space Telescope to emit pulsations only in gamma ray radiation, the first recorded of its kind.^[24]
• PSR J2007+2722, a 40.8-hertz 'recycled' isolated pulsar was the first pulsar found by volunteers on data taken in February 2007 and analyzed by distributed computing project Einstein@Home.^[45]
• PSR J1311–3430, the first millisecond pulsar discovered via gamma-ray pulsations and part of a binary system with the shortest orbital period.^[46]

Variable star

From Wikipedia, the free encyclopedia

A variable star is a star whose brightness as seen from Earth (its apparent magnitude) fluctuates.
This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as either:

• 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.

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]

A photogenic variable star, Eta Carinae, embedded in the Carina Nebula.

Discovery

An ancient Egyptian calendar of lucky and unlucky days composed some 3200 years ago may be the oldest preserved historical document of the discovery of a variable star, the eclipsing binary Algol.^[2][3]

Of the modern astronomers, 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^[4] (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.

Detecting 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, evidence for a pulsating star is found in its shifting spectrum because its surface periodically moves toward and away from us, with the same frequency as its changing brightness.

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 ageing 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 swell and shrink, affecting the brightness and spectrum. Pulsations are generally split into: radial, where the entire star expands and shrinks as a whole; and non-radial, where one part of the star expand while another part shrinks. Some scientists consider non-radial pulsations to encompass everything, with radial pulsations as a special case, but considering them as mutually exclusive is convenient for variable stars since they generally vary with one type or the other.
Depending on the type of pulsation and its location within the star, there is a natural or fundamental frequency which determines the period of the star. Stars may also pulsate in a harmonic or overtone which is a higher frequency, corresponding to a shorter period. Pulsating variable stars sometimes have a single well-defined period, but often they pulsate simultaneously with multiple frequencies and complex analysis is required to determine the separate interfering periods. In some cases, the pulsations do not have a defined frequency, causing random variation, referred to as stochastic. The study of stellar interiors using their pulsations is asteroseismology.

A pulsation in a star must be caused by an unbalanced driving force with a feedback mechanism. In pulsating variable stars the driving force is the internal energy of the star, usually from nuclear fusion, but in some cases just from stored energy, always attempting to propagate outwards. At certain locations on the HR diagram, corresponding to particular combinations of temperatures, size, and internal chemistry, the outward flow of energy by radiation varies strongly with the density or temperature of the material it is passing through. When the opacity of a layer is high that layer expands, and if the decrease of temperature or pressure causes the opacity to drop again, there is a feedback mechanism to create regular pulsations. This generally occurs as the ionisation level of the material changes, for example the ionisation of helium in yellow stars on the instability strip.

The expansion phase of a pulsation is caused by the blocking of the internal energy flow by material with a high opacity, but this must occur at a particular depth of the star to create visible pulsations. If the expansion occurs below a convective zone then nothing will be visible at the surface. If the expansion occurs too close to the surface then there may be no restoring force to create a pulsation. The restoring force to create the contraction phase of a pulsation can be pressure if the pulsation occurs in a non-degenerate layer deep inside a star, and this is called an acoustic or pressure mode of pulsation, abbreviated to p-mode. In other cases, the restoring force is simple gravity and this is called a g-mode. Pulsating variable stars typically pulsate in only one of these modes.

Cepheids and cepheid-like variables

This group consists of several kinds of pulsating stars, all found on the instability strip, 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. Each of the subgroups on the instability strip has a fixed relationship between period and absolute magnitude, as well as a relation between period and mean density of the star. The period-luminosity relationship was first established for Delta Cepheids by Henrietta Swan Leavitt, and makes the high luminosity Cepheids 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.

Note that the Cepheids are named only for Delta Cephei, while a completely separate class of variables is named after Beta Cephei.

Classical Cepheid variables

Classical Cepheids (or Delta Cephei variables) are population I (young, massive, and luminous) 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.

Type II Cepheids

Type II Cepheids (historically termed W Virginis stars) have extremely regular light pulsations and a luminosity relation much like the δ Cephei variables, so initially they were confused with the latter category. Type II Cepheids stars belong to Population II, older stars than the type I Cepheids. They have somewhat lower metallicity, much lower mass, somewhat lower luminosity, and a slightly offset period luminosity relationship, so it is always important to know which type of star is being observed.

RR Lyrae variables

These stars are somewhat similar to Cepheids, but are not as luminous and with shorter periods. They are older than type I Cepheids, belonging to Population II, but of lower mass than type II Cepheids. 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.

Delta Scuti variables

Delta Scuti (δ Sct) variables are similar to Cepheids but much fainter and with much 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.

Rapidly oscillating Ap variables

These stars of spectral type A or occasionally F0, a sub-class of δ Scuti variables found on the main sequence. They have extremely rapid variations with periods of a few minutes and amplitudes of a few thousandths of a magnitude.

Long period variables

The long period variables are cool evolved stars that pulsate with periods in the range of weeks to several years.

Mira variables

Mira variables are AGB red giants. Over periods of many months they fade and brighten by between 2.5 and 11 magnitudes, a sixfold to 30 thousandfold change in luminosity. 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. The very large visual amplitudes are mainly due to the shifting of energy output between visual and infra-red as the temperature of the star changes. In a few cases, Mira variables show dramatic period changes over a period of decades, thought to be related to the thermal pulsing cycle of the most advanced AGB stars.

Semiregular variables

These are red giants or supergiants. Semiregular variables may show a definite period on occasion, but more often show less well-defined variations that can sometimes be resolved into multiple periods. 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). At least some of the semi-regular variables are very closely related to Mira variables, possibly the only difference being pulsating in a different harmonic.

Slow irregular variables

These are red giants or supergiants with little or no detectable periodicity. Some are poorly studied semiregular variables, often with multiple periods, but others may simply be chaotic.

Beta Cephei variables

Beta Cephei (β Cep) variables (sometimes called Beta Canis Majoris variables, especially in Europe)^[8] 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.

Slowly pulsating B stars

Slowly pulsating B (APB) stars are hot main sequence stars slightly less luminous than the Beta Cephei stars, with longer periods and larger amplitudes.^[9]

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, a type of Extreme helium star.

RV Tauri variables

These are yellow supergiant stars (actually low mass post-AGB stars at the most luminous stage of their lives) 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. They lie near the instability strip, cooler than type I Cepheids more luminous than type II Cepheids. Their pulsations are caused by the same basic mechanisms related to helium opacity, but they are at a very different stage of their lives.

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. 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.

Gamma Doradus variables

Gamma Doradus (γ Dor) variables are non-radially pulsating main sequence stars of spectral classes F to late A. Their periods are around one day and their amplitudes typically of the order of 0.1 magnitudes.

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;^[10] DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB;^[11] and GW Vir stars, with atmospheres dominated by helium, carbon, and oxygen. GW Vir stars may be subdivided into DOV and PNNV stars.^[12][13]

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 one of the main areas of active research in the field of asteroseismology.

Eruptive variable stars

Eruptive variable stars show irregular or semi-regular brightness variations caused by material being lost from the star, or in some cases being accreted to it. Despite the name these are not explosive events, those are the cataclysmic variables.

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.

Giants and supergiants

Large stars lose their matter relatively easily. For this reason variability due to eruptions and mass loss 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. They have permanent high mass loss, but at intervals of years internal pulsations cause the star to exceed its Eddington limit and the mass loss increases hugely. Visual brightness increases although the overall luminosity is largely unchanged. Giant eruptions observed in a few LBVs do increase the luminosity, so much so that they have been tagged supernova impostors, and may be a different type of event.

Yellow hypergiants

These massive evolved stars are unstable due to their high luminosity and position above the instability strip, and they exhibit slow but sometimes large photometric and spectroscopic changes due to high mass loss and occasional larger eruptions, combined with secular variation on an observable timescale. The best known example is Rho Cassiopeiae.

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, but at irregular intervals they suddenly fade by 1 – 9 magnitudes (2.5 to 4000 times dimmer) before recovering to their initial brightness over months to years. Most are classified as yellow supergiants by luminosity, although they are actually post-AGB stars, but there are both red and blue giant R CrB stars. R Coronae Borealis (R CrB) is the prototype star. DY Persei variables are a subclass of R CrB variables that have a periodic variability in addition to their eruptions.

Wolf–Rayet variables

Wolf–Rayet stars are massive hot stars that sometimes show variability, probably due to several different causes including binary interactions and rotating gas clumps around the star. They exhibit broad emission line spectra with helium, nitrogen, carbon and oxygen lines. Variations in some stars appear to be stochastic while others show multiple periods.

Gamma Cassiopeiae variables

Gamma Cassiopeiae (γ Cas) variables are non-supergiant fast-rotating B class emission line 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 the rapid rotational.

Flare stars

In main-sequence stars major eruptive variability is exceptional. It is common only among the flare stars, also known as the UV Ceti variables, 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.

RS Canum Venaticorum variables

These are close binary systems with highly active chromospheres, including huge sunspots and flares, believed to be enhanced by the close companion. Variability scales ranges from days, close to the orbital period and sometimes also with eclipses, to years as sunspot activity varies.

Cataclysmic or explosive variable stars

Images showing the expansion of the light echo of a red variable star, the V838 Monocerotis

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 sizeable 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 (~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 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

How eclipsing binaries vary in brightness

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, and all of the planets and planet candidates detected by the Kepler Mission.