Stellar rotation is the angular motion of a star

Star

A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

 about its axis. The rate of rotation can be measured from the spectrum of the star, or by timing the movements of active features on the surface.

The rotation of a star produces an equatorial bulge due to centrifugal force

Centrifugal force

Centrifugal force can generally be any force directed outward relative to some origin. More particularly, in classical mechanics, the centrifugal force is an outward force which arises when describing the motion of objects in a rotating reference frame...

. As stars are not solid bodies, they can also undergo differential rotation

Differential rotation

Differential rotation is seen when different parts of a rotating object move with different angular velocities at different latitudes and/or depths of the body and/or in time. This indicates that the object is not solid. In fluid objects, such as accretion disks, this leads to shearing...

. Thus the equator

Equator

An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

 of the star can rotate at a different angular velocity

Angular velocity

In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per...

 than the higher latitudes. These differences in the rate of rotation within a star may have a significant role in the generation of a stellar magnetic field

Stellar magnetic field

A stellar magnetic field is a magnetic field generated by the motion of conductive plasma inside a star. This motion is created through convection, which is a form of energy transport involving the physical movement of material. A localized magnetic field exerts a force on the plasma, effectively...

.

The magnetic field

Stellar magnetic field

A stellar magnetic field is a magnetic field generated by the motion of conductive plasma inside a star. This motion is created through convection, which is a form of energy transport involving the physical movement of material. A localized magnetic field exerts a force on the plasma, effectively...

 of a star interacts with the stellar wind

Stellar wind

A stellar wind is a flow of neutral or charged gas ejected from the upper atmosphere of a star. It is distinguished from the bipolar outflows characteristic of young stars by being less collimated, although stellar winds are not generally spherically symmetric.Different types of stars have...

. As the wind moves away from the star its rate of angular velocity slows. The magnetic field of the star interacts with the wind, which applies a drag to the stellar rotation. As a result, angular momentum is transferred from the star to the wind, and over time this gradually slows the star's rate of rotation.

Measurement

Unless a star is being observed from the direction of its pole, sections of the surface have some amount of movement toward or away from the observer. The component of movement that is in the direction of the observer is called the radial velocity. For the portion of the surface with a radial velocity component toward the observer, the radiation is shifted to a higher frequency because of Doppler shift. Likewise the region that has a component moving away from the observer is shifted to a lower frequency. When the absorption lines of a star are observed, this shift at each end of the spectrum causes the line to broaden. However, this broadening must be carefully separated from other effects that can increase the line width.
The component of the radial velocity observed through line broadening depends on the inclination

Inclination

Inclination in general is the angle between a reference plane and another plane or axis of direction.-Orbits:The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit...

 of the star's pole to the line of sight. The derived value is given as , where v_e is the rotational velocity at the equator and i is the inclination. However, i is not always known, so the result gives a minimum value for the star's rotational velocity. That is, if i is not a right angle

Right angle

In geometry and trigonometry, a right angle is an angle that bisects the angle formed by two halves of a straight line. More precisely, if a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles...

, then the actual velocity is greater than . This is sometimes referred to as the projected rotational velocity.

For giant star

Giant star

A giant star is a star with substantially larger radius and luminosity than a main sequence star of the same surface temperature. Typically, giant stars have radii between 10 and 100 solar radii and luminosities between 10 and 1,000 times that of the Sun. Stars still more luminous than giants are...

s, the atmospheric microturbulence

Microturbulence

Microturbulence is a form of turbulence that varies over small distance scales. -Stellar:Microturbulence is one of several mechanisms that can cause broadening of the absorption lines in the stellar spectrum...

 can result in line broadening that is much larger than effects of rotational, effectively drowning out the signal. However, an alternate approach can be employed that makes use of gravitational microlensing

Gravitational microlensing

Gravitational microlensing is an astronomical phenomenon due to the gravitational lens effect. It can be used to detect objects ranging from the mass of a planet to the mass of a star, regardless of the light they emit. Typically, astronomers can only detect bright objects that emit lots of light ...

 events. These occur when a massive object passes in front of the more distant star and functions like a lens, briefly magnifying the image. The more detailed information gathered by this means allows the effects of microturbulence to be distinguished from rotation.

If a star displays magnetic surface activity such as starspot

Starspot

Starspots are equivalent to sunspots but located on other stars. Spots the size of sunspots are very hard to detect since they are too small to cause fluctuations in brightness...

s, then these features can be tracked to estimate the rotation rate. However, such features can form at locations other than equator and can migrate across latitudes over the course of their life span, so differential rotation of a star can produce varying measurements. Stellar magnetic activity is often associated with rapid rotation, so this technique can be used for measurement of such stars. Observation of starspots has shown that these features can actually vary the rotation rate of a star, as the magnetic fields modify the flow of gases in the star.

Equatorial bulge

Gravity tends to contract celestial bodies into a perfect sphere, the shape where all the mass is as close to the center of gravity as possible. But a rotating star is not spherical in shape, it has an equatorial bulge.

As a rotating proto-stellar disk contracts to form a star its shape becomes more and more spherical, but the contraction doesn't proceed all the way to a perfect sphere. At the poles all of the gravity acts to increase the contraction, but at the equator the effective gravity is diminished by the centrifugal force. The final shape of the star after star formation is an equilibrium shape, in the sense that the effective gravity in the equatorial region (being diminished) cannot pull the star to a more spherical shape. The rotation also gives rise to gravity darkening

Gravity darkening

Gravity darkening, also referred to as Gravity Brightening, is an astronomical phenomenon where a star rotates so rapidly that it has a detectably oblate spheroid shape, such as in Regulus in the Leo constellation....

 at the equator, as described by the von Zeipel theorem.

An extreme example of an equatorial bulge is found on the star Regulus A

Regulus

Regulus is the brightest star in the constellation Leo and one of the brightest stars in the night sky, lying approximately 77.5 light years from Earth. Regulus is a multiple star system composed of four stars which are organized into two pairs...

 (α Leonis A). The equator of this star has a measured rotational velocity of 317 ± 3 km/s. This corresponds to a rotation period of 15.9 hours, which is 86% of the velocity at which the star would break apart. The equatorial radius of this star is 32% larger than polar radius. Other rapidly rotating stars include Alpha Arae, Pleione

Pleione (star)

Pleione is a binary star in the Pleiades star cluster , located roughly 390 light years away in the constellation of Taurus. Pleione was not given a Bayer designation, but did receive a Flamsteed number—hence its designation 28 Tauri...

, Vega

Vega

Vega is the brightest star in the constellation Lyra, the fifth brightest star in the night sky and the second brightest star in the northern celestial hemisphere, after Arcturus...

 and Achernar

Achernar

Achernar , sometimes spelled Achenar, is the brightest star in the constellation Eridanus and the ninth-brightest star in the night sky. Of the top ten apparent brightest stars —Sirius, Canopus, Alpha Centauri, Arcturus, Vega, Capella, Rigel, Procyon, Achernar and Betelgeuse—Achernar is the hottest...

.

The break-up velocity of a star is an expression that is used to describe the case where the centrifugal force at the equator is equal to the gravitational force. For a star to be stable the rotational velocity must be below this value.

Differential rotation

Surface differential rotation

Differential rotation

Differential rotation is seen when different parts of a rotating object move with different angular velocities at different latitudes and/or depths of the body and/or in time. This indicates that the object is not solid. In fluid objects, such as accretion disks, this leads to shearing...

 is observed on stars such as the Sun when the angular velocity varies with latitude. Typically the angular velocity decreases with increasing latitude. However the reverse has also been observed, such as on the star designated HD 31993.) The first such star, other than the Sun, to have its differential rotation mapped in detail is AB Doradus

AB Doradus

AB Doradus is a pre-main sequence trinary star system in the constellation Dorado. The primary is a flare star that shows periodic increases in activity....

.
The underlying mechanism that causes differential rotation is turbulent convection

Convection

Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....

 inside a star. Convective motion carries energy toward the surface through the mass movement of plasma. This mass of plasma carries a portion of the angular velocity of the star. When turbulence occurs through shear and rotation, the angular momentum can become redistributed to different latitudes through meridional flow

Meridional flow

Meridional flow is a meteorological term meaning that the general flow pattern is north to south, or south to north, along the Earth's longitude lines . Extratropical cyclones in this environment tend to be stronger and move slower...

.

The interfaces between regions with sharp differences in rotation are believed to be efficient sites for the dynamo processes

Dynamo theory

In geophysics, dynamo theory proposes a mechanism by which a celestial body such as the Earth or a star generates a magnetic field. The theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time...

 that generate the stellar magnetic field

Stellar magnetic field

A stellar magnetic field is a magnetic field generated by the motion of conductive plasma inside a star. This motion is created through convection, which is a form of energy transport involving the physical movement of material. A localized magnetic field exerts a force on the plasma, effectively...

. There is also a complex interaction between a star's rotation distribution and its magnetic field, with the conversion of magnetic energy into kinetic energy modifying the velocity distribution.

Rotation braking

Stars are believed to form as the result of a collapse of a low-temperature cloud of gas and dust. As the cloud collapses, conservation of angular momentum causes any small net rotation of the cloud to increase, forcing the material into a rotating disk. At the dense center of this disk a protostar

Protostar

A protostar is a large mass that forms by contraction out of the gas of a giant molecular cloud in the interstellar medium. The protostellar phase is an early stage in the process of star formation. For a one solar-mass star it lasts about 100,000 years...

 forms, which gains heat from the gravitational energy

Potential energy

In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...

 of the collapse.

As the collapse continues, the rotation rate can increase to the point where the accreting protostar can break up due to centripetal force

Centripetal force

Centripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens...

 at the equator. Thus the rotation rate must be braked during the first 100,000 years to avoid this scenario. One possible explanation for the braking is the interaction of the protostar's magnetic field

Stellar magnetic field

A stellar magnetic field is a magnetic field generated by the motion of conductive plasma inside a star. This motion is created through convection, which is a form of energy transport involving the physical movement of material. A localized magnetic field exerts a force on the plasma, effectively...

 with the stellar wind

Stellar wind

A stellar wind is a flow of neutral or charged gas ejected from the upper atmosphere of a star. It is distinguished from the bipolar outflows characteristic of young stars by being less collimated, although stellar winds are not generally spherically symmetric.Different types of stars have...

. The expanding wind carries away the angular momentum and slows down the rotation rate of the collapsing protostar.

Average
rotational
velocities

Stellar class	ve (km/s)
O5	190
B0	200
B5	210
A0	190
A5	160
F0	95
F5	25
G0	12

Most main sequence

Main sequence

The main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Hertzsprung and Henry Norris Russell...

 stars with a spectral class between O5 and F5 have been found to rotate rapidly. For stars in this range, the measured rotation velocity increases with mass. This increase in rotation peaks among young, massive B-class stars. As the expected life span of a star decreases with increasing mass, this can be explained as a decline in rotational velocity with age.

For main sequence

Main sequence

The main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Hertzsprung and Henry Norris Russell...

 stars, the decline in rotation can be approximated by a mathematical relation:


where is the angular velocity at the equator and t is the star's age. This relation is named Skumanich's law after Andrew P. Skumanich who discovered it in 1972. Gyrochronology

Gyrochronology

Gyrochronology is a method for deriving the age of a low-mass star like the Sun from its rotation period.The term is derived from the Greek words gyros, chronos and logos, roughly translated as rotation, age and study respectively....

 is the determination of a star's age based on the rotation rate, calibrated using the Sun.

Stars slowly lose mass by the emission of a stellar wind from the photosphere. The star's magnetic field exerts a torque on the ejected matter, resulting in a steady transfer of angular momentum away from the star. Stars with a rate of rotation greater than 15 km/s also exhibit more rapid mass loss, and consequently a faster rate of rotation decay. Thus as the rotation of a star is slowed because of braking, there is a decrease in rate of loss of angular momentum. Under these conditions, stars gradually approach, but never quite reach, a condition of zero rotation.

Close binary systems

A close binary star

Binary star

A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, comes, or secondary...

 system occurs when two stars orbit each other with an average separation that is of the same order of magnitude

Order of magnitude

An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...

 as their diameters. At these distances, more complex interactions can occur, such as tidal effects, transfer of mass and even collisions. Tidal interactions in a close binary system can result in modification of the orbital and rotational parameters. The total angular momentum of the system is conserved, but the angular momentum can be transferred between the orbital periods and the rotation rates.

Each of the members of a close binary system raise tides on the companion star through gravitational interaction. However the bulges can be slightly misaligned with respect to the direction of gravitational attraction. Thus the force of gravity produces a torque component on the bulge, resulting in the transfer of angular momentum. This causes the system to steadily evolve, although it can approach a stable equilibrium. The effect can be more complex in cases where the axis of rotation is not perpendicular to the orbital plane.

For contact or semi-detached binaries, the transfer of mass from a star to its companion can also result in a significant transfer of angular momentum. The accreting companion can spin up to the point where it reaches its critical rotation rate and begins losing mass along the equator.

Degenerate stars

After a star has finished generating energy through thermonuclear fusion, it evolves into a more compact, degenerate state. During this process the dimensions of the star are significantly reduced, which can result in a corresponding increase in angular velocity.

White dwarf

A white dwarf

White dwarf

A white dwarf, also called a degenerate dwarf, is a small star composed mostly of electron-degenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored...

 is a star that consists of material that is the by-product of thermonuclear fusion during the earlier part of its life, but lacks the mass to burn those more massive elements. It is a compact body that is supported by a quantum mechanical effect known as electron degeneracy pressure

Electron degeneracy pressure

Electron degeneracy pressure is a particular manifestation of the more general phenomenon of quantum degeneracy pressure. The Pauli Exclusion Principle disallows two half integer spin particles from occupying the same quantum state at a given time. The resulting emergent repulsive force is...

 that will not allow the star to collapse any further. Generally most white dwarfs have a low rate of rotation, most likely as the result of rotational braking or by shedding angular momentum when the progenitor star lost its outer envelope. (See planetary nebula

Planetary nebula

A planetary nebula is an emission nebula consisting of an expanding glowing shell of ionized gas ejected during the asymptotic giant branch phase of certain types of stars late in their life...

.)

A slow-rotating white dwarf star can not exceed the Chandrasekhar limit

Chandrasekhar limit

When a star starts running out of fuel, it usually cools off and collapses into one of three compact forms, depending on its total mass:* a White Dwarf, a big lump of Carbon and Oxygen atoms, almost like one huge molecule...

 of 1.44 solar mass

Solar mass

The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...

es without collapsing to form a neutron star

Neutron star

A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

 or exploding as a Type Ia supernova

Type Ia supernova

A Type Ia supernova is a sub-category of supernovae, which in turn are a sub-category of cataclysmic variable stars, that results from the violent explosion of a white dwarf star. A white dwarf is the remnant of a star that has completed its normal life cycle and has ceased nuclear fusion...

. Once the white dwarf reaches this mass, such as by accretion or collision, the gravitational force would exceed the pressure exerted by the electrons. If the white dwarf is rotating rapidly, however, the effective gravity is diminished in the equatorial region, thus allowing the white dwarf to exceed the Chandrasekhar limit. Such rapid rotation can occur, for example, as a result of mass accretion that results in a transfer of angular momentum.

Neutron star

A neutron star

Neutron star

A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

 is a highly dense remnant of a star that is primarily composed of neutron

Neutron

The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

s—a particle that is found in most atomic nuclei and has no net electrical charge. The mass of a neutron star is in the range of 1.35 to 2.1 times the mass of the Sun

Solar mass

The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...

. As a result of the collapse, a newly formed neutron star can have a very rapid rate of rotation; on the order of a hundred rotations per second.

Pulsar

Pulsar

A pulsar is a highly magnetized, rotating neutron star that emits a beam of electromagnetic radiation. The radiation can only be observed when the beam of emission is pointing towards the Earth. This is called the lighthouse effect and gives rise to the pulsed nature that gives pulsars their name...

s are rotating neutron stars that have a magnetic field. A narrow beam of electromagnetic radiation

Electromagnetic radiation

Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

 is emitted from the poles of rotating pulsars. If the beam sweeps past the direction of the Solar System then the pulsar will produce a periodic pulse that can be detected from the Earth. The energy radiated by the magnetic field gradually slows down the rotation rate, so that older pulsars can require as long as several seconds between each pulse.

Black hole

A black hole

Black hole

A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

 is an object with a gravitational field that is sufficiently powerful that it can prevent light from escaping. When they are formed from the collapse of a rotating mass, they retain all of the angular momentum that is not shed in the form of ejected gas. This rotation causes the space within an oblate spheroid-shaped volume, called the "ergosphere", to be dragged around with the black hole. Mass falling into this volume gains energy by this process and some portion of the mass can then be ejected without falling into the black hole. When the mass is ejected, the black hole loses angular momentum (the "Penrose process

Penrose process

The Penrose process is a process theorised by Roger Penrose wherein energy can be extracted from a rotating black hole...

"). The rotation rate of a black hole has been measured as high as 98.7% of the speed of light

Speed of light

The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

.