Stellar rotation is the angular motion of a
star
A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth make ...
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
In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is parallel ...
. As stars are not solid bodies, they can also undergo
differential rotation. Thus the
equator
The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can al ...
of the star can rotate at a different
angular velocity
In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an objec ...
than the higher
latitudes
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...
. These differences in the rate of rotation within a star may have a significant role in the generation of a
stellar magnetic field.
The
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and t ...
of a star interacts with the
stellar wind. 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
The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who ...
. 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
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a Plane of reference, reference plane and the orbital plane or Axis of rotation, axis of direction of the orbiting object ...
of the star's pole to the line of sight. The derived value is given as
, where
is the rotational velocity at the equator and
is the inclination. However,
is not always known, so the result gives a minimum value for the star's rotational velocity. That is, if
is not a
right angle, then the actual velocity is greater than
.
This is sometimes referred to as the projected rotational velocity. In fast rotating stars
polarimetry
Polarimetry is the measurement and interpretation of the polarization of transverse waves, most notably electromagnetic waves, such as radio or light waves. Typically polarimetry is done on electromagnetic waves that have traveled through or ha ...
offers a method of recovering the actual velocity rather than just the rotational velocity; this technique has so far been applied only to
Regulus.
For
giant star
A giant star is a star with substantially larger radius and luminosity than a main-sequence (or ''dwarf'') star of the same surface temperature.Giant star, entry in ''Astronomy Encyclopedia'', ed. Patrick Moore, New York: Oxford University Press ...
s, the atmospheric
microturbulence 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 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
Starspots are stellar phenomena, so-named by analogy with sunspots.
Spots as small as sunspots have not been detected on other stars, as they would cause undetectably small fluctuations in brightness. The commonly observed starspots are in gen ...
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.
Physical effects
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 at the equator, as described by the
von Zeipel theorem.
An extreme example of an equatorial bulge is found on the star
Regulus A (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,
Vega
Vega is the brightest star in the northern
Northern may refer to the following:
Geography
* North, a point in direction
* Northern Europe, the northern part or region of Europe
* Northern Highland, a region of Wisconsin, United Sta ...
and
Achernar.
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 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.
The underlying mechanism that causes differential rotation is turbulent
convection
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the c ...
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.
The interfaces between regions with sharp differences in rotation are believed to be efficient sites for the
dynamo processes that generate the
stellar magnetic field. 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
During formation
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 forms, which gains heat from the
gravitational energy
Gravitational energy or gravitational potential energy is the potential energy a massive object has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field, which is released (conve ...
of the collapse.
As the collapse continues, the rotation rate can increase to the point where the accreting protostar can break up due to
centrifugal force
In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is parallel ...
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
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and t ...
with the
stellar wind in
magnetic braking. The expanding wind carries away the angular momentum and slows down the rotation rate of the collapsing protostar.
Most
main-sequence 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."
After formation
For main-sequence stars, the decline in rotation can be approximated by a mathematical relation:
:
where
is the angular velocity at the equator and
is the star's age. This relation is named ''Skumanich's law'' after Andrew P. Skumanich who discovered it in 1972.
Gyrochronology Gyrochronology is a method for estimating the age of a low-mass (cool) Main sequence, main sequence star (spectral class F8 V or later) from its stellar rotation, rotation period. The term is derived from the Greek language, Greek words ''gyros, chr ...
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.
At the end of the main sequence
Ultracool dwarfs and
brown dwarf
Brown dwarfs (also called failed stars) are substellar objects that are not massive enough to sustain nuclear fusion of ordinary hydrogen (hydrogen-1, 1H) into helium in their cores, unlike a main sequence, main-sequence star. Instead, they have ...
s experience faster rotation as they age, due to gravitational contraction. These objects also have magnetic fields similar to the coolest stars. However, the discovery of rapidly rotating brown dwarfs such as the T6 brown dwarf WISEPC J112254.73+255021.5 lends support to theoretical models that show that rotational braking by stellar winds is over 1000 times less effective at the end of the main sequence.
Close binary systems
A close
binary star system occurs when two stars orbit each other with an average separation that is of the same
order of magnitude 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 raises tides on the other 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 (
tidal acceleration). 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
Thermonuclear fusion is the process of atomic nuclei combining or “fusing” using high temperatures to drive them close enough together for this to become possible. There are two forms of thermonuclear fusion: ''uncontrolled'', in which the re ...
, 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
A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is comparable to the Earth's. A white dwarf's faint luminosity comes ...
is a star that consists of material that is the by-product of
thermonuclear fusion
Thermonuclear fusion is the process of atomic nuclei combining or “fusing” using high temperatures to drive them close enough together for this to become possible. There are two forms of thermonuclear fusion: ''uncontrolled'', in which the re ...
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 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.)
A slow-rotating white dwarf star can not exceed the
Chandrasekhar limit of 1.44
solar mass
The solar mass () is a standard unit of mass in astronomy, equal to approximately . It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxies and black holes. It is approximately equal to the mass o ...
es without collapsing to form a
neutron star
A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. w ...
or exploding as a
Type Ia supernova. 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
A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. w ...
is a highly dense remnant of a star that is primarily composed of
neutron
The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...
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 1.2 to 2.1 times the
mass of the Sun
The solar mass () is a standard unit of mass in astronomy, equal to approximately . It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxies and black holes. It is approximately equal to the mass of ...
. 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
A pulsar (from ''pulsating radio source'') is a highly magnetized rotating neutron star that emits beams of electromagnetic radiation out of its magnetic poles. This radiation can be observed only when a beam of emission is pointing toward E ...
s are rotating neutron stars that have a magnetic field. A narrow beam of
electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible ...
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
A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can defo ...
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"). The rotation rate of a black hole has been measured as high as 98.7% of the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
.
References
External links
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Rotation
Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
Rotation