Stellar rotation is the angular motion of a star 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 centripedal force. The centripetal force is the external force required to make a body follow a curved path As stars are not solid bodies, they can also undergo differential rotation. Thus the equator of the star can rotate at a different angular velocity than the higher latitudes. The equator (sometimes referred to colloquially as "the Line") is the intersection of the Earth 's surface with the plane perpendicular to the Do not confuse with Angular frequency The unit for angular velocity is rad/s Latitude, usually denoted symbolically by the Greek letter phi ( Φ) gives the location of a place on Earth (or other planetary body north or south of the These differences in the rate of rotation within a star may have a significant role in the generation of a stellar magnetic field. A stellar magnetic field is a Magnetic field generated by the motion of conductive plasma inside a Main sequence ( Hydrogen -burning [1]
The magnetic field of a star interacts with the stellar wind. A stellar magnetic field is a Magnetic field generated by the motion of conductive plasma inside a Main sequence ( Hydrogen -burning A stellar wind is a flow of neutral or charged gas ejected from the upper atmosphere of a Star. 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.
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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 proportion 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) named after Christian Doppler, is the change in Frequency and Wavelength of a Wave for 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. A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from an excess or deficiency of photons in a narrow frequency range compared [2] 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 of the star's pole to the line of sight. Inclination in general is the Angle between a Reference plane and another plane or axis of direction The derived value is given as 
, where ve 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, then the actual velocity is greater than . In Geometry and Trigonometry, a right angle is an angle of 90 degrees corresponding to a quarter turn (that is a quarter of a full circle [2] This is sometimes referred to as the projected rotational velocity.
For giant stars, the atmospheric microturbulence can result in line broadening that is much larger than effects of rotational, effectively drowning out the signal. A giant star is a Star with substantially larger Radius and Luminosity than a Main sequence star of the same surface temperature. Microturbulence is a form of Turbulence that varies over small distance scales However, an alternate approach can be employed that makes use of gravitational microlensing events. Gravitational microlensing is an astronomical phenomenon due to the Gravitational lens effect These occur when a massive object passes in front of the more distance 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. [3]
If a star displays magnetic surface activity such as starspots, then these features can be tracked to estimate the rotation rate. Starspots are equivalent to sunspots but located on other stars 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. [4] 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. [5]
Physical effects
Equatorial bulge
The rotation of a star produces a net centripetal force in a direction perpendicular to the axis. The centripetal force is the external force required to make a body follow a curved path At the pole the centripetal force is zero, so the gravitational force of the star is unopposed. Around the equator, however, the centripetal force is non-zero and it partly opposes the gravitational force. In order to balance out the difference in net forces at the pole and the equator, the surface of the star bulges outward along the equator and the star forms an oblate spheroid. An oblate Spheroid is a rotationally symmetric Ellipsoid having a polar axis shorter than the diameter of the equatorial circle whose plane
An extreme example of an equatorial bulge is found on the star Regulus A (α Leonis A). Regulus (α Leo / α Leonis / Alpha Leonis is the brightest star in the Constellation Leo and one of the brightest stars in the nighttime sky 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. [6] Other rapidly rotating stars include Alpha Arae, Vega and Achernar. Alpha Arae (α Ara / α Arae is the second brightest Star in the Constellation Ara. Vega (α Lyr / α Lyrae / Alpha Lyrae ( or) is the brightest Star in the Constellation Lyra, the fifth brightest star in the night Achernar (α Eri / α Eridani / Alpha Eridani sometimes spelled Achenar, is the brightest star in the Constellation Eridanus and the eighth-brightest
The break-up velocity of a star is an expression that is used to describe the case where the centripetal force at the equator is equal to the gravitational force. For a star to be stable the rotational velocity must be below this value. [7]
Differential rotation
Surface differential rotation is observed on stars such as the Sun when the angular velocity varies with latitude. Differential rotation is seen when different parts of a rotating object move with different angular velocities (rates of Rotation) Typically the angular velocity decreases with increasing latitude. However the reverse has also been observed, such as on the star designated HD 31993. )[8][9] The first such star, other than the Sun, to have its differential rotation mapped in detail is AB Doradus. AB Doradus is a pre-main sequence trinary star system in the Constellation Dorado. [10] [11]
The underlying mechanism that causes differential rotation is turbulent convection inside a star. Convection in the most general terms refers to the movement of molecules within Fluids (i 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 is a meteorological term meaning that the general flow pattern is north to south along the earth's Longitude lines (the opposite of Zonal flow [12][13]
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. The dynamo theory proposes a mechanism by which a celestial body such as the Earth generates a Magnetic field. A stellar magnetic field is a Magnetic field generated by the motion of conductive plasma inside a Main sequence ( Hydrogen -burning 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. [11]
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. In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position At the dense center of this disk a protostar forms, which gaining heat from the gravitational energy of the collapse. A protostar is a large object that forms by contraction out of the gas of a Giant molecular cloud in the Interstellar medium. Potential energy can be thought of as Energy stored within a physical system
As the collapse continues, the rotation rate can increase to the point where the accreting protostar can break up due to centripetal force at the equator. The centripetal force is the external force required to make a body follow a curved path 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 with the stellar wind. A stellar magnetic field is a Magnetic field generated by the motion of conductive plasma inside a Main sequence ( Hydrogen -burning A stellar wind is a flow of neutral or charged gas ejected from the upper atmosphere of a Star. The expanding wind carries away the angular momentum and slows down the rotation rate of the collapsing protostar. [14][15]
| Stellar class |
ve (km/s) |
|---|---|
| O5 | 190 |
| B0 | 200 |
| B5 | 210 |
| A0 | 190 |
| A5 | 160 |
| F0 | 95 |
| F5 | 25 |
| G0 | 12 |
Most main sequence stars with a spectral class between O5 and F5 have been found to rotate rapidly. In Astronomy, stellar classification is a classification of Stars based initially on photospheric temperature and its associated Spectral characteristics The main sequence is the name for a continuous and distinctive band of stars that appear on a plot of stellar color versus brightness In Astronomy, stellar classification is a classification of Stars based initially on photospheric temperature and its associated Spectral characteristics [6][17] 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 stars, the decline in rotation can be approximated by a mathematical relation:
where ve is the angular velocity at the equator and t is the star's age. The main sequence is the name for a continuous and distinctive band of stars that appear on a plot of stellar color versus brightness [18] This relation is named Skumanich's law after Andrew P. Skumanich who discovered it in 1972. [19] Gyrochronology is the determination of a star's age based on the rotation rate. [20]
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. [21]
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. A binary star is a Star system consisting of two Stars orbiting around their Center of mass. 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 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. [22]
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. [22]
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. [23]
Degenerate stars
After a star has finished generating energy through thermonuclear fusion, it evolves into a more compact, degenerate state. In Physics and Nuclear chemistry, nuclear fusion is the process by which multiple- like charged atomic nuclei join together to form a heavier nucleus 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 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. A white dwarf, also called a degenerate dwarf, is a small Star composed mostly of Electron-degenerate matter. In Physics and Nuclear chemistry, nuclear fusion is the process by which multiple- like charged atomic nuclei join together to form a heavier nucleus 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. Electron degeneracy pressure is a consequence of the Pauli exclusion principle, which states that two Fermions cannot occupy the same Quantum state at the 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. [24] (See planetary nebula. A planetary nebula is an Emission nebula consisting of a glowing shell of Gas and plasma formed by certain types of Stars when they die )
A slow-rotating white dwarf star can not exceed the Chandrasekhar limit of 1. The Chandrasekhar limit limits the mass of bodies made from Electron-degenerate matter, a dense form of matter which consists of nuclei immersed in a gas of Electrons 44 solar masses without collapsing to form a neutron star or exploding as a Type Ia supernova. The solar mass is a standard way to express Mass in Astronomy, used to describe the masses of other Stars and galaxies. A neutron star is a type of remnant that can result from the Gravitational collapse of a massive Star during a Type II, Type Ib or Type A Type Ia supernova is a sub-category of cataclysmic Variable 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 centripetal force at the equator can counter-balance the gravitational force and allow the mass 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. [25]
Neutron star
A neutron star is a highly dense remnant of a star that is primarily composed of neutrons—a particle that is found in most atomic nuclei and has no net electrical charge. A neutron star is a type of remnant that can result from the Gravitational collapse of a massive Star during a Type II, Type Ib or Type This article is a discussion of neutrons in general For the specific case of a neutron found outside the nucleus see Free neutron. The mass of a neutron star is in the range of 1. 35 to 2. 1 times the mass of the Sun. The solar mass is a standard way to express Mass in Astronomy, used to describe 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 thousand rotations per second. A millisecond pulsar ( MSP) often referred to as "recycled pulsar", is a Pulsar with a rotational period in the range of about 1-10 Milliseconds [26]
Pulsars are rotating neutron stars that have a magnetic field. Pulsars are highly magnetized rotating Neutron stars that emit a beam of Electromagnetic radiation in the form of radio waves A narrow beam of electromagnetic radiation is emitted from the poles of rotating pulsars. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. 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. [27]
Black hole
A black hole is an object with a gravitation field that is sufficiently powerful that it can prevent light from escaping. Black hole#Major features of rotating black holes A rotating black hole is a Black hole that possesses Angular momentum. A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e When they are formed from the collapse of a rotating mass, they retain angular momentum. 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 can then be ejected without falling into the black hole. When the mass is ejected, the black hole loses angular momentum. [28] The rotation rate of a black hole has been measured as high as 98. 7% of the speed of light. [29]
References
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- ^ a b Hut, P. (1999). "Tidal evolution in close binary systems". Astronomy and Astrophysics 99 (1): 126–140.
- ^ Weaver, D. ; Nicholson, M. (December 4, 1997). One Star's Loss is Another's Gain: Hubble Captures Brief Moment in Life of Lively Duo. NASA Hubble. Retrieved on 2007-07-03. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 324 - Battle of Adrianople Constantine I defeats Licinius, who flees to Byzantium.
- ^ Willson, L. A. ; Stalio, R. (1990). Angular Momentum and Mass Loss for Hot Stars, 1st edition, Springer, pp. 315-16. ISBN 0792308816.
- ^ Yoon, S. -C. ; Langer, N. (2004). "Presupernova evolution of accreting white dwarfs with rotation". Astronomy and Astrophysics 419: 623–644. doi:. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.
- ^ Lochner, J. ; Gibb, M. (December, 2006). Neutron Stars and Pulsars. NASA. Retrieved on 2007-06-27. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1358 - Republic of Dubrovnik is founded 1709 - Peter the Great defeats Charles XII of Sweden
- ^ Lorimer, D. R. (August 28, 1998). Binary and Millisecond Pulsars. Max-Planck-Gesellschaft. Retrieved on 2007-06-27. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1358 - Republic of Dubrovnik is founded 1709 - Peter the Great defeats Charles XII of Sweden
- ^ Begelman, Mitchell C. (2003). "Evidence for Black Holes". Science 300 (5627): 1898–1903. doi:. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.
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External links
- Staff (February 28, 2006). Stellar Spots and Cyclic Activity: Detailed Results. ETH Zentrum. Retrieved on 2007-06-26. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 363 - Roman Emperor Julian is killed during the retreat from the Sassanid Empire.
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