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| [[File:Achernar.jpg|right|thumb|280px|This illustration shows the oblate appearance of the star [[Achernar]] caused by rapid rotation.]]
| | 42 yr old Ship's Master Winfred from King City, has numerous hobbies and interests that include rocking aids babies, [http://ganhardinheiro.comoganhardinheiro101.com como ganhar dinheiro na internet] and netball. Has been a travel enthusiast and in recent past made vacation to Auschwitz Birkenau. |
| '''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. | |
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| The rotation of a star produces an equatorial bulge due to [[centrifugal force]]. 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]]. These differences in the rate of rotation within a star may have a significant role in the generation of a [[stellar magnetic field]].<ref name="donati2003"/>
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| The [[stellar magnetic field|magnetic field]] 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.
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| ==Measurement==
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| 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 line]]s of a star are observed, this shift at each end of the spectrum causes the line to broaden.<ref name="mnras89">{{cite journal
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| | author=Shajn, G.; Struve, O.
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| | title=On the rotation of the stars
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| | journal=Monthly Notices of the Royal Astronomical Society
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| | year=1929 | volume=89 | pages=222–239
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| | bibcode=1929MNRAS..89..222S }}</ref> However, this broadening must be carefully separated from other effects that can increase the line width.
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| [[File:V sin i.png|left|thumb|340px|This star has inclination ''i'' to the line-of-sight of an observer on the Earth and rotational velocity ''v<sub>e</sub>'' at the equator.]]
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| The component of the radial velocity observed through line broadening depends on the [[inclination]] of the star's pole to the line of sight. The derived value is given as <math>v_e \cdot \sin i</math>, where ''v<sub>e</sub>'' 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 <math>v_e \cdot \sin i</math>.<ref name="mnras89" /> This is sometimes referred to as the projected rotational velocity.
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| For [[giant star]]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.<ref>{{cite journal
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| | last=Gould | first=Andrew
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| | title=Measuring the Rotation Speed of Giant Stars from Gravitational Microlensing
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| | journal=Astrophysical Journal
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| | year=1997 | volume=483
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| | issue=1 | pages=98–102
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| | bibcode=1996astro.ph.11057G
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| | doi=10.1086/304244 |arxiv = astro-ph/9611057 }}</ref>
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| If a star displays magnetic surface activity such as [[starspot]]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.<ref>{{cite journal
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| | author=Soon, W.; Frick, P.; Baliunas, S.
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| | title=On the rotation of the stars
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| | journal=The Astrophysical Journal
| |
| | year=1999 | volume=510 | issue=2 | pages=L135–L138
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| | bibcode=1999ApJ...510L.135S
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| | doi=10.1086/311805 |arxiv = astro-ph/9811114 }}</ref> 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.<ref>{{cite journal
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| | author=Collier Cameron, A.; Donati, J.-F.
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| | title=Doin' the twist: secular changes in the surface differential rotation on AB Doradus
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| | journal=Monthly Notices of the Royal Astronomical Society
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| | year=2002 | volume=329 | issue=1 | pages=L23–L27
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| | bibcode=2002MNRAS.329L..23C
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| | doi=10.1046/j.1365-8711.2002.05147.x |arxiv = astro-ph/0111235 }}</ref>
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| {{-}}
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| ==Physical effects==
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| ===Equatorial bulge===
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| {{see also|Equatorial bulge}}
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| 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.
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| 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]].
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| An extreme example of an equatorial bulge is found on the star [[Regulus|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.<ref name="apj628">{{cite journal
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| | author=McAlister, H. A., ten Brummelaar, T. A., et al.
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| | title=First Results from the CHARA Array. I. An Interferometric and Spectroscopic Study of the Fast Rotator Alpha Leonis (Regulus).
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| | journal=The Astrophysical Journal
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| | year=2005 | volume=628
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| | issue=1 | pages=439–452
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| | doi=10.1086/430730
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| | bibcode=2005ApJ...628..439M|arxiv = astro-ph/0501261 }}</ref> Other rapidly rotating stars include [[Alpha Arae]], [[Pleione (star)|Pleione]], [[Vega]] and [[Achernar]].
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| 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.<ref>{{cite conference
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| | author=Hardorp, J.; Strittmatter, P. A.
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| | title =Rotation and Evolution of be Stars
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| | booktitle=Proceedings of IAU Colloq. 4 | page=48
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| | publisher=Gordon and Breach Science Publishers
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| | date=September 8–11, 1969
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| | location=Ohio State University, Columbus, Ohio
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| | bibcode=1970stro.coll...48H
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| }}</ref>
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| ===Differential rotation===
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| 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.)<ref>{{cite journal
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| | author=Kitchatinov, L. L.; Rüdiger, G.
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| | title=Anti-solar differential rotation
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| | journal=Astronomische Nachrichten
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| | year=2004 | volume=325 | issue=6 | pages=496–500
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| | bibcode=2004AN....325..496K
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| | doi=10.1002/asna.200410297 |arxiv = astro-ph/0504173 }}</ref><ref>{{cite journal
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| | author=Ruediger, G.; von Rekowski, B.; Donahue, R. A.; Baliunas, S. L.
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| | title=Differential Rotation and Meridional Flow for Fast-rotating Solar-Type Stars
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| | journal=Astrophysical Journal
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| | year=1998 | volume=494 | issue=2 | pages=691–699
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| | doi=10.1086/305216
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| | bibcode=1998ApJ...494..691R}}</ref> The first such star, other than the Sun, to have its differential rotation mapped in detail is [[AB Doradus]].<ref name="donati2003">{{cite web
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| | last=Donati | first=Jean-François | date=November 5, 2003
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| | url=http://www.ast.obs-mip.fr/users/donati/diffrot.html
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| | title=Differential rotation of stars other than the Sun
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| | publisher=Laboratoire d’Astrophysique de Toulouse
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| | accessdate = 2007-06-24 }}</ref>
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| <ref>{{cite journal
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| | author=Donati, J.-F.; Collier Cameron, A.
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| | title=Differential rotation and magnetic polarity patterns on AB Doradus
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| | journal=Monthly Notices of the Royal Astronomical Society
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| | year=1997 | volume=291 | issue=1 | pages=1–19
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| | bibcode=1997MNRAS.291....1D }}</ref>
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| The underlying mechanism that causes differential rotation is turbulent [[convection]] 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]].<ref>{{cite web
| |
| | last=Korab | first=Holly | date=June 25, 1997
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| | url=http://access.ncsa.uiuc.edu/Stories/97Stories/WOODward.html
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| | title=NCSA Access: 3D Star Simulation
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| | publisher=National Center for Supercomputing Applications
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| | accessdate=2007-06-27 }}</ref><ref>{{cite journal
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| | author=Küker, M.; Rüdiger, G.
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| | title=Differential rotation on the lower main sequence
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| | journal=Astronomische Nachrichten
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| | year=2004 | volume=326 | issue=3 | pages=265–268
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| | bibcode=2005AN....326..265K
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| | doi=10.1002/asna.200410387 |arxiv = astro-ph/0504411 }}</ref>
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| The interfaces between regions with sharp differences in rotation are believed to be efficient sites for the [[Dynamo theory|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.<ref name="donati2003" />
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| ==Rotation braking==
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| 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 [[potential energy|gravitational energy]] of the collapse.
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| As the collapse continues, the rotation rate can increase to the point where the accreting protostar can break up due to [[centrifugal force]] 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 [[stellar magnetic field|magnetic field]] 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.<ref>{{cite journal
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| | author=Ferreira, J.; Pelletier, G.; Appl, S.
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| | title=Reconnection X-winds: spin-down of low-mass protostars
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| | journal=Monthly Notices of the Royal Astronomical Society
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| | year=2000 | volume=312
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| | issue=2 | pages=387–397
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| | bibcode=2000MNRAS.312..387F
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| | doi=10.1046/j.1365-8711.2000.03215.x }}</ref><ref>{{cite news
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| | first=Terry | last=Devitt
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| | title=What Puts The Brakes On Madly Spinning Stars?
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| | publisher=University of Wisconsin-Madison
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| | date=January 31, 2001
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| | url=http://www.news.wisc.edu/5732
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| | accessdate=2007-06-27 }}</ref>
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| {| class="wikitable" style="float: right;"
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| |+Average<br>rotational<br>velocities<ref>{{cite journal
| |
| | last = McNally | first = D.
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| | title=The distribution of angular momentum among main sequence stars | journal=The Observatory
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| | year=1965 | volume=85 | pages=166–169
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| | bibcode=1965Obs....85..166M }}</ref>
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| |-
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| ![[Stellar class|Stellar<br />class]]
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| !''v<sub>e</sub>''<br />(km/s)
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| |-
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| |style="text-align: center;"|O5 ||style="text-align: center;"| 190
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| |-
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| |style="text-align: center;"|B0 ||style="text-align: center;"| 200
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| |-
| |
| |style="text-align: center;"|B5 ||style="text-align: center;"| 210
| |
| |-
| |
| |style="text-align: center;"|A0 ||style="text-align: center;"| 190
| |
| |-
| |
| |style="text-align: center;"|A5 ||style="text-align: center;"| 160
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| |-
| |
| |style="text-align: center;"|F0 ||style="text-align: center;"| 95
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| |-
| |
| |style="text-align: center;"|F5 ||style="text-align: center;"| 25
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| |-
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| |style="text-align: center;"|G0 ||style="text-align: center;"| 12
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| |}
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| Most [[main sequence|main-sequence]] stars with a [[spectral class]] between O5 and F5 have been found to rotate rapidly.<ref name="apj628" /><ref>{{cite conference
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| | author=Peterson, Deane M. ''et al.''
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| | title =Resolving the effects of rotation in early type stars
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| | booktitle=New Frontiers in Stellar Interferometry, Proceedings of SPIE Volume 5491
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| | page=65
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| | publisher=The International Society for Optical Engineering
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| | year=2004
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| | location=Bellingham, Washington, USA
| |
| | bibcode=2004SPIE.5491...65P
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| }}</ref> 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.
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| For main-sequence stars, the decline in rotation can be approximated by a mathematical relation:
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| :<math>\Omega_e \propto t^{-\frac{1}{2}}</math>
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| where <math>\Omega_e</math> is the angular velocity at the equator and ''t'' is the star's age.<ref>{{cite book
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| | first=Jean-Louis | last=Tassoul | year=1972
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| | title=Stellar Rotation | location=Cambridge, MA
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| | publisher=Cambridge University Press
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| | url=http://assets.cambridge.org/97805217/72181/sample/9780521772181ws.pdf
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| | accessdate=2007-06-26
| |
| | isbn=0-521-77218-4 }}</ref> This relation is named ''Skumanich's law'' after Andrew P. Skumanich who discovered it in 1972.<ref>{{cite journal
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| | first=Andrew P. | last=Skumanich
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| | title=Time Scales for CA II Emission Decay, Rotational Braking, and Lithium Depletion
| |
| | journal=The Astrophysical Journal
| |
| | year=1972 | volume=171 | page=565
| |
| | doi=10.1086/151310 | bibcode=1972ApJ...171..565S}}</ref> [[Gyrochronology]] is the determination of a star's age based on the rotation rate, calibrated using the Sun.<ref>{{cite journal
| |
| | first = Sydney A. | last = Barnes
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| | title = Ages for illustrative field stars using gyrochronology: viability, limitations and errors
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| | journal = The Astrophysical Journal
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| | year=2007 | volume=669 | issue=2 | pages=1167–1189
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| | doi=10.1086/519295
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| | arxiv=0704.3068 | bibcode=2007ApJ...669.1167B}}</ref>
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| 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.<ref>{{cite journal
| |
| | last = Nariai | first = Kyoji
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| | title=Mass Loss from Coronae and Its Effect upon Stellar Rotation
| |
| | journal=Astrophysics and Space Science
| |
| | year=1969 | volume=3
| |
| | issue = 1 | pages=150–159
| |
| | bibcode=1969Ap&SS...3..150N
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| | doi=10.1007/BF00649601 }}</ref>
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| ==Close binary systems==
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| 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.<ref name="aaa99">{{cite journal
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| | last=Hut | first=P.
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| | title=Tidal evolution in close binary systems
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| | journal=Astronomy and Astrophysics
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| | year=1999 | volume=99 | issue=1 | pages=126–140
| |
| | bibcode=1981A&A....99..126H }}</ref>
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| 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.<ref name="aaa99" />
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| 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.<ref>{{cite web
| |
| | author=Weaver, D.; Nicholson, M. | date=December 4, 1997
| |
| | url=http://hubblesite.org/newscenter/archive/releases/1997/39/text/
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| | title=One Star's Loss is Another's Gain: Hubble Captures Brief Moment in Life of Lively Duo
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| | publisher=NASA Hubble
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| | accessdate=2007-07-03 }}</ref>
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| ==Degenerate stars==
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| 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.
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| ===White dwarf===
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| {{main|White dwarf}}
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| 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. 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.<ref>{{cite book
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| | author=Willson, L. A.; Stalio, R. | year=1990
| |
| | title=Angular Momentum and Mass Loss for Hot Stars
| |
| | edition=1st | pages=315–16 | publisher=Springer
| |
| | isbn=0-7923-0881-6 }}</ref> (See [[planetary nebula]].)
| |
| | |
| A slow-rotating white dwarf star can not exceed the [[Chandrasekhar limit]] of 1.44 [[solar mass]]es without collapsing to form a [[neutron star]] 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.<ref>{{cite journal
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| | author=Yoon, S.-C.; Langer, N.
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| | title=Presupernova evolution of accreting white dwarfs with rotation
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| | journal=Astronomy and Astrophysics
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| | year=2004 | volume=419
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| | issue=2 | pages=623–644
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| | bibcode=2004A&A...419..623Y
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| | doi=10.1051/0004-6361:20035822 |arxiv = astro-ph/0402287 }}</ref>
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| ===Neutron star===
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| {{main|Pulsar}}
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| [[File:Pulsar schematic.jpg|right|thumb|250px|The neutron star (center) emits a beam of radiation from its magnetic poles. The beams are swept along a conic surface around the axis of rotation.]]
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| A [[neutron star]] is a highly dense remnant of a star that is primarily composed of [[neutron]]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 [[solar mass|mass of the Sun]]. 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.
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| [[Pulsar]]s are rotating neutron stars that have a magnetic field. A narrow beam of [[electromagnetic radiation]] 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.<ref>{{cite web
| |
| | last = Lorimer | first = D. R. | date =August 28, 1998
| |
| | url=http://relativity.livingreviews.org/Articles/lrr-1998-10/
| |
| | title=Binary and Millisecond Pulsars
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| | publisher=Max-Planck-Gesellschaft
| |
| | accessdate=2007-06-27 }}</ref>
| |
| | |
| ===Black hole===
| |
| {{main|Rotating black hole}}
| |
| A [[black hole]] 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]]").<ref>{{cite journal
| |
| | last = Begelman | first = Mitchell C.
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| | title=Evidence for Black Holes
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| | journal=Science | year=2003 | volume=300
| |
| | issue=5627 | pages=1898–1903
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| | doi=10.1126/science.1085334
| |
| | pmid = 12817138 |bibcode = 2003Sci...300.1898B }}</ref> The rotation rate of a black hole has been measured as high as 98.7% of the [[speed of light]].<ref>{{cite news
| |
| | first=Lee | last=Tune
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| | title=Spin of Supermassive Black Holes Measured for First Time
| |
| | publisher=University of Maryland Newsdesk
| |
| | date=May 29, 2007
| |
| | url=http://www.newsdesk.umd.edu/scitech/release.cfm?ArticleID=1447
| |
| | accessdate=2007-06-25 }}</ref>
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| ==References==
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| {{reflist|2}}
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| ==External links==
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| *{{cite web
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| | author=Staff | date=February 28, 2006
| |
| | url=http://helene.ethz.ch/research/stars/starspots/results/results_nf.html
| |
| | title=Stellar Spots and Cyclic Activity: Detailed Results
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| | publisher=ETH Zürich | accessdate=2009-10-22 }}
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| {{Star}}
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| {{good article}}
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| [[Category:Stellar astronomy]]
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