Stellar rotation: Difference between revisions

[[File:V sin i.png|left|thumb|340px|This star has inclination ''<math>i''</math> to the line-of-sight of an observer on the Earth and rotational velocity ''v_e'' at the equator.]]

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_ev_\mathrm{e} \cdot \sin i</math>, where ''v<submath>v_\mathrm{e}</submath>'' is the rotational velocity at the equator and ''<math>i''</math> is the inclination. However, ''<math>i''</math> is not always known, so the result gives a minimum value for the star's rotational velocity. That is, if ''<math>i''</math> is not a [[right angle]], then the actual velocity is greater than <math>v_ev_\mathrm{e} \cdot \sin i</math>.<ref name="mnras89" /> This is sometimes referred to as the projected rotational velocity. In fast rotating stars [[polarimetry]] offers a method of recovering the actual velocity rather than just the rotational velocity; this technique has so far been applied only to [[Regulus]].<ref>{{cite journal|doi=10.1038/s41550-017-0238-6|title=Polarization due to rotational distortion in the bright star Regulus|journal=Nature Astronomy|volume=1|issue=10|pages=690–696|year=2017|last1=Cotton|first1=Daniel V|last2=Bailey|first2=Jeremy|last3=Howarth|first3=Ian D|last4=Bott|first4=Kimberly|last5=Kedziora-Chudczer|first5=Lucyna|last6=Lucas|first6=P. W|last7=Hough|first7=J. H|bibcode=2017NatAs...1..690C|arxiv=1804.06576|s2cid=53560815 }}</ref>

| doi=10.1086/304244 |arxiv = astro-ph/9611057 | s2cid=16920051
}}</ref>

| doi=10.1086/311805 |arxiv = astro-ph/9811114 | s2cid=9517804
}}</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

| doi=10.1046/j.1365-8711.2002.05147.x | doi-access=free
|arxiv = astro-ph/0111235 | s2cid=11292613
}}</ref>

| bibcode=2005ApJ...628..439M|arxiv = astro-ph/0501261 | s2cid=6776360
}}</ref> Other rapidly rotating stars include [[Alpha Arae]], [[Pleione (star)|Pleione]], [[Vega]] and [[Achernar]].

| doi=10.1002/asna.200410297 |arxiv = astro-ph/0504173 | s2cid=59497102
}}</ref><ref>{{cite journal

| last=Korab
| first=Holly
| date=June 25, 1997

| access-date=2007-06-27 }}</ref><ref>{{cite journal

| doi=10.1002/asna.200410387 |arxiv = astro-ph/0504411 | s2cid=119386346
}}</ref>

:<math>\Omega_eOmega_\mathrm{e} \propto t^{-\frac{1}{2}},</math>

where <math>\Omega_eOmega_\mathrm{e}</math> is the angular velocity at the equator and ''<math>t''</math> is the star's age.<ref>{{cite book

| isbn=978-0-521-77218-1 }}</ref> This relation is named ''Skumanich's law'' after Andrew P. Skumanich who discovered it in 1972,.<ref>{{cite journal

| doi=10.1086/151310 | bibcode=1972ApJ...171..565S| doi-access=free}}</ref><ref>{{cite book|last1=Skumanich|first1=Andrew P.|last2=Eddy|first2=J. A.|editor1-last=Bonnet|editor1-first=R. M.|editor2-last=Dupree|editor2-first=A. K.|title=Aspects of Long-Term Variability in Sun and Stars – In: Solar Phenomena In Stars and Stellar Systems|date=1981|publisher=D. Reidel|location=Hingham, MA|pages=349–398}}</ref> but which had actually been proposed much earlier by [[Évry Schatzman]].<ref>{{cite journal | last1 name= Mestel | first1 = L. | author-link = Leon Mestel | year = 1968 | title = Magnetic Braking by a Stellar Wind—I| journal = MNRAS | volume = 138 | issue = 3| pages = 359–391 | doi=10.1093/mnras/138.3.359|bibcode = 1968MNRAS.138..359M | doi-access = free }}</ref"S2023"> [[Gyrochronology]] is the determination of a star's age based on the rotation rate, calibrated using the Sun.<ref>{{cite journal

| arxiv=0704.3068 | bibcode=2007ApJ...669.1167B| s2cid = 14614725
}}</ref>

[[Ultra-cool dwarf|Ultracool dwarfs]] and [[brown dwarf]]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<ref>{{cite journal|last1=Route|first1=M.|last2=Wolszczan|first2=A.|title=Radio-flaring from the T6 Dwarf WISEPC J112254.73+255021.5 with A Possible Ultra-short Periodicity|journal=The Astrophysical Journal Letters|date=20 April 2016|volume=821|issue=2|page=L21|doi=10.3847/2041-8205/821/2/L21|arxiv=1604.04543|bibcode=2016ApJ...821L..21R|s2cid=118478221 |doi-access=free }}</ref> 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.<ref>{{cite journal|last1=Route|first1=M.|title=Is WISEP J060738.65+242953.4 Really a Magnetically Active, Pole-on L Dwarf?|journal=The Astrophysical Journal|date=10 July 2017|volume=843|issue=2|page=115|doi=10.3847/1538-4357/aa78ab|arxiv=1706.03010|bibcode=2017ApJ...843..115R|s2cid=119056418 |doi-access=free }}</ref>

| doi=10.1051/0004-6361:20035822 |arxiv = astro-ph/0402287 }}</ref>| s2cid=2963085

| pmid = 12817138 |bibcode = 2003Sci...300.1898B | s2cid = 46107747
}}</ref> The rotation rate of a black hole has been measured as high as 98.7% of the [[speed of light]].<ref>{{cite news