25:
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would have to resolve this entire range of scales in each of the three dimensions. Consequently, all solar differential rotation models must involve some approximations regarding momentum and heat transport by turbulent motions that are not explicitly computed. Thus, modeling approaches can be classified as either mean-field models or large-eddy simulations according to the approximations.
706:
723:
The highly turbulent nature of solar convection and anisotropies induced by rotation complicate the dynamics of modeling. Molecular dissipation scales on the Sun are at least six orders of magnitude smaller than the depth of the convective envelope. A direct numerical simulation of solar convection
294:
Gradients in angular rotation caused by angular momentum redistribution within the convective layers of a star are expected to be a main driver for generating the large-scale magnetic field, through magneto-hydrodynamical (dynamo) mechanisms in the outer envelopes. The interface between these two
246:
measurements of solar "p-modes" it is possible to deduce the differential rotation. The Sun has very many acoustic modes that oscillate in the interior simultaneously, and the inversion of their frequencies can yield the rotation of the solar interior. This varies with both depth and (especially)
719:
On the Sun, the study of oscillations revealed that rotation is roughly constant within the whole radiative interior and variable with radius and latitude within the convective envelope. The Sun has an equatorial rotation speed of ~2 km/s; its differential rotation implies that the angular
226:
in stars which is a movement of mass, due to steep temperature gradients from the core outwards. This mass carries a portion of the star's angular momentum, thus redistributing the angular velocity, possibly even far enough out for the star to lose angular velocity in
277:
TVLM 513-46546, astronomers were able to measure subtle changes in the arrival times of the radio waves. These measurements demonstrate that the radio waves can arrive 1–2 seconds sooner or later in a systematic fashion over a number of years. On the Sun,
685:
312:
Solar differential rotation causes shear at the so-called tachocline. This is a region where rotation changes from differential in the convection zone to nearly solid-body rotation in the interior, at 0.71 solar radii from the center.
742:
Disk galaxies do not rotate like solid bodies, but rather rotate differentially. The rotation speed as a function of radius is called a rotation curve, and is often interpreted as a measurement of the mass profile of a galaxy, as:
470:
377:
583:
239:
There are many ways to measure and calculate differential rotation in stars to see if different latitudes have different angular velocities. The most obvious is tracking spots on the stellar surface.
282:
are common sources of radio flares. The researchers concluded that this effect was best explained by active regions emerging and disappearing at different latitudes, such as occurs during the solar
809:
590:
535:
1129:
http://www.astro.physik.uni-goettingen.de/~areiners/DiffRot/interactive.htm A simulation of the effects of differential rotation on stellar absorption-line profiles by Ansgar
Reiners
720:
velocity decreases with increased latitude. The poles make one rotation every 34.3 days and the equator every 25.05 days, as measured relative to distant stars (sidereal rotation).
404:
907:
851:
270:
at the equator and poles. See also plot 2. Solar differential rotation is also seen in magnetograms, images showing the strength and location of solar magnetic fields.
490:
927:
871:
1023:
Wolszczan, A.; Route, M. (10 June 2014). "Timing
Analysis of the Periodic Radio and Optical Brightness Variations of the Ultracool Dwarf, TVLM 513-46546".
709:
Internal rotation in the Sun, showing differential rotation in the outer convective region and almost uniform rotation in the central radiative region.
324:
222:
that they form from into rotating motion as they coalesce. Given this average rotation of the whole body, internal differential rotation is caused by
543:
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It may be possible to measure the differential of stars that regularly emit flares of radio emission. Using 7 years of observations of the M9
42:
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746:
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is the angle between the line of sight and the rotation axis, permitting the study of the rotational velocity's line-of-sight component v
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The inner differential rotation is one part of the mixing processes in stars, mixing the materials and the heat/energy of the stars.
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89:
61:
215:
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reported that the Sun had different rotational periods at the poles and at the equator, in good agreement with modern values.
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regions is where angular rotation gradients are strongest and thus where dynamo processes are expected to be most efficient.
68:
46:
122:
75:
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explanation of increased angular velocity at equatorial latitude due to overshoot of mass arriving from heated core
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The relative differential rotation rate is the ratio of the rotational shear to the rotation rate at the equator:
57:
35:
943:
587:
The
Doppler rotation rate in the Sun (measured from Doppler-shifted absorption lines), can be approximated as:
1128:
472:
is the difference in angular velocity between pole and equator, called the strength of the rotational shear.
680:{\displaystyle {\frac {\Omega }{2\pi }}=(451.5-65.3\cos ^{2}\theta -66.7\cos ^{4}\theta )\,\mathrm {nHz} }
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is the lap time, i.e. the time it takes for the equator to do a full lap more than the poles.
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On the feasibility of the detection of differential rotation in stellar absorption profiles
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231:. Differential rotation thus depends on temperature differences in adjacent regions.
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Differential rotation affects stellar optical absorption-line spectra through
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The broadened shapes of absorption lines in the optical spectrum depend on v
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For observed sunspots, the differential rotation can be calculated as:
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465:{\displaystyle \Delta \Omega =(\Omega _{0}-\Omega _{\mathrm {pole} })}
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is seen when different parts of a rotating object move with different
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Stellar
Photospheres; The Observations and Analysis of: Third Edition
184:
164:
1037:
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of the body and/or in time. This indicates that the object is not
372:{\displaystyle \Omega =\Omega _{0}-\Delta \Omega \sin ^{2}\Psi }
176:
18:
578:{\displaystyle \alpha ={\frac {\Delta \Omega }{\Omega _{0}}}}
804:{\displaystyle v_{c}(R)={\sqrt {\frac {GM(<R)}{R}}}}
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Stars and planets rotate in the first place because
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usually show differential rotation; examples in the
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266:of the line shapes, using equation (2) below for v
1078:Annu. Rev. Astron. Astrophys. 2003. 41:599–643
530:{\displaystyle {\frac {2\pi }{\Delta \Omega }}}
691:is the co-latitude (measured from the poles).
8:
1107:A. Reiners, J. H. M. M. Schmitt, (2002),
979:"Magnetic reversals of Jupiter and Saturn"
1097:, chapter 8, Cambridge University Press,
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914:
909:is the total mass enclosed within radius
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109:Learn how and when to remove this message
500:The reciprocal of the rotational shear
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1084:10.1146/annurev.astro.41.011802.094848
218:turns random drifting of parts of the
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47:adding citations to reliable sources
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1088:The Internal Rotation of the Sun
977:Hathaway, David H. (July 1986).
853:is the rotation speed at radius
216:conservation of angular momentum
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34:needs additional citations for
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1003:10.1016/0019-1035(86)90177-6
309:across the stellar surface.
123:Differential rotation matrix
16:Variations in rotation rates
399:{\displaystyle \Omega _{0}}
1175:
1117:10.1051/0004-6361:20011801
1111:, A&A 384 (1) 155–162
1055:10.1088/0004-637X/788/1/23
731:
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262:. This is calculated from
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1025:The Astrophysical Journal
902:{\displaystyle M(<R),}
846:{\displaystyle v_{c}(R),}
121:Not to be confused with
58:"Differential rotation"
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190:Around the year 1610,
1149:Astrophysics concepts
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494:heliographic latitude
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485:{\displaystyle \Psi }
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129:Differential rotation
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43:improve this article
1047:2014ApJ...788...23W
995:1986Icar...67...88H
200:rotation of the Sun
198:and calculated the
1154:Co-orbital objects
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264:Fourier transforms
244:helioseismological
204:Christoph Scheiner
133:angular velocities
1103:978-0-521-85186-2
922:{\displaystyle R}
866:{\displaystyle R}
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137:rates of rotation
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99:December 2009
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60: –
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54:Find sources:
48:
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32:This article
30:
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20:
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1087:
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1024:
1018:
1006:. Retrieved
989:(1): 88–95.
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175:include the
173:Solar System
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79:
72:
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53:
41:Please help
36:verification
33:
235:Measurement
202:. In 1630,
1143:Categories
965:References
732:See also:
713:See also:
247:latitude.
224:convection
169:protostars
69:newspapers
1063:119114679
1038:1404.4682
1031:(1): 23.
734:Milky Way
660:θ
657:
641:−
638:θ
635:
619:−
604:π
597:Ω
565:Ω
560:Ω
557:Δ
548:α
522:Ω
519:Δ
514:π
480:Ψ
440:Ω
436:−
427:Ω
417:Ω
414:Δ
388:Ω
367:Ψ
364:
351:Ω
348:Δ
345:−
336:Ω
329:Ω
242:By doing
194:observed
141:latitudes
1159:Rotation
1008:25 April
933:See also
696:Examples
196:sunspots
165:Galaxies
161:shearing
1043:Bibcode
991:Bibcode
959:Sunspot
492:is the
290:Effects
181:Jupiter
143:and/or
83:scholar
1101:
1061:
983:Icarus
811:where
687:where
379:where
185:Saturn
145:depths
85:
78:
71:
64:
56:
1059:S2CID
1033:arXiv
616:451.5
210:Cause
153:fluid
151:. In
149:rigid
90:JSTOR
76:books
1099:ISBN
1010:2024
888:<
786:<
736:and
644:66.7
622:65.3
183:and
167:and
135:(or
62:news
1113:doi
1080:doi
1051:doi
1029:788
999:doi
701:Sun
648:cos
626:cos
355:sin
268:rot
260:rot
252:rot
177:Sun
45:by
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1115::
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917:R
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891:R
885:(
882:M
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827:c
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789:R
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780:M
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764:R
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756:c
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674:z
671:H
668:n
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112:)
106:(
101:)
97:(
87:·
80:·
73:·
66:·
39:.
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