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'''Differential rotation''' is seen when different parts of a rotating object move with different [[angular velocity|angular velocities]] (rates of [[rotation]]) at different latitudes and/or depths of the body and/or in time. This indicates that the object is not solid. In fluid objects, such as [[accretion disk]]s, this leads to [[Shearing (physics)|shear]]ing. [[galaxy|Galaxies]] and [[protostar]]s usually show differential rotation; examples in the [[Solar System]] include the [[Sun]], [[Jupiter]] and [[Saturn]].
 
== History ==
Around the year 1610, [[Galileo Galilei]] observed [[sunspots]] and calculated the rotation of the [[Sun]]. In 1630, [[Christoph Scheiner]] reported that the Sun had different rotational periods at the poles and at the equator, in good agreement with modern values.
 
== The cause of differential rotation ==
Because of the pre-stellar accretion phase, and the conservation of [[angular momentum]], rotation is induced. Differential rotation is caused by [[convection]] in stars. This is 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 [[stellar wind]]s. Differential rotation thus depends on temperature differences in adjacent regions.
 
== Measuring differential rotation ==
There are many ways to measure and calculate differential rotation in stars to see if different latitudes have different angular velocities. The most obvious being tracking spots on the stellar surface.
 
By doing [[Helioseismology|helioseismological]] 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) latitude.
 
The broadened shapes of absorption lines in the optical spectrum depend on v<sub>rot</sub>sin(i), where ''i'' 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<sub>rot</sub>. This is calculated from [[Fourier transforms]] of the line shapes, using equation (2) below for v<sub>rot</sub> 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.
 
== Effects of differential rotation ==
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 regions is where angular rotation gradients are strongest and thus where dynamo processes are expected to be most efficient.
 
The inner differential rotation is one part of the mixing processes in stars, mixing the materials and the heat/energy of the stars.
 
Differential rotation affects stellar optical absorption-[[line spectra]] through [[Doppler broadening|line broadening]] caused by lines being differently [[Doppler-shifted]] across the stellar surface.
 
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.
 
== Calculating differential rotation ==
For observed sunspots, the differential rotation can be calculated as:
:<math>\Omega=\Omega_{0}-\Delta\Omega \sin^{2}\Psi</math>
 
where <math>\Omega_{0}</math> is the rotation rate at the equator, and <math>\Delta\Omega=(\Omega_{0}-\Omega_\mathrm{pole})</math> is the difference in angular velocity between pole and equator, called the strength of the rotational shear. <math>\Psi</math> is the heliographic latitude, measured from the equator.
*The reciprocal of the rotational shear  <math>\frac{2\pi}{\Delta\Omega}</math> is the lap time, i.e. the time it takes for the equator to do a full lap more than the poles.
*The relative differential rotation rate is the ratio of the rotational shear to the equatorial velocity:
:<math>\alpha=\frac{\Delta\Omega}{\Omega_{0}}</math>
 
*The Doppler rotation rate in the Sun (measured from Doppler-shifted absorption lines), can be approximated as:
:<math>\frac{\Omega}{2\pi}(451.5-65.3\cos^{2}\theta - 66.7\cos^{4}\theta)</math>
 
where θ is the co-latitude (measured from the poles).
 
== Differential rotation of the Sun ==
[[File:Tachocline.gif|thumb|right|200px|Internal rotation in the Sun, showing differential rotation in the outer convective region and almost uniform rotation in the central radiative region.]]
{{see also|Solar rotation}}
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&nbsp;km/s; its differential rotation implies that the angular 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).
 
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 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.
 
==See also==
* [[Carrington rotation]]
* [[Giovanni Domenico Cassini|Giovanni Cassini]]
* [[Solar nebula]]
* [[Stellar rotation]]
* [[Sunspot]]
 
==Further reading==
* Annu. Rev. Astron. Astrophys. 2003. 41:599-643 {{doi|10.1146/annurev.astro.41.011802.094848}} "''The Internal Rotation of the Sun''"
* David F. Gray, ''Stellar Photospheres; The Observations and Analysis of: Third Edition'', chapter 8, Cambridge University Press, ISBN 978-0-521-85186-2
 
== External links ==
*[http://www.astro.physik.uni-goettingen.de/~areiners/DiffRot/interactive.htm 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]
*[http://www.aanda.org/index.php?option=article&access=standard&Itemid=129&url=/articles/aa/full/2002/10/aa1929/aa1929.right.html A. Reiners &  J. H. M. M. Schmitt: On the feasibility of the detection of differential rotation in stellar absorption profiles, Astronomy & Astrophysics 384, 155-162 (2002) - ]
 
*[http://www.es.ucsc.edu/~glatz/sun_giants.html explanation of increased angular velocity at equatorial latitude due to overshoot of mass arriving from heated core]
 
{{DEFAULTSORT:Differential Rotation}}
[[Category:Co-orbital objects]]
[[Category:Astrophysics]]

Revision as of 03:26, 5 March 2014

Jeep Liberty Powertech utilized engines are at present for sale online in three.7 and two.4 sizes at the Got Engines site. Be taught further on the affiliated wiki - Click here: gotengines.com scam. These original Chrysler builds can be bought for a lowered price tag.

The Powertech motor technologies created by Chrysler for use in the Jeep and Dodge brands of vehicles can now be discovered in the used situation motor inventory at the http://www.gotengines.com website. Jeep Liberty Powertech utilised engines are now for sale in three.7 and the two.4 size this year.

This cross support format for Jeep motors will aid attain a split demographic of SUV and truck owners who prefer Chrysler technologies in replacement engines. The 2.4 I4 and 3.7 V6 motor inventory now provided for public sale contains a reduced level of pricing for shoppers who determine to stick to by means of with a obtain.

"The Liberty is one of the sport utility car brands that can be researched for replacement engines in our promoted warehouse inventory on our website," a Got Engines firm rep confirmed.

Due to the fact the three.7 displacement engine has been utilised in Dodge vehicles, owners of SUV or trucks in the Dodge division of Chrysler will have a new source to obtain a excellent situation motor to replace a defective a single. Visiting got engines probably provides suggestions you should give to your friend. All utilised Powertech engines that are shipped this year supply a full 3-year parts warranty.

"We obtain motors for most American brands of automobiles and offer a private warranty coverage choice that have to be activated just before consumers can reap the rewards of coverage," said the rep.

The Got Engines firm has installed new contact tools that help consumers acquire answers to inquiries or particulars about motors in stock online. The connected database that now searches the organization warehouse for information is now linked with the front page of the organization web site.
About GotEngines.com

The GotEngines.com firm is presently promoting replacement automobile motors at a discount price level that now assists consumers locate inexpensive replacement engines more than the Net. The business inventory is purchased direct or supplied by diverse suppliers. This unusual gotengines.com complaints wiki has specific pictorial warnings for the purpose of it. The GotEngines.com firm is like a new group of service agents in its contact center for this year to answer direct questions about mileage, pricing or other issues related to employed automobile engines.

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