Differential rotation
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Differential rotation is seen when different parts of a rotating object move with different
Around the year 1610,
Cause
Stars and planets rotate in the first place because
Measurement
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.
By doing 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 vrotsin(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 vrot. This is calculated from
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 ultracool dwarf 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, active regions 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 sunspot cycle.[2]
Effects
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
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.
Surface level
For observed sunspots, the differential rotation can be calculated as:
- The reciprocal of the rotational shear 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 rotation rate at the equator:
- The Doppler rotation rate in the Sun (measured from Doppler-shifted absorption lines), can be approximated as: where θ is the co-latitude (measured from the poles).
Examples
Sun
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 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.
Disk galaxies
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:
- is the rotation speed at radius
- is the total mass enclosed within radius
See also
- Solar rotation
- Giovanni Cassini
- Solar nebula
- Stellar rotation
- Sunspot
References
- . Retrieved 25 April 2024.
- S2CID 119114679.
Further reading
- Annu. Rev. Astron. Astrophys. 2003. 41:599–643 "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
- A. Reiners, J. H. M. M. Schmitt, (2002), On the feasibility of the detection of differential rotation in stellar absorption profiles, A&A 384 (1) 155–162