# Solar rotation

The solar rotation can be seen in the background

Solar rotation is able to vary with latitude because the Sun is composed of a gaseous plasma. The rate of rotation is observed to be fastest at the equator (latitude φ=0 deg), and to decrease as latitude increases. The differential rotation rate is usually described by the equation:

$\omega=A+B\,\sin^2(\varphi)+C\,\sin^4(\varphi)$

where ω is the angular velocity in degrees per day, φ is the solar latitude and A, B, and C are constants. The values of A, B, and C differ depending on the techniques used to make the measurement, as well as the time period studied.[1] A current set of accepted average values[2] is:

A= 14.713 deg/day (± 0.0491)
B= -2.396 deg/day (± 0.188)
C= -1.787 deg/day (± 0.253)

## Sidereal rotation

At the equator the solar rotation period is 24.47 days. This is called the sidereal rotation period, and should not be confused with the synodic rotation period of 26.24 days, which is the time for a fixed feature on the Sun to rotate to the same apparent position as viewed from Earth. The synodic period is longer because the Sun must rotate for a sidereal period plus an extra amount due to the orbital motion of the Earth around the Sun. Note that astrophysical literature does not typically use the equatorial rotation period, but instead often uses the definition of a Carrington rotation: a synodic rotation period of 27.2753 days (or a sidereal period of 25.38 days). This chosen period roughly corresponds to rotation at a latitude of 26 deg, which is consistent with the typical latitude of sunspots and corresponding periodic solar activity. When the Sun is viewed from the "north" (above the Earth's northern pole) solar rotation is counterclockwise. Sunspots viewed from Earth (its Northern hemisphere) appear to move from left to right across the face of the Sun.

## Using sunspots to measure rotation

The rotation constants have been measured by measuring the motion of various features ("tracers") on the solar surface. The first and most widely used tracers are sunspots. Though sunspots had been observed since ancient times, it was only when the telescope came into use that they were observed to turn with the Sun, and thus the period of the solar rotation could be defined. The English scholar Thomas Harriot was probably the first to observe sunspots telescopically as evidenced by a drawing in his notebook dated December 8, 1610, and the first published observations (June 1611) entitled “De Maculis in Sole Observatis, et Apparente earum cum Sole Conversione Narratio” ("Narration on Spots Observed on the Sun and their Apparent Rotation with the Sun") were by Johannes Fabricius who had been systematically observing the spots for a few months and had noted also their movement across the solar disc. This can be considered the first observational evidence of the solar rotation. Christopher Scheiner (“Rosa Ursine sive solis”, book 4, part 2, 1630) was the first to measure the equatorial rotation rate of the Sun and noticed that the rotation at higher latitudes is slower, so he can be considered the discoverer of solar differential rotation.

Each measurement gives a slightly different answer, yielding the above standard deviations (shown as +/-). St. John (1918) was perhaps the first to summarise the published solar rotation rates, and concluded that the differences in series measured in different years can hardly be attributed to personal observation or to local disturbances on the Sun, and are probably due to time variations in the rate of rotation, and Hubrecht (1915) was the first one to find that the two solar hemispheres rotate differently. A study of magnetograph data showed a synodic period in agreement with other studies of 26.24 days at the equator and almost 38 days at the poles. [3]

## Internal Solar Rotation

Internal rotation in the Sun, showing differential rotation in the outer convective region and almost uniform rotation in the central radiative region. The transition between these regions is called the tachocline.

Until the advent of helioseismology, the study of wave oscillations in the Sun, very little was known about the internal rotation of the Sun. The differential profile of the surface was thought to extend into the solar interior as rotating cylinders of constant angular momentum.[4] Through helioseismology this is now known not to be the case and the rotation profile of the Sun has been found. On the surface the Sun rotates slowly at the poles and quickly at the equator. This profile extends on roughly radial lines through the solar convection zone to the interior. At the tachocline the rotation abruptly changes to solid body rotation in the solar radiation zone.[5]

## References

1. ^ Beck, J. (2000). "A comparison of differential rotation measurements". Solar Physics 191: 47–70. Bibcode:2000SoPh..191...47B. doi:10.1023/A:1005226402796.
2. ^ Snodgrass, H.; Ulrich, R. (1990). "Rotation of Doppler features in the solar photosphere". Astrophysical Journal 351: 309–316. Bibcode:1990ApJ...351..309S. doi:10.1086/168467.
3. ^ 5. Astronomy and Astrophysics (ISSN 0004-6361), vol. 233, no. 1, July 1990, p. 220-228. http://adsabs.harvard.edu/full/1990A%26A...233..220S
4. ^ Glatzmaier, G. A (1985). "Numerical simulations of stellar convective dynamos III. At the base of the convection zone". Solar Physics 125: 1–12.
5. ^ Christensen-Dalsgaard J. and Thompson, M.J. (2007). The Solar Tachocline:Observational results and issues concerning the tachocline. Cambridge University Press. pp. 53–86.

, Ed. "Allen's Astrophysical Quantities", 4th Ed, Springer, 1999.

• Javaraiah, J., 2003. Long-Term Variations in the Solar Differential Rotation. Solar Phys., 212 (1): 23-49.
• St. John, C., 1918. The present condition of the problem of solar rotation, Publications of the Astronomical Society of the Pacific, V.30, No. 178, 318-325.