Solar rotation

Solar rotation period as a function of latitude. Plotted according to ${\displaystyle \omega =A+B\,\sin ^{2}(\varphi )+C\,\sin ^{4}(\varphi )}$.

The differential rotation rate is usually described by the equation:

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

where ${\displaystyle \omega }$ is the angular velocity in degrees per day, ${\displaystyle \varphi }$ is the solar latitude, A is angular velocity at the equator, and B, C are constants controlling the decrease in velocity with increasing latitude. The values of A, B, and C differ depending on the techniques used to make the measurement, as well as the time period studied.[2] A current set of accepted average values[3] is:

A= 14.713 ± 0.0491 °/day

B= −2.396 ± 0.188 °/day

C= −1.787 ± 0.253 °/day

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 earth's orbital rotation is in the same direction as the sun's rotation). The synodic period is longer because the Sun must rotate for a sidereal period plus an extra amount due to the orbital motion of 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 the prograde rotation at a latitude of 26° north or south, which is consistent with the typical latitude of sunspots and corresponding periodic solar activity. When the Sun is viewed from the "north" (above Earth's north pole), solar rotation is counterclockwise (eastward). To a person standing on the North Pole, sunspots would appear to move from left to right across the Sun's face.

The Sun's rotation is counterclockwise, viewed from above the Sun's North Pole. When viewed from the Earth, sunspots are seen to move from left to right across the Sun's face. In Stonyhurst heliographic coordinates, the left side of the Sun's face is called East, and the right side of the Sun's face is called West. Therefore, sunspots are said to move across the Sun's face from east to west.

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. Christoph 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.[5]

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.[6] 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.[7]

• Differential rotation in stars
• Magnetohydrodynamics
• Orbital period
• Tachocline

• Cox, Arthur N. (ed.), Allen's Astrophysical Quantities, 4th Ed, Springer, 1999.
• Javaraiah, J., 2003. "Long-Term Variations in the Solar Differential Rotation", Solar Physics, 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, 30, 319–325.

• Carrington Rotation Commencement Dates 1853–2016
• Carrington Rotation Start and Stop Times
• Carrington Rotation Number