Solar rotation is the rotation of the Sun about its own axis. The Sun is not a solid body, but is composed of a gaseous plasma, and different latitudes rotate with different periods. The solar rotation period is 25.67 days at the equator and increases with increasing latitude, reaching 33.40 days at 75 degrees of latitude. The source of this differential rotation is an area of current research in solar astronomy.
Axis of rotation The Sun's axis of rotation is inclined slightly from the axis of Earth's orbit in the ecliptic plane, resulting in observers on Earth seeing more of the Sun's north pole in September and more of the Sun's south pole in March. The direction of the Sun's axis of rotation was first inferred from the proper motion of sunspots. The standard values used to define the axis of rotation were derived in this manner by Richard C. Carrington in 1863. He found that the inclination angle between the Sun's equator and the plane of the ecliptic was 7.25 degrees and the longitude between the cross point of the solar equator with the ecliptic and the March equinox was 73.67 degrees for the year 1850.
Surface rotation as an equation
The differential rotation rate of the photosphere can be approximated by the equation:
ω = A + B sin 2 ( φ ) + C sin 4 ( φ ) {\displaystyle \omega =A+B\,\sin ^{2}(\varphi )+C\,\sin ^{4}(\varphi )}
where ω {\displaystyle \omega } is the angular velocity in degrees per day, φ {\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. A current set of accepted average values is:
A = 14.713 ± 0.0491 ∘ / day {\displaystyle A=14.713\pm 0.0491\ ^{\circ }/{\text{day}}}
B = − 2.396 ± 0.188 ∘ / day {\displaystyle B=-2.396\pm 0.188\ ^{\circ }/{\text{day}}}
C = − 1.787 ± 0.253 ∘ / day {\displaystyle C=-1.787\pm 0.253\ ^{\circ }/{\text{day}}}
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 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 Earth's North Pole at the time of equinox, sunspots would appear 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.
Bartels' rotation number Bartels' rotation number is a serial count that numbers the apparent rotations of the Sun as viewed from Earth, and is used to track certain recurring or shifting patterns of solar activity. For this purpose, each rotation has a length of exactly 27 days, close to the synodic Carrington rotation rate. Julius Bartels arbitrarily assigned rotation day one to 8 February 1832. The serial number serves as a kind of calendar to mark the recurrence periods of solar and geophysical parameters.
Carrington rotation
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