SOLAR ROTATION
SOLAR ROTATION

Dragan Roša and Darije Maričić
Zagreb Astronomical Observatory

Fig.1 The Photosphere of the Sun with sunspots. Sunspots can be enough large to be seen with the naked eye (often during the sunset or through partly transparent clouds). One of the oldest astronomical recordings is related to sunspots in ancient China . Telescopic observations of apparent motion of sunspots across the solar disc show that sun rotate.

The solar rotation was detected by observing the motion of dark spots (sunspots) across the solar disc. The discovery is related to Galileo Galilei, the first person who used the telescope to observe the sky at the beginning of the 17thcentury. Monitoring the changing positions of sunspots from day to day, Galileo concluded that our star rotates.† The Sun rotates in the same direction as the Earth. But the Sun's rotation is not so similar to the rotation of the Earth. The Sun does not rotate rigidly (solid-body rotation), like a billiard ball, or the solid planets and their moons. The Sun is a sphere of hot gas (plasma) and the rotation rate varies with the latitude on the Sun.

Christopher Scheiner was the first who noticed (around 1630) that the rotation rate at higher Sun's latitudes is slower. The equatorial regions rotate faster (with a period of about 25 days) than the polar regions which complete rotation in 30 days. This so-called "differential rotation" is a property of gaseous bodies like stars (Jupiter shows also differential rotation), but the physical mechanism of it is still a topic of research.


Fig.2 Scheiner's drawings of apparent movements of the sunspots across the solar disk, for two sets of observations taken six months apart. Scheiner concluded that the Sun's rotation axis is tilted by 7į with respect to the perpendicular on the ecliptic.

The rate of the solar differential rotation was first accurately measured in the 19thcentury by Richard Carrington. He used the position of prominent sunspots as "tracers", and found that the synodic rotation period of the equatorial parts of the Sun is about 27 days. The synodic rotation period is the time for a fixed feature on the Sun to rotate to the same apparent position as viewed from Earth. The sidereal period of rotation is determined with respect the fixed stars. The Earth's orbital motion around the Sun causes that the synodic period is longer than the sidereal one. For complete synodic period, the Sun must rotate for the sidereal period plus an extra amount due to the orbital Earth's motion which is in the same direction as the direction of the solar rotation.

The heliographic co-ordinate system is determined from the observations of solar rotation. In that way we can define the rotation axis and the solar equator. The system is rather arbitrary and corresponds to the average rotation of equatorial regions. The sidereal period of rotation of the solar equator is chosen to be 25,38 days (Carrington period). For historical reasons, rotations are identified by Carrington numbers. They are numbered starting with 9 November 1853 . The rotation axis is tilted by about 7,25 degrees from the axis of the Earth's orbit around the Sun. In March we see more of the Sun's south polar parts and more of its north polar parts is visible during September.

Fig.3† Illustration of the solar differential rotation with the position of fictitious sunspots. Second position (right picture) is approximately after five days after first (left picture). Regions near the Sunís equator rotate faster.

Aside from sunspots and sunspots groups, the solar differential rotation is frequently studied using various others tracers at or above the solar surface (such as filaments, microwave low temperature regions or coronal bright points). The differential rotation rate can be obtained by Doppler measurements of the surface plasma flows.

The rate of rotation and gas flow in the solar interior can be established by helioseismologic methods. Detailed Doppler shift measurements of the solar surface (photosphere) show that the Sun oscillates at a variety of frequencies. The rising and falling surface gas produces a regular pattern. There are millions of oscillations due the large number of different waves travelling through the solar interior and surface. Careful analysis of solar oscillations helped scientists to understand the physical conditions below the visible solar surface. Because the rotation influences the effective speed of the sound waves within the Sun it was possible to determine the rotation rate at different depths of the Sun. It was found that the Sun's interior has about the same rotation period as the surface. At a distance about 0.7 solar radius out from the centre of the Sun there is a change from differential rotation to solid-body rotation. Different latitudes of the deep Sun's layers are rotating at the almost same rate.

Fig. 4 The rotation rate of the solar interior for three latitudes (00, 300, 600) determined from helioseismology. On the horizontal axis is the distance from the Sun's centre as a fraction of the solar radius. The rotation rate is expressed in unitsí nHz ( Nan hertz), as a frequency (f) of rotation. The period of rotation can be easily calculated from the relationT= 1/f). Notice that a solar core (until the distance of 0.7 radius) rotates as a solid body.

Studies of solar rotation are very important in constructing a dynamo model, which generate solar magnetic fields and the 11-year cycle of solar activity. If the Sun would rotate rigidly, the magnetic field would remain weak and similar to Earth's dipole magnetic field. Astronomers believe that the differential rotation of the Sun stretches and twists magnetic fields lines beneath the photosphere. This is possible because the Sun's magnetic field is "frozen" into the hot gas (plasma). If the gas moves, so does the field.

Fig. 5 Due to the solar differential rotation the dipole solar magnetic field of quiet Sun at the beginning of a solar cycle becomes twisted. Subsurface magnetic field lines change configuration from a dipole into toroidal one. Coils develop a kink that protrudes through the photosphere and forms active region with sunspots and other phenomena.

The picture of the solar activity is generally accepted, but it is still a mystery in many details. We may say that the investigations in this field are just beginning. Many different instruments on Earth and spacecraft's are monitoring solar phenomena witch occur in our neighbourhood. Solar activity influences the Earth and Earth's space environment. There are also indications that solar variations are correlated with Earth's climate or weather patterns. On the other hand similar activity cycles are also found for some other stars in the Universe. We have opportunity to use stellar and solar data to complement each other.




17.10.2005
Dragan Roša and Darije Maričić
Zagreb Astronomical Observatory

ADDRESS

Opaticka 22, Zagreb, Croatia
Astronomical Observatory
CROATIA, Zagreb

E-mail:drosa@hpd.botanic.hr
††††††††††† darije.maricic@zg.htnet.hr

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