But the umbra is relatively stable and may present a global rotating structure. So, we analyze the different parts umbra and penumbra of sunspots to determine which one is better for obtaining the real rotation.
In the following, we present two examples to show how to analyze the sunspot rotation. The AR consists of four main sunspots: "P1" and "P2" with positive magnetic polarity, and "Fa" and "Fb" with negative magnetic polarity, shown in Figure 1. At the begining of February 14, the four sunspots are forming. On February 15 and 16, these four sunspots can be distinguished clearly. Figure 1. We analyze the four sunspots individually.
The radii are fixed in inner umbra, outer umbra, and penumbra to produce time slices. Figure 2 shows the fixed radii of time slices. Figure 2. The white circles in the sunspots are the radii to produce time-slice figures.
Diagonal lines in the time-slice images show a clear pattern of rotation. Some points show clockwise motion and others counterclockwise motion. The trends are even more complicated, and it is hard to determine the real rotational directions of the sunspots. Figure 3. Time slices at different radii of P1 in AR The green lines show that this sunspot rotates counterclockwise. The sunspot alway rotates counterclockwise on the time period.
There are clockwise and counterclockwise rotational tendencies at the same time. The situation is the same as in panel b. Figure 4.
Time slices at different radii of P2 in AR The green lines show counterclockwise uniform rotation of the sunspot. The colored lines mark the rotational tendency of the sunspot. There are clockwise and counterclockwise rotations at the same time. So panel a reflects the real rotation of the sunspot. Figure 5. Time slices at different radii of Fa in AR The sunspot rotates clockwise. The rotational clockwise and counterclockwise directions both exist the entire time.
The time-slice umbra may be more suitable for obtaining the rotation of the sunspot. Figure 6. Time slices at different radii of Fb in AR At the begining, there are some black features that show clockwise rotation.
On February 14, there are some explosions. There are some clockwise black streaks and counterclockwise white streaks rotational features. It is hard to determine the real rotation of the sunspot. There are some clockwise and counterclockwise rotation features, but not obvious.
So panel a may reflect the real rotation of the sunspot. The green lines of Figure 3 a show sunspot P1, which rotates counterclockwise. They all show a uniform rotational tendency at different areas and on different time periods from 14 UT to 16 UT. However, there are streaks showing different rotational tendency in Figure 3 b. The red lines represent the clockwise rotation. The green lines mark the counterclockwise rotational features, and the yellow lines mark the nonrotational features.
Different rotational tendencies lines with different color exist at the same time, as shown in the figure. This indicates that the motion of the outer umbra is complicated. It is not easy to determine the rotational direction from this part. In the region of the penumbra, the situation is the same as the outer umbra, which is shown in Figure 3 c.
There are lines with different colors in the same time period. This means that there are features with different rotational patterns at the same time. So we cannot obtain the uniform rotational tendency of the sunspot from the region.
In Figure 4 a , the green lines show counterclockwise uniform rotation of sunspot P2. The red and green lines in b and c show that there are clockwise and counterclockwise rotations in the same time period.
The rotational tendency in b and c is complicated and cannot be determined. The rotational features in the inner umbra may reflect the real rotation of the sunspot. Sunspot Fa mainly rotates clockwise in the umbra, which is shown in Figure 5 a with red lines. The black streaks in the figure mainly have the tendency to move down i. The red lines, green lines, and yellow lines in b and c show that there are clockwise and counterclockwise rotations and nonrotating parts at the same time. It means that the motion in the large radius penumbra is complicated.
The rotational tendency in the penumbra may not be the same as the rotational tendency in the umbra. The analysis in the umbra may be suitable for obtaining rotation of the sunspot. In Figure 6 a , the red lines show that sunspot Fb rotates clockwise. At the begining before February 14 , there are some features black streaks that show clockwise rotation. Starting from February 14, many C class flares occurred. The motion in this area is much larger.
In the time-slice figure, there are some black streaks showing clockwise rotation, and there are also some white streaks showing counterclockwise rotation.
After February 14, there are also some black streaks showing clockwise rotational tendency. However, there are clockwise and counterclockwise rotations at the same time in Figures 6 b and c. It is hard to determine the rotational tendency of the sunspot.
In Figure 6 c , there are some clockwise and counterclockwise rotation features, but not obvious. According to the above discussion, we find that the umbra rotates clockwise. The motion in the penumbra mainly comes from the consequence of the flares. It may be different from the rotation of the umbra. From these time-slice figures, we can see that the rotational tendency is uniform at small radius inner umbra with black streaks.
However, at large radius penumbra , the rotational tendency is complicated. Some points show clockwise rotation, but other points show counterclockwise rotation at the same time. For the complicated sunspots, we suggest that the small radius in the umbra shows the true rotation. The large-radius cases may contain the flow motion of the penumbra. It may not be the true rotation of the sunspots. Its structure changes very little during this period. The rotational tendency is shown in Figure 8.
The red line shows that the sunspot rotates clockwise. So the rotational tendencies on the small and large radii are always the same and show that this sunspot rotates clockwise. Figure 7. Figure 8. Time slices at different radii of AR The regimes all show the clockwise rotation of the sunspot. The rotational tendency can be obtained from the umbra or penumbra. According to the above discussion, we choose the radius r c to be near or inside the umbra for the complicated sunspots.
With the aligned data, we use the method described in Section 3 to analyze the rotation of sunspots. Figure 9. The uncurling starts at the westward direction and proceeds counterclockwise about the spot. After choosing the point of maximum intensity of the magnetograms as the center of the circle with a radius of 35 pixels 17 5 , shown in Figure 9 b , we uncurl the whole sunspot from the Cartesian frame to the polar frame.
From Figure 10 , some features varying with time can be seen, indicating that the sunspot was rotating. To display the rotational properties better, we select the circles with radii ranging from 3 pixels 1 5 to 32 pixels 16 0 Figure 9 b to obtain time slices.
Figure There are some bright and dark streaks in the figure. Before the invention of the telescope, the Sun was thought to be an unchanging and perfect sphere. We now know that the Sun is in a perpetual state of change: its surface is a seething, bubbling cauldron of hot gas.
Areas that are darker and cooler than the rest of the surface come and go. Vast plumes of gas erupt into the chromosphere and corona. Occasionally, there are even giant explosions on the Sun that send enormous streamers of charged particles and energy hurtling toward Earth.
When they arrive, these can cause power outages and other serious effects on our planet. Figure 1. Sunspots: This image of sunspots, cooler and thus darker regions on the Sun, was taken in July You can see the dark, central region of each sunspot called the umbra surrounded by a less dark region the penumbra.
The largest spot shown here is about 11 Earths wide. Although sunspots appear dark when seen next to the hotter gases of the photosphere, an average sunspot, cut out of the solar surface and left standing in the night sky, would be about as bright as the full moon. The first evidence that the Sun changes came from studies of sunspots , which are large, dark features seen on the surface of the Sun caused by increased magnetic activity. They look darker because the spots are typically at a temperature of about K, whereas the bright regions that surround them are at about K Figure 1.
We emphasize what your parents have surely told you: looking at the Sun for even a brief time can cause permanent eye damage. While we understand that sunspots look darker because they are cooler, they are nevertheless hotter than the surfaces of many stars. If they could be removed from the Sun, they would shine brightly. They appear dark only in contrast with the hotter, brighter photosphere around them.
Individual sunspots come and go, with lifetimes that range from a few hours to a few months. If a spot lasts and develops, it usually consists of two parts: an inner darker core, the umbra , and a surrounding less dark region, the penumbra. Many spots become much larger than Earth, and a few, like the largest one shown in Figure 1 have reached diameters over , kilometers. Frequently, spots occur in groups of 2 to 20 or more.
The largest groups are very complex and may have over spots. Figure 2. On March 30, , this group of sunspots extended across an area about 13 times the diameter of Earth. This region produced many flares and coronal mass ejections. By recording the apparent motions of the sunspots as the turning Sun carried them across its disk Figure 2. Galileo , in , demonstrated that the Sun rotates on its axis with a rotation period of approximately 1 month.
Our star turns in a west-to-east direction, like the orbital motions of the planets. The Sun, however, is a gas and does not have to rotate rigidly, the way a solid body like Earth does.
We call this behavior differential rotation. Between and , Heinrich Schwabe , a German pharmacist and amateur astronomer, kept daily records of the number of sunspots. What he was really looking for was a planet inside the orbit of Mercury, which he hoped to find by observing its dark silhouette as it passed between the Sun and Earth.
He failed to find the hoped-for planet, but his diligence paid off with an even-more important discovery: the sunspot cycle. The change of the horizontal Lorentz force exerted at and below the photosphere can be formulated as:. At UT in phase 2, the clockwise torque exerted on f 1 relative to the centre marked as the cross in Fig.
We caution that our calculation has a large uncertainty due to the assumption of h and ignorance of the differential rotation nature of f 1. The DAVE4VM technique based on the magnetic induction equation is employed to track both the horizontal and vertical components of the photospheric plasma flows. The vertical component of Poynting flux across the plane S at the photospheric level can be derived as 46 :.
Contributions from flux emergence and surface shearing motions are represented by the first and second terms, respectively. According to ref. Similarly, the magnetic helicity flux across S can be expressed by the combination of an emerging and a shearing terms 47 :.
As the helicity flux density is not a gauge invariant quantity, we study the helicity flux integrated over the whole AR. These were determined by ref. All the data used in the present study are publicly available. How to cite this article: Liu, C.
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