Sunspots and the rotation of the Sun

Josée SERT
"EAAE Summerschools" Working Group
CLEA - France
The activities presented here should always be done from pupils'observations and plottings : because it is important to show them that, from observations performed with a very simple equipment, we can infer important characteristics of the Sun. However, as mapping the positions of sunspots requires observing over several days, it is not always easy to get them at school. So, you can use either results got by another person, either slides (CLEA's for example). But in that case, an essential requirement is that students should first observe themselves the image of the Sun and even map sunspots once.

I. OBSERVATION

      

CAREFUL !
The observation of the Sun can turn out to be very dangerous, nobody must observe the Sun directly through an optical instrument (binoculars, telescope,...) without any protection. As the retina is not sensitive to pain, we can suffer irreversible injuries without noticing it at the very moment. On another hand, a long exposure of the instrument to the Sun may damage it seriously, even if filters are used. One of the only safe methods is to observe the Sun by projecting its image on a sheet of paper. See Figure 1.

With adhesive tape, fix a piece of light millimetered paper on the screen P after having drawn a 7 cm-radius circle on it (prepare several of them). Adjust the distance of the projection device so that the image of the Sun is the same size (or choose another radius for the circles). The difficulty is that the Earth is turning, and that the image of the Sun moves very fast. It is better to be two persons to do it : one who handles the instrument with flexibles, the other who plots the sunspots with a pencil.

  1. The first one moves the instrument in sort that the image of the Sun comes exactly upon the drawn circle, the other one looks at the spots on the millimetered paper. The first one tells the other the exact instant when the image coincides with the circle so that at that very moment he or she can plot the exact position of one spot with the help of the square. Do the same with every spot, and then draw the shape and size as well as possible. See Figure 2.

  2. They have then to draw a direction of reference : that of the movement of the Sun, from East to West. To do that, choose one spot, plot its exact position "a" on the paper, then, without touching anything, let the image move. You have to plot a second position, for example "A", when that very spot crosses the circle. Then, draw a line between the two positions, with an arrow from the first position to the second one (it is better when the positions are far one from the other). See again Figure 2.

  3. Carefully note the date and time.

  4. Make such mapping over several days (not necesseraly consecutive), in sort to recognize the spots from one day to the other. See Document 1.

II. WORKING ON THE PLOTTING

A) ROTATION PERIOD OF THE SUN

On tracing paper, draw a circle of the same diameter than the plotting papers, draw also a direction (with an arrow) that will be the reference.
You have to recognize the same spot on the plotting papers, then, you put the tracing paper over them, with the circles superimposed and the reference lines exactly parallel with the arrows in the same direction, you draw the positions of the spot and you number it.
You can notice that it moved almost on a straight segment of line (in fact, a parallel to the Sun equator). See Figure 3.

You have to compute of what angle it moved : so, you draw the parallel, of which you can see a diameter [AB]. You can show the movement by drawing half a circle corresponding to the visible part of that parallel (its diameter [A'B']), then by drawing with perpendicular lines the positions of the spot from 1' to 4'. You can then measure the angle between the furthest positions.
That angle a corresponds to the duration d = t4 - t1 between the furthest plottings. You can then infer the synodic rotation period t (as seen from the Earth) :

t = ( d / a ) x 360.

To find the actual rotation period of the Sun T, you have to follow the argument written in the "Additional informations".
You have then :

(1 / t = (1 / T) - (1 / 365,25) , and you can find T knowing t .

B) ARE THEY REALLY SPOTS ON THE SURFACE ?

When Galileo discovered the spots, people were puzzled. As many were reluctant to accept the day star to be spotted, they fancied that they were tiny planets on very close orbits.

Activity : (solution on Figure 4)

  1. A planet orbits at a little distance around the Sun. Draw seven positions when it turns by 30° : first you draw it as seen from "above" the orbit, then as seen by an observer located on the orbital plane : what would he or she see in front of the orbital disk ?

  2. An object is steady on the solar Equator : draw seven positions when the Sun turns around by 30° : first as seen from "above" one pole of the Sun, then as seen by an observer located in the Equator plane (we can consider that, as he or she was very far, he or she can see all of them).

  3. Observing on the plotting papers one spot (if possible near the edge in its first, or final, position), show that the most likely hypothesis is that the Sun rotates and has spots on its surface.

III. CLEA SLIDES

A) THE SETS

Two sets are proposed :

the A set (from A1 to A12) : March 1982 ;
the B set (from B1 to B7) : July 1982 ; A0 shows the equipment that was used.

The first slide in each set (i.e. slides 2 and 14) is a positive copy. The spots appear dark against a bright background. This is what students would see if they would observe an image of the Sun projected onto a screen. The following slides are negatives : they are direct copies of the negatives obtained with the equipment. For that reason, the details are crisper and more accurate.

B) HOW TO USE THE SLIDES

Either one of the set is projected onto a screen. Everyone will easily notice that the positions of the Sun change from day to day. Now, let us study their apparent motion. To that purpose, a circle representing the Sun (diameter : 10 cm) should first be drawn on a large sheet of white paper (A4 or A/B size) that will act as a screen. The distance between the projector and the screen should be adjusted so that the image exactly fits into the circle (about 90cm for a slide projector fitted with an 85-mm lens). The positions of the spots observed during those days are then recorded. See Figure 5.

a) Direction of rotation and position of the axis

If the slide has been correctly inserted in the projector, North is up and East is left. The successive positions of the spots show that the Sun's rotation is prograde (i.e. the visible part of the sphere rotates from East to West). The position of the rotational axis is determined by recording the motion of a spot over an interval of several days. In principle, its apparent part is an arc of ellipse except around two dates in the year, as the Equator of the Sun is tilted about 7° to the plane of the ecliptic : see Figure 6.

In fact, that arc of ellipse is very close to a chord. It is therefore possible to draw a line perpendicular to that chord going through the center. The angle between the axis so determined and the North-South axis is then measured with a protractor. Varying with the dates when the slides were exposed, the result is - 25° (March) and + 4° (July). See Figure 7. The angle is reckoned positively eastward from the North point of the Sun's disk.

b) We can of course determine the synodic period, then the sideral rotation period of the Sun as we did on the plotting papers.

c) More easily than on the plotting papers, we can see the differential rotation of the Sun : choose a spot located about the Equator, find its rotation period out, do the same thing with a spot the furthest from the Equator as possible, then compare.

IV. ADDITIONAL INFORMATIONS

A) SYNODIC AND SIDERAL PERIODS

The Sun is a sphere of gas in rotation around an axis, that rotation being faster in the equatorial areas than about the poles. It can be observed from the Earth only as the surface of the Sun shows details, the easiest to observe being the spots, that can be a marker ; we can measure the synodic period of rotation only, as the Earth is moving in relation to the Sun (see Figure 8).

After a sideral period T, the marker (a spot for example) comes back in the direction of the same star, but not in the direction of the Earth, as the Earth moved off. A little after, after a synodic period , the marker comes back in the direction of the Earth. After (in days), the Earth turned of an angle on its orbit, and the marker turned of (360° + ) on the surface of the Sun. So we have :

b = (360 x t ) / 365,25 on one hand and 360° + b = (360 x t ) / T on the other hand.
Hence (1 / t ) + (1 / 365,25) = 1 / T .

As we observe t , we compute T : so, as T varies from 25 to 29 days, we measure a period t from 26,8 days to 31,5 days from our observations.

B)THE SUNSPOTS

The sunspots are cooler places on the photosphere, that is the superficial layer of the Sun, where the light that goes out from the Sun forms : they appear, evolve and disappear. The number of spots depends on an 11-years activity cycle of the Sun.