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Sunspot Lab

A Web-Based Lab using current data
from the SOHO spacecraft

Summary: The proximity of the Sun, the nearest star, allows for detailed observations that are impossible to make for the other, far more distant stars. Early observations of the Sun by Galileo (starting in 1610) revealed the presence of dark spots on the surface of the Sun, known as sunspots. Sunspots appear dark by contrast with the surrounding surface of the Sun because they are cooler. The surface, or photosphere, of the Sun has a temperature of about 5800K while sunspots are typically 1800K cooler and therefore less luminous. Note that this puts the sunspot temperature at about 4000K, enough to make any metal white hot! This localized drop in surface temperature is due to enhanced magnetic fields in sunspots, up to about 10000 times greater than the field at the surface of the Earth. Sunspots come and go, isolated or in groups, and can be large or very small. The number of sunspots visible follows a cycle of solar activity of approximately 11 years. The last maximum occurred in 2000. Sunspots also reveal that the Sun is rotating!

In this lab, you will download pictures of the Sun taken by the Solar and Heliospheric Observatory (SOHO), a NASA/ESA satellite in orbit near the Earth and analyze the images to learn about how sunspots appear and evolve and to determine the period of rotation of the Sun.

Needed Supplies: log book, protractor and compass.

1. Download images: You will find the images on the SOHO web site. Go to the column entitled "List of individual images". Each number below that heading corresponds to an image of the Sun. For example, "20010918_2048" is an image taken on 9/18/2001 at 20:48 ("military time"). Click on the number and the image will appear on the screen. Look at a few images spanning about two weeks (old or recent) and identify a sunspot that you can track across most of the disk of the Sun. As you can see, the rotation of the Sun is quite evident. Print 7-8 images, fairly evenly spaced in time that show the march of your chosen sunspot across the disk, preferably including images where the sunspot appears very near the edge of the disk. Label that sunspot on each image. In each image, North is up and East (in the sky) is to the left. Note that according to the geographic convention, East is to the right for someone standing on the surface of the Sun.

2. The appearance and evolution of sunspots: Based on the images that you have printed, comment on the appearance of the sunspots visible (different kinds?) and how the change (if at all) over time, how long they last, etc. Given that the diameter of the Sun is 1.4 million km (870 000 miles), compute the diameter (in km) of several sunspots (label them!) and comment on the size of these features on the Sun. For example, compare their sizes to that of a familiar large objects, like the Earth.

3. The apparent path of a sunspot: Trace the position of your chosen sunspot on each image onto the earliest image showing the sunspot to show its apparent motion across the disk of the Sun. Label each position with the date. Be careful to properly register each image and to maintain the correct orientation.

4. Direction of rotation: In which direction does the Sun rotate (be careful about the definition of East and West!)? How does that compare with the Earth's direction of rotation? With the direction of the Earth's revolution around the Sun? Note: As seen from above the North pole, the Earth goes counterclockwise around the Sun.

   
   

   Figure 1

5. The tilt of the Sun's axis: It is very likely that the path of the sunspot is not a straight line across the disk but shows some curvature. This can be understood from the fact that the Sun's axis of rotation is not perpendicular to our line of sight. In other words, its axis of rotation is not perpendicular to the plane of Earth's orbit, the ecliptic. Figure 1 illustrates the varying viewing geometry during a 6 month period. The line across the disk is the Sun's equator and the poles are shown by small dots. The tilt of the Sun's axis (a few degrees) results in an apparent wobbling motion as we go around it, with the north pole tilted toward us for 6 months and the south pole tilted toward us for the rest of the year. Only at two points along our orbit do we see the equator straight on (middle image in Fig. 1) and the sunspots will then appear to move across the disk along straight lines. You can recreate the same effect by walking around a globe of the Earth. Note that the SOHO images that you downloaded are rotated so that the Sun's North is always at the top (the left-right tilting that you see in Figure 1 has been taken out).

   Now that we understand why the sunspot's path is curved, it should be obvious that the larger the angle of tilt, the greater the curvature of the path of the sunspot. Therefore, we can use a measure of the amount of curvature of the path to determine the amount of tilt of the Sun's axis along the line of sight at the time of your "observations." Figure 2 shows more detailed view of the situation. The path of the sunspot is a projected circle, i.e. an ellipse. The amount of curvature is simply given by the ratio b/a. When the spot moves in a straight line, b/a=0. Figure 3 show the Sun seen sideways to illustrate the geometry (when the N pole is tilted toward the Earth). Study the figure until you understand it. The angle of tilt toward (or away from) the Earth is i. This angle is given by

   sin i=b/a

   Use the path that you traced in part #3 above to measure both a and b and calculate the angle of tilt along the line of sight i. Which pole (N or S) is tilted toward us? A sunspot that would cross the center of the disk would have a positive or negative solar latitude? Keep in mind that the angle that you calculate is only the projected angle along the line of sight, and it varies with the time of year. The true angle of tilt of the Sun is fixed and can be observed directly only twice a year (first and last panels of Figure 1). Would you expect the Sun's actual angle of tilt to be larger or smaller than the one you have determined?

   
   

   Figure 2

   
   
   
   

   Figure 3

6. The Sun's period of rotation: It is quite obvious that the images you printed allow you to determine the period of rotation of the Sun. There are some subtleties however and we need to do a bit more geometry. The Sun is a sphere and the sunspot's motion from image to image is affected by the projection of the spherical surface of the Sun onto the plane of the sky (or equivalently, the flat surface of the sheet of paper). As a result, the sunspots appear to move more slowly toward the edges of the Sun than they do when near the center. We need to account for that. Figure 4 shows the Sun seen from the Earth (i.e. the images you printed) and the Sun seen from above its North pole (SNP; only the half visible from the Earth is shown). The latter shows that the sunspot actually moves on a circle and that this circle is usually smaller than the diameter of the Sun, unless the sunspot happens to be exactly on the Sun's equator. For now, assume that it traveled in a straight line joining the points on the limb of the Sun where it appeared/disappeared.

   Starting from the diagram you made in #3 above (which corresponds to the top panel in the figure) and using a compass and a ruler, produce the lower part of the figure. Do this as accurately as possible, especially for the images where the sunspot is very near the edge of the disk. Because of foreshortening, a small error in position near the edge of the disk result s in a large error on the angle of rotation. Note that the semi-circle has a diameter equal to the length of the long axis of the ellipse traced by the sunspot (2a in Fig. 2), NOT the diameter of the Sun's disk. Project the observed positions (top panel) onto the semi-circle (dotted lines). The angle A is the amount of rotation that your sunspot incurred between the first and last image. Measure A on your diagram, using a protractor. The rotation period of the Sun can be obtained simply from

   P (days) = (360^o/A)xT(days)

   where T is the time in days between the first and last image.

7. A closer look at the Sun's period of rotation: The period you just obtained in part #6 is what we observe from the Earth (called the synodic period). However, the Earth is not fixed in space but goes around the Sun! This means that our determination of the period is altered by our own motion (think of the track-cam that followed runners around at the track at the Sydney Olympic Games). Now you need to think about how you will remove this effect so you can compute the actual period of rotation of the Sun, as seen from a fixed point in space (the sidereal period). To guide your thinking, make a sketch of the rotating Sun and the orbiting Earth as seen from above. You can also think of someone walking around (on the ground) a rotating merry-go-round and how that person would go about figuring out the period of the merry-go-round for someone standing still on the ground. Remember that the Earth makes one revolution around the Sun in 365.25 days. Keep in mind your answer to part #4! Explain your reasoning.

   Determine the sidereal period of the Sun based on your "observations", reasoning and calculations.

8. Questions:

   1. Compare your determinations of the synodic and sidereal periods of rotation for the Sun with the accepted values (P_sid=25.38 days, P_syn=27.27 days). Comment on your results and on possible sources of error.

   2. Based on the evolution of sunspots and sunspot groups (part #2) on your images and the synodic period your calculated, would you expect sunspots or groups of sunspots to come back for another pass in front of the disk? Explain.

9. Your report: In your logbook include the printed images, your diagram showing the motion of the chosen sunspot (both parts), all calculations, notes on the appearance and evolution of sunspots and answers to the questions.




Figure 4