Assignment 1: Rotation Period of the Sun

Due: Before 5 pm, Thursday, 5 October 2006.

The Solar and Heliospheric Observatory, SOHO is a joint European Space Agency and NASA project to study the high energy radiation produced by the Sun. We will use SOHO images to determine the rotation period for the Sun. Look at the images acquired by SOHO during February 2001 given here.

1. Tne above files contain approximately two weeks of SOHO images of the Sun; February 1 to 16, 2001. To determine the rotation rate for the Sun, find long-lived sunspot groups and then follow them across the disk of the Sun (using the sixteen images). Make a plot of the position of a Sunpot (or group) on the disk of the Sun versus the day.

2. Determine the rotation period for the Sun based on the rate sunpot groups move across the face of the Sun. To perform this exercise, consider the picture below:

In the above figure, the vantage point is from the North. You, the observer sits in the equatorial plane of the Sun, the bottom of the picture, and watches as sunspots along the equator of the Sun. The sunspot groups move from left-to-right across your line-of-sight. In the two marked intervals, the spot is carried 45^o around the circle by the rotation of the Sun, that is, the Sun rotates for one-eighth of its rotation period in each interval. For you, observing from the bottom of the figure, the sunspot group appears to move at different rates even though the Sun rotates steadily. When the Sunpot is near the limb of the Sun (the edge of the Sun), the Sunspot appears to move more slowly than when it is near the center of the Sun (the length A is smaller than the length B).

• You may correct formally for this effect quite easily. Make a circle on a sheet of paper (as in the above figure).
• Plot your observations (and mark the date and time for which they were made) on the horizontal axis, the axis perpendicular to your line-of-sight.
• Draw a line perpendicular to the horizontal axis and find where it intersects the circle. Connect the intersection point to the center of the circle.
• The angle swept out by this line (from your initial observation) tells the fraction of the rotation period of the Sun which has elapsed since your first measurement. Use this result to estimate the rotation period for the Sun.
• Perform this exercise for all of your measurements, average your result for the rotation period of the Sun. What is your answer?

Use your method on several sunspot groups (choose ones at different Solar latitudes, if possible). Do you get the same rotation period for all of the sunspot groups? Can you show that the rotation period depends on Solar latitude (from your data)?

3. What are some sources of error in your result for the rotation period of the Sun?