Mandatory Term Project PHYS 1070.03 Solar Rotation

Due Date: 6 December (4pm, in Petrie 128) Grading: 15% of the course mark

Introduction:

In the Sky & Telescope lab, The Rotation of the Sun, the solar rotation period is determined using photos it provides. The objective of this exercise is the same, except that some of the data must be provided through your own observations of the Sun and the rest will be taken from satellite data. Your own data will be acquired by displaying an image of the Sun on a television monitor captured by a video camera that is attached to a small, wide-field refracting telescope mounted on York's 40 cm telescope. You are NOT required to do the Sky & Telescope lab. But because it provides excellent introductory and background information, as well as a good description of the reduction technique, it makes a good reference. Read it thoroughly (at least the first four pages) before you observe and again before beginning your write-up. You should also refer to Solar Telescope Operating Instructions handed out earlier in the term.

All bodies in the universe, including the Sun, possess angular momentum and therefore rotate. The Sun's rotation is an artifact of the primordial angular momentum of the gas cloud from which the Solar system formed some 4.6 Gyr ago.

Your ultimate goal is to measure the sidereal rotation period of the Sun, that is, the rotation period it would have in a frame of reference fixed with respect to the stars. This is achieved by measuring the synodic rotation period as seen by an observer on Earth, who of course is moving as a result of Earth's orbital motion around the Sun. Knowing Earth's period of revolution, it is easy then to determine the sidereal rotation period.

Read these instructions carefully. Precisely what you must do is outlined below, though you are always free to do more. You must hand in a typed, formal report in the following format; a) an introduction describing the background and rationale (0.5-1 page: don't regurgitate what is written here), b) presentations of the observations including a brief description of the technique and a complete log of the observations, c) reductions and calculations including the de-projection procedure, angles measured and synodic period derived with uncertainties, and d) conclusions and answers to questions contained in section IV below, including your result for the sidereal period of rotation.

Even though you will acquire your data in a group, you must perform the analysis and write the report on your own. Note clearly who your partners are on the cover page of the write-up as well as in the observing log. I. Purpose: To determine the sidereal rotation period of the Sun by observing sunspots.

II. Observational Procedure:

One must NEVER look directly at the Sun, either with the naked eye or through a telescope. For this reason, to study the Sun's surface we must project an image of the Sun onto a screen, either directly using an eyepiece or by using a video camera. A portion of the data you will use to measure the solar rotation period will be obtained by recording an image of the Sun projected on a TV monitor fed by a video camera that is attached to a small wide-field refracting telescope mounted on York's 40 cm telescope. Refer to the Solar Telescope Operating Instructions document for details about the instrumentation, including how to locate the Sun through the telescope. You will record your measurements on a transparency that is pre-marked with a circle representing the solar disk as it should appear on the TV monitor. The following outlines the basic procedure you should follow:

1. 1. Assuming you have been authorized to use the telescope, pick up the key to the dome along with water-soluble transparency markers from the Physics and Astronomy office in Petrie 128, normally between 9:00am and 4:30pm (except for noon- 2pm when the office is closed). You must leave your student card with a secretary that will be returned to you once the key and marker are returned. The secretary will also record your name/date of observation. 2. 2. Once you have successfully opened the dome and pointed the telescope at the Sun, lightly tape your transparency to the TV monitor. Centre the Sun's image on the pre-marked circle by following the instructions in the Solar Telescope Operating document. The Sun's disk should fit exactly within the circle. If the Sun’s limb is really fuzzy, adjust the focus of the wide-field refracting telescope using the focus wheel. If this doesn’t work, then contact appropriate observatory personnel for assistance, because something is wrong. (The Sun will move slightly with time because its motion differs slightly from the sidereal rate.) 3. 3. On your transparency, carefully trace the outline of all the sunspots visible on the solar disk using the marker. Sketch any other structures visible on the Sun's surface. 4. 4. You must be able to align images taken on different days. Thus, you must have a way of discerning absolute directions on your sketch. Therefore, before you finish observing, make sure you mark E—W and N—S clearly on your sketch. For example, you can use the hand paddle to move the telescope east. The Sun will move off the TV monitor, in a direction that is exactly west of where you are moving. It is absolutely essential that you provide direction indicators for each observation otherwise you will not be able to "combine" data from different days and complete your experiment! 5. 5. Record the date and time (EST or EDT, carefully noting which), on your transparency. Also write down the Sun's altitude (above the horizon), based upon the altitude scale on the mount of the 40 cm telescope. Record the observing conditions, too (e.g., clear, partly cloudy, windy, etc.). 6. 6. Shut down the observatory according to the instructions in the Solar Telescope Operating Instructions document, and return the transparency markers and key to Petrie 128. As soon as convenient, either trace or photocopy all the information on the transparency to a piece of paper. Then wipe the transparency clean with a damp cloth or tissue. It can now be used for the next observing session. 7. 7. An observing log summarizing all the information on each drawing must be generated for the final write-up. Include in this log the number of sunspots present each day. All your raw data must be included with your write-up. Remember to keep track of everything! Do NOT leave this exercise to the last minute. Clear weather is not something you can count on!

Each student must acquire 2-3 good-quality images of the Sun over a time span between 5 and 9 days. These data will be supplemented by data taken by the SOHO (The Solar and Heliospheric Observatory) satellite. The SOHO website is http://sohowww.nascom.nasa.gov/. You are permitted to retrieve continuum images of the Sun’s surface taken by the Michelson Doppler Interferometer (MDI) instrument. To find these images, click on “The Sun Now” in the top left-hand corner of the SOHO main page. This will take you to “The very latest SOHO images,” which include the MDI Continuum images, as well data from other wavelengths. To see the latest MDI image or any other wavelength image, click on the appropriate picture. To access the MDI archives, click on “512 × 512” directly below the MDI continuum image. You will now see a list of individual (archived) images, normally 2-3 images per day. For example, consider the three images: 20030107_0136, 20030107_0950, and 20030107_2224. These were taken at 1:36, 9:50 and 22:24 UT on January 7, 2003. Each of these is a gif file about 150 kb in size containing a visible image of the Sun. It is wise to download the appropriate SOHO images within a week after you have successfully obtained your own tracings. If not, you may always retrieve the data from a link at the bottom of the 512×512 image page, “list of all individual images.” (Note that the SOHO images are oriented such that the North Pole of the Sun is “up” and East to the left.)

You are permitted to download and print one 512 × 512 image per day for each day between your first and last ground-based images. For example, if you have tracings for Oct 18, 20 and 24, then you may download one MDI image for each of Oct 19, 20, 21, 22, and 23. No other data are permitted. Reduce, use and hand in the MDI and ground- based data together. Note that you may have to enlarge or reduce the MDI images using a photocopier so that they are as close as possible to the diameter/scale of the Sun in your own tracings.

III. Reduction Procedure:

If you have spot data for more than one latitude, you will have to repeat some of the following procedures for each latitude. (Data from two different latitudes is sufficient unless you want to do more!) If you have problems, follow the Sky & Telescope lab. Refer to the introduction for details of the write-up. 1. On a single page, trace the location of a particular sunspot or sunspot group (at a given latitude), as it appeared when you observed it. Be sure to align the individual images using the E-W/N-S indicators. Connect the traced spots with a best-fit (by eye) line of latitude running across the Sun, like the figure on page 4 of the Sky & Telescope lab (NB: it helps to orient the solar rotation axis parallel to one side of the page, but you may have to do some fiddling to figure out how to orient your individual images so that this happens). Having defined a line of latitude, mark the north and south poles of the Sun. Note that the Sun's axis of rotation is not aligned with Earth's axis of rotation, so the north and south Poles

of the Sun are NOT aligned with the north-south directions defined by Earth (how good the alignment is depends upon where Earth is in its orbit). 1. 2. Because of projection effects, the data may seem strangely spaced. You must therefore de-project the data before analysis can take place. Either above or below your “Sun,” draw a semi-circle so that the diameter of the semi-circle is equal to the length of your latitude line. If you now draw lines perpendicular to the latitude line from the spots to the semi-circle, you can see where the spots actually were on the surface of the Sun. Draw lines connecting the centre of the semi-circle to the semi-circle with the spots. (You cannot add data from more than one latitude on a single diagram.) 2. 3. As shown in the Sky & Telescope lab, measure the angle that each well- identified spot moved through during your observations. Note that you do not have to do this for every pair of angles. Measure at least 6 to a maximum of 20 angles. 3. 4. Calculate the (synodic) rotation period for each well-identified spot at the given latitude, average the periods, and provide an informal (but reasonable) estimate of the uncertainty of this quantity (e.g., based on the range of values you obtained, not a formal fit).

IV. Answer the following Questions:

1. 1. What assumption about sunspots is fundamental for determining the rotation of the Sun by this method? 2. 2. Since Earth has moved in its orbit around the Sun during your measurements, you have measured the synodic rotation period. Calculate the sidereal rotation period (and its uncertainty). 3. 3. For the largest single spot in your or the SOHO data, estimate the relative size of the spot in solar diameters, and then in kilometres. Relative to Earth’s radius, how large was this spot? 4. 4. a) At what (solar) latitude were your sunspots? b) At this point, what part of the Solar Cycle is the Sun in (look it up if you are unsure)? 5. 5. a) If you observed spots at widely different latitudes, compare their rotation periods. What does this reveal about the nature of the Sun? If you didn't observe spots at different latitudes, find out how the rotation period of the Sun varies with latitude; in particular, list the accepted rotation periods for the equator and poles of the Sun. b) In light of this, what does the "true" rotation period mean for a body like the Sun? 6. 6. On the SOHO website there are images (and archives) for other wavelengths taken by other instruments on the satellite. From the “Latest SOHO images” webpage, describe very briefly what the “EIT 284” data tell us about the Sun.