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The Spinning Sun

The Spinning Sun
This is a small research project suitable for undergraduate Astronomy and Physics students. It was put together by Helmut Jerjen from the Research School of Astronomy and Astrophysics (ANU). Please send me an e-mail if you are planning to do this project. I would be delighted to hear more about your own results. Enjoy and have fun!
INTRODUCTION

SUNSPOTS: The surface of the Sun, called the photosphere, is at a temperature of 5800 degrees Kelvin. Sunspots are cooler features (3800 degrees Kelvin) wandering across the disk of the Sun that have been observed since ancient times.

When viewed through special telescopes (*never look into the sun with the naked eye, binoculars or normal telescopes!*), they have a dark central region known as the umbra, surrounded by a somewhat lighter region called the penumbra.

Sunspots are the site of strong magnetic fields. They typically grow over a few days and last anywhere from a few days to a few months. They can be very large, as much as 50,000 km in diameter. The number of sunspots you can count on the Sun's surface is not always the same, but varies over time. Solar activity is directly related to the frequency of sunspots. Here is a plot showing the number of sun spots since 1995:


ROTATION: The sun does not rotate as a rigid body. It is a gas from its outermost layers down to its centre. The equatorial region of the photosphere rotates faster than do regions at higher and lower latitudes. This is called differential rotation. The differential rotation of the Sun's latitudes causes its magnetic field lines to become twisted together over time, causing magnetic field loops to erupt from the Sun's surface and trigger the formation of the Sun's dramatic sunspots and solar prominences.

SOHO: To follow the Sun's activities closely, the ESA/NASA solar observatory SOHO was launched into an orbit around the Sun, rather than an orbit around the Earth on December 1995. This assures that SOHO would provide solar data 24 hours a day. At no time would the Sun be hidden from SOHO by the Earth. SOHO's position is around a point called the L1 Lagrangian point, a rather stable location at which the gravitational pull from Earth equals the gravitational pull from the Sun. L1 lies on the direct line between the Earth and the Sun, approximately 1% the distance from the Earth to the Sun. This allows SOHO to travel with the Earth as it revolves around the Sun, but at a distance of 1,500,000 km closer to the Sun. SOHO is tracked and data is collected by the Deep Space Network (DSN), a series of three deep space communications facilities strategically placed on three continents, approximately 120 degrees apart around the world: Goldstone, CA (USA), Madrid (Spain), and Canberra (Australia).

TOOLS

  • Image Analysis Software for your computer: ImageJ (from the National Institutes of Health, USA) is freely available for MaxOSX, Windows, and Linux x86.
  • Plotting Software such as MS Excel, IgorPro, or any of the free plotting software.
  • Julian Date converter software for Windows , MacOSX. Web calculator can be found here .


    PROJECT

  • Go to the Australian Space Weather Agency to learn more about the observed monthly sunspot numbers. Do sunspots appear and disappear randomly or are there any patterns observable over the years, decades, centuries? How many sunspots have been observed in May 2003? In which month were the largest number of sunspots detected from 1995 to 2007?
  • Look at the SOHO Michelson Doppler Imager data from a "good" year when the sunspots number frequency was particularly high.
  • Browse through the images and search for one that shows a big, well-defined sunspot.
  • Save this image on your computer and open it with the Image Analysis Software ImageJ.
  • ImageJ allows you to find the x and y coordinates of the sunspot or any other feature on the sun. Just move the cursor over the image and see how the coordinates change. What are the coordinates of your sunspot? You may want to use the "zoom" to increase the acuracy of your answer. Also determine the coordinates of the center and the pixel diameter of the sun? When you compare that number with the sun's real diameter of 1 380 000 km, how big is one pixel in reality? How many pixels in size would the Earth be on such an image?
  • The next task is to download a complete time series of images that illustrate how your sunspot is moving due to the sun's rotation. For that purpose, search carefully for all images that show your sunspot from appearing on the left edge of the disk, moving across, to disappearing on the right edge of the disk. If you have difficulties to find a suitable sunspot you may want to use either sunspot1 at x=542, y=350 or sunspot2 at x=560, y=644 on the image MDI_int_1999.12.23_14_00.gif.
  • Now we are going to analyse all images of the time series. Load the image with the earliest date into ImageJ and measure the x and y coordinates of your sunspot. Write these numbers into a spreadsheet of your plotting program. Also record the Julian date of the image by converting the date as given in the image name into the Julian date. A Julian date converter can be found here. For example, the three numbers for sunspot1 on image MDI_int_1999.12.23_14_00.gif are: 2451536.08333, 542, 350. Repeat this procedure for all the other images in the time series. Once this is done you can plot your results. The composite image on the left shows the sunspots' motion and if you plot for instance the date and x-coordinate value from each image you can get a graph like the one on the right:

    What does the slope of the curve tell you?
  • The time has come to work out the differential rotation of the sun. Let's go back to the time series. By comparing the dates of the first and last image (see image names) you can get a rought estimate of the rotational period. What do you get? Did you take into account that you observed only have of the rotation? The value that you got is the rotation period for the latitude of the sunspot. Let's work out the latitute of your sunspot. To do this you need the trigonometric equation:

    Can you work this equation out yourself? The latitudes of sunspot1 and sunspot2 are: 18.7 and -16.3 degrees. Now, we need many more of these observations. Go back to the SOHO Michelson Doppler Imager data and find more sunspots that occur at various solar latitudes. Find for each sunspot the "first" and "last" image, estimate the rotational period and calculate the solar latitude. .......................
  • Browse through the images and search carefully for one sunspot that last for several months (very tricky).
  • Find sunspots that cover a range in solar latitude (close to and away from the solar equator). Once you have found a set of (5-10) suitable sunspots use a graphic program to measure and record accurate x (longitude) and y (latitude) coordinates of the selected sunspots on every image (2-4 images per day) over as many days as possible as long as they are visible (note: the zero point of the coordinate system can be chosen arbitrarily.)
  • Plot the x and y coordinates of each sunspot as a function of time (time series). The apparent motion of a sunspot across the Sun's disk at constant velocity follows a sine function: slower motion when appearing and disappearing and faster motion when crossing the center of the disk. Use a Mathematical program to fit a sine function at the observed data. The result could look like this. Note the gaps in the time series due to the sunspots being unaccessible while travelling on the backside of the sun.
  • Determine the rotation periods for all sunspots. Do you have to apply a correction for the motion of the SOHO satellite around the Sun? Compare the results with their latitude coordinate to find evidence for differential rotation. The plot could look like this .
  • Discuss your results within the context of other people's findings reported on the internet and on ADS by the professional astronomers (e.g. Tang 1980 or Newton & Nunn 1951) What are effects not taken into account in our experiment (2nd and 3rd order effects) and how could the experiment be improved?


    LINKS

    History of Solar Physics


    Images credits: Courtesy of SOHO consortium. SOHO is a project of international cooperation between ESA and NASA.
    Comments and feedback: jerjen@mso.anu.edu.au
    Last update: October, 2007