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SUNSPOTS Lesson Plan Resource Guide

Background Material: Research Activity

Please be sure to read all the lesson pages, as they provide background for the research activity. Open the folder SUNSPOTS to start the lesson, and use the navigation links at upper right to access all sections.

Activity
Read these lesson pages by selecting the "ACTIVITY" tab near the upper right corner of the screen.

Scientists compare images taken in different wavelengths of light and try to find relationships between the images. They  look for correlations that may point to physical relationships and processes that were previously unknown. Visible light images of the sun show sunspots on the photosphere, while x-ray images show us x-ray active regions in the corona. 

Scientists would like to know more about whether and how the x-ray active regions are connected to sunspots. Finding a correlation between their respective areas on the solar disk would be evidence suggesting a physical connection; for example, possibly the x-rays are emitted by coronal plasma interacting with the magnetic field loops that terminate in the sunspots. However, this may be difficult to investigate, even with the latest data.  Imagine trying to establish a correlation between the size of a flame and the size of a burning match tip on a rotating sphere, especially if conditions like the air around the flame are not constant. In this analogy, the flame is like the x-ray active areas; the match tip corresponds to the sunspots seen in visible light images.

In our interviews on this project, solar scientist George Fisher suggested the idea of trying to measure and quantify the relationship between sunspots and x-ray activity.  It is commonly assumed among scientists that the hot active regions in coronal images and visible sunspots are somehow two views of the same structure, but Fisher believes no one has yet established the connection with a formal investigation.  If the correlation were well established, and especially if it could be well quantified, this would be a very useful tool for inferring levels of x-ray activity from older, visible light images. The Yohkoh satellite produces  daily images in both visible and x-ray light which can be compared over a number of days to address this question, so a Java "applet" program was written to measure the areas and plot the data.  (The term applet is a diminutive form of  "application.")

The QuickTime movies in the first page (activity.html) show the sun over a period of about 2 months, as a series of images in soft (relatively low-energy) x-rays on the left, and in visible light on the right.  The sun makes a complete rotation about every 28 days.  You may notice that the x-ray areas seem to change rapidly in brightness, this may be partly  due to a "beacon" effect, dependent on whether the hot region, which may be at some altitude above the solar surface, is rotated toward the satellite's telescope.  The interview with George Fisher presents the correlation problem  in terms of several quantities, which he thinks are likely to be correlated, and possibly proportional:  sunspot area, magnetic flux, and x-ray energy emitted. 
NOTE: if you do not have QuickTime, the same movie sequences appear in the RealMedia interview clip.

The Java applet program is launched from the second page,  activity2.html. Activity2 also serves as  a self-contained "quick-start" guide for using the applet. Three more pages of supporting material, can be accessed from links in the sidebars of pages 2 and 3.  These pages are also displayed sequentially if one continues to use the "next" arrows at the top and bottom of each page. These links are shown, and the page contents summarized briefly  in the table below. 

using the applet icon Page 3 gives a detailed account of how to operate the applet. This is important for students who are less experienced computer users, or otherwise have a hard time starting.
about the images icon Page 4 describes how the data are gathered using the Soft X-ray Telescope (SXT) aboard the Yohkoh satellite and how the images are created. Supplementary material.
active x-ray regions icon Page 5 gives detailed descriptions of what the features in the x-ray images show, as interpreted by scientists. This information is important for standardizing the measurements from one student or group to another, and for understanding what areas seem most likely to be related to sunspots.

Students should be  urged to use these pages, as the information will help them make better decisions about their experimental procedure in measuring the images. Having the applet in a separate window allows students to keep navigating through the pages of supporting material as they work.  

The Java applet program is a tool for comparing sunspot and x-ray active areas using the image pixels as your unit of measurement. Each pixel represents an area roughly the size of the earth superimposed on the surface of the Sun. Here are some tips that may be helpful:

The x-ray images used come from the Yohkoh satellite's Soft X-ray Telescope (SXT). Visible (white) light images are from a camera, also on Yohkoh. Colors are consistent over the data set. For example, a pixel with 100 photon counts is the same color in every one of the x-ray images. All images are from a solar maximum (January, 1992), and so are similar to what the sun may look like as we approach a new maximum in the year 2000.  Current daily images are available at: 

http://solar.physics.montana.edu/YPOP/ProjectionRoom/latest.htmlá (goes to Yohkoh SXT site)

Not all features in the X-ray images  are "active regions" for our purposes. Like the shades of gray in a medical x-ray film, the colors in the x-ray images represent varying levels of non-visible x-ray emissions. Large spots in white-to-bright-yellow that are completely within the disk are active regions. They can be much larger than the visible sunspots and may vary in brightness and color as they rotate across the disk. Tiny bright spots of 1 or 2 pixels are not showing the same kind of activity as the larger regions, and shouldn't be counted. Areas extending outside the disk shouldn't be counted, because they would be connected to sunspots that have rotated to the edge of the visible disk, and don't show in visible images. Students may want to study the QuickTime  movie on page activity5.html  to get a better idea of the dynamic changes of  the x-ray active areas from day to day .

Examples of values and a plot generated by a teacher using the Java applet are shown below. The plot indicates a roughly linear correlation. Each point in the plot shows white light area vs. areas of intense x-ray activity.  Although the scatter of the points looks  bi- or even tri-modal (3 different slopes), the plot has a consistent average slope, with about the same number of points falling above and below a  central line. Since the scale of the x-ray axis is  an order of magnitude (x10) greater than the sunspot axis, the degree of vertical scatter is not too surprising. The sample and graph also appear in pages activity 2 and activity 3. These are meant as a rough guide only. Students should not be saddled with  the idea that their data should look just like the sample; every researcher's measurements will be a little different.

sample values table sample plot

Linear Correlation is the simplest case of what students may find. This seems to be the case in our example plot, where the points with x=sunspot area and y=x-ray area seem to cluster about a line with a definite slope. The relationship between the two quantities might also be expressed in an algebraic expression, like the linear equation y = mx + b, where x = sunspot area, y = x-ray area, and b = y intercept (value of y at x = 0).  If
 y intercept b = 0 the slope m =  y/x
y intercept b > 0 the slope m = ( y - b)/x may be positive or negative
y intercept b < 0 the slope m = ( y - b)/x m must be positive.* 

*However, this implies that some negative values of y correspond to positive values of x, which signals a non-physical situation, since area cannot be negative. Some unknown quantity is probably not taken into account; systematic error is the most likely.

If  b = ▒0, the slope  m is the  factor by which the x-ray area is proportional to the sunspot area, and m is approximated by the average of y/x for all the points measured:  1/n i=1Sn yi/xiNote also that the slope is then without units, as it should be, since both x and y are in units of pixels and these cancel out when divided. You may wish to have students perform a least squares fit to a straight line, if calculators or a computer program are available for this.

Note also that time does not appear as one of the variables in the correlation plot. These relationships do not depend on the passage of time; it is assumed that if the (sunspots vs. x-ray active area) correlation exists, it is time invariant. The absence of a time axis may disorient students who have not done much graphing. If your students need to approach the goal of the research activity more slowly, start with plotting the areas measured on the images against time. 

Plotting sheets are included for graphing each of the white light and x-ray data sets against time:  Sunspot area vs. date ; X-ray active area vs. date. Horizontal time axes span the month of January 1992, and vertical axes have appropriate scales for the two types of images. The time graphs will have some shape, not necessarily linear or smoothly curved-- they may have sudden jumps as spots and x-ray areas appear and disappear because of the sun's rotation, or as active areas become brighter and dimmer. Both the evolution of the sunspots or active regions and the rotation of the sun (once per 28 days) affects each day's data. For sunspots, the effect of rotation will likely dominate, as the sunspots evolve on a time-scale of  several weeks or months.  X-ray regions may vary on much shorter time scales.

Compare the two time graphs:  if the two graphs show a similar overall shape, comparing them may help students discover the correlation themselves. The more the shapes are alike, the closer the correlation graph would be to a straight line. Remember that the vertical scales of the two time graphs are different, so that a similarity indicates the x-ray and sunspot areas are proportional, not identical. Encourage students to make guesses about what the x-ray vs. sunspot graph would look like.

The applet program does not "do science" by itself.  Students must learn how to use the program correctly and a great deal of the benefit of this activity lies in the critical thinking required to interpret the images, and make an intelligent interpretation of the resulting graphs, with some accounting for sources of error. Team and class presentations, or  discussions, using questions like those suggested in the lesson plan, are useful in completing the lesson.

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