Interstellar dust is obvious to us because it scatters light. If a dust cloud is dense enough, it blocks out so much light that a "dark patch" appears in the sky. However, because the dust grains are just about the same size as the wavelength of visible light, long wavelength red light scatters less than shorter wavelength blue light. Therefore, dark patches are more clearly outlined in blue light than in red.
In this exercise, you will use three photographs of a dark patch and the surrounding sky to calculate the "extinction" of light due to dust. The three photographs used three different wavelength fileters, but the exposure time varied. You will determine the extinction in each photograph, and come up with a value for the extinction (in magnitudes) as a function of wavelength.
The photographs are of a region called the Coalsack Nebula, a relatively nearby dark patch located around 200pc from earth. The three photographs were taken with filters for blue light (J-Band, centered on 420nm), red light (R-band, centered on 640nm), and infrared light (I-band, centered on 800nm). Notice how the dark patch (in the upper left part of the photographs) is most clearly seen in the blue image. Don't be confused by the fact that the red and infrared photographs were taken for shorter exposure times.
We will assume that all the stars in the field are behind the dark cloud. Therefore you can simply use a count of the number of stars per unit area, both within and outside the dark cloud, to estimate how much light is absorbed by the cloud. Using a piece of paper and some scissors, cut out a window of convenient size and shape. Only count stars brighter than some specific size within the window, and make sure you keep that minimum size the same when you count inside and outside the dark cloud. Make the window large enough so that you get at least 20 or 30 stars within the cloudy portion, otherwise the random statistical fluctuations in your count will make it more difficult to interpret your results. You may want to try this a couple of times with the window in different places so you can check that you get consistent answers.
The density of stars would look pretty much constant all through this region if it were not for the obscuring dust. Therefore the extinction Dm (i.e. "Delta m") is reflected in the ratio between the number of stars, N, per unit area in the cloudy region, and the number, N0, in the region outside the cloud. That is, the magnitude m of stars outside the cloud is reduced to m-Dm through the cloud, and some fall below the limiting magnitude in your count. Since magnitude goes like 2.5 times the logarithm of the flux, we have 2.5Dm=D[logN]=logN-logN0, so
Calculate the extinction Dm for each of the three photographs. Plot the extinction as a function of the inverse wavelength (1/lambda). Compare to Zeilik Fig.19-6. (Note that the textbook plots extinction versus wavelength on a reversed logarithmic scale, so it is equivalent in shape to plotting the inverse wavelength.) Keep your results on the worksheet.
Answer the following question: We needed to assume that all the stars visible in the direction of the cloud were in fact behind the cloud, and not in the foreground. Is this a good assumption? Use the fact that the cloud is 200pc away and covers about 6 arc minutes on the sky. Also use the fact that the density of stars in our neighborhood is about one per 10 cubic parsecs.