Assignment #9 Star Colors & the B-V Index

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1 Name Class Date Assignment #9 Star Colors & the B-V Index Millions of stars are scattered across the sky. Astronomers want to study these stars as carefully as possible. This means measuring everything we can possibly measure about them. Unfortunately, it's not easy to measure anything that's a septillion miles away! As we've discussed in class, astronomers really only measure three properties of stars: 1) Position 2) Color 3) Brightness We've already had practice using two methods to measure a star's position the Altitude/Azimuth method and the Right Ascension/Declination method. Now it's time to look at the second stellar property: color. It may not be obvious to you that stars even have colors some people are convinced that stars only come in white! This is not true. Carefully comparing one star to another reveals that stars come in a variety of colors and brightnesses. PART A Astronomers can learn a wealth of information about stars from carefully studying their colors. It turns out, however, that it's not so easy to define a star's color. This is because, of course, no star emits only a single color of light. In fact, all stars emit every color light! The color we see when we look at a star (or any other glowing object, for that matter), is the sum of all the colors the star is emitting. Usually, however, a star will emit most of its light at a particular color, making that color the dominant color of the star. As we discussed in class, the graph of the intensity of light emitted by a star versus the color of light is usually a distinctive curve called a Black-Body curve or Black-Body spectrum. A typical Black- Body spectrum looks like Figure 1: Figure 1 1

2 What this graph shows is that at very short wavelengths (to the left on the x-axis), the star gives off very little energy. In other words, it's very dim at those colors. The same is true at very long wavelengths (to the right on the x-axis). Most of the star's energy is given off at a small range of wavelengths - in this case, around 7 x 10-7 m or 7000 Angstroms (1 Angstrom (Å)= 1 x meters = meters). So light at around this wavelength will give the star it's distinctive color. Here's a real star's spectrum: Figure 2 This looks like a messy version of Figure 1! The messiness comes from the absorption lines, as we discussed in class. Let's ignore them for now. The typical Black-Body curve is easily seen behind the messiness. Draw a smooth curve through the top of the spectrum in Figure 2 that follows the general direction of the black body curve. IGNORE ANY SMALL BUMPS OR DIPS. This imaginary curve will reach a maximum or peak at which wavelength? Remember, wavelength is measured on the horizontal or x- axis. Peak wavelength (λ peak ) = Å What color will this star appear to us if we looked at it in the sky? Well, as you remember from class, wavelength is just a fancy way of saying color, right? So let's convert one to the other. Below, in Figure 3, is a picture of the visible light spectrum, with corresponding wavelengths listed (you'll need a color monitor or printer to see the colors). Figure 3 2

3 Using λ peak, the peak wavelength you just measured, estimate the color of our star, using Figure 3. What color will our star will appear to be? As you also might remember from our lectures or textbook, we can use this same peak wavelength to determine the temperature of the star, using Wien's law. Wien's law, in mathematical terms, says that, for a glowing Black Body (like a star), the brightest wavelength of light given off by the object, also known as the peak wavelength, is given by = 30,000,000 Formula 1 where T is the temperature of the star, measured in degrees Kelvin, and wavelength (λ) is measured in Angstroms. If we rearrange things in Formula 1 we get = 30,000,000 Formula 2 Use Wien's Law (Formula 2) to figure out the temperature of the star whose spectrum is shown in Figure 2. Remember, you measured λ peak, the peak wavelength, from Figure 2! T = So we can roughly measure a star's temperature by seeing what color it is! Pretty amazing! Of course, don't forget that when we look at a star we're really seeing a bunch of colors all mixed together, so what we're really doing is roughly measuring a star's temperature by seeing what it's brightest color is. PART B Of course it's not so easy to decide on the color of a star by just looking at it with your eyes. Astronomers have a much more precise way of measuring a star's color. They use something called the B- V Index. The idea of the B-V index is to take the magnitude of a star at two precisely defined colors, one in the Blue section of the spectrum (B), and one in the green-yellow, visual part of the spectrum (V). We then subtract the V-magnitude from the B-magnitude to get the B-V index. For example, a very hot star will give off more blue light than green-yellow light, so its B- magnitude will be less than its V-magnitude (remember, a smaller magnitude means a brighter star!), and therefore its B-V index will be a small number minus a bigger number, which will be a negative number. Similarly, a cooler star will have a smaller V magnitude than a B magnitude, so its B-V index will be a positive number. As discussed in class, you can make a precise relationship between a star's B-V Index and its temperature. The graph in Figure 4 below can be used to make that relationship precise. To find a star's temperature, you simply measure its B-V Index, then find where that B-V Index value hits the curve on the graph, and follow vertically down to the x-axis to find the star's temperature. 3

4 Figure4 Let's see how this works. Start Stellarium. Turn off the Atmosphere and Fog. Click on ten random stars, and estimate each star's color as best as you can on screen by looking at it. Also, record each star's B-V Index in Table 1 below. The B-V Index is listed in parentheses after the Magnitude reading in the 1 st line of the Information that appears on screen underneath the line with the star's name. Try to find as many stars of different colors (and hence, temperatures) as possible! You may have to move to a different part of the sky to see more stars of different colors. Table 1 Star name Estimated Star color B-V Index Temperature (from graph) 4

5 Given what you learned about the relationship between temperature and color from Wien's Law in Part A, do your results make sense? Explain Now use the graph in Figure 4 to answer the following questions: Roughly what temperature would you expect a star with B-V index of to be? Roughly what temperature would you expect a star with B-V index of to be? What would the B-V index be for a star that is 20,000 K? Now use your graph and Formula 1 and Figure 3 to answer the following questions: What color would you expect a star with B-V index of -0.2 to be What color would you expect a star with B-V index of to be What color would you expect a star with B-V index of 0.75 to be? The B-V Index turns out to be a very useful tool for quickly calculating a star's temperature, based on its magnitude at two carefully chosen colors. Astronomers can build precise machines to accurately measure a star's magnitude at those two colors, and calculate B-V indexes very accurately, thereby allowing them to find a star's temperature much more accurately than they could by just looking at a star with their eyes and guessing it's color! By precisely specifying a star's B-V index, we can know it's temperature! This is a much more accurate way of estimating a star's temperature than just using Wien's law and guessing the dominant color of a star. Star colors not only make the night sky more beautiful, but provide astronomers with essential information to determine the properties of stars and our universe. Write a conclusion describing what you learned in this exercise. 5