Nebraska Astronomy Applet Project Student Guide to the H-R Diagram Applet _____________________________ Pre-test in EDU Before working through the student guide, take the pre-test in EDU. Record your score here / 10. Directions: The next section covers information contained on the HR Diagram background page and the supplements on luminosity and spectral type. Read those pages, and then complete the text below by filling in the blanks. Where indicated, open the mini-applets to answer some questions. Section 1: Historical Background on the H-R Diagram The H-R diagram was named after the two discovering astronomers, Ejnar _________ and Henry Norris _________. It is a plot of the luminosity vs. surface temperature of a sampling of stars, such as those in a cluster. The temperature scale along the bottom axis goes from about 3000 K on the right to about ______ on the left. ___________ (the other axes) is a measure of the total energy radiated by a star each second. The Sun is nearly in the middle of both the temperature and luminosity scales on the diagram relative to other stars. Approximately 90% of stars lie along a nearly straight diagonal line known as the Spectral classes are one way of categorizing stars by their temperatures. The main spectral classes in order from hottest to coolest are __, B, __, __, G, __, and __. Stellar luminosities depend on both the surface temperature and the radius of a star. They are given by the product of two quantities -- the star's surface area (4R2) and its flux (the amount of energy coming from each square meter of the star’s surface each second) . The flux is given by a relation known as the ________-___________ Law (F = T4). Since the 4, , and are constants, we can think of luminosity as being equal to L = R2T4 in solar units. So that a star twice as big as the sun and the same temperature would have a luminosity of __________. Stars fall into three general categories; ______ ________ stars, ______ ________, and _______ _______ largely on the basis of size. Bright, cool stars have a very ______ radius. Since they have the same luminosity as main sequence stars, but are cooler, they must have larger surface areas. Antares is a good example of a bright cool star, known as a ______ ________. Smaller, hot stars are called White Dwarfs and lie below the main sequence There is a correlation between a main sequence star's mass and its luminosity. Stars that have higher ________ and are on the main sequence have a greater mass than fainter stars. The mass luminosity relation was discovered by __________ in 1924. It says that the stars luminosity is proportional to the ________ power of its mass. Once you know the mass and radius of a star you can calculate its average density. It is important to classify stars so that they can be studied in groups whose members all have similar properties. This helps astronomers to better understand how each type of star functions and at what point it is in its evolution. One method is to classify stars into ____________ ____________ based on the thickness of their spectral lines. More luminous stars have ________ spectral lines than less luminous ones of the same spectral class. Lines from a _______ star are much narrower than those of a dim star lined up below it on the H-R Diagram. Our Sun is classified as ____________ class G2 and ___________ class V. At some points in their life cycle a star may not be in perfect equilibrium. When stars are in a state of imbalance or instability, they are crossing an area called the ____________ ________ on the H-R diagram. Stars called ___________ variables are an important type of star in this unstable state. They are used as distance indicators (standard candles) because the ________ of their pulsation varies in proportion with their luminosity. Section 2: Applet Walkthrough This portion of the student guide is designed to familiarize you with the H-R Diagram Applet. By reading it and completing the simple exercises you will gain an understanding of the purpose and functionality of each part of the applet. Take special care to notice how each action affects different areas of the applet. For example, when you move the temperature slider, what happens to the size and color of the stars in the Relative Size box? Why does this occur? Section 2.1 First, move the temperature slider back and forth. Notice as you move the slider, the white dot moves horizontally on the H-R diagram matching the temperature you have moved to. The temperature is in degrees Kelvin, or absolute temperature. It increases from right to left on the diagram, opposite the motion of the slider. The luminosity slider is directly below the temperature slider. It shows the luminosity of a star located where the white dot is on the H-R diagram. Moving the slider will move the dot vertically on the diagram. The luminosity is given in solar luminosities and increases as you move up the diagram. Quick Exercise 2.1: Move the luminosity slider to 1 L (actually1*100 L) and the temperature slider to near 5770 K. Where does the white dot move to on the diagram? Is it on the Main Sequence? Section 2.2 In the black box just below the diagram, the radius of a star at the selected position can be found. In that same box is the name of the last star that was selected, or clicked on, by the user (either from the provided star list or a user defined list). Select the 34 Nearest Stars option in the Star Selection area. Now click on the yellow dot set to indicate the Sun on the H-R diagram. It is labeled underneath with the word Sun. Notice that the temperature and luminosity sliders read about what they did when you set them to the Sun's values previously. Now it should say the star name (Sun) and the star's radius in the black box below the diagram. Now click on a different star. Notice the name and radius, as well as the temperature and luminosity, change to match the description of the new star. If you click on the diagram in a place where there is no star, the temperature, luminosity, and radius will change, but the star name will remain that of the last star selected. Obviously there are many more stars than can be shown on a single diagram (entering all the data would take a very long time!), so only a small sampling of stars are provided. While there may be a star (or many, many stars) in a specific location, the applet can only give the star name for the stars in its database. Later in this guide you will be shown how to add your own stars to the diagram. Quick Exercise 2.2: Click on "25 Brightest Stars". Select the star that is nearest the top right of the diagram. What is this star called? What is its radius? Notice that this radius is larger than that of the Sun ( L > 1 *100 L ). How does the temperature compare to the Sun's? The luminosity? This bright Red Giant star is called Betelgeuse. It is cooler than the Sun and has a much larger radius. Section 2.3 The "IsoRadius Lines" button adds lines of constant radius to the diagram. The lines are labeled in solar radii. Click on "IsoRadius Lines" and look at where the R = 1*100 R line intersects the main sequence. Again you have found very near the Sun's position on the diagram. As you can see the radius values increase as you move toward brighter cooler stars. Find the white dwarf region of the diagram and click anywhere in that area. You can see that white dwarfs have a much smaller radius than our main sequence Sun. Right next to the "IsoRadius Lines" button is the "Instability Strip" button. The "Instability Strip" button adds the instability strip region to the diagram. Stars in this region are in a period of their life where they are not in equilibrium and therefore vary in brightness with some periodicity. For example, an RR Lyrae star near the bottom of the instability strip might vary by anywhere from 0.2 to 1.2 Mv and have a period of ~0.5 days. By now you have noticed that in the upper left corner of the applet is the Relative Size box. As you have been using the applet the size and color of those stars in the box have been varying. The star on the right always represents the Sun. The other star shows the relative size and the color of the selected star on the diagram. The color represents the effective temperature of the star, which of course is what determines a star's color in reality. Increasing or decreasing its luminosity can change the size of the star. This is due to the dependence of a star’s luminosity on its surface area. Quick Exercise 2.3: Move the temperature slider until the left star in the Relative Size box is white or very light blue. Now change its size until it is much smaller than the Sun. What kind of star is this? Even though the temperature is very high do you think this star would be easy to see? Why or why not? This type of star is called a White Dwarf. Notice there is a White Dwarf region on the diagram. Move the dot on the diagram along this region. What properties do you notice that stay about the same? This almost constant radius for White Dwarfs is a consequence of how these hot, compact stars were formed. Section 2.4 As we have seen, in the Star Selection box (lower left) you can choose which stars you want plotted on the diagram. There is also a Find feature that can be used to locate a specific star in the database of stars already in the applet (25 brightest stars and 34 nearest stars) or a userdefined star. To use this feature, select a star in the drop down menu and then click Find. To select a star in the drop down menu you must have something other than No Stars Plotted selected. Once you have selected a star from the menu, click Find to put a green crosshair on the star. To select the star's properties you must then click there on the diagram. If you want to add a new star or group of stars to the plot select one of the User Defined spots in the Star Selection box. Next adjust the temperature and luminosity to the values you want for your new star, or click on the diagram where you want the star to be placed. Finally, click on Adding Star to Plot in the Adding Stars to Groups box and type in the name you want for the star. Clicking OK will add the new star to the plot. This star will now show up every time you select that User Defined group in the Star Selection box. Add more stars the same way. Clicking the Clearing Stars from Group will erase all the stars in the selected user defined group. Stars may also be added to other selected groups in this manner, by clicking on the desired group and adding the star. Clearing the stars from a group cannot erase stars already in the applet by default. Quick Exercise 2.4: Click on User Defined group #1. Move the temperature slider to 9550 K and the luminosity slider to 2.6*100 L. Next, click on Adding Star to Plot. Enter the name Vega and click OK. Now, click anywhere on the diagram. Go to the drop down menu in the Star Selection box and select your newly added star. Click on Find. Now your new star has a green crosshair on it on the diagram. To select this star you must click on the crosshair. You can add other stars in this manner to create your own diagram. If you use a random sampling of stars for this you will find that most of the stars lie along a smooth curve. This curve will agree with the Main Sequence. Section 3: The Applet Exercises Exercise 1: Exploring the Stefan-Boltzmann Law The purpose of this exercise is to gain some insight into how the Stefan-Boltzmann law relates to the H-R Diagram. Step 1: First select the Sun on the diagram by clicking the 34 Nearest Stars option and then clicking on the spot that represents the Sun on the diagram. Make sure the luminosity slider reads 1*100 (we will call this luminosity L). Now, by moving the temperature slider a small amount, make the radius as close to 1*100 as possible (label this R). The purpose of this was to make the numbers in this exercise as easy as possible (so we are starting at R = 1R and L = 1L). Also take note of the temperature (T) once you have the other two values set. Step 2: Next, turn on the IsoRadius Lines. Drag your star along the R = 1R line until the temperature has doubled. What has happened to the luminosity? Write down this new luminosity and label it Lstar1. Add a star at this location named Star 1 in case you want to reference it at the end of this exercise. Step 3: Move your star position back to the original values for the Sun (L, R, T). This time move the star so that T stays the same while the radius doubles (to make R = 2R try moving the luminosity slider). Once you have done this note the luminosity and label it Lstar2. Add a star named Star2 here for future reference. Questions: 1.) Which changed the luminosity the most step 2 or step 3? 2.) These results are due to the luminosity relation L = 4R2)(T4), where is a constant. If we consider this equation in solar luminosities and solar radii we get L = (R2)(T4). Given this and assuming you used exactly L = 1*100and R = 1*100, what values would you expect to find for Lstar1 and Lstar2? 3.) Did your “experimental” values obtained in steps 2 and 3 agree with this? Why or why not? Exercise 2: Predicting Star Types For this exercise the main goal is for you to understand how to categorize a star using its temperature and luminosity. What makes a star a main sequence star, a white dwarf, or a red giant? It is important that you really think about your predictions before moving on to using the applet to plot the stars. Step 1: Below is a table listing temperatures (in Kelvin) and luminosities (in solar luminosities) for some unknown types of stars. The first star listed is the Sun. It is a main sequence star and its temperature and luminosity are listed as closely to the actual values as this applet allows. From this table each star can be placed on the H-R diagram. Before using the applet to place the stars, can you predict where they might go? In the spaces provided, predict whether the star is a main sequence star, a white dwarf, a giant or a super giant. Remember, the Sun is a main sequence star. Use this to help you guess what the others are. Star Name Sun Star 1 Star 2 Star 3 Star 4 Star 5 Star 6 L(L) 1.0*100 1.0*10-1 2.0*102 2.0*102 5.01*10-3 3.16*101 1.58*105 T(K) Prediction of Type 5754 main sequence 3890 3890 13183 13183 9120 4467 Step 2: Now that you have filled in the table above, select Both Groups from the star selection box on the applet and add these stars to the H-R diagram. Go back and make sure that your predictions were correct. All of these stars are fairly typical for their type. Questions: 1.) What is the name of a star near Star 2 on the diagram? Near Star 3? 2.) What property of Stars 1-6 were we really trying to determine in our predictions? Which stars had the most extreme values of this property? Post-test in EDU Before working through the student guide, take the post-test in EDU. Record your score here / 10.