The Hertzsprung-Russell Diagram Lab Instructions

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Apr 3, 2024

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The Hertzsprung-Russell Diagram Lab Instructions These lab activities have evolved over years of use in Clemson University’s Department of Physics and Astronomy general astronomy laboratory. Contributors include Tom Collins, Mark Leising, Neil Miller, Peter Milne, Grant Williams, Donna Mullenax, Jessica Crist, Keith Davis, Amber Porter, Lea Marcotulli, and David Connick. Please direct all questions, complaints, and corrections to David Connick (dconnic@clemson.edu) who is responsible for all errors and omissions. I. Introduction In 1911 Einar Hertzsprung, a Danish astronomer, compared the stars in a cluster by plotting their apparent magnitudes against their colors. In 1913 the American astronomer Henry Norris Russell made a similar investigation of stars (of known distance) by plotting their absolute magnitudes versus their spectral classes, we will look at spectral classes in detail in the next lab. Hertzsprung and Russell made the very important discovery that the luminosities of most stars have a direct relation to their colors or spectral classes and therefore to their temperatures. The vertical axis (y axis) of a Hertzsprung-Russell (HR) diagram can be apparent magnitude, absolute magnitude, or luminosity. The horizontal axis (x axis) may be spectral class, temperature, or color index. Whichever combination of the above is plotted, most HR diagrams have similar characteristics. If all of the stars whose absolute magnitudes are known are plotted on the same HR diagram a pattern of preferred locations can be seen. Most stars will fall along a roughly diagonal band from upper left to lower right. This band is called the main sequence. Very hot stars and very luminous stars (large negative absolute magnitude) are at the upper left end of this band while relatively cool stars with low luminosities (large positive absolute magnitudes) lie at the lower right end. We now know that these stars are in the stable "adult" part of their lives during which their energy comes primarily from core hydrogen burning. The Sun is one of these stable core hydrogen-burning stars. The following table shows the lifetime of a star on the main sequence (hydrogen burning lifetime) as determined by its spectral type. Spectral Type Color Index (B-V) Lifetime (years) O -0.4 <10 6 B -0.2 3x10 7 A 0.2 4x10 8 F 0.5 4x10 9 G 0.7 1x10 10 K 1.0 6x10 10

M 1.6 >10 11 Fully developed stars that are not on the main sequence have exhausted their core hydrogen and are further along in their evolution. The cores of these stars are in a more advanced stage in which the fusion of elements heavier than hydrogen may be involved. Stars that lie above the main sequence are more luminous than main sequence stars of the same temperature and are therefore larger (giants or supergiants). Stars below the main sequence are less luminous than main sequence stars of the same temperature and are therefore smaller (e.g., the white dwarfs). We can use our knowledge about the spectral classes of stars and the HR diagram to determine what stars in the rest of the Galaxy are like. HR diagrams can tell us quite a bit about stars but we must interpret them carefully; there are logical pitfalls in drawing general conclusions using observations involving a limited number of stars. II. Figure 1 Analysis Figure 1 in the ‘H-R Diagram lab figures’ document shows an H-R Diagram with some example stars given in the major categories. Study Figure 1 and answer questions 1-5 on the worksheet. III. Figure 2 Analysis Hipparcos was a satellite that made precise measurements of stars over a period of years. Among the measurements it made were parallaxes, the apparent wobbles of stars due to the Earth’s motion around the Sun, which provides excellent distances for nearby stars. With precise distances the location of a star on an H-R diagram can be shown very accurately. Figure 2 shows a plot of the brightest stars we see from earth combined with a plot of the closest stars to earth using Hipparcos data. Use figure 2 to answer questions 6-8 on the worksheet. IV. Structure of our Galaxy You will need to open the Starry Night program. Once the program is open you should load the “HRgalaxy.skyset” file. You should see the night sky with an H-R diagram in the bottom left of the view screen. We will use the H-R diagram to compare the stars in the plane of our Milky Way galaxy with those outside the plane. The left vertical axis of the H-R diagram is the absolute magnitude while the bottom horizontal axis is the spectral class. With your FOV at about 20 degrees center the screen on a view of the Milky Way galaxy. The denser area you can find the better. In a moment you will move your view away from the Milky Way galaxy. Watch the H-R diagram as you change your view and answer questions 9-11 on the worksheet.

V. Open Clusters and Globular Clusters We will now look at the types of star clusters and where they can be seen. It will help to turn off the Stars and H-R diagram for a moment to declutter our view. Go to the gear and in the ‘Stars’ dropdown uncheck the box for ‘show stars’ and ‘show H-R diagram’. You will likely need to move your view around within the program to find the circles that represent the clusters. The empty dashed circles represent open clusters while the solid circles with plus signs inside are globular clusters. Make sure your FOV is smaller than 40 degrees so these deep sky objects will appear on the screen. Open the info panel and click on the clusters as you move around the screen. In the info panel will be an image of the star cluster as viewed from Earth. Answer questions 12-14 as you explore the clusters in the Starry Night program. VI. Age of Clusters There are certain advantages to constructing an H-R Diagram with a cluster rather than with a random distribution of stars. First, all the stars in a cluster are at nearly the same distance from us. Therefore one can use the stars’ apparent magnitudes rather than absolute magnitude as the ordinate. Second, specific information about the age of the cluster can be determined from an H-R Diagram of its stars. It is logical to assume that all the stars in a cluster formed from the same large cloud of gas at about the same time. Therefore all the stars in a given cluster have about the same age. However, very high mass stars evolve quickly and have a shorter lifetime than their lower mass kin. These high mass stars have a greater fuel supply than lower mass stars but they are burning that fuel at a much faster rate. High mass main sequence stars at the upper left corner of an H-R diagram begin to move to the right (by expanding) off the main sequence. As time passes, stars farther down the main sequence begin to “turn off” the main sequence. The line that traces where the stars are at a given time is peeling away from the original main sequence, from the top down. The result is that at a single given time the H-R Diagram for stars in a cluster will show a distinct “turn off” that tells immediately the age of the cluster. Figure 3 shows the H-R diagram of many star clusters. Use the information from Figure 3 and the table from the introduction to answer questions 15-18 on the worksheet. VII. Constructing an H-R Diagram Finally we will create our own H-R diagram in google sheets. Open the ‘H-R lab plot’ excel file in google sheets. In the file is information for some of the brightest stars in the Beehive cluster. The information for 3 stars is missing. Search for the Beehive cluster in Starry Night and collect the data from the 3 stars the program shows. (You will need to show the stars by checking the ‘show stars’ box in the settings under ‘Stars”. Check the more information box in the information panel to see all the required information.) The Henry Draper catalog number shows up as HD# in the info panel of the Starry Night program.

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Record your data in the spreadsheet. Note that the last column in the spreadsheet already has a number in the top cell. If you click on that cell in that column you will see a formula called the distance modulus equation, which relates the apparent magnitude, m, and the distance in parsecs, d, to the absolute magnitude M. M = m + 5 – 5 log d The last column is for the luminosity of each star in terms of solar units. The equation in the top of the column calculates the luminosity of each star relative to the luminosity of the sun. A value of 10 means a star is 10 times more luminous than the sun. After you have entered the missing data drag the absolute magnitude equation down to populate the absolute magnitude for all of the stars. Then drag the luminosity equation down to populate the luminosity for each star. Create a scatter chart with the B-V color index as the x axis and the luminosity as the y axis (series data in chart setup). You will want to customize the y axis to be in log scale and choose a max and min that shows the data well (We suggest a y range of 0 to 500 and an x range of - 0.5 to 2). Add a title and labels to your chart. Copy the chart into your worksheet and answer questions 19-21 on the worksheet.

The Hertzsprung-Russell Diagram Lab Instructions

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