Wk07-HR_Diagram_Intro_Worksheet_avaiceman

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Oct 30, 2023

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Student Name: Lab TA: Partners Names: Astronomy 1101 The Hertzsprung-Russell Diagram Laboratory Worksheet One of the most fundamental physical properties of a star is its luminosity , the rate at which it radiates energy into space as light. Unfortunately, we cannot directly observe the luminosity of a star. What we can observe is the apparent brightness (or just brightness for short) of the star, which is a measurement of how bright it appears to us as seen from a distance here on the Earth. The brightness of a star depends on its luminosity and its distance : if two stars have the same luminosity, the more distant one appears fainter. This is the same effect as seeing two 100-watt light bulbs (which have same luminosity) at different distances — the one across the street appears fainter than the one on the table next to you because light from the distant bulb gets spread out over a much larger area before it reaches you. To estimate the luminosity of a star we must measure its brightness and its distance. Distances to nearby stars are measured using their parallaxes . The other fundamental observable property of a star is its color . The color of a star depends on the temperature of its surface. Hotter stars have bluer colors and cooler stars have redder colors. The Sun has a surface temperature of ~6,000 Kelvin, and it emits primarily pale-yellow light. Astronomers typically describe color quantitatively as a color index , which gives the ratio of the star’s brightness seen two different wavelengths (e.g., the ratio of red light to blue light). For purposes of this lab, you just need to know that the color index is a number that lies between - 0.5 and + 2.5, and that red stars have a positive color index and blue stars have a negative color index. In other words, color index is a quantitative measure of “redness.” In this lab, you will first compute the luminosities of a few stars using their observed brightness and distance. You will then make and examine a Hertzsprung-Russell (or H- R) Diagram, a plot of luminosity vs. color index. The H-R diagram is one of the primary tools that astronomers use to understand the properties of stars. The first versions of the such diagrams were made by the Danish astronomer Ejnar Hertzsprung and the American astronomer Henry Norris Russell around 1910.

Part 1: Distance, Brightness, and Luminosity The relation between Distance (d), Brightness, and Luminosity is Brightness = Luminosity ÷ (4π × d 2 ) where d is the distance. If you move a star 2 times farther away from you it will appear to be 2 2 = 4 times fainter than before, but its total energy output (luminosity) stays the same. If we measure a star’s brightness and its distance, we can determine its luminosity by reordering this equation: Luminosity = Brightness × (4π × d 2 ) The star Alpha Centauri (α Cen) is one of the closest stars to the Sun, at a distance of d = 4.37 light years = 4.13 × 10 16 meters. The apparent brightness of α Cen is Brightness = 2.71 × 10 - 8 watts/m 2 (watts per square meter). 1. From the above equation, what is the luminosity of α Cen, in watts? Luminosity of α Cen = (2.71 × 10 - 8) X (4π × (4.13 × 10 16 ) 2 ) (2.71 × 10 - 8) X (4π × (1.71 × 10 33 ) ) = 5.808 X 10 26 2. What is the ratio of the luminosity of α Cen to the luminosity of the Sun, 3.828 × 10 26 watts? (Luminosity of α Cen / Luminosity of Sun) = ( 5.808 X 10 26 ) / (3.828 × 10 26 ) = 1.5174 If you did everything right, your answer to the last question should be about 1.5. Now do the same calculation for: Betelgeuse, the red star that is the left shoulder of the constellation Orion: Brightness = 9.90 × 10 - 8 watts/m 2 Distance = 6.08 × 10 18 m 3. (Luminosity of Betelgeuse / Luminosity of Sun) = (4.6 X 10 31 ) / (3.828 X 10 26 ) =1.2 X 10 5

Rigel, the blue star that is the right knee of the constellation Orion: Brightness = 5.68 × 10 - 8 watts/m 2 Distance = 8.02 × 10 18 m 4. (Luminosity of Rigel / Luminosity of Sun) = (4.7 X 10 31 )/ (3.828 X 10 26 )=1.23 X 10 5 Sirius b, a faint blue star that is a binary companion to the bright star Sirius: Brightness = 1.20 × 10 - 10 watts/m 2 Distance = 8.14 × 10 16 m 5. (Luminosity of Sirius b / Luminosity of Sun) = ( 1 X 10 25 )/ (3.828 X 10 26 ) =2.6 X 10 -2 Part 2: Making an H-R diagram The table below lists the color index and luminosity of 50 stars, whose distances were determined via parallax measurements using the Hipparcos satellite. Luminosities are all expressed in units of the Sun’s luminosity, i.e., an entry of 0.01 means that the star is (1/100) of the solar luminosity (100 times less luminous than the Sun). 6. Plot the positions of these 50 stars on the graph on the next page. The stars with the * next to them in the table have been plotted for you; check that you understand their locations on the plot. After you have finished the first ten stars, check your plot with your lab partner to see that you agree. Plotting these points will take some time but watch for patterns as they emerge. Color Index Luminosity Color Index Luminosity 0.89 0.2* - 0.08 77 1.02 8* 0.45 5 0.55 0.0002* 1.04 34 1.04 0.1* 1.36 0.05 1.02 0.15 0.80 18 0.74 0.3 0.61 4.6 1.10 0.1 1.14 0.1 0.50 8 0.89 27 1.42 0.08 1.62 0.0009 0.32 7.6 1.12 0.07 0.20 14 1.08 21 0.39 8.7 0.96 0.1 0.24 8.8 0.52 3.7 1.41 0.03 1.47 0.004

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0.72 2.4 0.97 0.2 0.31 13 0.77 0.3 1.08 29 0.65 1 1.02 0.2 0.69 3 0.08 58 0.86 0.6 - 0.07 58 1.07 0.2 0.50 2 0.93 29 1.03 31 0.53 9.4 0.72 0.7 0.13 27 0.36 0.0003 0.96 0.2 0.18 0.0006 0.26 0.0006

7. The color index of α Cen is 0.69. Plot it on your graph and label it. 8. The color index of Sirius b is - 0.03. Plot it on your graph and label it. 9. Where do Rigel and Betelgeuse, from part 1, appear on this diagram? Around the upper left and upper right corners. 10. Write down two things you notice about your handmade graph. Each of your observations or inferences should be written as a complete sentence: A. I can see a group of coordinates between 0.9 and 1.2. B. They all go in approximately a line with some outliers. Part 3 – Temperature, Area, and Luminosity The luminosity (L) of a star depends on its temperature (T) and its radius (R) by L = 4 p R 2 s T 4  Where 4 p and s are numbers, not variables. Think of them like the ‘G’ in the formula for the force due to gravity.  4 p R 2 is the surface area of a sphere.  s T 4 is the amount of flux given off by a hot opaque object (a blackbody) per surface area. You can just take this formula as given, it’s a basic result of thermodynamics. This equation tells us:  If two stars have the same temperature (same color index), the larger star is more luminous.  If two stars have the same radius, the hotter (bluer) star is more luminous. 11. With this information in mind, label the four corners of the H-R diagram (the one on which you plotted points by hand) to indicate where you find the stars corresponding to the list below.  hot and large radius – upper left  hot and small radius - bottom left  cool and large radius – upper right  cool and small radius – bottom right 12. Based on the H-R diagram, what do you think is the approximate color index of the Sun? Explain your answer in a complete sentence.

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I think the approximate color index of the sun would be around 0.7. 13. On your hand-plotted H-R diagram, mark and label (A, B, C) the location of a hypothetical star that is A. the same luminosity as the Sun but has a cooler surface temperature B. the same temperature as the Sun but has a larger radius C. the same luminosity as the Sun but has a smaller radius Part 4: Making sense of the H-R diagram The next graph has 1500 stars on it instead of 50, so that you can see more details. Spend a few minutes discussing this plot with your lab partner.

14. Write down 2 more qualitative observations or inferences about things you and your partner notice in the H-R diagram. Part 3 may help you make new deductions. Each of these observations should be expressed as a complete sentence. A. The stars relatively lie in a line with a slight jump around 1.3 color index. B. There are clusters of outlying stars. Part 5: Spectral Lines We use light to measure all sorts of things about astronomical objects and the “spectrum” of an object is a basic way to look at its light. In this part of the lab, you will draw a spectrum based on more observations of the arc lamps with your spectrometer tool, your diffraction glasses. Compare 3 different spectral tubes of the elements Hydrogen, Helium, and Neon wearing your diffraction glasses. A. Describe in a sentence or two what you see when observing Hydrogen. I observed the colors red and blue showing up. B. Compare in a sentence or two what you see comparing Hydrogen to the other two elements. Helium showed most of the colors, neon only showed red, and hydrogen had red and blue. C. Knowing what you know already from this course, what color(s) would you expect to see when you look out into the Universe and see hot gasses? In addition, write 2-3 sentences about why spectra are important to understanding the space and the objects around us. I think we could see reds and blues from hot gasses, like what we saw from the helium, hydrogen, and neon. Spectra is important because it can provide us with lots of information. We can understand temperature, density, composition, and more.