Wk07-HR_Diagram_Intro_Worksheet

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 ÷ (4 π × 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 × (4 π × 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 = 5.8 x 10^34 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) = 1.5 x 10^8 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) = 1.19 x 10^25 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) = 119931981 Sirius b, a faint blue star that is a binary companion to the bright star Sirius: Brightness = 1.20 × 10 − 10 watts/m 2

0.24 8.8 0.52 3.7 1.41 0.03 1.47 0.004 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

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. I think that the sun will be in the middle with t the average 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. We can see the shape at the H-R B. It has an even amount of outliers 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 see a more red, orange and darker colors involved. B. Compare in a sentence or two what you see comparing Hydrogen to the other two elements. That the other element, are more compatible since they have more electrons. The more electrons the more color. 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. Spectra allows us to identify what kinds of elements, exist around us. It allows us to tell if a planet with a star can Bring about life. The color will be more red and orange and dark colors as it totals more helium and other elements.