HR Diagram

HR Diagram – Student Guide Background Information Work through the background sections on Spectral Classification, Luminosity, and the Hertzsprung-Russell Diagram. Then complete the following questions related to the background information. Question 1: The table below summarizes the relationship between spectral type, temperature, and color for stars. Note that the surface temperature of the stars in the table increases. Question 2: Complete the following table related to stellar luminosities in solar units using the equation 2 4 L R T  . NAAP – HR Diagram Explorer 1/9 Star Surface Temperature K Spectral Type Color Betelguese 3530 M2 Red Arcturus 4,300 K5 Orange Sun 5830 G2 Yellow Procyon A 6530 F5 Yellow-White Sirius A 9145 A1 White Rigel A 11,000 B9 White Delta Orionis 33200 O9 Blue Radius (R ⊙ ) Temperature (T ⊙ ) Luminosity (L ⊙ ) 1 1 1 1 2 16.8 3 1 9 1 1/2 .057

Question 3: The mass luminosity relation 3.5 L M  describes the mathematical relationship between luminosity and mass for main sequence stars. It describes how a star with a mass of 2 M ⊙ would have a luminosity of ______11.31371_______ L ⊙ while a star with luminosity of 3,160 L ⊙ would have an approximate mass of _______10_________ M ⊙. HR Diagram Explorer Open the HR Diagram Explorer . Begin by familiarizing yourself with the capabilities of the Hertzsprung-Russell Diagram Explorer through experimentation.  An actual HR Diagram is provided in the upper right panel with an active location indicated by a red x. This active location can be dragged around the diagram. The options panel allows you to control the variables plotted on the x-axis: (temperature, B- V, or spectral type) and those plotted on the y-axis (luminosity or absolute magnitude). One can also show the main sequence, luminosity classes, isoradius lines, or the instability strip. The Plotted Stars panel allows you to add various groups of stars to the diagram.  The Cursor Properties panel has sliders for the temperature and luminosity of the active location on the HR Diagram. These can control the values of the active location or move in response to the active location begin dragged. The temperature and luminosity (in solar units) are used to solve for the radius of a star at the active location.  The Size Comparison panel in the upper left illustrates the star corresponding to the active location on the HR Diagram. Note that the size of the sun remains constant. NAAP – HR Diagram Explorer 2/9

Question 6: The equation below describes the luminosity of a star in terms of its radius and temperature. Use this equation to explain the results you found in the table of the previous question. Stars can have the same surface temperature, but can vary in size and Lumosity. Stars in the lower left of the diagram may be as small as .00010 the size of the Sun and still have the same very high temperature as blue giants in the top left of the diagram.  In addition to the isoradius lines, check show luminosity classes . This green region (dwarfs V) is known as the main sequence and contains all stars that are fusing hydrogen into helium as their primary energy source. Over 90% of all stars fall in this region on the HR diagram. Move the active cursor up and down the main sequence and explore the different values of stellar radius. Question 7: Describe the sizes of stars along the main sequence. What are stars like near the top of the main sequence, the middle, and the bottom? Stars at the top of the main sequence have greater temperature, radius, and luminosity. These aspects gradually decline with the location of the main sequence. Stars that sit just below the middle of the main sequence have temperature, radius, and luminosity similar to our Sun. Stars at the bottom of the main sequence are the lowest temperature, radius, and luminosity of the main sequence stars. NAAP – HR Diagram Explorer 4/9 2 4 4 L R T   

L  The background pages of this module talked about the mass-luminosity relationship for stars on the main sequence: Question 8: What can you conclude about the masses of stars along the main sequence? It can be concluded that as move up the main sequence, you will find that the mass is increasing along with the luminosity. Question 9: Use the results from the previous 5 questions to construct a “conceptual” HR Diagram. You simply want to draw arrows showing the direction in which variables are increasing. a) Draw in an arrow on the y axis showing the direction of increasing “intrinsic luminosity” of the stars. (This is complete for you.) b) Draw in an arrow on the x-axis showing the direction of increasing surface temperature of the stars. c) Draw in an arrow showing the direction of increasing radius on the diagram. (hint: this must be perpendicular to the isoradius lines.) d) Draw in an arrow showing the direction of increasing mass for main sequence stars on the diagram. (Note that his arrow only applies to main sequence stars, but that is over 90% of stars.) NAAP – HR Diagram Explorer 5/9 3.5 L M 

 Uncheck show luminosity classes and check show instability strip . Note that this region of the HR Diagram indicates where pulsating stars are found such as RR Lyrae stars and Cepheid variable stars. These stars vary in brightness because they are pulsating – alternately growing bigger and smaller – which changes their radii and surface temperatures and resulting their luminosities. Question 10: Describe the characteristics of stars that are found in the instability strip. You should cover their range of temperatures, colors, luminosities, and sizes. (Hint: Comparing them to the sun is useful.) Are variable stars necessarily on the main sequence? Stars in the variable strip range in temperature from approx. 5100K to 8400K. Our own Sun sits withing this range at a temperature of 5800K. These variable stars also range in luminosity from 20 luminosity to 1600. These two factors also show that the radius of these variable stars fall between 2.3R to 48R. Variable stars in the instability strip can also fall along a small portion of the main sequence as well as red giants.  Check the plotted stars option the nearest stars . You should cover their range of temperatures, colors, luminosities, and sizes. Question 11: Describe the characteristics of the nearest stars. The nearest stars range in temperatures from 9500K to 2300K and fall along the lower half of the main sequence. These stars also have less than 29 Luminosity. Some of the colors of these stars are light blue, white, light yellow, yellow, orange and red. The smallest of these stars are around .098R while the largest is around 1.7R. Question 12: Do you think these stars are rare or very common among all of the stars of our galaxy? Explain your reasoning. Are any assumptions involved in your reasoning? I think that these stars are some of the most common of the stars as the current understood age of the universe is nearly 14 billion years old while our sun is only 4.6 billion years old. This makes be believe that most stars fall within this range due to this being the early life stages of stellar evolution. NAAP – HR Diagram Explorer 7/9

 Uncheck the plotted stars option the nearest stars and check the brightest stars . Why are these stars the brightest in the sky? Three students debate this issue: Student A: “I think it’s because these stars must be very close to us. That would make them appear brighter to us in the sky.” Student B: “I think it’s because these stars are very luminous. They are putting out a tremendous amount of energy.” Student C: “I think it’s because these stars are very close and very luminous.” Question 13: Use the tools of the HR Diagram to support the views of one of the three students. Why are the stars we perceive as bright in the night sky really bright?” (hint: You may find the options labeled both the nearest and brightest stars and the overlap useful.) I believe that Student C makes a valid point. There are stars that are very bright but are also very far away, almost compensating for their distance with luminosity. There are also stars dimmer than our own Sun, but because they are closer to us it makes them appear brighter. It would take a very distant star to have a large amount of luminosity in order to appear bright to us. This is why the bright stars fall along the upper half of the HR Diagram where their luminosity and radii are much larger than our Sun. Question 14: Do you think that these bright stars are very common (make up a large percentage of all stars in general)? Explain your reasoning. I think that these bright stars do not make up the largest percentage of all stars in general. There could be many very distant stars that have low luminosity and are therefore harder for astronomers to find. Having a distant star be extremely bright helps us be able to identify it. NAAP – HR Diagram Explorer 8/9