Lab 7 HR Diagram 2

Name: NAAP – HR Diagram Explorer 1/9 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  . Star Surface Temperature K Spectral Type Color Betelguese M2 Arcturus 4,300 G2 Yellow Procyon A F5 Yellow-White Sirius A A1 White Rigel A 11,000 Delta Orionis O9 Radius (R ⊙ ) Temperature (T ⊙ ) Luminosity (L ⊙ ) 1 1 1 2 1 9 1 1/2 Eden Adams 8,388aass classy 4,388 3888 m're pay 3,948 101700 101045 sis.osa.is 0 88 3,500K oramge KS alphacentmi A 5,800K 6,500k 9,100K 138 Light Blue 33,000K Blue I 16 3 1116

NAAP – HR Diagram Explorer 2/9 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 _____________ L ⊙ while a star with luminosity of 3,160 L ⊙ would have an approximate mass of ________________ 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. 11.31 10

NAAP – HR Diagram Explorer 4/9 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.  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?  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? 2 4 4 L R T    3.5 L M  This equation states that the total luminosity radiated per unit surface area is equal to the temperature T tothe 4th Power Ta and the surface area of the star 417123 This explains howvariation in temp radius a luminosity are related which determines the type of star foundin different regions of the HR diagram like the table above Near the top of themain sequence stars have alarge radiust high temp large blue Near the middle of the main sequence stars have a medium radius t med temp midsize white At the bottom of the main sequence stars haveasmall radius t low temp small red The mass of stars along the main sequence vary greatly with moremassive stars around the top t less massive starsalong the bottom

NAAP – HR Diagram Explorer 5/9 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.) Figure 1: Conceptual HR Diagram L 9 r i didnt radius increasing mass for main sequence stars Infamy ng surface

NAAP – HR Diagram Explorer 7/9 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.) 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. Based on the fact that there is hardly any overlap between the brightest t nearest stars onthe HR diagram I support theanswer of Student B The brightest starshave high luminosity andallthe closest starsto us have muchlower luminosity are not considered as bright These bright stars fall pretty close to themain sequence line which includes about 9090 of all stars so I wouldn't say these stars are uncommon but they definitely don't make up most of the stars in the galaxy

NAAP – HR Diagram Explorer 8/9 Deriving the Isoradius Lines (optional, mathematical section) Question 15: The HR Diagram is a log-log plot of the solar units equation L=R 2 T 4 . Use the boxed equations to argue that isoradius lines on the HR Diagram must be parallel lines. Question 16: Complete the table below. Then add the points to the following HR Diagram and use them to draw in the isoradius lines for 1, 10, and 100 solar radii. Symbol L (L u ) R (R u ) T (T u ) x 1 1 1 A 1 4 10 B 1 10 C 10 1 D 1,000 10 E 10 10 F 100 1 G 100 2 H 100 0.5 2 4 2 4 2 4 ( ) 2 4 L R T log L log R T log L log R logT log L log R logT      