Lab_9__Stars_and_Selection_Effects_S24

Lab 9: Stars and Selection Effects Name: Group Name: Lab 9: Stars and Selection Effects Open the NAAP Labs application, and then open 9. Hertzprung-Russell Diagram . PART A - 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. A1. The table below summarizes the relationship between spectral type, temperature, and color for stars. Fill in the blanks, noting that the surface temperature of the stars in the table increases as you move downward. (3 pts) Star Surface Temperature (K) Spectral Type Color Betelguese M2 Arcturus 4,300 Sun G2 Yellow Procyon A F5 Yellow-White Sirius A A1 Rigel A 11,000 Delta Orionis O9 1

Lab 9: Stars and Selection Effects A2. Complete the following table related to stellar radius, surface temperature, and luminosity (all in solar units) using the equation . Show your work in the space below. See the next page for some math hints that may be useful. (4 pts) Radius (R ⊙ ) Temperature (T ⊙ ) Luminosity (L ⊙ ) 1 1 1 1 2 1 9 1 1/2 2 64 2

Lab 9: Stars and Selection Effects Math Hint: If y ∝ x 4 , you can invert the proportionality to find that x ∝ y 1/4 . Math Hint: The “ ∝ ” sign means proportional to. Let’s take the example of y ∝ x 4 . This is shorthand for ‘y scales with x 4 , and there is a constant of proportionality A such that y = A x 4 , but we don’t need to worry about the value of A for our purposes today”. Let’s say you know that x 1 = 2 and y 1 = 32. We also know that x 2 = 3, and we want to know what y 2 is. You can set up the problem as: By using ratios in this way, the constant of proportionality cancels out! Solve for y 2 and then substitute in values for x 1 , x 2 , and y 1 : A3. The mass luminosity relation describes the mathematical relationship between luminosity and mass for main sequence stars (that is—adult stars that are fusing Hydrogen in their cores). The sun is a main-sequence star with 1 M ⊙ and 1 L ⊙ . The mass-luminosity relation then implies that a main-sequence star with a mass of 2 M ⊙ would have a luminosity of (don’t forget your units! Show your work!; 1 pt): 3

Lab 9: Stars and Selection Effects A4. Meanwhile a main-sequence star with luminosity of 3,160 L ⊙ would have an approximate mass of: (1 pt) PART B - HR Diagram Explorer In the NAAP Labs application, 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 and y-axis —we’ll leave these at defaults today. 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 being 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. 4