2023 Woksheet - HR Diagrams

Worksheet — Hertzsprung-Russell Diagrams Page 1 of 8 Astronomy BPHYS 101 Worksheet — Hertzsprung-Russell Diagrams Identify Yourself (LIMIT 3 PEOPLE) Background Information Read through the background sections on Spectral Classification , Luminosity , and the Hertzsprung - Russell Diagram . (Links to these are on the Canvas page for this assignment.) Then complete the following questions related to the background information. Question 1: (Refer to the Spectral Classification webpage) The table below summarizes the relationship between spectral type, temperature, and color for stars. The stars in this table are arranged in order of increasing surface temperature. Star Surface Temperature [kelvin] Spectral Type Color Betelgeuse M2 Arcturus 4,300 G2 Yellow Procyon A F5 Yellow-White Sirius A A1 White Rigel A 11,000 Delta Orionis O9 Question 2: (Refer to the Luminosity webpage) Complete the following table related to stellar luminosities in solar units using the proportionality relationship ? ∝ 𝑅 2 𝑇 4 . When working in solar units ( 𝑅 ⨀ , 𝑇 ⨀ , ? ⨀ ), the relationship is ? = 𝑅 2 𝑇 4 . Radius [ 𝑅 ⨀ ] Temperature [ 𝑇 ⨀ ] Luminosity [ ? ⨀ ] 1 1 1 2 1 9 1 0.5 Name 1: Name 2: Name 3:

Worksheet — Hertzsprung-Russell Diagrams Page 2 of 8 Question 3: The mass-luminosity relation ? ∝ ? 3.5 describes the mathematical relationship between luminosity and mass for main sequence stars. Complete the table below. When working in solar units ( ? ⨀ , ? ⨀ ), the relationship is ? = ? 3.5 . Luminosity [ ? ⨀ .] Mass [ ? ⨀ .] 3160 2 HR Diagram Explorer Open the HR Diagram Explorer . Begin by familiarizing yourself with the capabilities of the Hertzsprung - Russell diagram Explorer through experimentation. An 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, BV, 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. Exercises Drag the active location around on the HR Diagram. Note the resulting changes in the temperature and luminosity sliders. Now manipulate the temperature and luminosity sliders and note the corresponding change in the active location. Question 4: Mark ( ✓ ) the region of the HR diagram corresponding to each description below. Description Top Right Bottom Left Hot stars are found at the: Faint stars are found at the: Luminous stars are found at the: Cool stars are found at the:

Worksheet — Hertzsprung-Russell Diagrams Page 4 of 8 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: ? ∝ ? 3.5 Question 8: What can you conclude about the masses of stars along the main sequence?

Worksheet — Hertzsprung-Russell Diagrams Page 5 of 8 Question 9: Use the results from the previous questions to construct a “conceptual” HR Diagram. You simply want to draw arrows showing the direction in which variables are increasing. a) Draw an arrow on the vertical- axis showing the direction of increasing “intrinsic luminosity” of the stars. (This is complete for you.) b) Draw an arrow on the horizontal-axis showing the direction of increasing surface temperature of the stars. c) Draw an arrow showing the direction of increasing radius on the diagram. (Hint: This must be perpendicular to the isoradius lines.) d) Draw an arrow showing the direction of increasing mass for main sequence stars on the diagram. (Note that this arrow only applies to main sequence stars, but that is over 90% of stars.) 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 the resulting 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?

Worksheet — Hertzsprung-Russell Diagrams Page 7 of 8 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. Deriving the Isoradius Lines The HR Diagram is a log-log plot of the solar units equation ? = 𝑅 2 𝑇 4 Question 15: 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 ? [ ? ⨀ ] 𝑅 [ 𝑅 ⨀ ] 𝑇 [ 𝑇 ⨀ ] × 1 1 1 A 1 √10 4 B 1 0.5 C 10 1 D 1000 10 E 10 √10 F 100 1 G 100 2 H 100 0.5

Worksheet — Hertzsprung-Russell Diagrams Page 8 of 8 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000 1000000 0.1 1 10 Luminosity 𝐿 [ 𝐿 ⨀ ] Temperature T [ T ⨀ ] Hertzsprung - Russell Diagram (Axes expressed in Solar Units)