Lab 6 HR Diagram

The H-R Diagram Background Information Work through the background material on Spectral Classification, Luminosity, and the Hertzsprung-Russell Diagram. Then complete the following questions related to the background information. Remember to type your answer in blue text. Question 1: The table below summarizes the relationship between spectral type, temperature, and color for stars. Fill in the blank boxes using the simulator found under the Spectral Classification link in the background material. Question 2: Complete the following table related to stellar luminosities. All units are expressed in terms of the sun, or in solar units. Remember that luminosity is proportional to radius squared and temperature to the fourth power. ( L = R 2 T 4 w hen solarunitsare used ). Star Surface Temperature K Spectral Type Color Betelguese 3,530 M2 Orange Arcturus 4,300 K5 Yellow Sun 5,830 G2 Yellow Procyon A 6530 F5 Yellow-White Sirius A 9,145 A1 White Rigel A 11,000 B9 White-Blue Delta Orionis 33,200 O9 Blue Radius (R ⊙ ) Temperature (T ⊙ ) Luminosity (L ⊙ ) 2 1 4 2 2 64 4 1 16 1/2 1/2 0.015625

Question 3: The mass luminosity relation describes the mathematical relationship between luminosity and mass for main sequence stars. It describes how a star with a mass of 3 M ⊙ would have a luminosity of   L ⊙ , while a star with luminosity of 35,780 L ⊙ would have an approximate mass of   M ⊙. H-R Diagram Explorer Open the H-R Diagram Explorer . Begin by familiarizing yourself with the capabilities of the Hertzsprung- Russell Diagram Explorer through experimentation.  An actual H-R 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 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.  Drag the active location around on the H-R 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: Check one box in each row of the table below that corresponds to appropriate region of the H-R diagram. Question 1: Question 2: Description Top Right Bottom Left Faint stars are found at the: X Luminous stars are found at the: X Hot stars are found at the: X Cool stars are found at the: X

The background page on the Hertzsprung-Russell Diagram detailed the mass-luminosity relationship for stars on the main sequence: Question 7: Note how Luminosity changes on the H-R diagram. What can you conclude about the relative masses of stars as you go from the bottom to the top of the main sequence? Question 8: Uncheck show luminosity classes and check show instability strip . Note that this region of the H-R Diagram indicates where pulsating (variable) stars are found, which are extremely important for finding distances. These stars vary in brightness because they are pulsating – alternately growing bigger and smaller – which changes their radii and surface temperatures and resulting luminosities. Question 8: Describe the characteristics of stars that are found in the instability strip. You should describe their range of temperatures, colors, luminosities, and sizes. (Comparing them to the sun is useful.) What name do we have for variable stars near the bottom of the instability strip? What name do we have for variable stars near the top of the instability strip? Question 4: The star grows by 3.5 in mass as the luminosity increases. Like the background information stated in the lab, the stars that are above the main sequence have a chance of collapsing and the stars below the main sequence have a chance of blowing apart. Uncheck show luminosity classes and check show instability strip . Note that this region of the H-R Diagram indicates where pulsating (variable) stars are found, which are extremely important for finding distances. These stars vary in brightness because they are pulsating - alternately growing bigger and smaller - which changes their radii and surface temperatures and resulting luminosities. Question 5: The name for variable stars near the bottom of the instability strip are giants (red giants), the name that we have for variable stars near the top of the instability strip are called super giants (blue giants). The luminosities range from about 20-1800, the colors are blue. The temperature range is from 5100k to 8500k. The sizes of these stars are a significant amount bigger than the sun.

L Question 9: Use the results from the previous questions to construct a “conceptual” H-R Diagram. Use the Arrow drawing tool in Shapes under the Insert tab to draw arrows showing the direction in which variables are increasing. Use the Scribble drawing tool or insert a text box to label each of the arrows. a) Draw and label (with an L) an arrow on the y axis showing the direction of increasing luminosity of the stars. (This has been completed for you.) b) Draw and label (with a T) an arrow on the x-axis showing the direction of increasing surface temperature of the stars. c) Draw and label (with an R) an arrow showing the direction of increasing radius on the diagram. (hint: this must be perpendicular to the isoradius lines.) d) Draw and label (with an M) an arrow showing the direction of increasing mass for main sequence stars on the diagram. Figure 1: Conceptual H-R Diagram

Question 13: Do you think that these brightest stars are very common (do they make up a large percentage of all stars in our galaxy)? Explain your reasoning . Summary/Conclusion (5 points): Roughly 90% of all stars lie along the main sequence but, depending on their position on the H-R diagram, they spend drastically different amounts of time on the main sequence. Explain why bright stars spend a relatively short amount of time on the main sequence, why dim stars spend a very long time on the main sequence, and how this affects the relative numbers of bright and dim stars found in our galaxy. Question 9: The brightest stars are not very common and do not make up a large percentage of all stars in our galaxy. This is because the majority of stars, about 90%, lie along the main sequence. However, the time a star spends on the main sequence depends on its mass. High-mass stars are brighter, but they burn through their fuel much faster, so they spend less time on the main sequence. On the other hand, low-mass stars are less bright, but they burn their fuel more slowly, so they spend a longer time on the main sequence. Therefore, while the brightest stars are noticeable and significant, they are not the most common type of star in our galaxy. The most common stars are those along the main sequence, with a wide range of brightness levels. The lifespan of a star on the main sequence is determined by its mass and the rate at which it consumes its hydrogen fuel. Bright stars, which are more massive, have a higher pressure and temperature at their cores, leading to a faster rate of nuclear fusion. This rapid fusion process causes them to burn through their hydrogen fuel quickly, resulting in a shorter lifespan on the main sequence. On the other hand, dim stars, which are less massive, have lower core pressure and temperature. This results in a slower rate of nuclear fusion, allowing them to consume their hydrogen fuel at a much slower pace. Consequently, they spend a longer time on the main sequence. The relative numbers of bright and dim stars in our galaxy are affected by these lifespans. Since bright stars burn out quickly, they are less common in the galaxy. Conversely, dim stars, due to their longer lifespans, are more abundant. This is why, despite the fact that bright stars are easier to see, dim stars (like red dwarfs) are actually the most common type of star in our galaxy.