Understanding Our Universe
3rd Edition
ISBN: 9780393614428
Author: PALEN, Stacy, Kay, Laura, Blumenthal, George (george Ray)
Publisher: W.w. Norton & Company,
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Chapter 15, Problem 43QAP
To determine
The time most massive stars will explode.
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Question 41
.Suppose you are looking at H-R diagrams of two similar star clusters. The most luminous main
sequence stars in the Porcini cluster are much more luminous than the most luminous main
sequence stars in the Morel cluster. What can you conclude?
O the Porcini cluster is younger than the Morel cluster
O the Porcini cluster is farther away than the Morel cluster
O the Porcini cluster is lower in metallicity than the Morel cluster
O the Porcini cluster is larger in diameter than the Morel cluster
If the RR Lyrae stars in a globular cluster have average apparent magnitudes of +19, how far away (in pc) is the cluster? (Hints: See the following figure, and use the magnitude-distance formula: d = 10(mv - My+5)/5.)
Туре
(Classical)
Cepheids
104
103
Туре II
Cepheids
102
RR Lyrae stars
0.3
1
10
30
100
Pulsation perlod (days)
pc
Absolute magnitude
Luminosity, L L.
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 4 M⊙ would have a luminosity of ______ L⊙.
If a star has a radius 1/2 that of the Sun and a temperature 4 that of the Sun, how many times higher is the star's luminosity than that of the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125)
If a star has a radius 2 times larger than the Sun's and a luminosity 1/4th that of the Sun, how many times higher is the star's temperature than that of the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125)
If a star has a surface temperature 2 times lower than the Sun's and a luminosity the same as the Sun, how many times larger is the star than the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125)
Chapter 15 Solutions
Understanding Our Universe
Ch. 15.1 - Prob. 15.1CYUCh. 15.2 - Prob. 15.2CYUCh. 15.3 - Prob. 15.3CYUCh. 15.4 - Prob. 15.4CYUCh. 15 - Prob. 1QAPCh. 15 - Prob. 2QAPCh. 15 - Prob. 3QAPCh. 15 - Prob. 4QAPCh. 15 - Prob. 5QAPCh. 15 - Prob. 6QAP
Ch. 15 - Prob. 7QAPCh. 15 - Prob. 8QAPCh. 15 - Prob. 9QAPCh. 15 - Prob. 10QAPCh. 15 - Prob. 11QAPCh. 15 - Prob. 12QAPCh. 15 - Prob. 13QAPCh. 15 - Prob. 14QAPCh. 15 - Prob. 15QAPCh. 15 - Prob. 16QAPCh. 15 - Prob. 17QAPCh. 15 - Prob. 18QAPCh. 15 - Prob. 19QAPCh. 15 - Prob. 20QAPCh. 15 - Prob. 21QAPCh. 15 - Prob. 22QAPCh. 15 - Prob. 23QAPCh. 15 - Prob. 24QAPCh. 15 - Prob. 25QAPCh. 15 - Prob. 26QAPCh. 15 - Prob. 27QAPCh. 15 - Prob. 28QAPCh. 15 - Prob. 29QAPCh. 15 - Prob. 30QAPCh. 15 - Prob. 31QAPCh. 15 - Prob. 32QAPCh. 15 - Prob. 33QAPCh. 15 - Prob. 34QAPCh. 15 - Prob. 35QAPCh. 15 - Prob. 36QAPCh. 15 - Prob. 37QAPCh. 15 - Prob. 38QAPCh. 15 - Prob. 39QAPCh. 15 - Prob. 40QAPCh. 15 - Prob. 41QAPCh. 15 - Prob. 42QAPCh. 15 - Prob. 43QAPCh. 15 - Prob. 44QAPCh. 15 - Prob. 45QAP
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- You can use the equation in Exercise 22.34 to estimate the approximate ages of the clusters in Figure 22.10, Figure 22.12, and Figure 22.13. Use the information in the figures to determine the luminosity of the most massive star still on the main sequence. Now use the data in Table 18.3 to estimate the mass of this star. Then calculate the age of the cluster. This method is similar to the procedure used by astronomers to obtain the ages of clusters, except that they use actual data and model calculations rather than simply making estimates from a drawing. How do your ages compare with the ages in the text? Figure 22.10 NGC 2264 HR Diagram. Compare this HR diagram to that in Figure 22.8; although the points scatter a bit more here, the theoretical and observational diagrams are remarkably, and satisfyingly, similar. Figure 22.12 Cluster M41. (a) Cluster M41 is older than NGC 2264 (see Figure 22.10) and contains several red giants. Some of its more massive stars are no longer close to the zero-age main sequence (red line). (b) This ground-based photograph shows the open cluster M41. Note that it contains several orange-color stars. These are stars that have exhausted hydrogen in their centers, and have swelled up to become red giants. (credit b: modification of work by NOAO/AURA/NSF) Figure 22.13 HR Diagram for an Older Cluster. We see the HR diagram for a hypothetical older cluster at an age of 4.24 billion years. Note that most of the stars on the upper part of the main sequence have turned off toward the red-giant region. And the most massive stars in the cluster have already died and are no longer on the diagram. Characteristics of Main-Sequence Starsarrow_forwardIf the Sun were a member of the cluster NGC 2264, would it be on the main sequence yet? Why or why not?arrow_forwardExplain how an HR diagram of the stars in a cluster can be used to determine the age of the cluster.arrow_forward
- You have discovered two star clusters. The first cluster contains mainly main-sequence stars, along with some red giant stars and a few white dwarfs. The second cluster also contains mainly main-sequence stars, along with some red giant stars, and a few neutron stars-but no white dwarf stars. What are the relative ages of the clusters? How did you determine your answer?arrow_forwardIn the HR diagrams for some young clusters, stars of both very low and very high luminosity are off to the right of the main sequence, whereas those of intermediate luminosity are on the main sequence. Can you offer an explanation for that? Sketch an HR diagram for such a cluster.arrow_forwardAccording to the text, a star must be hotter than about 25,000 K to produce an H II region. Both the hottest white dwarfs and main-sequence O stars have temperatures hotter than 25,000 K. Which type of star can ionize more hydrogen? Why?arrow_forward
- If we plot the apparent brightnesses of stars in a globular cluster versus their surface temperatures in a similar way as in the HR diagram , there will be a horizontal branch . Which of the following statements about these horizontal branch stars is wrong ? (A)They have the same absolute magnitude . (B)They have different sizes . (C)Their sole source of energy is hydrogen shell burning . (D)They can help us estimate the distance of the globular cluster from us .arrow_forwardA star population is composed of stars with masses in the range between 1M and 150M. The initial mass function is = (M/M)-2.3, where = (Mo). The luminosity of a star scales with its mass as L/L = (M/M) 3.3. Calculate the percentage of the total luminosity of the stars in the population which is produced by stars with mass between 120M and 150M.arrow_forwardConsider two different clusters with approximately the same turnoff luminosity. Cluster A has a main sequence 0.5 magnitudes bluer than cluster B. What property is different between clusters A and B? Explain the physical process that makes the stars of cluster A bluer.arrow_forward
- The sketch below shows an H-R diagram for a star cluster. Consider the star to which the arrow points. How is it currently generating energy? Temperature A. by hydrogen shell burning around an inert helium core B. by gravitational contraction C. by core hydrogen fusion D.by core helium fusion combined with hydrogen shell burning E. by both hydrogen and helium shell burning around an inert carbon core Luminosity -→arrow_forwardFor the PP chain 0.7% of the mass participating in nuclear fusion is liberated as energy which produces a star's luminosity. Assume that the core of a main sequence star consists of 10% of its total mass. Hence, estimate the lifetime of a star on the main sequence in terms of its luminosity L/L. Give your answer in years. You may use the observed mass-luminosity relation L x M³.5, where M is the star's total mass. Using typical values, calculate estimates for the main sequence lifetime of a KO star and a 05 star. Describe briefly why your estimate might be more accurate for K stars compared to O stars.arrow_forwardIf an open cluster contains 500 stars and is 25 pc in diameter, what is the average distance between the stars?arrow_forward
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