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 13, Problem 22QAP
To determine
The reason for high-mass star to not become degenerate.
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A red giant star might have radius = 104 times the solar radius,
and luminosity = 1730 times solar luminosity.
Use the data given below to calculate the temperature
at the surface of the red giant star.
Data:
solar radius R = 7 x 108 meters
solar luminosity L = 4 x 1026 watts
Stefan-Boltzmann constant
a = 5.67 x 10-8 W m² K-4
(in K)
A: 1226 OB: 1434 OC: 1678 OD: 1963 OE: 2297 OF: 2688 OG: 3145 OH: 3679
For 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.
What are the main products of the fusion reactions that take place in low mass main sequence stars?
Chapter 13 Solutions
Understanding Our Universe
Ch. 13.1 - Prob. 13.1CYUCh. 13.2 - Prob. 13.2CYUCh. 13.3 - Prob. 13.3CYUCh. 13.4 - Prob. 13.4CYUCh. 13.5 - Prob. 13.5CYUCh. 13.6 - Prob. 13.6CYUCh. 13 - Prob. 1QAPCh. 13 - Prob. 2QAPCh. 13 - Prob. 3QAPCh. 13 - Prob. 4QAP
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- If a 100 solar mass star were to have a luminosity of 107 times the Sun’s luminosity, how would such a star’s density compare when it is on the main sequence as an O-type star, and when it is a cool supergiant (M-type)? Use values of temperature from Figure 18.14 or Figure 18.15 and the relationship between luminosity, radius, and temperature as given in Exercise 18.47. Figure 18.15 Schematic HR Diagram for Many Stars. Ninety percent of all stars on such a diagram fall along a narrow band called the main sequence. A minority of stars are found in the upper right; they are both cool (and hence red) and bright, and must be giants. Some stars fall in the lower left of the diagram; they are both hot and dim, and must be white dwarfs. Figure 18.14 HR Diagram for a Selected Sample of Stars. In such diagrams, luminosity is plotted along the vertical axis. Along the horizontal axis, we can plot either temperature or spectral type (also sometimes called spectral class). Several of the brightest stars are identified by name. Most stars fall on the main sequence.arrow_forwardBetelgeuse is a nearby supergiant that will eventually explode into a supernova. Let's see how awesome it would look. At peak brightness, the supernova will have a luminosity of about 10 billion times the Sun. It is 600 light-years away. All stellar brightnesses are compared with Vega, which has an intrinsic luminosity of about 60 times the Sun, a distance of 25 light-years, an absolute magnitude of 0.6 and an apparent magnitude of 0 (by definition). a) At peak brightness, how many times brighter will Betelgeuse be than Vega? b) Approximately what apparent magnitude does this correspond to? c) The Sun is about -26.5 apparent magnitude. What fraction of the Sun's brightness will Betelgeuse be?arrow_forwardObservations show that stellar luminosity, L, and mass, M, are related by L x M3.5 for main sequence stars. Obtain an expression that relates the main sequence life time and the mass of a star. You should assume that the luminosity is constant throughout a star's main sequence life time, and that the amount of mass converted into energy by a star while it is on the main sequence is given by AM main sequence life time of a 20 Solar mass star given that the Sun is expected to spend 1010 years on the main sequence. Comment on the significance of your answer. fM, where f is a constant. Estimate thearrow_forward
- 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)arrow_forwardQUESTION 16 Use the figure shown below to complete the following statement: A low-mass protostar (0.5 to 8M the mass compared to our sun) remains roughly constant in decreases in until it makes a turn towards the main sequence, as it follows its evolutionary track. Protostars of different masses follow diferent paths on their way to the main sequence. 107 Luminosity (L) 10 105 10 107 10² 101 1 10-1 10-2 10-3 Spectral type 0.01 R 0.001 Re 60 M MAIN SEQUENCE 40,000 30,000 20 Mau 10 Mgun 5 Mun 0.1 Run Ren radius; temperature luminosity; radius 3 Min. 05 BO temperature; luminosity Oluminosity: temperature radius: luminosity 1 M 10,000 6000 Surlace temperature (K) 1,000 Rs 2 M STAR L 0.8 M B5 AO FOGO КБ МБ -10 +10 3000 Absolute visual magnitude andarrow_forwardFor a main sequence star with luminosity L, how many kilograms of hydrogen is being converted into helium per second? Use the formula that you derive to estimate the mass of hydrogen atoms that are converted into helium in the interior of the sun (LSun = 3.9 x 1026 W). (Note: the mass of a hydrogen atom is 1 mproton and the mass of a helium atom is 3.97 mproton. You need four hydrogen nuclei to form one helium nucleus.)arrow_forward
- A 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_forwardUsing solar units, we find that a star has 4 times the luminosity of the Sun, a mass 1.25 times the mass of the Sun, and a surface temperature of 4090 K (take the Sun's surface temperature to be 5784 K for the sake of this problem). This means the star has a radius of.................... solar radii and is a .................... star (use the classification).arrow_forwardIn the H-R diagram we see that stellar masses__________ downward along the main sequence. At the upper end of the main sequence, the hot, luminous O stars can have masses as high as _________ or more times that of the Sun. On the lower end, cool, dim M stars may have as little as __________ times the mass of the Sun. Many more stars fall on the lower end of the main sequence than on the upper end, which tells us that _________stars are much more common than __________ stars.arrow_forward
- QUESTION 21 In a Type Ia supernova, the cause of the violent outburst is: 1) the sudden emission of a shell of stellar material from a dying low-mass star 2) the collapse of a very massive protostar to the main sequence 3) an enormous release of neutrinos during a sudden episode of hydrogen fusion 4) the transfer of so much mass from a companion star that a white dwarf goes "over the limit" and collapses, causing an enormous amount of sudden fusion 5) two neutron stars colliding with each otherarrow_forwardOne way to calculate the radius of a star is to use its luminosity and temperature and assume that the star radiates approximately like a blackbody. Astronomers have measured the characteristics of central stars of planetary nebulae and have found that a typical central star is 16 times as luminous and 20 times as hot (about 110,000 K) as the Sun. Find the radius in terms of the Sun’s. How does this radius compare with that of a typical white dwarf?arrow_forwardWhy massive stars are short lived?arrow_forward
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