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 37QAP
To determine
The percentage loss in the mass of O star during its main-sequence lifetime.
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If an X-ray binary consists of a 17-solar-mass star and a neutron star orbiting each other every 23.2 days, what is their average separation? (Hints: Use the version of Kepler's third law for binary stars,
MA + MB = a^3/p^2
make sure you express quantities in units of AU, solar masses, and years. Assume the mass of the neutron star is 1.4 solar masses.)
What is the free-fall time of a 10 MSun main-sequence star?
O 100 hours
O 10 hours
O 1 hour
O 0.1 hours
One 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?
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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- According 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_forwardBefore the star that became SN 1987A exploded, it evolved from a red supergiant to a blue supergiant while remaining at the same luminosity. As a red supergiant, its surface temperature would have been approximately 4000 K, while as a blue supergiant, its surface temperature was 16,000 K. How much did the radius change as it evolved from a red to a blue supergiant?arrow_forwardIf a 3 and 8 MSunstar formed together in a binary system, which star would: A. Evolve off the main sequence first? B. Form a carbon- and oxygen-rich white dwarf? C. Be the location for a nova explosion?arrow_forward
- What physical properties are different for an M giant with a luminosity of 1000 LSunand an M dwarf with a luminosity of 0.5 LSun? What physical properties are the same?arrow_forwardWhat is the radius of the progenitor star that became SN 1987A? Its luminosity was 100,000 times that of the Sun, and it had a surface temperature of 16,000 K.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_forward
- If an X-ray binary consists of a 16 solar mass star and a neutron Star orbiting each other every 15.4 days, what is their average separation? (Hint: Use the version of Keller's third law for binary stars, Ma + Mb = a^3 /p^2 ; make sure you express quantities in unites of AU, solar masses, and years. Assume the mass of a neutron Star is 1.6 solar masses.) ___________ AUarrow_forwardThe 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_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
- 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.arrow_forwardA 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: 3679arrow_forwardIf a neutron Star has a radius of 12 km and a temperature of 8.0 x 10^6 K, how luminous is it? Express your answer in watts and also in solar luminosity units. (Hint: Use the relation L/L= (R/R)^2(T/T)^4 . Use 5,800 K for the surface temperature of the Sun. The luminosity of the sun is 3.83 x 10^26W) luminosity in watts ________ W luminosity in solar luminosity units ______ Larrow_forward
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