Foundations of Astronomy
13th Edition
ISBN: 9781305079151
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 13, Problem 24RQ
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How the life of
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A main sequence star of mass 25 M⊙has a luminosity of approximately 80,000 L⊙. a. At what rate DOES MASS VANISH as H is fused to He in the star’s core? Note: When we say “mass vanish '' what we really mean is “gets converted into energy and leaves the star as light”. Note: approximate answer: 3.55 E14 kg/s b. At what rate is H converted into He? To do this you need to take into account that for every kg of hydrogen burned, only 0.7% gets converted into energy while the rest turns into helium. Approximate answer = 5E16 kg/s c. Assuming that only the 10% of the star’s mass in the central regions will get hot enough for fusion, calculate the main sequence lifetime of the star. Put your answer in years, and compare it to the lifetime of the Sun. It should be much, much shorter. Approximate answer: 30 million years.
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.
For 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.)
Chapter 13 Solutions
Foundations of Astronomy
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- Observations 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_forwardWhy does a type II supernova explode? in two sentences.arrow_forwardQUESTION 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_forward
- A supernova’s energy is often compared to the total energy output of the Sun over its lifetime. Using the Sun’s current luminosity, calculate the total solar energy output, assuming a 1010 year main-sequence lifetime. Using Einstein’s formula E=mc2 calculate the equivalent amount of mass, expressed in Earth masses. [Hint: The total energy output of the Sun over its lifetime is given by its current luminosity times the number of seconds in a year times its ten billion-year lifetime; ; mass of earth = 6×1024kg; c = 3×108m/s. Your answer should be 200-300 Earth masses.]arrow_forwardUse t = 1 M2.5 to compute the life expectancy of a 0.6-solar-mass star. (A solar lifetime is approximately 10 billion years.) yrWhy might this be an underestimate if the star is fully mixed by convection? a) If the star is fully mixed its mass will be much larger than 0.6 solar masses. b) If the star is fully mixed its mass will be much smaller than 0.6 solar masses. c) If the star is fully mixed it will be able to use a larger portion of its hydrogen in fusion than the Sun. d) If the star is fully mixed it will be able to use a smaller portion of its hydrogen in fusion than the Sun.arrow_forwardHow is a nova different from a type Ia supernova? How does it differ from a type II supernova?arrow_forward
- How would the spectra of a type II supernova be different from a type Ia supernova? Hint: Consider the characteristics of the objects that are their source.arrow_forwardWould you be more likely to observe a type II supernova (the explosion of a massive star) in a globular cluster or in an open cluster? Why?arrow_forwardA supernova can eject material at a velocity of 10,000 km/s. How long would it take a supernova remnant to expand to a radius of 1 AU? How long would it take to expand to a radius of 1 light-years? Assume that the expansion velocity remains constant and use the relationship: expansiontime=distanceexpansionvelocity .arrow_forward
- 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_forwardWhat observations from SN 1987A helped confirm theories about supernovae?arrow_forwardIf 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_forward
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