Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 20, Problem 36E
H II regions can exist only if there is a nearby star hot enough to ionize hydrogen. Hydrogen is ionized only by
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If the hottest star in the Carina Nebula has a surface temperature of 51,000 K, at what wavelength (in nm) does it radiate the most energy?
Hint: Use Wien's law:
?max =
2.90 ✕ 106 nm · K
T
How does that compare with 91.2 nm, the wavelength of photons with just enough energy to ionize hydrogen?
-The wavelength calculated above is shorter than 91.2 nm. Photons at this calculated wavelength will have more than enough energy to ionize hydrogen.
-The wavelength calculated above is longer than 91.2 nm. Photons at this calculated wavelength will have more than enough energy to ionize hydrogen.
-The wavelength calculated above is shorter than 91.2 nm. Photons at this calculated wavelength will not have enough energy to ionize hydrogen.
-The wavelength calculated above is longer than 91.2 nm. Photons at this calculated wavelength will not have enough energy to ionize hydrogen.
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,
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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.
Let us imagine that the spectrum of a star is collected and we find the absorption line of Hydrogen-Alpha (the deepest absorption line of hydrogen in the visible part of
the electromagnetic spectrum) to be observed at 656.5 nm instead of 656.3 nm as measured in a lab here on Earth. What is the velocity of this star in
m/s? (Hint: speed of light is 3*10^8 m/s; leave the units off of your answer)
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Chapter 20 Solutions
Astronomy
Ch. 20 - Identify several dark nebulae in photographs in...Ch. 20 - Why do nebulae near hot stars look red? Why do...Ch. 20 - Describe the characteristics of the various kinds...Ch. 20 - Prepare a table listing the different ways in...Ch. 20 - Describe how the 21-cm line of hydrogen is formed....Ch. 20 - Describe the properties of the dust grains found...Ch. 20 - Why is it difficult to determine where cosmic rays...Ch. 20 - What causes reddening of starlight? Explain how...Ch. 20 - Why do molecules, including H2 and more complex...Ch. 20 - Why can’t we use visible light telescopes to study...
Ch. 20 - The mass of the interstellar medium is determined...Ch. 20 - Where does interstellar dust come from? How does...Ch. 20 - Figure 20.2 shows a reddish glow around the star...Ch. 20 - If the red glow around Antares is indeed produced...Ch. 20 - Even though neutral hydrogen is the most abundant...Ch. 20 - The terms H II and H2 are both pronounced “H two.”...Ch. 20 - Suppose someone told you that she had discovered H...Ch. 20 - Describe the spectrum of each of the following: A....Ch. 20 - According to the text, a star must be hotter than...Ch. 20 - From the comments in the text about which kinds of...Ch. 20 - One way to calculate the size and shape of the...Ch. 20 - New stars form in regions where the density of gas...Ch. 20 - Thinking about the topics in this chapter, here is...Ch. 20 - Stars form in the Milky Way at a rate of about 1...Ch. 20 - The 21-cm line can be used not just to find out...Ch. 20 - Astronomers recently detected light emitted by a...Ch. 20 - We can detect 21-cm emission from other galaxies...Ch. 20 - We have said repeatedly that blue light undergoes...Ch. 20 - Suppose that, instead of being inside the Local...Ch. 20 - Suppose that, instead of being inside the Local...Ch. 20 - A molecular cloud is about 1000 times denser than...Ch. 20 - Would you expect to be able to detect an H II...Ch. 20 - Suppose that you gathered a ball of interstellar...Ch. 20 - At the average density of the interstellar medium,...Ch. 20 - Consider a grain of sand that contains 1 mg of...Ch. 20 - H II regions can exist only if there is a nearby...Ch. 20 - In the text, we said that the five-times ionized...Ch. 20 - Dust was originally discovered because the stars...Ch. 20 - How would the density inside a cold cloud (T=10K)...Ch. 20 - The text says that the Local Fluff, which...
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- Let us imagine that the spectrum of a star is collected and we find the absorption line of Hydrogen-Alpha (the deepest absorption line of hydrogen in the visible part of the electromagnetic spectrum) to be observed at 656.5 nm instead of 656.3 nm as measured in a lab here on Earth. What is the velocity of this star in m/s? (Hint: speed of light is 3*10^8 m/s; leave the units off of your answer)arrow_forward12: A star with spectral type A0 has a surface temperature of 9600 K and a radius of 2.2 RSun. How many times more luminous is this star than the Sun? (if it is less luminous enter a number less than one) Answer: 36.854 13:This star has a mass of 3.3 MSun. what is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr. Please answer question 13 thank you.arrow_forwardA 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.arrow_forward
- 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.)arrow_forwardA star with spectral type A0 has a surface temperature of 9600 K and a radius of 2.2 RSun. How many times more luminous is this star than the Sun? (if it is less luminous enter a number less than one) This star has a mass of 3.3 MSun. Using the simple approximation that we made in class, what is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr. Compare this to the lifetime of a A0 star listed in Table 22.1 (computed using a more sophisticated approach). Is the value you calculated in the previous problem longer or shorter than what is reported in the table? (L for longer, S for shorter) (You only get one try at this problem.)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_forward
- Assuming that at the end of the He burning phase of the stellar core (r < R_core) has no H or He or other metals and is composed completely of Carbon, X=Y=0, X_c = 1 ; The envelope above the core has a normal stellar composition ( r > R_core). Calculate the length of time in years that a 1M_sol and 10M_sol star will live on the horizontal branch or the time between the start and end of the He burning phase. Assume that the normal relationship between mass and luminosity holds for horizontal branch stars. Please be as detailed as possiblearrow_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_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
- 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_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
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