Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN: 9781337399920
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 14, Problem 9RQ
To determine
The position of neutron star on the H-R diagram on the assumption that its temperature is approximately
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If 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 ______ L
A 1.8 M neutron and a 0.7 M white dwarf have been found orbiting each other with a period of 28 minutes. What is their average separation? Convert your answer to units of the Suns radius, which is 0.0047 AU. (hint: Use the version of Keller's third law for the binary stars Ma + Mb = a^3/p^2 ; make sure you express quantities in unites of AU, solar masses, and years. NOTE: a year is 3.2 x 10^7 s)
___________ solar radii
If a 1.40 MSun neutron star has a radius of 10.0 km, what is the radius (in km) of a 2.15 MSun neutron star? (Use the mass-radius relationship
R ∝ M−1/3)
What is the escape velocity (in km/s) from the surface of a 1.5 M neutron star? From a 3.0 M neutron star? (Hint: Use the formula for escape velocity,
Ve =
2GM
r
;
make sure to express quantities in units of meters, kilograms, and seconds. Assume a neutron star has a radius of 11 km and assume the mass of the Sun is 1.99 ✕ 1030 kg.)
1.5 M neutron star km/s3.0 M neutron star km/s
Chapter 14 Solutions
Foundations of Astronomy (MindTap Course List)
Ch. 14 - Prob. 1RQCh. 14 - Prob. 2RQCh. 14 - Prob. 3RQCh. 14 - Prob. 4RQCh. 14 - Prob. 5RQCh. 14 - Prob. 6RQCh. 14 - Prob. 7RQCh. 14 - Prob. 8RQCh. 14 - Prob. 9RQCh. 14 - Prob. 10RQ
Ch. 14 - Prob. 11RQCh. 14 - Prob. 12RQCh. 14 - Prob. 13RQCh. 14 - Prob. 14RQCh. 14 - Prob. 15RQCh. 14 - Prob. 16RQCh. 14 - If the Sun has a Schwarzschild radius, why isnt it...Ch. 14 - Prob. 18RQCh. 14 - Prob. 19RQCh. 14 - Prob. 20RQCh. 14 - Prob. 21RQCh. 14 - In what sense is a black hole actually black?Ch. 14 - If you are falling into a black hole and you point...Ch. 14 - Prob. 24RQCh. 14 - Prob. 25RQCh. 14 - Prob. 26RQCh. 14 - How Do We Know? How does peer review make fraud...Ch. 14 - Prob. 1PCh. 14 - Prob. 2PCh. 14 - Prob. 3PCh. 14 - Prob. 4PCh. 14 - Prob. 5PCh. 14 - Prob. 6PCh. 14 - Prob. 7PCh. 14 - Prob. 8PCh. 14 - Prob. 9PCh. 14 - Prob. 10PCh. 14 - Prob. 11PCh. 14 - Prob. 12PCh. 14 - Prob. 13PCh. 14 - Prob. 14PCh. 14 - Prob. 15PCh. 14 - Prob. 16PCh. 14 - Prob. 1SOPCh. 14 - Prob. 2SOPCh. 14 - Prob. 1LTLCh. 14 - Prob. 2LTLCh. 14 - Prob. 3LTLCh. 14 - Prob. 4LTLCh. 14 - Prob. 5LTL
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- Where in the Galaxy would you expect to find Type II supernovae, which are the explosions of massive stars that go through their lives very quickly? Where would you expect to find Type I supernovae, which involve the explosions of white dwarfs?arrow_forwardAs we have discussed, Sirius B in the Sirius binary system is a white dwarf with MB ∼ 1M , LB ∼ 0.024L ,and rB ∼ 0.0084r . For such a white dwarf, the temperature at the center is estimated to be ∼ 107 K.If Sirius B’s luminosity were due to hydrogen fusion, what is the upper limit of the mass fraction of thehydrogen in such a white dwarf?Step 1: Calculate the observed energy production rate per unit mass (remember luminosity is energy outputper unit time).Step 2: Use the per unit mass energy generation rate of hydrogen fusion (via PP chain) to estimate thepossible hydrogen mass fraction given the condition at the center of the white dwarf.arrow_forwardWhat is the peak wavelength (in nm) of a neutron star's luminosity if its temperature is 106 K?arrow_forward
- 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) 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_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_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_forward
- What is the escape velocity (in km/s) from the surface of a 1.1 M neutron star? From a 3.0 M neutron star?arrow_forwardWhat is the escape velocity (in km/s) from the surface of 1.1 M neutron star? (hint: Use the formula for the escape velocity Ve = 2GM/R ; make sure to express quantities in United of meters, kilograms, and seconds. Assume a neutron has a radius of 11 km and assume the mass of the sun is 1.99 x10^30 kg.) 1.1 M neutron Star = _________ km/s 3.0 neutron Star = __________ km/sarrow_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) 36.854 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.arrow_forward
- Calculate the Kepler speed grazing the surface of a) a white dwarf, b) a neutron star. Give your answers in terms of the speed of light. (Take RNS = 10 km, RWD = 10 000 km, and MWD = MNS = 1 Msun.)arrow_forwardA. Estimate the surface gravity of a neutron star with R = 10 km and M = 2M. . B. Determine the density of such a neutron star in g/cm³. C. How much would a teaspoon (5 cm³) of this neutron star weigh on Earth? This material is known as neutronium. Give your answer in pounds. D. Which would be heavier: a teaspoon of neutronium weighed on Earth, or a teaspoon of water weighed on the surface of a neutron star?arrow_forwardWhat is the free-fall time of a 10 MSun main-sequence star? O 100 hours O 10 hours O 1 hour O 0.1 hoursarrow_forward
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