8 Quiz
Answer the following questions in order to test your understanding of the key ideas that you have been learning about.
In the following questions you may use the following values of physical constants, as necessary:
Question 1
a.
Red giant stars are undergoing fusion of helium into carbon and oxygen.
b.
On the main sequence, stars convert hydrogen into helium.
c.
Stars spend less of their lives as red giants than they do on the main sequence.
d.
Supergiant stars have higher luminosities than red giant stars.
e.
More massive stars have shorter lives than less massive stars.
f.
High mass stars are more common than low mass stars.
The correct answers are a, b, c, d and e.
Answer
The first five statements are all true. The last one is false: high mass stars are much rarer than low mass stars.
Question 2
a.
110 million K
b.
240 million K
c.
320 million K
d.
550 million K
e.
630 million K
The correct answer is b.
Answer
Since helium-4, carbon-12 and oxygen-16 all have Ye = 0.5 electrons per nucleon, the electron number density is simply
The limiting temperature below which electrons in the core would be degenerate is
Putting in the numbers gives
Question 3
Match the following equations of state with the correct dependence on particle number density and temperature.
Using the following two lists, match each numbered item with the correct letter.
-
ultra-relativistic degenerate gas
-
non-relativistic degenerate gas
-
ideal gas
a.
b.
c.
- 1 = b
- 2 = a
- 3 = c
Answer
The equations of state for degenerate matter do not depend on temperature; they only depend on the particle density to some power. The equation of state for an ideal gas depends on particle density and temperature.
Question 4
a.
13%
b.
18%
c.
25%
d.
37%
e.
52%
The correct answer is c.
Answer
Since helium-4, carbon-12 and oxygen-16 all have Ye = 0.5 electrons per nucleon, the electron number density is simply
The Fermi kinetic energy can be written as
Putting in the numbers gives
Therefore EF = 2.05 × 10-14 J which is about 128 keV. Since the rest-mass energy of an electron is 511 keV, this means that EF is about 25% of the rest mass energy. (So the assumption that the electrons are non-relativistic may not be appropriate.)
Question 5
a.
0.25 R⊕
b.
0.36 R⊕
c.
0.58 R⊕
d.
0.82 R⊕
e.
0.93 R⊕
The correct answer is d.
Answer
The radius is given by
Putting in the numbers gives
So RWD = 5.25 × 106 m which is equivalent to 0.82 R⊕.
Question 6
Match the following compact remnants with the progenitor single star main-sequence mass.
Using the following two lists, match each numbered item with the correct letter.
-
He white dwarf
-
CO white dwarf
-
neutron star
a.MMS = 15 M☉
b.MMS = 0.15 M☉
c.MMS = 1.5 M☉
- 1 = b
- 2 = c
- 3 = a
Answer
Main-sequence stars with masses below 0.5 M☉ will form He white dwarfs, those with masses in the range 0.5–8 M☉ will form CO white dwarfs, and those with masses in the range 11–16 M☉ (or possibly up to 25 M☉) will form neutron stars.
Question 7
a.
1.4 × 1045 J
b.
1.6 × 1045 J
c.
1.8 × 1045 J
d.
1.4 × 1046 J
e.
1.6 × 1046 J
f.
1.8 × 1046 J
The correct answer is b.
Answer
First consider the helium nuclei. The number of helium-4 nuclei in the core is
The total energy absorbed by the helium-4 nuclei is therefore
Now consider the iron nuclei. The number of iron-56 nuclei in the core is
Note that each nucleus will contain 26 protons. Now assuming that each proton is converted into a neutron by electron capture, emitting a neutrino with energy 10 MeV, the energy removed by electron capture is
So the total energy removed is E = EHe + EFe = 1.6 × 1045 J
Question 8
a.
White dwarfs are always less massive than neutron stars.
b.
White dwarfs are smaller than neutron stars.
c.
White dwarfs are more dense than neutron stars.
d.
White dwarfs are supported by electron degeneracy pressure.
e.
Neutron stars are supported by proton degeneracy pressure.
f.
ONeMg white dwarfs are more common than CO white dwarfs.
g.
Neutron stars can have masses up to 3 times that of the Sun.
The correct answer is d.
Answer
Only the fourth statement is true. The most massive white dwarfs can be more massive than the least massive neutron stars; white dwarfs are always larger than neutron stars and always less dense too. Neutron stars are supported by neutron degeneracy pressure because neutrons far outnumber protons in their composition. CO white dwarfs are more common than ONeMg white dwarfs because they form from lower mass progenitor stars which are more common than higher mass progenitor stars. The maximum neutron star mass is no more than about 2.5 times the mass of the Sun.