Deck 16: Evolution of Low-Mass Stars

Question 1

Stars with masses similar to the Sun will lose approximately 30 percent of their mass before they become white dwarfs.

Answer 1

True

Question 2

If a main-sequence star were gaining mass by being in an interacting binary system, what would happen to that star's luminosity and why?

A) The luminosity would increase because the star would become a nova.
B) The luminosity would increase because the star's central pressure would rise and the rate of nuclear reactions would increase.
C) The luminosity would decrease because the outgoing energy has to pass through more layers in the star.
D) The luminosity would decrease because high-mass stars are fainter.
E) The luminosity would decrease because the star would quickly turn into a white dwarf.

Answer 2

The luminosity would increase because the star's central pressure would rise and the rate of nuclear reactions would increase.

Question 3

The Sun will become a red giant star in about 5 billion years.

Answer 3

True

Question 4

A star like the Sun will eventually become an electron degenerate white dwarf star.

Question 5

The percentage of hydrogen in the Sun's core today is roughly half of what it was originally.

Question 6

What factor is most important in determining a star's position on the main sequence and subsequent evolution?

A) temperature
B) pressure
C) mass
D) radius
E) color

Question 7

The Sun eventually could become a nova.

Question 8

A low-mass star that burns helium in its core and hydrogen in a shell surrounding the core is more luminous than a similar star that burns only hydrogen in a shell around a dead core.

Question 9

When a star burns hydrogen in a shell, it will never produce as much energy (per unit time) as when it burns hydrogen in the core because the core has a higher temperature.

Question 10

Which star spends the longest time as a main-sequence star?

A) 0.5 M _$\odot$
B) 1 M _$\odot$
C) 3 M _$\odot$
D) 6 M _$\odot$
E) 10 M _$\odot$

Question 11

If a main-sequence star's core temperature increased, fusion reaction rates would decrease because the protons would be moving faster.

Question 12

Binary stars can evolve to become novae and supernovae because small differences in the stars' masses can mean large differences in their main-sequence lifetimes.

Question 13

Pressure from degenerate electrons keeps the core of a red giant star from collapsing.

Question 14

Once the core of a low-mass main-sequence star runs out of hydrogen, fusion in the star stops until the core temperature is high enough for helium fusion to begin.

Question 15

The more massive a star is, the more hydrogen it has to burn, and the longer its main-sequence lifetime lasts.

Question 16

A Type I supernova can be as luminous as 10 billion L _$\odot$ .

Question 17

A 10M _$\odot$ star will evolve through the same phases as a 1M _$\odot$ star.

Question 18

The main-sequence lifetime of a star is given by the equation:

A) " $\tau$ $\infty$ M/L"
B) " $\tau$ $\infty$ L/M"
C) " $\tau$ $\infty$ M ²/L"
D) " $\tau$ $\infty$ L²/L"
E) " $\tau$ $\infty$ M/L²"

Question 19

The evolutionary cutoff between low- and high-mass stars occurs at approximately:

A) 1.5 M _$\odot$
B) 1 M _$\odot$
C) 3 M _$\odot$
D) 5 M _$\odot$
E) 10 M _$\odot$

Question 20

Stars evolve primarily because they use up the fuel in their cores.

Question 21

The Sun will likely stop being a main-sequence star in:

A) 5,000 years
B) 5 million years
C) 50 million years
D) 500 million years
E) 5 billion years

Question 22

Use the following graph and the relationship $\tau$ $\infty$ M/L to estimate the main-sequence lifetime of a star with a mass equal to 10 times that of the Sun. Note that the Sun's main-sequence lifetime is about 10¹⁰ years.

A) 3 million years
B) 30 million years
C) 300 million years
D) 3 billion years
E) 30 billion years

Question 23

During evolutionary phase A in the figure below, the star is _________. In evolutionary phase B, it is _________.

A) expanding; expanding
B) expanding; contracting
C) contracting; losing mass
D) contracting; contracting
E) gaining mass; contracting

Question 24

Using this diagram, identify the star with the smallest radius.

A) star A
B) star B
C) star C
D) star D
E) star E

Question 25

A main-sequence star is unique because:

A) hydrostatic equilibrium exists at all radii
B) energy transport occurs via convection throughout much of its interior
C) carbon burning occurs in its core
D) it emits strong surface winds
E) hydrogen burning occurs in its core

Question 26

If there were mixing processes in a main-sequence star with a radiative zone (there aren't) that churned up all the material in the interior, we would expect that the main-sequence lifetime would be _________ because _________.

A) shorter, because the star would turn into a giant faster
B) shorter, because the star would burn hydrogen faster and have a higher luminosity
C) longer, because helium nuclei have a higher mass than hydrogen nuclei
D) shorter, because the star would never turn into a red giant
E) longer, because more hydrogen would be available to burn

Question 27

As a main-sequence star burns its core supply of hydrogen, what happens?

A) Helium begins to fuse throughout the core.
B) Helium fuses in a shell surrounding the core.
C) Helium fusion takes place only at the very center of the core, where temperature and pressure are highest.
D) Helium builds up as ash in the core.
E) Helium builds up everywhere in the star's interior.

Question 28

When a spectral-type G2 star like the Sun leaves the main sequence:

A) its luminosity and surface temperature both stay the same
B) its luminosity and surface temperature both decrease
C) its luminosity increases and its surface temperature decreases
D) its luminosity and surface temperature both increase
E) its luminosity decreases and its surface temperature increases

Question 29

When a star depletes its core supply of hydrogen, _________ causes the core to collapse while increased gas _________ is exerted on the atmosphere.

A) pressure; pressure
B) radiation; gravity
C) gravity; gravity
D) gravity; pressure
E) gravity, radiation

Question 30

If the Milky Way formed stars at approximately a constant rate over the last 14 billion years, what fraction of the M-type stars that ever formed in it can still be found as main-sequence stars today? Note that M-type stars have a mass of approximately 0.5 M _$\odot$ .

A) 10 percent
B) 33 percent
C) 50 percent
D) 75 percent
E) 100 percent

Question 31

A low-mass red giant star's energy comes from:

A) hydrogen burning to helium in its core
B) helium burning to carbon in its core
C) hydrogen burning to helium in a shell surrounding its core
D) helium burning to carbon in a shell surrounding its core
E) hydrogen burning to carbon in a shell surrounding its core

Question 32

The luminosity of a star depends on:

A) its mass and age
B) its mass
C) its age
D) its distance
E) its mass, age, and distance

Question 33

You observe a 0.8 M _$\odot$ white dwarf in a binary orbit around a main-sequence star of mass 1.4 M _$\odot$ . Which of the following is most likely the original mass of the star that became the white dwarf?

A) 0.5 M _$\odot$
B) 1 M _$\odot$
C) 0.8 M _$\odot$
D) 1.4 M _$\odot$
E) 3 M _$\odot$

Question 34

What is the radius of a red giant star that has a luminosity of 300 L _$\odot$ and a temperature of 4000 K? (Note that the temperature of the Sun is 5800 K.)

A) 8 R _$\odot$
B) 13 R _$\odot$
C) 25 R _$\odot$
D) 36 R _$\odot$
E) 65 R _$\odot$

Question 35

Degenerate refers to a state of matter at:

A) low density
B) high density
C) low luminosity
D) high luminosity
E) high temperature

Question 36

Using the data in the table below, identify the spectral type of a star that has a main-sequence lifetime of about 10 billion years.

A) A5
B) F5
C) K0
D) G2
E) M8

Question 37

How long will a 2 M _$\odot$ star live as a main-sequence star?

A) 12 million years
B) 180 million years
C) 1.8 billion years
D) 12 billion years
E) 18 billion years

Question 38

Place the following evolutionary stages in order from youngest to oldest.

A) 1, 2, 3
B) 2, 3, 1
C) 3, 2, 1
D) 3, 1, 2
E) 2, 1, 3

Question 39

As a red giant star evolves, hydrogen shell burning proceeds increasingly faster due to:

A) rotational energy from the star's rapid rotation
B) heat released from the core's contraction
C) pressure from the contracting envelope
D) release of energy stored in magnetic fields
E) energy from the fusion of heavier elements

Question 40

For low-mass main-sequence stars in hydrostatic equilibrium, at any interior radius there exists a balance between the downward gravitational force at that radius and:

A) the pressure from a degenerate electron core
B) the convective force of material rising from the interior
C) the energy released from fusion reactions in the core
D) the outward gas pressure from the material inside that radius
E) the energy released by fusion reactions in a shell surrounding the degenerate core

Question 41

As a subgiant star becomes a red giant, its luminosity increases while its temperature remains approximately constant. What does this mean?

A) The radius is decreasing.
B) The radius is increasing.
C) The star is getting hotter.
D) The star is losing mass.
E) The star is rotating more slowly.

Question 42

During which phase of the evolution of a low-mass star does it have two separate regions of nuclear burning occurring in its interior?

A) pre-main sequence
B) main sequence
C) red giant
D) horizontal branch
E) white dwarf

Question 43

A white dwarf with a temperature of 30,000 K would shine brightest at what wavelength?

A) 4 nm, X-rays
B) 100 nm, ultraviolet
C) 400 nm, blue visible
D) 1 $\mu$ m, infrared
E) 10 $\mu$ m, infrared

Question 44

A star's surface temperature during the horizontal branch phase is determined primarily by its:

A) luminosity
B) mass and chemical composition
C) magnetic field strength
D) rotation rate
E) radius

Question 45

As a low-mass main-sequence star runs out of fuel in its core, it grows more luminous. How is this possible?

A) It explodes.
B) It begins to fuse helium in the core.
C) The core expands as it runs out of fuel.
D) The core shrinks, bringing more hydrogen fuel into the burning region.
E) Convection takes place throughout the interior, bringing more fuel to the core.

Question 46

Helium burns in the core of a horizontal branch star via _________ and produces _________.

A) the triple-alpha reaction; carbon
B) the proton-proton chain; lithium
C) the triple-alpha reaction; oxygen
D) the proton-proton chain; iron
E) the proton-proton chain; calcium

Question 47

When helium fusion begins in the core of a red giant star, the situation quickly gets out of control because electron-degeneracy pressure does not respond to changes in:

A) luminosity
B) density
C) gravity
D) temperature
E) magnetic field strength

Question 48

A particular asymptotic giant branch star has approximately the same mass as the Sun but 100 times its radius. Compared to the Sun, what is the escape velocity from that star?

A) 0.01 times that of the Sun
B) 0.1 times that of the Sun
C) the same as that of the Sun
D) 10 times that of the Sun
E) 100 times that of the Sun

Question 49

Asymptotic giant-branch stars have _________ luminosities, _________ radii, and _________ escape velocities.

A) large; large; large
B) large; small; large
C) large; large; small
D) small; large; small
E) small; small; large

Question 50

What is the escape velocity from the surface of a 1 M _$\odot$ AGB star that has a radius of 100 R _$\odot$ ?

A) 60 km/s
B) 120 km/s
C) 240 km/s
D) 620 km/s
E) 800 km/s

Question 51

What ionizes the gas in a planetary nebula and makes it visible?

A) X-ray photons emitted by a pulsar
B) ultraviolet photons emitted by a white dwarf
C) the shock wave from a supernova
D) hydrogen burning in the nebular gas
E) infrared photons from a nova explosion

Question 52

Asymptotic giant branch stars have high-mass loss rates because:

A) they are rotating quickly
B) they have weak magnetic fields
C) they have strong magnetic fields
D) they have low surface gravity
E) they have high surface temperatures

Question 53

A star like the Sun will lose about _________ of its mass before it evolves to become a white dwarf.

A) 3 percent
B) 30 percent
C) 60 percent
D) 75 percent
E) 90 percent

Question 54

When a low-mass star becomes an AGB star and has a temperature of 3300 K, at what wavelength will it shine the brightest?

A) 650 nm, red visible
B) 880 nm, infrared
C) 2.5 $\mu$ m, infrared
D) 1 mm, microwave
E) 10 m, radio

Question 55

What is a planetary nebula?

A) a planet surrounded by a glowing shell of gas
B) the disk of gas and dust surrounding a young star that will soon form a star system
C) the ejected envelope of a giant star surrounding the remnant of a star
D) a type of young, medium-mass star
E) leftover gas from a supernova explosion

Question 56

What would you need to measure about a planetary nebula to determine how long ago its parent star died?

A) the mass of the white dwarf
B) the mass and radius of the white dwarf
C) the nebula's temperature and radius
D) the nebula's radius and expansion velocity
E) the composition of the gas in the nebula

Question 57

The gas in a planetary nebula is composed of:

A) primarily hydrogen from the surrounding interstellar medium
B) primarily hydrogen from the post-asymptotic giant branch star
C) hydrogen and heavier elements like helium and carbon processed in the core of the post-asymptotic giant branch star
D) primarily helium from the post-asymptotic giant branch star
E) carbon and helium from the nuclear reactions that took place on the horizontal branch

Question 58

The Ring Nebula is a planetary nebula that currently has a radius of 1.2 * 10¹³ km and an expansion velocity of 250 km/s. Approximately how long ago did its parent star die and eject its outer layers?

A) 1,500 years ago
B) 3,200 years ago
C) 5,400 years ago
D) 8,000 years ago
E) 28,000 years ago

Question 59

What is the name of the nuclear reaction illustrated here?

A) the proton-proton chain
B) the CNO cycle
C) beta decay
D) the triple-alpha process
E) the alpha-beta reaction

Question 60

A low-mass main-sequence star's climb up the red giant branch is halted by:

A) the end of hydrogen shell burning
B) the beginning of helium fusion in the core
C) electron-degeneracy pressure in the core
D) instabilities in the star's expanding outer layers
E) an explosion that destroys the star

Question 61

As a white dwarf star gradually cools, its radius stays approximately constant. What is happening to the white dwarf's luminosity?

A) It stays the same.
B) It increases.
C) It increases then decreases periodically.
D) It decreases.
E) You can't tell from the information given.

Question 62

In what two ways does temperature affect the rate of nuclear reactions?

Question 63

A Type I supernova has a luminosity of approximately:

A) 10 thousand L _$\odot$
B) 10 million L _$\odot$
C) 1 billion L _$\odot$
D) 10 billion L _$\odot$
E) 10 trillion L _$\odot$

Question 64

Explain the two different forms of pressure that support the core of a low-mass main-sequence star and the core of a low-mass red giant star.

Question 65

Calculate the main-sequence lifetimes of the following stars of different spectral types: B0 (18 M _$\odot$ ), B5 (6 M _$\odot$ ), A5 (2 M _$\odot$ ), F5 (1.3 M _$\odot$ ), and M0 (0.5 M _$\odot$ ). What trend do you notice in your results?

Question 66

Describe the structure of a red giant star just before the helium flash takes place. How does this compare to the structure of a horizontal-branch star?

Question 67

How many times longer does a 2 M _$\odot$ main-sequence star live compared to a 10 M _$\odot$ main-sequence star?

Question 68

In a white dwarf, what is the source of pressure that halts its contraction as it cools?

A) thermal pressure of the extremely hot gas
B) electrons packed so closely that they become incompressible
C) neutrons that resist being pressed further together
D) carbon nuclei that repel each other strongly because they each contain six protons
E) rapid rotation

Question 69

Why does the core of a main-sequence star have to be hotter to burn helium into carbon than hydrogen into helium?

Question 70

A 1M _$\odot$ star in a binary system could create the following chemical element and eject it into the interstellar medium:

A) carbon
B) helium
C) iron
D) gold
E) all of the above

Question 71

If an 0.8 M _$\odot$ white dwarf could accrete matter from a binary companion at a rate of 10 ^{- 9} M _$\odot$ /yr, how long would it take before it exploded as a Type I supernova?

A) 600 thousand years
B) 20 million years
C) 200 million years
D) 600 million years
E) 1 billion years

Question 72

Consider a red giant star with a luminosity of 200 L _$\odot$ and a radius of 50 R _$\odot$ . Using the luminosity-temperature-radius relationship (L $\infty$ R²T ⁴), calculate how hot this star's surface temperature will be compared to the Sun, whose temperature is 5,800 K.

Question 73

One star in a binary will almost always become a red giant before the other because:

A) one star is always larger in radius than the other
B) binaries always have one star twice as massive as the other
C) small differences in main-sequence masses yield large differences in main-sequence ages
D) the more massive binary star always gets more mass from the less massive binary star when both are main-sequence stars
E) one star always spins faster than the other

Question 74

What are two ways that Type I supernovae can be produced?

A) mass transfer and stellar mergers
B) helium flash and stellar mergers
C) mass transfer and helium flash
D) helium burning and mass transfer
E) carbon burning and mass transfer

Question 75

Consider a 1 M _$\odot$ star's journey up the red giant branch. Its luminosity will change from 10 L _$\odot$ to nearly 1,000 L _$\odot$ . How will its temperature and radius change as the star ascends? (Recall that L $\infty$ R²T ⁴.)

Question 76

How can the core of a star be degenerate with respect to the electrons but nondegenerate with respect to the nuclei?

Question 77

A Type I supernova occurs when a white dwarf exceeds a mass of:

A) 0.8 M _$\odot$
B) 1.4 M _$\odot$
C) 2.3 M _$\odot$
D) 5.4 M _$\odot$
E) 10 M _$\odot$

Question 78

A nova is the result of which explosive situation?

A) mass transfer onto a white dwarf
B) helium burning in a degenerate stellar core
C) a white dwarf which exceeds the Chandrasekhar limit
D) the collision of members of a binary system
E) runaway nuclear reactions in the core

Question 79

Which of the stellar spectral types shown below would be the least likely to have planets with life?

A) B0
B) G2
C) K0
D) M0
E) M5

Question 80

What stops a red giant from cooling to continuously lower temperatures, and why?