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Chapter 18: Relativity
and Black Holes
Learning
Objectives.
Define the bold-faced vocabulary terms within the chapter.
18.1 Relative Motion Affects Measured
Velocities
Illustrate why relative motion causes two people to report
different observations of the same physical situation.
Multiple Choice: 1, 2, 4, 5, 7
Differentiate between the relative motion of a material
object and light as seen by two different observers.
Multiple Choice: 3, 6, 8
Short Answer: 1, 2
18.2 Special Relativity Explains How Time
and Space Are Related
Explain how traveling at relativistic speeds affects
measurements of time, length, speed, and energy.
Short Answer: 4, 5, 7, 9, 10, 12
Describe observational tests of special relativity.
Multiple Choice: 22, 26
Short Answer: 6, 11
Illustrate why relativistic space travel is highly
improbable.
Multiple Choice: 17, 18
Short Answer: 3, 8
18.3 Gravity Is a Distortion of Spacetime
Explain why “free fall is the same as free float.”
Multiple Choice: 45
Short Answer: 22
Illustrate how motion along a curved surface mimics motion in
a gravitational field.
Multiple Choice: 36, 42, 44
Short Answer: 16, 23
Illustrate how gravity is really motion of particles through
spacetime that has been curved by mass.
Multiple Choice: 35, 37, 47
Short Answer: 17, 19, 21
Describe observable consequences of general relativity.
Multiple Choice: 38, 39, 40, 43, 46, 48, 49, 50, 51, 52, 53
Short Answer: 15, 20
Describe observational tests of general relativity.
Short Answer: 18
Compare and contrast the accuracy of Newtonian vs.
relativistic physics.
Multiple Choice: 34, 41
Short Answer: 14
18.4 Black Holes
Explain the significance of the Schwarzschild radius (or
event horizon) of a black hole.
Multiple Choice: 54, 55, 60, 67
Short Answer: 25, 29, 30
Calculate the Schwarzschild radius of a black hole.
Multiple Choice: 56, 58, 59, 62, 66, 68, 69, 70
Assess whether an object is or is not likely to evolve into a
black hole.
Short Answer: 27
Describe why a black hole cannot be observed directly but how
it can be detected indirectly.
Multiple Choice: 57, 61, 63, 65
Short Answer: 24, 26
Summarize the observational evidence that black holes exist.
Multiple Choice: 64
Short Answer: 28
Working It Out 18.1
Calculate the relativistic effect of time dilation when
moving at high speeds.
Multiple Choice: 9, 10, 11, 12, 13
Working It Out 18.2
Calculate the masses of two stars in a binary system.
Short Answer: 13
MULTIPLE CHOICE
1.
What is the meaning of
the phrase inertial frame of reference?
a.
a reference frame that
is not accelerating
b.
a reference frame that
is stationary with respect to the Earth
c.
a reference frame that
is in motion at constant speed
d.
a reference frame that
is accelerating at a constant rate
e.
a reference frame in
which there are strong gravitational forces
2.
What will observers in
different inertial frames of reference always agree on?
a.
how the speed of light
varies with the motion of an observer
b.
the length of the
meter, but not the duration of the second
c.
the rate each frame is
accelerating
d.
the laws of physics
e.
whether events are
simultaneous or not
3.
Suppose that an object
is moving and it is emitting light toward you, in vacuum. What would you notice
about the light you observe?
a.
The wavelength gets
longer.
b.
The frequency gets
lower.
c.
The energy becomes
lower.
d.
The speed stays
constant.
e.
The speed is
increasing.
4.
You are driving on an
interstate at 70 mi/h and, in the adjacent lane in the same direction, another
car is passing you. From your point of view, the other car seems to advance at
10 mi/h, i.e., it is only slowly moving ahead of you. What is the speed that
the odometer should indicate inside the other car?
a.
70 mi/h
b.
10 mi/h
c.
80 mi/h
d.
60 mi/h
e.
75 mi/h
5.
You are driving on an
interstate at 70 mph and in the adjacent lane, but in the opposite direction,
another car is zipping by. From your point of view, the other car seems to pass
at 150 mph, which would seem crazy. What is the speed that the odometer should
indicate inside the other car?
a.
80 mph
b.
55 mpg
c.
220 mph
d.
110 mph
e.
150 mph
6.
You observe a distant
galaxy apparently moving away at one third the speed of light 
. If you could measure the speed at which
this galaxy’s light is passing the Earth, you would get
. If you could measure the speed at which
this galaxy’s light is passing the Earth, you would get
a.
b.
2 
c.
c.
d.
4 
e.
5 
7.
Stellar aberration
should be distinguished from stellar parallax in that
a.
stellar aberration
immediately allows for measurements of distances to stars.
b.
stellar parallax is
easily observable, whereas the aberration is impossible to measure.
c.
stellar aberration
depends on the Earth’s orbital speed around the Sun.
d.
stellar parallax
depends on the Earth’s orbital speed around the Sun.
e.
stellar aberration
demonstrates that the speed of light is infinite.
8.
Superluminal motions
were detected in jets of plasma launched by actively accreting compact objects.
This shows that
a.
special relativity has
a limited range of applications.
b.
observed superluminal
motions can be explained without violating the theory of relativity.
c.
black holes can
actually launch material jets that advance faster than light.
d.
general relativity
allows for faster-than-light motions, even though special relativity does not.
e.
the jets are aligned
with our line of sight, therefore we understand that their light is coming at
us faster than c speed.
9.
What is the Lorentz
factor for an object moving at 0.85c?
a.
1.00
b.
1.67
c.
1.89
d.
0.99
e.
2.05
10.
At what fraction of the
speed of light would the γ factor lead to a
10-fold time dilation?
a.
0.5
b.
0.95
c.
0.75
d.
0.995
e.
0.9999995
11.
If the Lorentz factor
is 2, what is the corresponding speed?
a.
0.86c
b.
1.55c
c.
0.27c
d.
0.52c
e. 0.9999c
12.
The second marked by a
clock aboard a fast (hypothetical) interstellar ship moving at v = 0.95c would be __________________
compared with the second marked by a clock at rest on Earth.
a.
70.71 times shorter
b.
70.71 times longer
c.
7.09 times shorter
d.
3.20 times longer
e.
3.20 times shorter
13.
A fast-moving muon
decays in 2 × 10−4 seconds, as
measured by an observer at rest. In the reference frame of the muon itself, its
lifetime is in fact only 2 × 10−6 seconds. What is
the muon's speed?
a.
0.05c
b.
0.50c
c.
0.95c
d.
0.995c
e.
0.99995c
14.
One consequence of
Einstein’s ideas about the speed of light is that
a.
if two events take
place at the same time for one observer, they will occur simultaneously for all
observers.
b.
whether events are seen
as simultaneous or not depends on the motions of observers.
c.
two events cannot
happen at the same time for two different observers.
d.
it is not possible to
know when an event happens.
e.
people could design and
fly interstellar spaceships moving as fast as light itself.
15.
What is the meaning of
the word spacetime?
a.
It is a mental
framework for keeping track of numbers in Newtonian physics.
b.
Space and time form a
two-dimensional region where physics takes place.
c.
The term has no special
meaning; it’s just a fancy way to sound important when talking about physics.
d.
It is the combined
treatment of space and time in the theory of relativity.
e.
It is the idea that
observers will always measure the same locations and times of events.
16.
According to Einstein’s
Theory of Special Relativity, which two quantities are different manifestations
of the same thing?
a.
mass and gravity
b.
light and energy
c.
energy and mass
d.
temperature and energy
e.
distance and time
17.
According to Special
Relativity, spacecraft that would travel faster than the speed of light are
a.
impossible, because
nothing can travel that fast.
b.
possible, but not
useful since they could not contain living beings.
c.
impossible, since
objects that travel that fast would get shorter and squeeze out space for the
astronauts to live.
d.
possible, if we are
clever enough with new technologies.
e.
impossible, because
they would require new energy sources that are not yet invented.
18.
Why can an object with
a nonzero mass never travel as fast as the speed of light?
a.
It would take an
infinite amount of energy to accelerate it to a speed of c.
b.
It would emit so much
radiation that its energy would decrease and it would slow down again.
c.
It would lose all its
mass and turn into neutrinos.
d.
An object can actually
travel as fast as light, but if it did it would disappear.
e.
If it were going at the
speed of light, it would be converted to pure energy since E = mc2.
19.
In an accelerator, a
massive particle may gain a relativistic speed for which its total energy is
1,000 time greater than its rest energy. This implies a Lorentz factor of
a.
0.999.
b.
10.
c.
1.
d.
1000.
e.
2.29.
20.
At what (relativistic)
speed does the length of a spacecraft become half of its rest length?
a.
0.40c
b.
0.27c
c.
0.99c
d.
0.87c
e.
0.10c
21.
What is true about
muons?
a.
They are always moving
at high speed, so they test relativity.
b.
Relativity explains why
we can see muons that are produced high in the atmosphere from cosmic rays.
c.
We can see them being
deflected from straight lines by the gravity of black holes.
d.
They have a mass that
does not increase if they are moving fast.
e.
They are examples of
Hawking radiation from black holes.
22.
Has relatively ever
been tested?
a.
No, because it would
require us to set up physics experiments in faraway galaxies.
b.
Yes, because even
ordinary motion in automobiles and airplanes produces easily noticeable effects
predicted by relativity.
c.
No, because no one has
been able to think of experiments that are able to measure the small differences
between the predictions of Newtonian physics and relativity.
d.
Yes, because (for
example) subatomic particles can be accelerated to speeds approaching that of
light.
e.
No, because the theory
of relativity contains paradoxes and contradictions, like the twin paradox.
23.
Which of the following
is a consequence of Einstein’s Special Theory of Relativity?
a.
Moving clocks run
quicker.
b.
The velocity of light
depends on the speed of the observer.
c.
Distances are shorter
for objects traveling close to the speed of light.
d.
Gravity arises because
mass distorts spacetime.
e.
Faster moving objects
require less force to accelerate them.
24.
The twin paradox shows
that special relativity
a.
explains many things
but can’t explain everything.
b.
is accurate but
contains some worrisome contradictions.
c.
is incorrect.
d.
is incomplete.
e.
correctly accounts for
the results of experiments in different reference frames.
25.
Which of the following
statements is not valid?
a.
If the speed of light
is finite, time must run differently for different observers.
b.
The results of physics
experiments are indistinguishable in inertial frames and freely falling frames.
c.
The high positional
accuracy provided by the GPS system is possible if relativistic corrections are
applied.
d.
Time is contracted and
distances dilated in moving frames.
e.
If the speed of light
is finite, telescopes could be seen as “time machines.”
26.
The Large Hadron
Collider at CERN in Switzerland can accelerate protons to amazing kinetic
energies of the order of 1.6 × 10−7J. What would be
the Lorentz factor for a proton of mass 1.67 × 10−27 kg at such speed?
a.
133
b.
1065
c.
70.79
d.
2
e.
999
27.
For a fast
(hypothetical) interstellar ship moving at v = 0.95c a distance of 10 ly between neighboring stars would
actually measure
a.
32 ly.
b.
10.5 ly.
c.
3.1 ly.
d.
9.5 ly.
e.
10 ly.
28.
In Special Relativity
the total energy of a fast moving object (kinetic plus rest energy) is given by
E = γmc2, where m
is the rest mass of the object. At what (relativistic) speed would the kinetic energy of a 100-ton spaceship be the same as its rest energy?
a.
1c
b.
0.999c
c.
0.5c
d.
0.25c
e.
0.87c
29.
Of all four muons
produced at 15 km above ground and schematically shown in the figure below,
which one would “see” the distance to the ground as a mere 200 m?
a.
the muon moving at 0.9c
b.
the muon moving at 0.99c
c.
the muon moving at
0.999c
d.
the muon moving at
0.9999c
e.
the muons would not
experience any relativistic effect because they are too tiny.
30.
Assume that a group of
explorers traveled to the Orion Nebula, which is the nearest star-forming cloud
and is at a distance of 1,300 light-years, using revolutionary technology that
allowed them to travel at a speed of 0.99c. Observers
back on Earth using Earth-bound clocks would say it took the explorers
__________ to get there, but the explorers with their moving clocks would say
it took them only __________ to get there.
a.
1,310 years; 185 years
b.
1,440 years; 630 years
c.
1,310 years; 390 years
d.
1,440 years; 425 years
e.
1,310 years; 1,300
years
31.
If you were to design a
spacecraft that could travel to the galactic center fast enough that the
astronauts aboard aged by only 25 years during the trip, how fast would the
spacecraft have to go? (Note: The galactic center is 25,000 light years away.)
a.
0.95c
b.
0.995c
c.
0.99995c
d.
0.9999995c
e.
0.999999995c
32.
Suppose you detect a
pulsar that gives us 1,000 radio pulses per second, but the pulsar is in a
distant galaxy that is apparently moving away from us at 50 percent of the
speed of light. An observer at rest with respect to the pulsar in that faraway
galaxy would measure a pulse rate of
a.
870 per second.
b.
1,150 per second.
c.
1,250 per second.
d.
1,366 per second.
e.
1,450 per second.
33.
The satellites from the
GPS network are in high orbits and their clocks fall behind ground-based clocks
by about 7 µs/day. Assuming that this dilation is entirely a special
relativistic effect, which is the best estimate for the orbital speed of a GPS
satellite?
a.
27,500 km/h
b.
14,000 km/h
c.
1,000 km/h
d.
67,000 km/h
e.
38,500 km/h
34.
When do the predictions
of Special Relativity match those of Newtonian physics?
a.
in terrestrial laboratories
b.
inside our Solar System
c.
when different
observers are at rest with each other
d.
when objects have a low
mass
e.
when objects are moving
slowly
35.
__________ is the
result of mass distorting the fabric of spacetime.
a.
Energy
b.
Radiation
c.
Fusion
d.
Gravity
e.
Electric charge
36.
What does gravity mean
in relativity?
a.
It is a result of mass
and energy being two forms of the same thing.
b.
It is a consequence of
distances getting shorter as objects move faster.
c.
It is the result of the
mass of falling bodies getting bigger because they are in motion.
d.
It is the force that
objects with mass exert on a body.
e.
It is the result of the
distortion in spacetime around an object with any energy density.
37.
A geodesic is
the name for the
a.
aberration of
starlight.
b.
gravitational field of
the Earth.
c.
solid crust of a
terrestrial planet.
d.
path followed by a
freely falling object in spacetime.
e.
shape of a body that
has mass.
38.
Gravitational lensing
occurs when _____________ distorts the fabric of spacetime.
a.
a star
b.
dark matter
c.
a black hole
d.
any massive object
e.
a white dwarf
39.
The bending of light
paths near a massive object is the essence of
a.
time dilation.
b.
the twin paradox.
c.
gravitational lensing.
d.
length contraction.
e.
mass increase.
40.
General relativity
predicts that coalescing (merging) massive objects would trigger
a.
pulses of
electromagnetic radiation.
b.
gravitational waves.
c.
high-energy particles.
d.
a slowing of clocks
here on the Earth.
e.
blueshifted light from
the surface of the object.
41.
How does relativity
compare with Newtonian physics?
a.
Relativity gives the
same result as Newtonian physics when objects are moving slowly.
b.
Relativity gives
results that contradict many predictions of Newtonian physics, so we know the
latter is incorrect.
c.
Relativity must be
better, because it is a newer theory than Newtonian physics.
d.
Newtonian physics and
relativity make the same predictions, but it’s easier to compute results using
relativity.
e.
Newtonian physics is
well accepted by scientists, whereas relativity is still controversial.
42.
You measure that an
object has a mass of exactly 1 kg. The Equivalence Principle says that the mass
you would measure by trying to accelerate it would be
a.
1 kg.
b.
greater than 1 kg.
c.
less than 1 kg.
d.
different from 1kg,
depending on what it’s made of.
e.
larger than 1 kg,
because of the Sun’s gravity.
43.
Photons have no mass,
and Einstein’s theory of general relativity says
a.
their paths through
spacetime are curved in the presence of a massive body.
b.
their apparent speeds
depend on the observer’s frame of reference.
c.
they should not be
attracted to a massive object.
d.
their wavelengths must
remain the same as they travel through spacetime.
e.
their wavelengths would
grow longer as they travel through empty space.
44.
The Equivalence
Principle says that
a.
the universe is
homogeneous and isotropic.
b.
being stationary in a
gravitational field is the same as being in an accelerated reference frame.
c.
at any radius inside a
star the outward gas pressure must balance the weight of the material on top.
d.
mass and energy are
interchangeable and neither can be destroyed.
e.
gravity does not exist
in space.
.
45.
Why do astronauts in
space feel no gravity?
a.
There is no gravity out
in space.
b.
Gravity happens only
when objects are accelerating.
c.
In space, the gravity
from the Moon and the Sun cancels out the Earth’s gravity.
d.
They and their
spaceship are both freely falling at the same rate in the gravitational field.
e.
The astronauts do not
have any mass when they are out in space.
46.
The Principle of
Equivalence states that the gravitational mass is equal to the
a.
mass when moving nearly
the speed of light.
b.
resistance to acceleration.
c.
mass when near a black
hole.
d.
weight of the object.
e.
density divided by the
volume.
47.
In the rubber-sheet
analogy for spacetime, what would you expect for objects (such as golf balls)
rolling around in the presence of a massive object that is stretching the
rubber sheet?
a.
Their paths will be
straight if they are moving slowly enough.
b.
Their paths will curve
more the closer they come to the massive object.
c.
Their paths will curve
by the same amount no matter how close they come to the mass.
d.
Their paths will curve
toward the mass if they pass close but bend away from the mass if they pass far
from the mass.
e.
Their paths will curve
less the closer they come to the massive object.
48.
The gravitational
redshift of light should be smallest for light emitted from the surface of
a.
a black hole.
b.
the Sun.
c.
a white dwarf.
d.
a planet like the
Earth.
e.
a neutron star.
49.
According to the theory
of relativity, a clock on top of Mount Everest would run ___________ compared
with a clock at sea level because ______________ .
a.
faster; of the high
altitude, which means a slightly weaker gravity
b.
faster; the air is a
lot thinner and there is less friction within the clock
c.
faster; it is closer to
the Moon and thus experiences stronger tide forces
d.
slower; of the low
pressure at that altitude
e.
identically; time is
the same for all clocks in the universe
50.
The Sun’s mass would
affect the spacetime in its proximal space and photons from distant stars would
follow curved geodesics rather than straight paths when passing close to our
star, as in the figure shown below. According to general relativity, an
observer on Earth would also expect the “apparent stars” to appear
a.
redder.
b.
hotter.
c.
more distant.
d.
bluer.
e.
more massive.
51.
Which of the following
applications (which affects many people) could not have been achieved without
implementing necessary relativistic effects and corrections?
a.
fast-moving automobiles
b.
GPS technology
c.
interstellar travel
d.
radar technology
e.
neutrino detectors
52.
Compared with a clock
on the surface of the Earth, a clock on the International Space Station runs
a.
at approximately the
same rate, but slightly slower.
b.
significantly slower.
c.
significantly faster.
d.
sometimes faster and
sometimes slower.
e.
at an equal rate,
except during eclipses.
53.
Light is increasingly
redshifted near a black hole because
a.
the photons are moving
away from us very quickly as they are sucked into the black hole.
b.
the photons are moving
increasingly faster in order to escape the pull of the black hole.
c.
the photons lose energy
because climbing out of the black hole’s gravity makes them weaker.
d.
the curvature of
spacetime is increasingly stretched near the black hole, which in turn
stretches the wavelengths of the photons.
e.
time is moving
increasingly slower as viewed from the observer’s frame of reference.
54.
The event horizon of a
black hole is defined as
a.
the point of maximum
gravity.
b.
the radius of the
original neutron star before it became a black hole.
c.
the radius from which
shock waves course through spacetime due to the strong gravitational distortion
of the black hole.
d.
the radius at which the
escape speed from the black hole equals the speed of light.
e.
the radius at which the
gravitational force is the same as that on the surface of the Sun.
55.
What is the
significance of the Schwarzschild radius around a black hole?
a.
It is the radius at
which an orbiting object would show a precession.
b.
It is the radius at
which gravitational redshift can be detected.
c.
It is the radius at
which the black hole’s spin equals the speed of light.
d.
It is the radius at
which the escape velocity equals the speed of light.
e.
It is the radius at
which a body falling onto the black hole would move at half the speed of light.
56.
The Schwarzschild
radius of a 10 M⊙ is
__________ the size of the Schwarzschild radius of a 5 M⊙ black hole.
a.
b.
c.
equal to
d.
2 times
e.
5 times
57.
Hawking radiation from
black holes refers to
a.
light emitted from
matter falling onto a black hole.
b.
the gravitational
redshift of light emitted near the event horizon.
c.
the radiation of
particles created near the event horizon.
d.
high-energy X-rays and
gamma rays from the formation of a black hole.
e.
the optical and
infrared light from an energetic supernova explosion.
58.
If the Sun suddenly
turned into a black hole, what would be the radius of its event horizon?
a.
3 m
b.
30 m
c.
300 m
d.
3 km
e.
30 km
59.
If the Earth were to
shrink in size until it became a black hole, its Schwarzschild radius would be
a.
1 cm.
b.
1 m.
c.
1 km.
d.
10 km.
e.
200 km.
60.
A person would
experience __________ as he or she approached the event horizon of a black
hole.
a.
extremely strong tidal
forces
b.
intense heating
c.
strong Hawking radiation
d.
strong infrared
radiation
e.
nothing
61.
Hawking radiation is
emitted by a black hole when
a.
the black hole rotates
quickly.
b.
the black hole accretes
material.
c.
a supernova explodes
and forms a black hole out of its core.
d.
synchrotron radiation
is emitted by infalling charged particles.
e.
a virtual pair of
particles is created near the event horizon.
62.
If the Sun were to be
instantly replaced by a 1 M⊙ black
hole, the gravitational pull of the black hole on Earth would be
a.
much greater than it is
now.
b.
the same as it is now.
c.
much smaller than it is
now.
d.
larger or smaller,
depending on the location of the Moon.
e.
irrelevant, because
Earth would quickly fall into the Sun and be destroyed.
63.
Even if a black hole
emitted no light, we can still detect it
a.
from sound waves produced
by material falling onto the black hole.
b.
by tides produced on
the Earth’s oceans.
c.
through its Hawking
radiation.
d.
through its
gravitational effect on surrounding gas or stars.
e.
by looking for dark
patches on the sky where the black hole swallows background light.
64.
A red giant star is
found to be orbiting an unseen object with a short orbital period. By measuring
the speed at which it orbits, astronomers deduce that the unseen object has a
mass of 10 M⊙. This
object is probably a ______________ because ________________.
a.
black hole; the giant
star is massive and could be in orbit only about something even more massive
b.
black hole; its mass is
too large to be a neutron star or a white dwarf
c.
neutron star; any
supernova that would have made a black hole would have destroyed the red giant
d.
M-dwarf star; only such
stars would be faint enough to go unseen in this system
e.
black hole; most red
giants orbit neutron stars, and neutron stars can turn into black holes
65.
Black holes that are
stellar remnants can be found by searching for
a.
dark regions at the
centers of galaxies.
b.
variable X-ray sources.
c.
extremely luminous
infrared objects.
d.
objects that emit very
faint radio emission.
e.
regular, repeated
pulsations at radio wavelengths.
66.
What black-hole mass
would have an event horizon radius comparable to the size of an atomic nucleus?
a.
100 kg
b.
1011
kg
c.
100 tons
d.
1024
kg
e.
0.1 kg
67.
Which of the following
are the only possible properties of black holes?
a.
mass, angular momentum,
and electrical charge
b.
mass, electrical
charge, and fraction of heavy nuclei
c.
electrical charge,
density, and dark matter content
d.
angular momentum, mass,
and elasticity
e.
mass, density of dark
matter, and temperature of Hawking radiation
68.
While traveling through
the galaxy in a spacecraft, you and a colleague set out to investigate the 106
M⊙ black
hole at the center of our galaxy. He hops aboard an escape pod and drops into a
circular orbit around the black hole, maintaining a distance of 10,000 km,
while you remain much farther away in the spacecraft. After doing some
experiments to measure the strength of gravity, your colleague signals his
results back to you by using a green laser. What would you see? Hint: You will
need to calculate the location of the event horizon.
a.
You would see your
colleague’s signals unaltered in wavelength, because he is orbiting well
outside the event horizon of the black hole.
b.
You would see your
colleague’s signals shifted to a much redder wavelength, because he is close to
the event horizon.
c.
You would never get to
see the escape pod carrying your colleague reaching the desired orbit; thus,
you’d never get any signals back from him.
d.
You would see nothing,
because no light can escape the gravitational pull of a black hole no matter
how far your colleague is from it.
e.
You would see your
colleague’s signals shifted to a much bluer wavelength, because black holes can
make highly energetic light.
69.
While traveling through
the galaxy in a spacecraft, you and a colleague set out to investigate the 106 M⊙ black
hole at the center of our galaxy. She hops aboard an escape pod and drops into
a circular orbit around the black hole, maintaining a distance of 1 AU, while
you remain much farther away in the spacecraft. After doing some experiments to
measure the strength of gravity, your colleague signals her results back to you
by using a green laser. What would you see? Hint: You will need to calculate
the location of the event horizon.
a.
Your colleague’s
signals are shifted only slightly toward the red, because she is orbiting well
outside the event horizon of the black hole.
b.
You would see your
colleague’s signals shifted to a much redder wavelength, because she is close
to the event horizon.
c.
You would see nothing,
because your colleague has crossed the event horizon around the black hole.
d.
You would see nothing,
because no light can escape the gravitational pull of a black hole no matter
how far your colleague is from it.
e.
You would see your
colleague’s signals shifted to a much bluer wavelength, because black holes can
make highly energetic light.
70.
While traveling through
the galaxy in a spacecraft, you and a colleague set out to investigate the 106 M⊙ black
hole at the center of our galaxy. She hops aboard an escape pod and drops into
a circular orbit around the black hole, maintaining a distance of 4 ×
106 km, while you remain much farther
away in the spacecraft. After doing some experiments to measure the strength of
gravity, your colleague signals her results back to you by using a green laser.
What would you see? Hint: You will need to calculate the location of the event
horizon.
a.
You would see your
colleague’s signals unaltered in wavelength, because she is orbiting well
outside the event horizon of the black hole.
b.
You would see your
colleague’s signals shifted to a much redder wavelength, because she is close
to the event horizon.
c.
You would see nothing,
because your colleague has crossed the event horizon around the black hole.
d.
You would see nothing,
because no light can escape the gravitational pull of a black hole no matter
how far your colleague is from it.
e.
You would see your
colleague’s signals shifted to a much bluer wavelength, because black holes can
make highly energetic light.
SHORT ANSWER
1.
Explain, in the context
of the special relativity, how a telescope is a kind of “time machine.”
2.
Let’s assume we know
that the semi-major axis of the “loop” described by a star’s position due to
stellar aberration is equal to the orbital speed of the Earth (expressed in
units of light speed c in vacuum). What would be the corresponding
angular opening of the cone in the figure below?
3.
Give a simple
explanation to why the speed cannot increase as suggested by the Newtonian
behavior shown as a straight line in the figure below.
4.
What is the central
idea in relativity concerning the speed of light? Describe at least two unusual
consequences of this idea.
5.
Explain what
four-dimensional spacetime means.
6.
What is the meaning of
the equation E = mc2?
7.
Explain why no object
that has mass can ever move at a speed equal to the speed of light. At what
velocity do massless particles (e.g., photons) travel in vacuum?
8.
Use the figure shown
below to explain that the implied acceleration has indeed a value close to the
accepted value for the acceleration of Earth’s gravity.
9.
Suppose we discovered
radio signals coming from the star Alpha Centauri, which is 4.4 light-years
from us, and we sent a crew in a spacecraft to visit it. If the spacecraft used
revolutionary technology allowing it to travel at a speed of 0.5c, how long would it take the spacecraft to get to Alpha
Centauri, and how much time would the astronauts say passed during the trip?
(Ignore the time it would take to accelerate the spacecraft to reach a velocity
of 0.5c.)
10.
Explain the
relativistic effects on clocks aboard the International Space Station compared
with synchronized clocks here on Earth.
11.
Muons are elementary
particles that decay into other particles in about 2.2 microseconds. They are
formed in the upper atmosphere of the Earth from high-energy cosmic rays and
can be detected on the ground even though they could travel only a few hundred
meters before decaying, according to Newtonian physics. How does relativity
explain that we can detect them on the ground? Explain both in our reference
frame and in the frame of the muon.
12.
The GPS system requires
time accuracy of the order of a few tens of nanoseconds (ns) for the clocks
aboard the satellites. At the high altitudes where the satellites are deployed,
their orbital speeds are about 20,000 km/h. Based on arguments Special
Relativity alone show that time dilation corrections are absolutely relevant
and necessary in order to maintain the aforementioned accuracy level.
13.
A 15-M⊙ star has been monitored for decades and scientists found
that it is orbiting in a highly eccentric ellipse about an unseen mass
(presumably a supermassive black hole [BH]) at the center of Milky Way with a
period of 15.6 years and a semimajor axis of about 1000 A.U. What is the mass
of the unseen object?
14.
Explain how Newtonian
physics is an approximation to relativity.
15.
What are gravitational
waves? Have they been detected?
16.
How would the Newtonian
theory explain the orbit of the Earth around the Sun? What would the
explanation be in general relativity?
17.
What is the “rubber
sheet” analogy for spacetime, and why is it useful for explaining gravity and
gravitational waves?
18.
Describe two early
classical tests of the general relativity.
19.
Explain why Einstein’s
theory of general relativity predicts the existence of gravitational lensing.
20.
How might we be able to
detect events like colliding neutron stars even if we don’t detect any light
from them?
21.
Explain how mass and
compactness would play into affecting the way an object distorts the fabric of
spacetime.
22.
What is the Equivalence
Principle? Describe a consequence of the equivalence principle for astronauts
orbiting in the space station.
23.
Galileo supposedly
experimented with gravity by dropping two objects of different masses from the
Leaning Tower of Pisa at the same instant and observing that they hit the
ground at the same time. If Albert Einstein had done the experiment, how would
his conclusion have differed from Galileo’s?
24.
What does singularity mean in the context of black holes?
25.
What is the difference
between the singularity and the event horizon of a black hole?
26.
Explain why Hawking
radiation may not be a practical way to observe black holes.
27.
Describe two possible
ways to make a stellar-size black hole.
28.
You repeatedly measure
the radial velocity of what seems to be a single main-sequence star like the
Sun but find that it in fact is in a tight orbit around another object that
remains unseen. From measurement of the velocity and orbital period, you
calculate that the unseen object has a mass 20 times that of the Sun-like star.
Why might this object be a black hole?
29.
Roughly estimate the
magnitude of the tidal acceleration between the feet and the head of an
astronaut when he is approaching a 1 M⊙ black hole (BH) and is
100 km from it, as in the figure shown below. Compare that acceleration with
the standard acceleration of gravity here on Earth. Would “spaghettification”
be a good way to describe the effect on the human being?
30.
Based the line of
reasoning you (hopefully) outlined in the previous problem, would it be more
likely for an astronaut to be subject of “spaghettification” when 100 km away
from the event horizon of a supermassive BH of 100 million solar masses or when
100 km away from the event horizon of a 1 solar mass BH?
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Chapter 19: Galaxies
Learning
Objectives.
Define the bold-faced vocabulary terms within the chapter.
19.1 Galaxies Come in Different Shapes and
Sizes
Evaluate how well Shapley and Curtis’s arguments about, and
Hubble’s measurements of, the nature of galaxies conform to the established
process of science laid out in this text.
Multiple Choice: 1, 2, 4, 11, 14, 16
Short Answer: 5, 6
Illustrate the essential morphological (shape)
characteristics of the Hubble types of galaxies.
Multiple Choice: 3, 5, 6, 7, 8, 28
Short Answer: 3, 4
Show how stellar orbits determine the morphology of a galaxy
or its components.
Multiple Choice: 15
Short Answer: 1
Compare and contrast spiral and elliptical galaxies in terms
of their gas and dust content, color, luminosity, stellar populations, and
mass.
Multiple Choice: 9, 10, 12, 13, 17, 18
Short Answer: 2
19.2 Astronomers Use Several Methods to
Find Distances to Galaxies
Illustrate why measurements to increasingly distant objects
require overlapping scales, each building on the previous “rung” of a “distance
ladder.”
Multiple Choice: 26
Short Answer: 8
Explain what is meant by “standard candle.”
Multiple Choice: 19, 22, 23
Compare and contrast the observations needed to use the
various distance indicators in this chapter, including Cepheids, Type Ia
supernovae, and Hubble’s law.
Multiple Choice: 20, 21, 24, 25, 27, 29
Short Answer: 9, 10, 11
19.3 Galaxies Are Mostly Dark Matter
Explain how the amount of matter inferred from
electromagnetic radiation can differ from that inferred from gravity.
Multiple Choice: 43
Short Answer: 17, 18
Illustrate how flat rotation curves imply the need for dark
matter.
Multiple Choice: 42, 52
Short Answer: 16, 19
Summarize the observational evidence for dark matter in
spiral and elliptical galaxies.
Multiple Choice: 44, 48, 49, 50, 51, 53
Short Answer: 15
Compare and contrast the behavior of normal and dark matter.
Multiple Choice: 45
Summarize the candidates for dark matter, and the
observational evidence supporting or refuting each candidate.
Multiple Choice: 46, 47
Short Answer: 14
19.4 Most Galaxies Have a Supermassive
Black Hole at the Center
Explain why astronomers initially believed quasars were
stars.
Multiple Choice: 59, 61, 68
Illustrate how the period of variability of an object places
limits on its physical size.
Multiple Choice: 63, 67, 69
Short Answer: 26, 30
Summarize the observational evidence for galaxies containing
supermassive black holes at their centers, since black holes emit no observable
radiation of their own.
Multiple Choice: 70
Explain how an AGN differs from the nucleus of an ordinary
galaxy.
Multiple Choice: 57, 60, 62, 64, 66
Short Answer: 22, 23, 25, 28, 29
Illustrate the unified model of AGN and how different
perspectives can lead to classification of the central engine as a different
type of AGN.
Multiple Choice: 58, 65
Short Answer: 21, 24, 27
Working It Out 19.1
Use the relationship between distance, luminosity, and
brightness to calculate the distance to a standard candle.
Short Answer: 7
Working It Out 19.2
Use Doppler shifts and the Hubble redshift-distance law to
relate recessional velocity, redshift, and distance.
Multiple Choice: 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41
Short Answer: 12, 13
Working It Out 19.3
Calculate the size, density, and accretion rate of a
supermassive black hole.
Short Answer: 20
MULTIPLE CHOICE
1.
What caused early
astronomers to believe that our galaxy is only about 6,000 light-years across?
a.
Telescopes were not
powerful enough to observe stars farther away.
b.
Interstellar dust
blocked visible light from stars farther away.
c.
Stars farther away
could not be resolved as individual objects.
d.
Astronomers
miscalculated the distances to stars, believing that the stars were 50 times
closer than they actually were.
e.
Astronomers assumed all
red stars were faint main- sequence stars, and they confused more luminous red
giants with them.
2.
In the Great Debate of
1920, Curtis and Shapley argued over whether or not
a.
the Big Bang occurred.
b.
the age of the universe
was 14 billion years.
c.
the universe was
contracting.
d.
life existed outside
Earth.
e.
the spiral nebulae were
located outside the Milky Way.
3.
Which of the following
Hubble images shows an edge-on disk galaxy?
4.
Astronomers have known
that galaxies are separate entities outside of our own for roughly the last
a.
35 years.
b.
60 years.
c.
90 years.
d.
150 years.
e.
210 years.
5.
The Hubble
classification scheme for galaxies sorts them by their
a.
evolutionary state.
b.
mass.
c.
amount of dust.
d.
amount of dark matter.
e.
visual appearance.
6.
What type of galaxy is
shown in the figure below?
a.
a giant elliptical
b.
an ordinary spiral
galaxy
c.
an irregular galaxy
d.
a barred spiral
e.
a dwarf elliptical
7.
What type of galaxy is
shown in the figure below?
a.
a giant elliptical
b.
a regular spiral galaxy
c.
an irregular galaxy
d.
a barred spiral
e.
a dwarf elliptical
8.
In spiral galaxies, the
size of the central bulge is correlated with the
a.
tightness of the spiral
arms.
b.
luminosity of the
galaxy.
c.
age of the galaxy.
d.
thickness of the disk.
e.
presence of an active
nucleus.
9.
Active star formation
does not typically occur in elliptical galaxies because they
a.
rotate too fast.
b.
contain little
molecular hydrogen.
c.
are too massive.
d.
are too far away.
e.
usually contain active
nuclei.
10.
Elliptical galaxies
appear red because they
a.
are moving away from
us.
b.
contain mostly ionized
hydrogen gas.
c.
contain mostly old
stars.
d.
contain lots of dust.
e.
contain a mix of old
and young stars.
11.
One of the first
philosophical speculations about the nature of spiral nebulae being “island
universes” like our Milky Way, only much farther, came from
a.
Charles Messier.
b.
Immanuel Kant.
c.
Edwin Hubble.
d.
Harlow Shapley.
e.
Heber Curtis.
12.
The dark features in
the HST image in in the figure shown below indicate
a.
collections of cool
stars.
b.
clumps of dark matter.
c.
copious amounts of dark
energy.
d.
large amounts of dust.
e.
faulty pixels on the
CCD camera.
13.
The receding speed of
spiral galaxies may also render their colors __________ due to
__________________.
a.
bluer; relativistic
beaming
b.
bluer; Doppler effect
c.
redder; relativistic
beaming
d.
redder; Doppler effect
e.
redder; galactic
interactions
14.
What did Edwin Hubble
study in the Andromeda Galaxy that proved it was an individual galaxy and not
part of our own Milky Way?
a.
Cepheid stars
b.
Type Ia supernovae
c.
globular clusters
d.
red giant stars
e.
RR Lyrae variables
15.
Stars in the disks of
spiral galaxies have orbits that are
a.
randomly oriented.
b.
constantly getting larger.
c.
mostly aligned in the
same plane.
d.
spiral-shaped.
e.
unaffected by dark
matter.
16.
The nearest big galaxy,
Andromeda, is at an estimated distance of
a.
780 Mpc.
b.
0.78 kpc.
c.
0.78 Mpc.
d.
2.5 × 106 kpc.
e.
250 × 103 Mpc.
17.
The disks of spiral
galaxies appear blue because
a.
they are moving toward
us.
b.
they contain a
relatively high concentration of low-mass stars.
c.
they contain active
regions of star formation.
d.
they contain more
metals that, when ionized, emit blue light.
e.
stars collide with each
other frequently in these dense regions and explode as Type Ia supernovae.
18.
Which of the following
would not be found in an elliptical
galaxy?
a.
low-mass stars
b.
Type Ia supernovae
c.
Type II supernovae
d.
planetary nebulae
e.
hot gas
19.
To be a standard
candle, an object must have a constant
a.
lifetime.
b.
brightness.
c.
luminosity.
d.
distance.
e.
mass.
20.
According to Hubble’s
law, as the distance of a galaxy ____________ its _______________ increases.
a.
increases; luminosity
b.
increases; recessional
velocity
c.
decreases; luminosity
d.
decreases; recessional
velocity
e.
decreases; peculiar
velocity
21.
Astronomers use
galactic redshift to estimate
a.
gravity.
b.
luminosity.
c.
velocity.
d.
mass.
e.
distance.
22.
Why can Type Ia
supernovae be used to determine a galaxy’s distance?
a.
Type Ia supernovae
occur only in very luminous galaxies.
b.
Most Type Ia supernovae
have approximately the same luminosity.
c.
Most Type Ia supernovae
have approximately the same size.
d.
A Type Ia supernova
occurs in a typical galaxy about once every 100 years.
e.
Type Ia supernovae
occur even in very small galaxies.
23.
Which distance indicator
can be used to measure the most distant objects?
a.
Cepheids
b.
Parallax
c.
Type Ia supernovae
d.
main-sequence fitting
e.
RR Lyrae stars
24.
If the distance of a
galaxy at a redshift z = 0.5 is 1,800 Mpc, how many years back into the past are we
looking when we observe this galaxy?
a.
500 million years
b.
2 billion years
c.
6 billion years
d.
9 billion years
e.
10 billion years
25.
The spectra of most
galaxies tell us that
a.
galaxies appear to be
moving away from us.
b.
their light comes
predominantly from objects other than stars.
c.
most galaxies contain
clouds of gas that are absorbing their favorite wavelengths.
d.
galaxies in the past
rotated at a faster rate than they do today.
e.
galaxies are rushing
through space in all directions.
26.
Which of the following
lists distance indicators from nearest to farthest?
a.
Cepheids, parallax,
main-sequence fitting, Type Ia supernovae
b.
parallax, main-sequence
fitting, Cepheids, Type Ia supernovae
c.
parallax, main-sequence
fitting, Type Ia supernovae, Cepheids
d.
main-sequence fitting,
parallax, Cepheids, Type Ia supernovae
e.
Cepheids, Type Ia
supernovae, main-sequence fitting, parallax
27.
The Tully-Fisher method
of determination of distances to galaxies is based on the correlation between
a.
color and redshift.
b.
star formation rate and
morphological type.
c.
width of emission lines
and black hole accretion rate.
d.
rotational speed and
luminosity.
e.
dark matter radial
profile and X-ray brightness.
28.
Which galaxies are
sometimes called “armless” disks?
a.
ellipticals
b.
irregulars
c.
dwarfs
d.
SOs
e.
barred spirals
29.
Type Ia supernovae have
an absolute magnitude of −19.3. If you discover a Type Ia supernovae in a distant
galaxy that has an apparent magnitude of 22, then how far away is this galaxy?
a.
0.3 Mpc
b.
40 Mpc
c.
1,200 Mpc
d.
1,800 Mpc
e.
3,500 Mpc
30.
The nearest known
quasar shows a redshift of z = 0.0516, which
means it is at a distance of
a.
220 Mpc.
b.
450 Mpc.
c.
100 Mpc.
d.
15400 Mpc.
e.
100 kpc.
31.
For the more distant
quasars, the emission lines that would normally occur in the visible domain
would be shifted into
a.
UV.
b.
X-rays.
c.
gamma rays.
d.
IR.
e.
radio.
32.
A certain spectral line
of rest wavelength lrest (i.e., laboratory value) is shifted by 100 nm in a quasar. A
second line with a rest wavelength half the (rest) value of the first one would
be shifted by
a.
200 nm.
b.
100 nm.
c.
500 nm.
d.
50 nm.
e.
1000 nm.
33.
If a galaxy has an
apparent velocity of 700 km/s, what is its distance if the Hubble constant is
assumed to be 70 km/s/Mpc?
a.
10 Mpc
b.
70 Mpc
c.
100 Mpc
d.
700 Mpc
e.
1,000 Mpc
34.
If you found a galaxy
with an Hα emission line that had a wavelength of 756.3 nm, what would
be the galaxy’s redshift? (Note that the rest wavelength of the Hα emission line is
656.3 nm.)
a.
0.05
b.
0.07
c.
0.10
d.
0.13
e.
0.15
35.
If the distance of a
galaxy is 10 Mpc, what is its recessional velocity if the Hubble constant is
assumed to be 70 km/s/Mpc?
a.
700 km/s
b.
1,000 km/s
c.
3,500 km/s
d.
5,000 km/s
e.
7,000 km/s
36.
You see a galaxy in
which the Hα line (rest wavelength = 656.3 nm) is
observed at a wavelength of 756.3 nm. What would be the observed wavelength of
a particular helium line that has a rest wavelength of 1,083 nm?
a.
1,083 nm
b.
1,183 nm
c.
1,248 nm
d.
1,440 nm
e.
3,142 nm
37.
If a galaxy has a
recessional velocity of 50,000 km/s, at what wavelength will you observe the Hαemission line?
(Note that the rest wavelength of the Hα emission line is
656.3 nm.)
a.
695.7 nm
b.
719.4 nm
c.
742.3 nm
d.
765.7 nm
e.
1750 nm
38.
If you found a galaxy
with an Hα emission line that had a wavelength of 756.3 nm, what would
be the galaxy’s distance if the Hubble constant is 70 km/s/Mpc? (Note that the
rest wavelength of the Hα emission line is 656.3 nm.)
a.
650 Mpc
b.
760 Mpc
c.
3,200 Mpc
d.
6,400 Mpc
e.
7,600 Mpc
39.
If the spectrum of a
distant galaxy is observed to have a calcium K absorption line that occurs at a
wavelength of 500.4 nm, what is this galaxy’s distance if the rest wavelength
of this absorption line is 393.4 nm? Assume the Hubble constant is 70 km/s/Mpc.
a.
720 Mpc
b.
952 Mpc
c.
1,166 Mpc
d.
2,580 Mpc
e.
3,730 Mpc
40.
In the figure shown
below, the upper spectrum is from hydrogen at rest in a laboratory, and the
lower spectrum is from a galaxy. How far away is this galaxy?
a.
110 Mpc
b.
170 Mpc
c.
230 Mpc
d.
280 Mpc
e.
340 Mpc
41.
You read about the discovery
of quasars with redshift z larger than 1. This means that
a.
their host galaxies are
receding at speeds exceeding the speed of light.
b.
the measurements of
redshift must be wrong, z cannot exceed 1.
c.
the relationship
between z and receding speed must account for relativistic corrections.
d.
the speed of light can
exceed c in the case of distant quasars.
e.
quasars must contain a
lot of dark matter.
42.
The rotation curve of a
galaxy is a plot of the rotation speed as a function of the
a.
galaxy’s luminosity.
b.
mass of the dark matter
halo.
c.
brightness of the
luminous matter in the galaxy.
d.
radius from the center.
e.
ages of star clusters.
43.
If you measure the
velocity of a cloud of gas that is rotating around the center of a galaxy in a
circular orbit with radius R, you can determine the
a.
total mass of the
galaxy.
b.
mass of the stars and
gas in the galaxy.
c.
mass of the galaxy
enclosed within the radius R.
d.
mass of the galaxy
located outside the radius R.
e.
mass of luminous matter
within the radius R.
44.
What makes up the
majority of the mass of an individual spiral galaxy?
a.
a central supermassive
black hole
b.
dark matter
c.
massive O- and B-type
stars
d.
cold molecular gas
clouds
e.
low-mass G-, K-, and
M-type stars
45.
Dust in galaxies does
not count as dark matter because
a.
it absorbs only some
wavelengths of light but not all wavelengths as dark matter does.
b.
it interacts with
light.
c.
it is found only in
spiral disks, whereas dark matter is also found in elliptical galaxies, too.
d.
dust is easily
destroyed by dark matter.
e.
there is never enough
to account for all the gravity in galaxies.
46.
Dark matter is most
likely made up of
a.
elementary particles
that have mass but do not interact much with normal matter.
b.
supermassive black
holes.
c.
faint stellar remnants
such as white dwarfs and neutron stars.
d.
free-floating Jupiter-mass
planets.
e.
cold concentrations of
dust.
47.
How have astronomers
searched for evidence of MACHOs in the halo of the Milky Way?
a.
They search for stars
that are binary companions of MACHOs.
b.
They search for rapidly
moving, massive gas clouds.
c.
They search for
disturbances in the background of gravitational waves.
d.
They search for distant
stars with light briefly amplified by gravitational lensing.
e.
They search for close
binary stars undergoing mass transfer.
48.
The density of ordinary
luminous matter can exceed the density of dark matter in which parts of
galaxies?
a.
everywhere inside
galaxies
b.
only in the outer
regions of galaxies
c.
only in star clusters
d.
near the centers of
galaxies
e.
only around an AGN
49.
Roughly what percentage
of the total mass of a galaxy is made up of luminous, or normal, matter?
a.
5–10 percent
b.
25–30 percent
c.
40–50 percent
d.
70–75 percent
e.
90–95 percent
50.
How did astronomers
determine that elliptical galaxies are composed mostly of dark matter?
a.
They measured the
velocities of stars in the inner regions of the galaxies.
b.
They measured the
rotation rates of gas as a function of distance from the centers of the
galaxies.
c.
They measured the
amount of gravitational pull elliptical galaxies have on companion galaxies.
d.
They assumed that the
proportion of dark matter was roughly the same as in spiral galaxies.
e.
They measured the X-ray
emission from hot gas gravitationally bound to the galaxies.
51.
How can we measure the
mass of an elliptical galaxy?
a.
by measuring the speeds
of stars in the nucleus
b.
by observing the
velocity of the hot, X-ray emitting gas that surrounds the galaxy
c.
by measuring the number
of H II regions in the galaxy
d.
by measuring how many
supernovae go off each century
e.
by measuring the amount
of blue light in the galaxy
52.
For which galaxies
would it be easiest to measure rotation curves?
a.
elliptical
b.
face-on barred spirals
c.
face-on normal spirals
d.
face-on S0s
e.
edge-on spirals
53.
If a galaxy had no dark
matter, how would the velocity (v) of a star that orbited far outside
the visible extent of the galaxy depend on its distance (r) from the
center of the galaxy? Hint: Think about the Keplerian motion of planets around
the Sun.
a.
v ∝ r−2
b.
v ∝ r−1
c.
d.
v ∝ r
e.
v ∝ r2
54.
Assume that when a
supermassive black hole accretes gas, approximately 20 percent of the accreted
mass is converted directly into energy, which is radiated away. If a quasar has
a luminosity of 1013 L⊙, then
what must be its mass accretion rate?
a.
1 M⊙ per year
b.
3.5 M⊙ per
year
c.
1 M⊙ per century
d.
3.5 M⊙ per century
e.
1 M⊙ per million years
55.
Which of the following
functions correctly illustrates the relation between mean density and black
hole mass?
a.
ρ ∝ M−2
b.
ρ ∝ M−1
c.
d.
ρ ∝ M
e.
ρ ∝ M2
56.
Scientists estimate
that the efficiency of mass accretion onto a supermassive black hole is about
15 percent. Compared with the energetic efficiency of the stellar fusion of
hydrogen into helium, the accretion is
a.
about 20 times more
efficient.
b.
about 20 times less
efficient.
c.
equally inefficient.
d.
twice as efficient.
e.
half as efficient.
57.
AGNs are most likely
powered by
a.
extremely dense star
clusters.
b.
accreting supermassive
black holes.
c.
ultradense molecular
clouds.
d.
decaying dark matter.
e.
supernova explosions.
58.
The unified model of
AGN suggests that quasars, Seyfert galaxies, and radio galaxies are
a.
unrelated, although
they are all very luminous galaxies at radio wavelengths.
b.
powered by similar mass
accretion rates onto supermassive black holes.
c.
driven by violent
mergers of two gas-rich spiral galaxies.
d.
similar phenomena but
viewed from different orientation angles.
e.
all powered by high
rates of star formation and supernova explosions.
59.
In most cases it is
impossible to observe the host galaxies of quasars because
a.
quasars outshine the
host galaxies by a few orders of magnitude.
b.
the supermassive black
holes have “eaten” all the stars in those galaxies.
c.
the host galaxies of
quasars have too much dark matter.
d.
the host galaxies of
quasars have too much obscuring dust.
e.
the galaxies hosting
quasars are much smaller than our own Milky Way.
60.
What happens to active
galaxies when their AGNs run out of fuel?
a.
The black holes
powering them collapse even further.
b.
They simply become
normal galaxies.
c.
They slowly dissipate
into clouds of gas and dust.
d.
They eventually pull in
material from farther out, starting the AGN process all over again.
e.
They explode as
gamma-ray bursts.
61.
Quasars were first
discovered in which region of the electromagnetic spectrum?
a.
X-ray
b.
gamma-ray
c.
radio
d.
infrared
e.
visible
62.
What do the broad
emission lines in quasar spectra tell astronomers about these objects?
a.
They are very far away.
b.
They are moving away
from us.
c.
They have rapid
internal motions.
d.
They are very dense.
e.
They have few heavy
elements.
.
63.
How do we know that
AGNs have sizes on the order of our Solar System?
a.
Quasars and Seyfert
galaxies are stellarlike sources.
b.
Their brightness varies
by factors of a few.
c.
The emission lines in
their spectra show gas rotating at speeds of thousands of km/s.
d.
Their brightness varies
on timescales ranging from hours to a day.
e.
We can measure their
angular size, which gives us the physical size when we know the distance.
64.
The formation of the
Solar System and the existence of AGNs both demonstrate the
a.
importance of how
luminosity varies with time.
b.
high efficiency of
nuclear fusion.
c.
importance of accretion
disks.
d.
importance of living in
the center of a galaxy.
e.
existence of dark
matter.
65.
In some radio galaxies,
we see only one side of the jet because
a.
the black hole produces
a jet in only one direction.
b.
of relativistic
beaming.
c.
the other side is
inside the black hole’s event horizon.
d.
of dust obscuration.
e.
of dark matter that
blocks the light from one side of the jet.
66.
We interpret the
presence of more AGNs in the past than today to indicate that
a.
there were fewer
galaxy-galaxy interactions in the past.
b.
there were more
galaxy-galaxy interactions in the past.
c.
supermassive black
holes were larger in the past.
d.
today’s AGNs are hidden
primarily by large amounts of cold gas and dust.
e.
AGNs had bigger central
black holes in the past.
67.
Quasars remain
unresolved sources, even with the best telescopic observations, because they
a.
are too luminous.
b.
occupy a very small
volume.
c.
are quite blue.
d.
produce copious amounts
of radio energy.
e.
host supermassive black
holes.
68.
Which of these
statements about quasars is false?
a.
Quasars are extremely
luminous.
b.
Quasars are rare in our
local vicinity.
c.
Quasars have high
brightnesses.
d.
Quasars are extremely
massive.
e.
Quasars are located at
the centers of some active galaxies.
69.
If a Seyfert galaxy’s
nucleus varies in brightness on the timescale of 10 hours, then what is the
approximate upper limit for the size of the emitting region?
a.
20 AU
b.
30 AU
c.
50 AU
d.
70 AU
e.
120 AU
70.
More luminous giant
galaxies tend to have __________ supermassive black holes at their centers.
a.
more massive
b.
radio quiet
c.
more luminous
d.
slower rotating
e.
less massive
SHORT ANSWER
1.
What determines the
three-dimensional shapes of galaxies?
2.
How do the current star
formation rates of spiral and elliptical galaxies compare?
3.
How did Hubble use his
tuning fork diagram to classify galaxies? Is there any significance to this
organization?
4.
How do we know that the
stellar disks in spiral galaxies are flat? How do we know that elliptical
galaxies are not flat?
5.
What were the positions
taken by Heber Curtis and Harlow Shapley in their “Great Debate,” and how were
both of them partially correct?
6.
How did Edwin Hubble
definitively prove that “spiral nebulae” were individual galaxies that were
separate from the Milky Way?
7.
The light curve of a
Cepheid variable star allows astronomers to infer its mean apparent magnitude
at 15.6 and the period of pulsation about 4.8 days. Utilizing the calibrated
relation between period and luminosity for Classical Cepheids, its absolute
magnitude is estimated at –3.6. What is the distance to that Cepheid star and,
implicitly, the distance to its host galaxy?
8.
Explain why the light
gray bands (labeled Radar, Parallax, etc.) that cover certain ranges of
distances in the figure shown below overlap with one another both at the beginning
and at the end?
9.
Name two “rungs” in the
distance ladder that let us estimate the value of the Hubble constant.
10.
Order the following
objects by the maximum distance they can be detected: Cepheid variables, RR
Lyrae stars, Type Ia supernovae, and low-mass main-sequence stars. Explain your
reasoning.
11.
Explain why the linear
Hubble’s law has no free term.
12.
The spectrum of a
galaxy is observed to have an Hα emission line at
a wavelength of 928.7 nm. What is its redshift? (Note that the rest wavelength
of the Hα emission line is 656.3 nm.)
13.
The spectrum of a
galaxy is observed to have an Hα emission line at
a wavelength of 856.3 nm. What is its distance if the Hubble constant is
assumed to be 70 km/s/Mpc? (Note that the rest wavelength of the Hα emission line is
656.3 nm.)
14.
What is the most likely
candidate for making up the dark matter in galaxies?
15.
How do we know that
many elliptical galaxies contain significant amounts of dark matter?
16.
What is plotted on a
rotation curve, and what can it tell us about a galaxy?
17.
If the rotational speed
of the gas in the disk of a spiral galaxy is 100 km/s at a distance of 26,000
light-years from its center, then what is the mass enclosed within this radius?
If the mass of luminous matter inside this radius is 5 billion M⊙ then what fraction of the galaxy’s mass is made of dark
matter (within that same radius)? (Hint: Recall the technique learned earlier
in Chapter 4.)
18.
Outside the dark matter
halo of a galaxy, how should the speed of an orbiting body such as a satellite
dwarf galaxy depend on its distance from the giant galaxy’s center?
19.
Estimate the total mass
enclosed within 100 kpc radius, based on the rotation curve shown in the figure
below. (Hint: Recall the technique learned earlier in Chapter 4.)
20.
Microquasars are scaled-down
versions of quasars, the former being powered by accretion onto stellar-sized
black holes, the material being provided by a companion star. The underlying
mechanism seems to be very similar in both microquasars and their supermassive
AGN. Typical microquasars have luminosities that are ten orders of magnitude
lower than ordinary quasars. What is the typical level of accretion rate in the
two cases?
21.
What are the main
components of an AGN?
22.
If there is a 4 million
M⊙ black hole at the center of our galaxy, why is our own
galaxy not an AGN?
23.
How do we explain that
“billions of galaxies are closer to Earth than is the nearest quasar”?
24.
Give three examples of
types of active galactic nuclei and give one reason why each is unique.
25.
What is the difference
between a Seyfert galaxy and a normal spiral galaxy?
26.
How do astronomers know
that AGNs are as small as our Solar System?
27.
How does the appearance
of an AGN depend on the viewing angle to the nucleus?
28.
What is the connection
between active galaxies and galactic mergers?
29.
Why is a higher
percentage of distant galaxies classified as AGNs compared with the percentage
of galaxies around us locally?
30.
If an AGN varies its
brightness on a timescale of 4 hours, then what is the size limit of the AGN
measured in AU?
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