Astronomy Homework 10
How does it compare with the amount of energy released by the Sun during its entire main-sequence lifetime?
(EsupernovaExplosion/ESunTotal)~10^2
Which of the following statements about gravitational waves are true?
-The emission of gravitational waves from merging black holes is predicted by Einstein's general theory of relativity. -The first direct detection of gravitational waves, announced in 2016, came from the LIGO observatory. -Two orbiting neutron stars or black holes will gradually spiral toward each other as a result of energy being carried away by gravitational waves.
Process of Science: Identifying Stellar Corpses C. The Chandra X-Ray Observatory has detected X rays from a star system that contains a main-sequence star of spectral type B6. The X-ray emission is strong and fairly steady, and no sudden bursts have been observed. Which of the following statements are reasonable conclusions about this system?
-The main-sequence star orbits either a neutron star or a black hole. -Gas from the main-sequence star makes an accretion disk around another object
Using this formula, estimate the amount of gravitational potential energy released in a massive star supernova explosion.
10^46 jouls
Based on current understanding, the minimum mass of a black hole that forms during a massive star supernova is roughly _________.
3 solar masses
How thick a layer would Earth form as it wraps around the neutron star's surface? Assume that the layer formed by Earth has the same average density as the neutron star. (Hint: Consider the mass of Earth to be distributed in a spherical shell over the surface of the neutron star and then calculate the thickness of such a shell with the same mass as Earth. The volume of a spherical shell is approximately its surface area times its thickness: Vshell=4πr2×thickness. Because the shell will be thin, you can assume that its radius is the radius of the neutron star.)
7mm
What is a nova? Describe the process that creates a nova, and what a nova looks like.
A nova is when a white dwarf gains back enough hydrogen to start fusion again and become a star. The flash causes a bright light flash that lasts few weeks.
Which of statement below about black holes is not true?
A spaceship passing near a 10 solar-mass black hole is much more likely to be destroyed than a spaceship passing at the same distance from the center of a 10 solar-mass main-sequence star.
Describe the mass, size, and density of a typical white dwarf. How does the size of a white dwarf depend on its mass?
A white dwarf is a type of star that is faint for its white-hot temperature. A white dwarf star has the mass of the sun and the radius of the earth, but does not have enough light or other radiation to be easily found. The white dwarfs are connected with stellar evolution. A white dwarf is the hot core of a star, left over after the star uses up its nuclear fuel and dies. It is made mostly of carbon and is topped by a thin layer of hydrogen and helium gases. The physical conditions inside the star are unusual. The central density is about 1 million times more than water!
Based on the curves shown here, which of the following statements best describes how we can distinguish a massive star supernova from a white dwarf supernova?
A white dwarf supernova is brighter at its peak and over a few months fades more steadily than a massive star supernova.
Choose the correct description of processes, which cause a white dwarf supernova.
A white dwarf supernova occurs when the white dwarf gains enough mass for the carbon interior of the star to begin carbon fusion. The fusion begins almost instantly throughout the star, so the entire star ignites and the white dwarf explodes completely.
Based on current evidence, which of the following statements about gamma ray bursts is true?
All those that we have detected occurred in distant galaxies.
Choose the correct description of what accretion disks are, and why do we find them only in close binary systems.
An accretion disk is a disk of orbiting material that is falling toward a central body, like a white dwarf. We see these only in close binary systems because they require material to be transferred from one star to another.
Consider the statement from Part A reading "a 3-solar-mass black hole may be hidden between Jupiter and Saturn." How do we know this statement is not true?
An object of that mass would disrupt the orbits of the planets in our solar system.
Sirius, the brightest star in the night sky, is actually a binary star system. Sirius A is main-sequence star and Sirius B is a white dwarf. Nearly all the visible light we see from Sirius comes from Sirius A. But when we photograph the system with X-ray light, as shown here, Sirius B is the brighter of the two stars. Why?
As a white dwarf, Sirius B is much hotter than Sirius A and thus emits more X rays.
Choose the correct description, of what happens to the electron speeds in a more massive white dwarf.
As the mass of a white dwarf increases, the pressure must increase to resist gravity. To do this, the electrons must move faster.
Choose the correct explanation of how does the accretion disk provide a white dwarf with a new source of energy that we can detect from Earth.
As the material falls onto a white dwarf, gravitational energy is turned into heat. The heat provides the white dwarf with a new energy source, allowing it to glow in the ultraviolet.
How is an X-ray burst (in an X-ray binary system) similar to a nova?
Both involve explosions on the surface of stellar corpse.
Which of the following statements about degeneracy pressure is not true?
Degeneracy pressure can arise only from interactions among electrons.
What is degeneracy pressure, and how is it important to the existence of white dwarfs and neutron stars? What is the difference between electron degeneracy pressure and neutron degeneracy pressure?
Degeneracy pressure is a type of pressure unrelated to an object's temperature, which arises when electrons or neutrons are packed so tightly that the exclusion and uncertainty principles come into play. Since white dwarfs are essentially the exposed core of a dead core, there has to be pressure pushing against gravity equally to prevent the white dwarf from crushing under gravities forces.
How does a black hole form from a massive star?
During a supernova, if a star is massive enough for its gravity to overcome neutron degeneracy of the core, the core will be compressed until it becomes a black hole.
Which of the following is closest in size (radius) to a white dwarf?
Earth
Which of the following diagrams best represents the scale of Earth in comparison to a neutron star?
Earth big. neutron star tiny.
What would happen if the Sun suddenly became a black hole without changing its mass?
Earth would remain in the same orbit.
Which of the following best describes why a white dwarf cannot have a mass greater than the 1.4-solar-mass limit?
Electron degeneracy pressure depends on the speeds of electrons, which approach the speed of light as a white dwarf's mass approaches the 1.4-solar-mass limit.
Which of the following statements about electron degeneracy pressure and neutron degeneracy pressure is true?
Electron degeneracy pressure is the main source of pressure in white dwarfs, whereas neutron degeneracy pressure is the main source of pressure in neutron stars.
No visible light can escape a black hole, but things such as gamma rays, X rays, and neutrinos can.
F
There is no upper limit to the mass of a neutron star.
F
The white dwarf at the center of the Helix Nebula has a mass three times the mass of our Sun.
False, because the maximum mass of a white dwarf is about 1.4 solar masses.
I observed a white dwarf supernova occurring at the location of a single (not binary) white dwarf.
False, white dwarf supernovae arise from mass transfer from a companion star and thus cannot occur outside binary systems.
In what direction would the gravitational force from the hoop pull on the person's head? In what direction would it pull on the person's feet?
Gamma-ray bursts originate from beyond the Milky Way Galaxy because they are distributed uniformly on the sky
Consider the statement from Part A reading "the singularity of a black hole has infinite density." Why is this statement in the "unknown" bin?
General relativity and quantum mechanics give different answers about the nature of singularity.
A binary system that looks like the one shown in this painting should shine brightly in X rays. Which one of the four labeled regions is the source of most of the X rays?
II
Choose the correct description, how does this behavior lead to the white dwarf limit for mass.
If mass of the white dwarf becomes so great that the electrons would have to move faster than light to resist the gravity, the white dwarf must collapse into a neutron star. This limit is about 1.4 MSun.
Which of the following statements about black holes is not true?
If the Sun magically disappeared and was replaced by a black hole of the same mass, Earth would soon be sucked into the black hole.
Suppose you are falling into a black hole. How will you perceive the passage of your own time? How will outside observers see time passing for you? Briefly explain why your trip into a stellarmass black hole is likely to be lethal.
If you fell into a black hole time would be mear seconds until you disappear into oblivion, you'd seem to be in a dead stop on the point of no return. It would be potentially deadly because gravity would stretch you in opposite directions, while the pressure would destroy you.
Which statement concerning black hole masses and Schwarzschild radii is not true?
In a binary system with a black hole, the Schwarzschild radius depends on the distance from the black hole to the companion star.
What makes us think that the star system Cygnus X-1 contains a black hole?
It emits X-ray characteristics of an accretion disk, but the unseen star in the system is too massive to be a neutron star.
What makes us think that the star system Cygnus X-1 contains a black hole?
It emits X-rays characteristic of an accretion disk, but the unseen star in the system is too massive to be a neutron star.
What is this a picture of?
It is a painting of close binary star system in which the star on the right is a white dwarf surrounded by an accretion disk filled with gas drawn by gravity from the companion star on the left.
What do we mean by the singularity of a black hole?
It is the center of the black hole, a place of infinite density where the known laws of physics cannot describe the conditions.
What do we mean by the event horizon of a black hole?
It is the point beyond which neither light nor anything else can escape.
What is the ultimate fate of an isolated white dwarf?
It will cool down and become a cold black dwarf
Viewed from a distance, how would a flashing red light appear as it fell into a black hole?
Its flashes would shift to the infrared part of the spectrum.
From Part B, you know that from afar you'll never see the in-falling rocket cross the event horizon, yet it will still eventually disappear from view. Why?
Its light will become so redshifted that it will be undetectable.
How does the gravity of an object affect light?
Light coming from a compact massive object, such as a neutron star, will be redshifted.
Process of Science: Identifying Stellar Corpses D. What is the key observation needed to determine whether the compact object in Part C is a neutron star or a black hole?
Measure Doppler shifts in the spectrum of the main-sequence star so that you can determine the mass of the compact object.
Process of Science: Identifying Stellar Corpses B. The following items describe observational characteristics that may indicate that an object is either a neutron star or a black hole. Match each characteristic to the correct object; if the characteristic could apply to both types of object, choose the bin labeled "Both neutron stars and black holes."
NEUTRON STAR ONLY: 1. may emit rapid pulses of radio waves 6. may be in a binary system that undergoes X-ray bursts BLACK HOLE ONLY: 2. is detectable only if it is accreting gas from other objects 5. can have a mass of 10 solar masses BOTH NEUTRON STARS AND BLACK HOLES : 3. may be surrounded by a supernova remnant 4. may be located in an X-ray binary
How do we know that pulsars are neutron stars?
No massive object, other than a neutron star, could spin as fast as we observe pulsars spin.
Will our Sun ever undergo a white dwarf supernova explosion? Why or why not?
No, because it is not orbited by another star.
What do we mean by the singularity of a black hole? How do we know that our current theories are inadequate to explain what happens at the singularity?
Nothing can stop the crushing of gravity in a black hole, all the matter that forms a black hole should ultimately be crushed to an infinitely tiny and dense point in the black holes center. We call this point a singularity. Both of the scientific claims make sense scientifically but oppose each other which means they are inadequate.
Imagine that our Sun were magically and suddenly replaced by a black hole of the same mass (1 solar mass). What would happen to Earth in its orbit?
Nothing. Earth's orbit would remain the same.
Why do we think that supernovae should sometimes form black holes? What observational evidence supports the existence of black holes?
People think super novae should sometimes form black holes because as soon as the core exceeds the neutron star limit, gravity overcomes the neutron degeneracy pressure and the core collapses once again. This time, no known force can keep the core from collapsing into oblivion as a black hole. The only observational evidence of black holes since black hole emit no light, is the black holes influence of its gravitational influence on its surroundings.
Each Voyager spacecraft carries a "postcard" designed to be understandable to any aliens that might someday encounter it. On the "postcard," scientists pinpointed the location of Earth by triangulating it between pulsars. Why did the scientists choose pulsars rather than some other type of star?
Pulsars are easy to identify by their almost perfectly steady periods of pulsation.
Which statement about pulsars is not thought to be true?
Pulsars can form only in close binary systems.
Which of the following is not true about differences between novae and supernovae?
Supernovae eject gas into space but novae do not.
All pulsars are neutron stars, but not all neutron stars are pulsars.
T
Key Concept: Black Holes Each statement below makes a claim about black holes. Based on current scientific understanding of black holes, sort the statements into the correct bin according to whether the statement is:
TRUE : 4. a black hole can have the mass of a star in a space less than a few kilometers across 5. a black hole is an object smaller than its own Schwarzschild radius 8. two orbiting black holes can merge and emit gravitational waves 9. material from a binary companion can form an X-ray-emitting accretion disk around a black hole 10. a black hole can form during a supernova explosion NOT TRUE : 2. a 3-solar-mass black hole may be hidden between Jupiter and Saturn 3. a black hole will suck in any binary companion star 7. you would be squashed by gravity at the event horizon of any black hole 11. black holes emit x-ray light from within their event horizons UNKNOWN : 1. black holes make up 1% of the mass of the Milky Way Galaxy 6. the singularity of a black hole has infinite density
How does an accretion disk around a neutron star differ from an accretion disk around a white dwarf?
The accretion disk around a neutron star is much hotter and emits higher-energy radiation.
Which of the following best describes what would happen if a 1.5-solar-mass neutron star, with a diameter of a few kilometers, were suddenly (for unexplained reasons) to appear in your home town?
The entire Earth would end up as a thin layer, about 1 cm thick, over the surface of the neutron star.
Which of the following statements about gamma ray bursts is not true?
The events responsible for gamma ray bursts apparently produce only gamma rays, and no other light that we can hope to detect.
This painting shows an accretion disk around a black hole in a close binary star system. What physical law explains why matter flowing from the companion star orbits rapidly as it nears the black hole?
The law of conservation of angular momentum
What happens to two neutron stars that are orbiting so close together they emit gravitational waves?
The neutron stars will spiral together and merge.
Which statement about accretion disks is not true?
The primary factor determining whether a white dwarf has an accretion disk is the white dwarf's mass. The primary factor is not mass, but rather it is whether the white dwarf is in a close binary system where gas from its companion can spill over.
This series of images shows the pulsar at the center of the Crab Nebula looking bright every 0.033 second. Based on these data and current theory of pulsars, what can we conclude?
The pulsar is a neutron star that makes one full rotation every 0.033 second
Suppose a white dwarf is gaining mass because of accretion in a binary system. What happens if the mass someday reaches the 1.4-solar-mass limit?
The white dwarf undergoes a catastrophic collapse, leading to a type of supernova that is somewhat different from that which occurs in a massive star but is comparable in energy
Suppose that a white dwarf gains enough mass to reach the 1.4 solar-mass limit?
The white dwarf will explode completely as a white dwarf supernova.
Suppose that a white dwarf is gaining mass through accretion in a binary system. What happens if the mass someday reaches the 1.4 solar mass limit?
The white dwarf will explode completely as a white dwarf supernova.
Suppose two neutron stars are closely orbiting one another. What do scientists suspect will eventually happen to them, and why?
Their orbits will spiral inward until the two neutron stars merge because of energy lost through gravitational waves.
Choose the correct way to distinguish white dwarf and massive star supernovae observationally.
These supernovae, unlike the massive star supernovae, lack hydrogen lines in their spectra, allowing astronomers to tell the two types of supernovae apart.
Consider again the civilization described in the previous question. (They live on a planet orbiting 10 AU from a close binary star system that consists of a 15 M Sun red giant star and a 10 M Sun black hole surrounded by an accretion disk.) Through a bizarre (and scientifically unexplainable) fluctuation in the space-time continuum, a copy of a book from that civilization arrives on your desk; it is titled Iguoonos: How We Evolved. In the first chapter, you learn that these beings evolved from organisms that lived 5 billion years ago. Which of the following statements should you expect to find as you continue to read this book?
They evolved on a different planet in a different star system and moved to their current location.
Suppose you drop a clock toward a black hole. As you look at the clock from a high orbit, what will you notice?
Time on the clock will run slower as it approaches the black hole, and light from the clock will be increasingly redshifted.
From the viewpoint of an observer in the orbiting rocket, what happens to time on the other rocket as it falls toward the event horizon of the black hole?
Time runs increasingly slower as the rocket approaches the black hole.
Gamma-ray bursts are more likely to be observed in galaxies that are rapidly forming new stars than in galaxies containing only old stars.
True, because the characteristic of GRBs made them hard to observe galaxies that are rapidly forming new stars than in galaxies containing only old stars.
From your point of view, an object falling toward a black hole will never cross the event horizon.
True, because the object takes forever to cross the event horizon. You' ll see how the object vanishes from view due to the huge gravitational red-shift of light
Process of Science: Identifying Stellar Corpses A. The following items describe observational characteristics that could indicate that an object is either a white dwarf or a neutron star. Match each characteristic to the correct object.
WHITE DWARF : 2. may be in a binary system that undergoes nova explosions 5. emits most strongly in visible and ultraviolet 6. may be surrounded by a planetary nebula NEUTRON STAR : 1. can have a mass of 1.5 solar masses 3. may repeatedly dim and brighten more than once per second 4. may be in a binary system that undergoes X-ray bursts 7. may be surrounded by a supernova remnant
Consider the statement from Part A reading "black holes make up 1% of the mass of the Milky Way Galaxy." Why is this statement in the "unknown" bin?
We cannot detect all black holes and therefore don't know the percentage of the galaxy's mass they make up.
How do we know what happens at the event horizon of a black hole?
We don't know for sure: we only know what to expect based on the predictions of general relativity.
Consider again the civilization described in the previous question. (They live on a planet orbiting 10 AU from a close binary star system that consists of a 15 M Sun red giant star and a 10 M Sun black hole surrounded by an accretion disk.) One foolhardy day, a daring individual in their space force (let's call him Major Tom) decides to become the first of his species to cross the event horizon of the black hole. To add to the drama, he decides to go in wearing only a thin space suit, which offers no shielding against radiation, no cushioning against any forces, and so on. Which of the following is most likely to kill him first (or at least to start the process of killing him first)?
X rays from the accretion disk
Explain how the presence of a neutron star can make a close binary star system appear to us as an X-ray binary. Why do some of these systems appear to us as X-ray bursters?
X-Ray Binary-intense x-ray emission, close binaries that contain accreting neutron stars X-ray bursters- accreting neutron stars sporadically erupt with a pronounced spike in luminosity. Because these eruptions release energy primarily in the form of X-rays we call them x-ray bursts and systems that produce them are known as X-ray bursters.
Which of these objects has the largest radius?
a 1.2MSun white dwarf
Which of these objects has the smallest radius?
a 1.2MSun white dwarf
Which of these black holes exerts the weakest tidal force on an object near its event horizon?
a 10^6 MSun black hole
Which of the following is closest in size (radius) to a neutron star?
a city
What is an accretion disk?
a disk of hot gas swirling rapidly around a white dwarf, neutron star, or black hole
A teaspoonful of white dwarf material on Earth would weigh
a few tons
This graph shows data collected by a gamma ray telescope. What kind of event is it showing?
a gamma ray burst from a distant galaxy
Which of these neutron stars must have had its angular momentum changed by a binary companion?
a pulsar that pulses 600 times per second
From a theoretical standpoint, what is a pulsar?
a rapidly rotating neutron star
A typical neutron star is more massive than our Sun and about the size (radius) of _________.
a small asteroid (10 km in diameter)
Degeneracy pressure is the source of the pressure that stops the crush of gravity in all the following except
a very massive main-sequence star
What kind of star is most likely to become a white-dwarf supernova?
a white dwarf star with a red giant binary companion
The maximum mass of a white dwarf is _________.
about 1.4 times the mass of our Sun
If you had something the size of a sugar cube that was made of neutron star matter, it would weigh _________.
about as much as a large mountain
If you were inside the rocket that falls toward the event horizon, from your own viewpoint you would __________.
accelerate as you fall and cross the event horizon completely unhindered
Which of these binary systems is most likely to contain a black hole?
an X-ray binary containing an O star and another objects of equal mass
According to our modern understanding, what is a nova?
an explosion on the surface of a white dwarf in a close binary system
From an observational standpoint, what is a pulsar?
an object that emits flashes of light several times per second or more, with near perfect regularity
What is the basic definition of a black hole?
an object with gravity so strong that not even light can escape
What is the basic definition of a black hole?
any object from which the escape velocity exceeds the speed of light
A typical white dwarf is _________.
as massive as the Sun but only about as large in size as Earth
If you had something the size of a sugar cube that was made of white dwarf matter, it would weigh _________.
as much as a truck
If you were inside the rocket that falls toward the event horizon, you would notice your own clock to be running __________.
at a constant, normal rate as you approach the event horizon
The white dwarf that remains when our Sun dies will be mostly made of ______.
carbon In its final stages of life, the Sun will fuse helium into carbon, but it will never become hot enough for carbon fusion.
A spacecraft is on a trajectory that happens to be taking it near a black hole. Which diagram shows how the spacecraft's orbit will be affected?
curve with dot not touching
After a massive-star supernova, what is left behind?
either a neutron star or a black hole
Where do gamma-ray bursts tend to come from?
extremely distant galaxies
Some gamma ray bursts are hypothesized to come from mergers of neutron stars or black holes. If this hypothesis is correct, what else should we in principle be able to detect from such mergers?
gravitational waves
According to present understanding, a nova is caused by _________.
hydrogen fusion on the surface of a white dwarf
When we see X rays from an accretion disk in a binary system, we can't immediately tell whether the accretion disk surrounds a neutron star or a black hole. Suppose we then observe each of the following phenomena in this system. Which one would rule out the possibility of a black hole?
intense X-ray bursts
What would happen to a neutron star with an accretion disk orbiting in a direction opposite to the neutron star's spin?
its spin would slow down
A 10-solar-mass main-sequence star will produce which of the following remnants?
neutron star
Prior to the 1990s, most astronomers assumed that gamma-ray bursts came from neutron stars with accretion disks. How do we now know that this hypothesis was wrong?
observations from the Compton Gamma-Ray Observatory show that gamma-ray bursts come randomly from all directions in the sky
The Schwarzschild radius of a black hole depends on ________.
only the mass of the black hole
The Schwarzschild radius of a black hole depends on ________.
only the mass of the black hole The greater the mass, the larger the Schwarzschild radius.
A typical white dwarf has a mass of about 1.0MSun and the radius of Earth (about 6400 kilometers). Calculate the average density of a white dwarf, in kilograms per cubic centimeter.
p=1800 kg/cm^3
Pulsars are thought to be _________.
rapidly rotating neutron stars
In some cases, a supernova in a binary system may lead to the eventual formation of an accretion disk around the remains of the star that exploded. All of the following statements about such accretion disks are true except
several examples of flattened accretion disks being "fed" by a large companion star can be seen clearly in photos from the Hubble Space Telescope.
As the falling rocket plunges toward the event horizon, an observer in the orbiting rocket would see that the falling rocket __________.
slows down as it approaches the event horizon and never actually crosses the event horizon
The more massive a white dwarf, the _________.
smaller its radius
Which of the following represents the true shape of a black hole as you'd see it (or measure it) as you flew past it in a spaceship?
sphere
When we see X rays from an accretion disk in a binary system, we can't immediately tell whether the accretion disk surrounds a neutron star or a black hole. Suppose we then observe each of the following phenomena in this system. Which one would force us to immediately rule out the possibility of a black hole?
sudden, intense, X-ray bursts
Evidence indicates that many gamma ray bursts are produced by __________.
supernovas of massive stars in distant galaxies
Which of the following observatories is most likely to discover a black hole in a binary system?
the Chandra X-Ray Observatory
Imagine an advanced civilization living on a planet orbiting at a distance of 10 AU (1.5 billion kilometers) from a close binary star system that consists of a 15 M Sun red giant star and a 10 M Sun black hole. The black hole is surrounded by an accretion disk. Sometime within the next million years or so, the civilization's planet is likely to be doomed because ________.
the red giant will probably supernova within the next million years
A neutron star is _________.
the remains of a star that died in a massive star supernova (if no black hole was created)
A white dwarf is _________.
what most stars become when they die
