Astronomy Chapter 10

Part D: Complete the following sentences. Use each choice only once. Drag a phrase from the left to the correct blank at the right. Ignoring any radiation, you could in principle survive the journey across the event horizon of a [Blank]. If you tried to fly into a [Blank], you would be killed by tidal forces before you crossed the event horizon. If you tried to visit a [Blank], you would probably be killed by radiation well before you reached the black hole itself.

- Ignoring any radiation, you could in principle survive the journey across the event horizon of a [supermassive black hole]. - If you tried to fly into a [10-solar-mass black hole], you would be killed by tidal forces before you crossed the event horizon.target 2 of 3 - If you tried to visit a [black hole in an X-ray binary system], you would probably be killed by radiation well before you reached the black hole itself.

First, launch the video below. Then, close the video window and answer the questions that follow. You can watch the video again at any point. Part A: Which of the following accurately describe some aspect of gravitational waves? Select all the statements that are true. - Gravitational waves are an extremely low-energy form of light. - Gravitational waves come from funnel-shaped regions of the universe. - The existence of gravitational waves is predicted by Einstein's general theory of relativity. - Gravitational waves are predicted to travel through space at the speed of light. - The first direct detection of gravitational waves came in 2015. - Gravitational waves carry energy away from their sources of emission. - The existence of gravitational waves is predicted by Newton's universal law of gravitation.

- The existence of gravitational waves is predicted by Einstein's general theory of relativity. - Gravitational waves are predicted to travel through space at the speed of light. - The first direct detection of gravitational waves came in 2015. - Gravitational waves carry energy away from their sources of emission.

Part 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 must orbit a black hole. - The main-sequence star must orbit a white dwarf. - The main-sequence star must orbit a neutron star. - Some time in the next few decades, this system will undergo a nova explosion. - The main-sequence star is emitting X rays. - 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. - The main-sequence star orbits either a white dwarf or a neutron star. Submit

- 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. The system is an X-ray binary, which means the companion to the main-sequence star can be either a neutron star or a black hole. The X rays come from the hot accretion disk consisting of gas that the compact object's gravity is pulling away from the main-sequence star.

Which of the following statements about gravitational waves are true? Select all that apply. -Although gravitational waves are an important theoretical prediction, we do not yet have any observational evidence that they exist. -Two orbiting neutron stars or black holes will gradually spiral toward each other as a result of energy being carried away by gravitational waves. -Scientists seek to detect gravitational waves by using powerful gamma-ray telescopes. -The first direct detection of gravitational waves, announced in 2016, came from the LIGO observatory. -The emission of gravitational waves from merging black holes is predicted by Einstein's general theory of relativity. -The emission of gravitational waves from merging black holes is predicted by Newton's universal law of gravitation.

-Two orbiting neutron stars or black holes will gradually spiral toward each other as a result of energy being carried away by gravitational waves. -The first direct detection of gravitational waves, announced in 2016, came from the LIGO observatory. -The emission of gravitational waves from merging black holes is predicted by Einstein's general theory of relativity. Einstein's general theory of relativity predicts that systems in which large masses are orbiting closely should emit substantial amounts of energy in the form of gravitational waves, thereby causing the orbits of the objects to decay until they eventually merge. Scientists first recognized evidence for the existence of gravitational waves in binary pulsar systems, in which the measured decay of the neutron star orbits agreed with the prediction of general relativity. Then, in 2016, scientists announced the first direct detection of gravitational waves, made at the LIGO facilities, with a signal consistent with the gravitational waves coming from the final merger of two orbiting black holes.

Match the words in the left-hand column to the appropriate blank in the sentences in the right-hand column. Use each word only once. 1. The radius of a white dwarf is determined by a balance between the inward force of gravity and the outward push of [Blank]. 2. A white dwarf in a close binary system will explode as a supernova if it gains enough mass to exceed the [Blank]. 3. A(n) [Blank] consists of hot, swirling gas captured by a white dwarf (or neutron star or black hole) from a binary companion star. 4. A(n) [Blank] occurs when hydrogen fusion ignites on the surface of a white dwarf in a binary system. 5. A(n) [Blank] can occur only in a binary system, and all such events are thought to have about the same luminosity. 6. A(n) [Blank] occurs when fusion creates iron in the core of a star.

1. The radius of a white dwarf is determined by a balance between the inward force of gravity and the outward push of [electron degeneracy pressure]. 2. A white dwarf in a close binary system will explode as a supernova if it gains enough mass to exceed the [white dwarf limit (1.4 solar masses)]. 3. A(n) [accretion disk] consists of hot, swirling gas captured by a white dwarf (or neutron star or black hole) from a binary companion star. 4. A(n) [nova] occurs when hydrogen fusion ignites on the surface of a white dwarf in a binary system. 5. A(n) [white dwarf supernova] can occur only in a binary system, and all such events are thought to have about the same luminosity. 6. A(n) [massive star supernova] occurs when fusion creates iron in the core of a star.

Part B: Determine the ratio of the mass of 1 cm3 of neutron star material to the mass of Mount Everest (≈ 5 × 10^10 kg). Express your answer using one significant figure.

10

Part C: What is the Schwarzschild radius of a 10 solar mass black hole?

30km

A typical neutron star has a mass of about 1.5MSun and a radius of 10 kilometers. Part A: Calculate the average density of a neutron star, in kilograms per cubic centimeter. Express your answer in kilograms per centimeter cubed to two significant figures.

7.2*10^11 kg/cm^3

Part A: Which of the following best describes a black hole?

A place from which the escape velocity exceeds the speed of light.

Part B: Listed following are several astronomical objects. Rank these objects based on their mass, from largest to smallest. (Be sure to notice that the main-sequence star here has a different spectral type from the one in Part A.)

A typical black hole (formed in a supernova) > A typical neutron star > A one-solar-mass white dwarf > Main-sequence star of spectral type M > Jupiter > The Moon Note that while the rankings shown are correct for "typical" white dwarfs, neutron stars, and black holes, each of these objects comes in a range of masses and so there may be some exceptions.

Part B: 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. The black hole would occassionallly eclipse Saturn, but we never see such eclipses. We would have by now detected it with X-ray telescopes. Black holes must have more than 3 solar masses.

An object of that mass would disrupt the orbits of the planets in our solar system. An object with 3 times the mass of our Sun would be the dominant mass of our solar system, so the planets could not have their current orbits around the Sun if such an object existed.

What predicted the existence of gravitational waves?

Einstein's general theory of relativity

Part C: 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. We have not yet detected X-ray emissions from a singularity. We have not yet detected gravitational waves from a singularity. The idea of singularlity is inconsistent with Newton's universal law of gravitation.

General relativity and quantum mechanics give different answers about the nature of singularity. The fact that two otherwise very successful theories make different claims about singularity means our knowledge of physics must be incomplete, and therefore that we cannot yet know the true nature of singularity.

What happens if a white dwarf reaches the 1.4 MSun limit?

It explodes as a white dwarf supernova

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 a white dwarf?

It is the remains of a star that ran out of fuel for nuclear fusion.

Which statement must be true for a rocket to travel from Earth to another planet?

It must attain escape velocity from Earth

Part B: Consider a binary system of two neutron stars. How should the emission of gravitational waves affect this system?

It should cause the orbits of the two objects to decay with time. Energy must be conserved, so the fact that gravitational waves are carrying energy away from the system means the system must be losing orbital energy, causing the orbits of the two neutron stars to decay with time. The same would also occur in other systems with two massive objects in close orbits, such as a system with two black hole or with a neutron star and a black hole.

Imagine that our Sun were magically and suddenly replaced by a black hole of the same mass (1 solar mass). How would Earth's orbit change?

It would not change; Earth's orbit would remain the same.

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. Objects in strong gravity experience gravitational redshift, so light that is red would have its wavelength shifted into the infrared part of the spectrum

Part A: A white dwarf has a mass of about 1.3 MSun and the radius of about 5800 kilometers. Calculate the average density of the white dwarf, in kilograms per cubic centimeter. Express your answer in kilograms per cubic centimeter to two significant figures.

MSun = 1.989 *10^30 Mass = 1.3 * 1.989*10^30 = 2.585*10^30kg Radius = 5800 * 1000 = 5.8*10^6 meter Density = Mass/Volume Volume = 4/3*3.14*r^2 4/3 * 3.14 (5.8*10^6)^3 = 8.167*10^20 cubic meter, 1 cubic meter = 10^6 cubic cm = 8.167*10^26 Density = 2.585*10^30kg/8.167*10^26 = 3200 kg/cm^3

Part A: Listed following are several astronomical objects. Rank these objects based on their diameter, from largest to smallest. (Note that the neutron star and black hole in this example have the same mass to make your comparison easier, but we generally expect black holes to have greater masses than neutron stars.)

Main-sequence star of spectral type A > Jupiter > A one-solar-mass white dwarf > The Moon > A two-solar-mass neutron star > The event horizon of a black hole The main-sequence star is obviously much larger than a planet such as Jupiter. A one-solar-mass white dwarf is about the size of Earth, which makes it larger than the Moon. A neutron star will be larger than a black hole of the same mass, because while light can escape from a neutron star, the same mass in a black hole must be more concentrated so that its gravity is strong enough to prevent light from escaping.

Part D: What is the key observation needed to determine whether the compact object in Part C is a neutron star or a black hole? - Obtain high-resolution images of the compact object, so that you can determine whether it emits any light. - Study the X-ray emission to determine the temperature of the gas in the accretion disk. -Measure Doppler shifts in the spectrum of the main-sequence star so that you can determine the mass of the compact object.

Measure Doppler shifts in the spectrum of the main-sequence star so that you can determine the mass of the compact object. The Doppler shifts will allow you to determine the speed (or at least the component of the speed that is in your line of sight) of the main-sequence star as it orbits the compact object. You can then use this speed along with the known mass of the main-sequence star to determine the compact object's mass (or a lower limit on its mass). If this mass is greater than the neutron star limit of about 3 solar masses, then the object must be a black hole.

Part 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: - May emit rapid pulses of radio waves - May be in a binary system that undergoes X-ray bursts Black Hole Only: - Is detectable only if it is accreting gas from other objects - Can have a mass of 10 solar masses Both: - May be located in an X-ray binary - May be surrounded by a supernova remnant Be sure you understand why each of these observations goes with the indicated object(s). For example, radio pulses and X-ray bursts cannot come from black holes, because both are caused by events that happen on the surface of a compact object. Note also that the fact that two important items go in the "Both" bin indicates that it can be more difficult to distinguish between neutron stars and black holes than between white dwarfs and neutron stars.

Part B: Each item below describes an observation of a hypothetical supernova. Classify each observation as either "Not surprising" if it fits in with our current understanding of supernovae, or "Surprising" if the observation would cause us to rethink our understanding of supernovae. Drag the appropriate items to their respective bins.

Not Surprising: - A white dwarf supernova in a galaxy of only old stars - Two massive star supernovae occur in the same young star cluster - A massive star supernova leaves behind no detectable compact object - A massive star in a binary system explodes. Surprising: - An isolated star like our Sun explodes as a white dwarf supernova - A young (5 million years) star explodes as a white dwarf supernova Note that either of the two "Surprising" observations would force us to reconsider our ideas about supernovae if we actually witnessed them (we haven't).

Part B: How does this compare to the mass of familiar objects? The mass of one cubic centimeter of white dwarf matter is comparable to the mass of an average person. The mass of one cubic centimeter of white dwarf matter is comparable to the mass of a car. The mass of one cubic centimeter of white dwarf matter is comparable to the mass of a feather. The mass of one cubic centimeter of white dwarf matter is comparable to the mass of a pen.

The mass of one cubic centimeter of white dwarf matter is comparable to the mass of a car.

Part C: Listed following are several astronomical objects. Rank these objects based on their density, from highest to lowest.

The singularity of a black hole > A typical neutron star > A one-solar-mass white dwarf > A main-sequence star The singularity of a black hole is a place where density approaches infinity, so it is clearly the most dense of the objects shown. Neutron stars are much more dense than white dwarfs, which in turn are much more dense than main-sequence stars.

What makes astronomers think that Cygnus X-1 contains a black hole?

The unseen object orbited by a luminous star is too massive to be a neutron star.

Part A: 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 (based on current science), meaning that scientists are confident in this statement based on current understanding of gravity (general relativity) and stellar evolution Not true, either because it contradicts current scientific theory or is contradicted by observations Unknown, meaning the statement makes a claim that may or may not be true, and for which we would need new science or new observations to decide which it is.

True (based on current science): - A black hole can have the mass of a star in a space less than a few kilometers across - A black hole is an object smaller than its own Schwarzschild radius - Two orbiting black holes can merge and emit gravitational waves - Material from a binary companion can form an X-ray-emitting accretion disk around a black hole - A black hole can form during a supernova explosion Not true: - A 3-solar-mass black hole may be hidden between Jupiter and Saturn - A black hole will suck in any binary companion star you would be squashed by gravity at the event horizon of any black hole - Black holes emit x-ray light from within their event horizons Unknown: - Black holes make up 1% of the mass of the Milky Way Galaxy - The singularity of a black hole has infinite density

Part D: 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. According to our understanding of stellar evolution, black holes should make up a much lower percentage of the galaxy's mass. According to our understanding of stellar evolution, black holes should make up a much higher percentage of the galaxy's mass. We do not know the mass of the Milky Way's central black hole.

We cannot detect all black holes and therefore don't know the percentage of the galaxy's mass they make up. The only black holes that we can detect at present are those with X-ray emitting accretion disks, and even then it takes a great deal of followup observation to determine whether the X-rays are coming from an accretion disk around a neutron star or a black hole. Therefore we do not have good statistics on the total number or mass of black holes in our galaxy.

Part A: Match the items below with the correct type of supernova. Drag the appropriate items to their respective bins.

White Dwarf Supernova: - Can only occur in a binary system - Spectra always lack strong hydrogen lines - Can occur in a very old star cluster - Star explodes completely, leaving no compact object behind - Has a brighter peak luminosity. Massive Star Supernova: - Black hole or neutron star left behind - Can only occur in a galaxy with ongoing star formation.

Part 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: - May be surrounded by a planetary nebula - Emits most strongly in visible and ultraviolet - May be in a binary system that undergoes nova explosions Neutron Star: - May be in a binary system that undergoes X-ray bursts - Can have a mass of 1.5 solar masses - May be surrounded by a supernova remnant - May repeatedly dim and brighten more than once per second Be sure you understand why each of these observations goes with the indicated object. For example, white dwarfs may be surrounded by planetary nebulae because they are the remains of low-mass stars, while neutron stars form only in supernovae.

Listed following are distinguishing characteristics of different end states of stars. Match these to the appropriate consequence of stellar death

White Dwarf: - Supported by electron degeneracy pressure - Typically about the size (diameter) of Earth - Has a mass no greater than 1.4 M Sun - In a binary system, it can explode as a supernova Neutron Star: - Sometimes appears as a pulsar - Usually has a very strong magnetic field Black Hole: - Size defined by its Schwarzschild radius - Viewed from afar, time stops at its event horizon

Part B: Explain your reasoning.

White dwarfs are the remains of low-mass stars, which are far more numerous than high-mass stars.

What is an accretion disk?

a disk of hot gas swirling rapidly around a white dwarf, neutron star, or black hole

A pulsar is

a rapidly rotating neutron star.

If you had something the size of a sugar cube that was made of white dwarf matter, it would weigh about as much as

a truck

If we see a nova, we know that we are observing

a white dwarf in a binary system.

The maximum mass of a white dwarf is __________.

about 1.4 times the mass of our Sun

What is the basic definition of a black hole?

an object with gravity so strong that not even light can escape

A typical white dwarf is __________.

as massive as the Sun but only about as large in size as Earth

Why does matter falling toward a white dwarf, neutron star, or black hole in a binary system form an accretion disk?

because the infalling matter has some angular momentum

Part D: LIGO detects gravitational waves because the lengths of its arms change as gravitational waves pass by. About how much are these lengths expected to change when LIGO detects gravitational waves from the merger of two neutron stars or two black holes?

by an amount smaller than the diameter of a proton

Part E: Given such small length changes (as noted in Part D), what can give scientists confidence that they have really detected a gravitational wave signal?

detecting the same changes at more than one location

Part B: The boundary from within which light cannot escape from a black hole is called the black hole's __________.

event horizon

Part C: With current technology, we expect to be able to detect (directly) gravitational waves from a binary system of two neutron stars or two black holes __________.

only from the instant when the two objects merge into one As the orbits decay, the two objects should eventually merge into one, and that event can produce gravitational waves strong enough for us to detect with instruments like LIGO.

The Schwarzschild radius of a black hole depends on __________.

only the mass of the black hole

The first gravitational waves that were detected directly came from

the merger of two black holes.

A neutron star is __________.

the remains of a star that died in a massive star supernova (if no black hole was created)

A neutron star is

the remains of a star that died in a supernova.

A white dwarf is

what most stars become when they die.

Part A: Which kind of these objects do you think is most common in our galaxy?

white dwarfs