Chapter 10 - The Bizarre Stellar Graveyard
What is an accretion disk?
a disk of hot gas swirling rapidly around a white dwarf, neutron star, or black hole
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
A neutron star is
the remains of a star that died in a supernova
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
Evidence for black holes -Accretion disks
- Due toconservation of angular momentum, gas falling into thegravitational wellcreated by a massive object will typically form a disc-like structure around the object. - The X-rays are produced by matter falling from one component, called thedonor(usually a relatively normalstar), to the other component, called theaccretor, which is very compact: aneutron starorblack hole.
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?
- Gas from the main-sequence star makes an accretion disk around another object. - The main-sequence star orbits either a neutron star or a black hole.
Consider all of the observations shown in the video. Which of the following are reasonable conclusions?
- Stars near the galactic center are much closer together than stars around our Sun. - There are strong magnetic fields in the central region of the galaxy. - Gas orbits the radio source called Sgr A*.
Which of the following accurately describe some aspect of gravitational waves?
- The first direct detection of gravitational waves came in 2015 - Gravitational waves carry energy away from their sources of emission. - Gravitational waves are predicted to travel through space at the speed of light. - The existence of gravitational waves is predicted by Einstein's general theory of relativity.
Which of the following statements about gravitational waves are true?
- 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.
You've just discovered another new X-ray binary, which we will call Hyp-X2 ("Hyp" for hypothetical). The system Hyp-X2 contains a bright, G2 main-sequence star orbiting an unseen companion. The separation of the stars is estimated to be 12 million kilometers, and the orbital period of the visible star is 5 days. 1. Use Newton's version of Kepler's third law to calculate the sum of the masses of the two stars in the system. Give your answer in kilograms. 2. Give your answer from the previous part in solar masses. (MSun = 2.0 × 10^30 kg) 3. Determine the mass of the unseen companion. (Hint: A G2 main-sequence star has a mass of 1MSun.) 4. Is it a neutron star or a black hole? Select the correct answer and explanation.
1. (M1 + M2) = R^3/P^2 P^2 = (5/365)^2 R^3 = ([12000000*(6.6845871226706*10^-9)])^3 R^3/P^2 = 2.75050945 2.75050945 (2*10^30) = 5.5010189*10^30 2. 2.75050945 3. 1.75050945 4. The unseen companion has a mass far too small for a black hole. It must be a neutron star.
If you tried to fly into a ______________, you would be killed by tidal forces before you crossed the event horizon.
10-solar-mass black hole
Look again at the orbit of the star with the highlighted orbit. By comparing the orbit to the scale bar shown on the diagram, you can estimate that this orbit has a semimajor axis of about _____.
1150 AU
To determine the mass of the central object, we must apply Newton's version of Kepler's third law, which requires knowing the orbital period and average orbital distance (semimajor axis) for at least one star. We could consider any of the stars shown in the figure, so let's consider the star with the highlighted orbit (chosen because its dots are relatively easy to distinguish). What is the approximate orbital period of this star?
20 yr
What is the Schwarzschild radius of a 10 solar mass black hole?
30 km
Based on the measurements discussed in part D, the mass of the central black hole is calculated to be about __________ times that of the Sun.
4 million
The following equation, derived from Newton's version of Kepler's third law, allows us to calculate the mass (M) of a central object, in solar masses, from an orbiting object's period (p) in years and semimajor axis (a) in astronomical units: M = a^3 / p^2 Using this formula with the values you found in Parts C and D, what is the approximate mass of the central object?
4 million solar masses
Which of the following best describes a black hole?
A place from which the escape velocity exceeds the speed of light.
What happens to a white dwarf when it accretes enough matter to reach the 1.4M_Sun limit? A. It explodes. B. It collapses into a neutron star. C. It gradually begins fusing carbon in its core.
A. It explodes.
How does the radius of the event horizon change when you add mass to a black hole? A. It increases. B. It decreases. C. It stays the same.
A. It increases.
What would the gas in an accretion disk do if there were no friction? A. It would orbit indefinitely. B. It would eventually fall in. C. It would blow away
A. It would orbit indefinitely.
Could there be neutron stars that appear as pulsars to other civilizations but not to us? A. Yes B. No
A. Yes
Is it easy or hard to fall into a black hole? A. easy B. hard Hint: A black hole with the same mass as the Sun wouldn't be much bigger than a college campus.
A. easy
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.
According to the conservation of angular momentum, what would happen if a star orbiting in a direction opposite the neutron's star rotation fell onto a neutron star? A. The neutron star's rotation would speed up. B. The neutron star's rotation would slow down. C. Nothing. The directions would cancel each other out.
B. The neutron star's rotation would slow down.
Why Pulsars Must Be Neutron Stars
Circumference of NS = 2π(radius) ~ 60 km Spin rate of fast pulsars ~ 1000 cycles per second - Surface rotation velocity ~ 60,000 km/s ~ 20% speed of light ~ escape velocity from NS Anything else would be torn to pieces!
What predicted the existence of gravitational waves?
Einstein's general theory of relativity
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, while neutron degeneracy pressure is the main source of pressure in neutron stars.
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
Consider the portion of the video that starts with the all-sky view of the Milky Way and then zooms in to the galactic center. All of the images except the first two show radio, infrared, or X-ray light. Why don't these images show visible light?
Interstellar dust in the galactic disk prevents us from seeing the galactic center with visible light.
What happens if a white dwarf reaches the 1.4 M_Sun limit?
It explodes as a white dwarf supernova
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.
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.
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.
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.
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 - can have a mass of 10 solar masses - is detectable only if it is accreting gas from other objects Both neutron stars and black holes - may be located in an X-ray binary - may be surrounded by a supernova remnant
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.
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
As discussed in the Extraordinary Claims box, scientific confidence in the existence of neutron stars and black holes arose through a combination of actual observations along with conclusions about those observations made with the aid of inferences based on models. Classify each statement below as an observation or an inference based on the current understanding of neutron stars and black holes.
Observations - pulsars dim and brighten with a short, steady period - pulsars are located within supernova remnants - some suspected black holes are strong X-ray sources - no white dwarf with a measured mass has a mass above 1.4 M_Sun Inferences from a model - adding mass to a 1.4 M_Sun white dwarf would cause it to collapse - pulsars are rapidly rotating neutron stars - a white dwarf rotating faster than about once per second would be torn apart - a collapsing stellar core of more than about 3 M_Sun will collapse to form a black hole - in a supernova, the collapsing stellar core will form a ball of neutrons
When Jocelyn Bell discovered the first pulsar, it was jokingly called an "LGM" for "little green men." What key piece of evidence suggested instead that the pulsar was the remains of a collapsed stellar core?
Pulsars were found to be located at the centers of supernova remnants.
If you wanted to observe the center of our galaxy, you would need to point a telescope in the direction of the constellation __________.
Sagittarius
Notice that some of the stars on the diagram are represented by a series of dots that are very close together, while others have their dots farther apart. Keeping in mind that all the stellar positions were measured at approximately one-year intervals, which stars are moving the fastest in their orbits during the time period indicated by the dots?
The fastest stars are the ones with the dots farthest apart
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.
Suppose two neutron stars or two black holes are closely orbiting one another. What do scientists predict will eventually happen to them, and why?
Their orbits will spiral inward until the two objects merge because of energy lost through gravitational waves
You've now found that the central object has a mass of about 4 million solar masses but is no more than about 70 AU in diameter—which means it cannot be much larger than the size of our planetary system. Why do these facts lead astronomers to conclude that the central object is a black hole?
There is no known way to pack so much mass into such a small volume without it collapsing into a black hole.
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.
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
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.
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
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 repeatedly dim and brighten more than once per second - 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
Match the items below with the correct type of supernova.
White dwarf supernova - Can only occur in a binary system - Star explodes completely, leaving no compact object behind. - Can occur in a very old star cluster - Spectra always lack strong hydrogen lines. - 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
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
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) typical neutron star a one-solar-mass white dwarf main-sequence star of spectral type M Jupiter the Moon
If we see a nova, we know that we are observing
a white dwarf in a binary system
A typical white dwarf is __________.
as massive as the Sun but only about as large in size as Earth
The maximum mass of a white dwarf is __________.
about 1.4 times the mass of our Sun
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
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??
an object with gravity so strong that not even light can escape
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
If you tried to visit a ______________, you would probably be killed by radiation well before you reached the black hole itself.
black hole in an X-ray binary system
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
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
The boundary from within which light cannot escape from a black hole is called the black hole's __________.
event horizon
To calculate the dashed orbits from the stellar positions, astronomers had to assume that __________.
if they observed for many more years, the dots would trace out ellipses
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 two-solar-mass black hole
From Part E you know the mass of the central object. Now consider its size. Based on what you can see in the diagram, you can conclude that the diameter of the central mass is __________.
no more than about 70 AU
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
A white dwarf has a mass of about 1.0 MSun and the radius of about 6400 kilometers. Calculate the average density of the white dwarf, in kilograms per cubic centimeter. How does this compare to the mass of familiar objects?
p=1800 kg/cm^3 The mass of one cubic centimeter of white dwarf matter is comparable to the mass of a car.
Astronomers are seeking to obtain an image of the region around the black hole's event horizon with a project called the Event Horizon Telescope. What type of light does this project seek to observe?
radio waves
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
Ignoring any radiation, you could in principle survive the journey across the event horizon of a
supermassive black hole
The first gravitational waves that were detected directly came from
the merger of two black holes.
What characteristics of the orbiting stars do we need to measure in order to calculate the mass of the central object, Sgr A*?
their orbital periods and average orbital distances
A white dwarf is
what most stars become when they die.
Neutron Stars
• A neutron star is the ball of neutrons left behind by a massive-star supernova. • Degeneracy pressure of neutrons supports a neutron star against gravity. Neutron Stars • A neutron star is about the same size as a small city.
Pulsars
• A pulsar is a neutron star that beams radiation along a magnetic axis that is not aligned with the rotation axis. • The radiation beams sweep through space like lighthouse beams as the neutron star rotates.
White Dwarfs and Accretion
• A star that started with less mass gains mass from its companion. • Eventually, the mass-losing star will become a white dwarf. • Mass falling toward a white dwarf from its close binary companion has some angular momentum. • The matter therefore orbits the white dwarf in an accretion disk. • What happens next?
What is spacetime?
• An object's number of dimensions is the number of independent directions in which movement is possible within the object.
Supernovae and Gamma-Ray Bursts
• Brief bursts of gamma rays coming from space were first detected in the 1960s • Observations in the 1990s showed that many gamma-ray bursts were coming from very distant galaxies. • They must be among the most powerful explosions in the universe—could be the formation of a black hole. • Observations show that at least some gamma-ray bursts are produced by supernova explosions. • Others may come from collisions between neutron stars.
Curvature Near Black Hole
• Continued shrinkage of Sun would eventually make curvature so great that it would be like a bottomless pit in spacetime: a black hole. • A black holeis an object whose gravity is so powerful that not even light can escape it. • Spacetime is so curved near a black hole that nothing can escape. • The "point of no return" is called the event horizon. • Event horizon is a three-dimensional surface.
Gravitational Lensing
• Curved spacetime alters the paths of light rays, shifting the apparent positions of objects in an effect called gravitational lensing. • Observed shifts precisely agree with general relativity. • Gravitational lensing can distort the images of objects. • Lensing can even make one object appear to be at two or more points in the sky. • Gravity of a foreground galaxy (center) bends light from an object almost directly behind it. • Four images of that object appear in the sky (Einstein's Cross). • Gravity of foreground galaxy (center) bends light from an object directly behind it. • A ring of light from the background object appears in the sky (Einstein Ring).
Limitations of the Rubber Sheet Analogy
• Masses do not rest "upon" the spacetime like they rest on a rubber sheet. • The rubber sheet shows only two dimensions of space.
Two Types of Supernovae
• Massive star supernova: - Iron core of a massive star reaches white dwarf limit and collapses into a neutron star, causing total explosion. • White dwarf supernova: - Carbon fusion suddenly begins as a white dwarf in close binary system reaches white dwarf limit, causing total explosion. • One way to tell supernova types apart is with a light curve showing how luminosity changes with time.
Neutron star in a close binary system
• Matter falling toward a neutron star forms an accretion disk, just as in a white dwarf binary • Much stronger gravity makes the accretion disk much hotter and denser • Some X-ray binaries contain compact objects of mass exceeding 3M_Sun, which are likely to be black holes.
Gravity and Spacetime
• Newton viewed gravity as a mysterious "action at a distance." • Einstein removed the mystery by showing that what we perceive as gravity arises from curvature of spacetime. - High-precision test of general relativity by the Cassini space probe (artist's impression): radio signals sent between the Earth and the probe (green wave) are delayedby the warping ofspacetime(blue lines) due to theSun's mass.
Rubber Sheet Analogy
• On a flat rubber sheet: - Free-falling objects move in straight lines. - Circles all have circumference 2pi*r. • Mass of Sun curves spacetime: - Free-falling objects near Sun follow curved paths. - Circles near Sun have circumference < 2pi*r. • Matter distorts spacetime in a manner analogous to how heavy weights distort a rubber sheet.
The White Dwarf Limit
• Quantum mechanics says that electrons must move faster as they are squeezed into a very small space. • As a white dwarf's mass approaches 1.4M_Sun, its electrons must move at nearly the speed of light. • Because nothing can move faster than light, a white dwarf cannot be more massive than 1.4M_Sun, the white dwarf limit(or Chandrasekhar limit).
Neutron Star Limit
• Quantum mechanics says that neutrons in the same place cannot be in the same state • Neutron degeneracy pressure can no longer support a neutron star against gravity if its mass exceeds about 3M_sun • Some massive star supernovae can make a black hole if enough mass falls onto core • Beyond the neutron star limit, no known force can resist the crush of gravity • As far as we know, gravity crushes all the matter into a single point known as a singularity
The major ideas of general relativity
• Special relativity showed that space and time are not absolute • Instead, they are inextricably linked in a four-dimensional combination called spacetime
Curvature Near Sun
• Sun's mass curves spacetime near its surface • If we could shrink the Sun without changing its mass, curvature of spacetime would become greater near its surface, as would strength of gravity.
Nova or Supernova?
• Supernovae are MUCH MUCH more luminous (about 100 thousand times)!!! • Nova: H to He fusion of a layer of accreted matter, white dwarf left intact • Supernova: complete explosion of white dwarf, nothing left behind
"Surface" of a Black Hole
• The "surface" of a black hole is the radius at which the escape velocity equals the speed of light • This spherical surface is known as the event horizon • Nothing can escape from within the event horizon because nothing can go faster than light • No escape means there is no more contact with something that falls in. It increases the hole mass, changes the spin or charge, but otherwise loses its identity • The radius of the event horizon is known as the Schwarzschild radius • The event horizon of a 3M_Sun black hole is about as big as a small city • The event horizon is larger for black holes of larger mass • A black hole's mass strongly warps space and time in the vicinity of its event horizon • If the Sun became a black hole, its gravity would be different only near the event horizon • Light waves take extra time to climb out of a deep hole in spacetime, leading to a gravitational redshift • Time passes more slowly near the event horizon.
Nova
• The temperature of accreted matter eventually becomes hot enough for hydrogen fusion • Fusion begins suddenly and explosively, causing a nova • The nova star system temporarily appears much brighter • The explosion drives accreted matter out into space
What would it be like to visit a black hole?
• Tidal forces near the event horizon of a 3M_Sun black hole would be lethal to humans. • Tidal forces would be gentler near a supermassive black hole because its radius is much bigger.
Discovery of Neutron Stars
• Using a radio telescope in 1967, Jocelyn Bell noticed very regular pulses of radio emission coming from a single part of the sky. • The pulses were coming from a spinning neutron star—a pulsar.
White Dwarfs
• White dwarfs are the remaining cores of dead stars. • Electron degeneracy pressure supports them against the crush of gravity. • White dwarfs cool off and grow dimmer with time
Size of a White Dwarf
• White dwarfs with same mass as Sun are about same size as Earth. • Higher-mass white dwarfs are smaller.
X-Ray Bursts
•High temperatures cause the disk to radiate powerful x-rays • Matter accreting onto a neutron star can eventually become hot enough for helium fusion. • The sudden onset of fusion produces a burst of X rays.
