Astronomy Homework 14
What is true of a White dwarf supernova?
(1) Can only occur in a binary system. (2) Spectra always lack strong hydrogen lines. (3) Can occur in a very old star cluster. (4) Star explodes completely, leaving no compact object behind. (5) Has a brighter peak luminosity.
What is true of a Massive star supernova?
(1) Can only occur in a galaxy with on going star formation (2) Black hole or neutron star left behind
What are some aspects of gravitational waves?
(1) Gravitational waves are predicted to travel through space at the speed of light (2) The first direct detection of gravitational waves came in 2015 (3) The existence of gravitational waves is predicted by Einstein's general theory of relativity (4) Gravitational waves carry energy away from their sources of emission
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 -the moon -Jupiter -a two-solar-mass neutron star -a one-solar-mass white dwarf -the event horizon of a two-solar-mass black hole
(1) Main sequence star (2) Jupiter (3)1Msun white dwarf (4) the Moon (5) 2Msun Neutron star (6) 2Msun event horizon of a black hole
What evidence do we have that black holes exist?
(1) The gravitational influence on the motion of objects in their vicinity. (2) A direct image of the material in the accretion disk around a black hole. (3)Detection of gravitational waves from mergers of black holes in binary systems.
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? (1) The main-sequence star orbits either a neutron star or a black hole. (2) Some time in the next few decades, this system will undergo a nova explosion. (3) The main-sequence star must orbit a black hole. (4) The main-sequence star orbits either a white dwarf or a neutron star. (5) Gas from the main-sequence star makes an accretion disk around another object. (6) The main-sequence star must orbit a white dwarf. (7) The main-sequence star is emitting X rays. (8) The main-sequence star must orbit a neutron star.
(1) The main-sequence star orbits either a neutron star or a black hole. (2) 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.)
What are the characteristics of a white dwarf?
(1) Typically about the size (diameter) of Earth. (2) Supported by electron degeneracy pressure. (3) Has a mass no greater than 1.4 MSun. (4) In a binary system, it can explode as a supernova.
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.) -main-sequence star of spectral type M -the moon -a typical black hole (formed in a supernova) -a typical neutron star -a one-solar-mass white dwarf -Jupiter
(1) a typical black hole (formed in a supernova) (2) a typical neutron star (3) a one-solar-mass white dwarf (4) main-sequence of spectral type M (5) Jupiter (6) the Moon
What are some characteristics of a black hole?
(1) size defined by its Schwarzschild radius. (2) Viewed from afar, time stops at its event horizon.
What are some characteristics of a neutron star?
(1) sometimes appears as a pulsar (2) usually has a very strong magnetic field
Rank these objects based on their density, from highest to lowest. -a typical neutron star -a main-sequence star -a one-solar-mass white dwarf -the singularity of a black hole
(1) the singularity of a black hole (2) a typical neutron star (3) a one-solar-mass white dwarf (4) 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)
How does it compare with the amount of energy released by the Sun during its entire main-sequence lifetime?
(EsupernovaExplosion/ESunTotal)~10^2
What are the observational characteristics that could indicate that an object is a 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 (neutron stars form only in supernovae)
What are the observational characteristics that could indicate that an object is a 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 (white dwarfs may be surrounded by planetary nebulae because they are the remains of low-mass stars)
For the white dwarf supernova, the luminosity 175 days after it reaches peak brightness is about what % of the luminosity at peak brightness.
1%
A mini-black hole with the mass of the Moon.
1.1×10^−7 km
Approximately how many days does it take for a massive star supernova to decline to 10% of its peak brightness?
100 days
Using this formula, estimate the amount of gravitational potential energy released in a massive star supernova explosion. In a massive star supernova explosion, a stellar core collapses down to form a neutron star roughly 10 kilometers in radius. The gravitational potential energy released in such a collapse is approximately equal to GM^2/r where M is the mass of the neutron star, r is its radius, and G=6.67×10^−11m^3/kg×s^2 is the gravitational constant.
10^47 joules
A 5MSun black hole that formed in the supernova of a massive star.
15 km
A 10^8MSun black hole in the center of a quasar. Express your answer using two significant figures.
3.00x 10^8 km
Approximately how many days does it take for a white dwarf supernova to decline to 10% of its peak brightness?
30 days
Approximately how many days does it take for a massive star supernova to decline to 1% of its peak brightness?
300 days
At peak brightness, the white dwarf supernova is approximately how many times as luminous as the massive star supernova at its peak brightness?
3x
Which of these objects has the smallest radius? - a 1.2Msun white dwarf - a 0.6Msun white dwarf - Jupiter
A 1.2Msun white dwarf
Neil Gehrels is the head of the Swift satellite team. Why is he certain the burst he discovered is not from the explosion of a massive star?
Because the galaxy where the burst was detected only has old stars; all the massive ones already exploded. [Elliptical galaxies are full of old stars, and do not experience many if any massive-star supernova explosions]
What was so strange about the July 24 burst, the one that the scientists think might be caused by a black hole swallowing a neutron star, compared to the July 9 burst?
Both had flares 100 seconds after the initial blast, but the July 24 burst was 5 times more powerful, and flared yet again half a day later [Scientists hypothesize that the burst one-half day later was caused by material that was expelled during the collision, but eventually fell back into the black hole. That material experienced tidal stretching and compression, heating up for one last flash of light before it disappeared beyond the event horizon.]
What would happen if Jupiter turned into a black hole?
Earth would continue orbiting the Sun, unaffected by this event.
The radius of a white dwarf is determined by a balance between the inward force of gravity and the outward push of what?
Electron degeneracy pressure
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]
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.
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. (Viewed from afar the light of the in-falling rocket becomes increasingly redshifted. As it approaches the event horizon, the redshift approaches infinity, meaning all its light is stretched to such enormous wavelengths that no detector could see it, even in principle.)
What is the key observation needed to determine whether the compact object in the previous question 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 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]
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." (1) may emit rapid pulses of radio waves (2) may be located in an X-ray binary (3) may be surrounded by a supernova remnant. (4) may be in a binary system that undergoes X-ray bursts. (5) is detectable only if it is accreting gas from other objects (6) can have a mass of 10 solar masses.
Neutron Star: (1) may emit rapid pulses of radio waves (2) may be in a binary system that undergoes X-ray bursts. Black Hole: (1) is detectable only if it is accreting gas from other objects (2) can have a mass of 10 solar masses. Both: (1) may be located in an X-ray binary (2) may be surrounded by a supernova remnant. (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)
What would be considered surprising and what would be considered not surprising in the observation of supernovas? (1)A white dwarf supernova in a galaxy of only old stars. (2)Two massive star supernovae occur in the same young star cluster. (3)A massive star supernova leaves behind no detectable compact object. (4)A massive star in a binary system explodes. (5)An isolated star like our Sun explodes as a white dwarf supernova. (6)A young (5 million years) star explodes as a white dwarf supernova.
Not surprising: (1)A white dwarf supernova in a galaxy of only old stars. (2)Two massive star supernovae occur in the same young star cluster. (3)A massive star supernova leaves behind no detectable compact object. (4)A massive star in a binary system explodes. Surprising: (1)An isolated star like our Sun explodes as a white dwarf supernova. (2)A young (5 million years) star explodes as a white dwarf supernova.
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.]
If you could measure the orbital speeds of particles in an accretion disk around a black hole, what would you notice?
Particles near the center are moving the fastest.
Dr. Lamb and Dr. Whitcomb discuss their paper on collisions and gravity waves and the LIGO project, which is a ground-based experiment to detect gravity waves from space. What is their main contribution to the news discussed in "Scientists Trace Gamma Rays to Collisions of Dead Stars"?
Such collisions are predicted to create gravitational waves, which could be detected by gravity wave detectors like LIGO.
What technology enabled the first detection of gravitational waves in space?
The crucial measurement was to discern the change in length of the two arms of the gravitational wave detector.
When were Spaces waves (gravitational waves) first detected?
The detection of waves in spacetime, or gravitational waves, were reported for the very first time in February, 2016.
From the viewpoint of an observer in the orbiting rocket, what happens to time on the a rocket as it falls toward the event horizon of the black hole?
Time runs increasingly slower as the rocket approaches the black hole.
Why are the scientists so confident that they have succeeded in making a detection?
Two independent sites detected the same event at nearly the same time.
Which of these objects has the largest radius? -a 1.2 Msun white dwarf -a 1.5 Msun Neutron star -a 3.0Msun black hole
a 1.2 Msun white dwarf
Which of these black holes exerts the weakest tidal forces on an object near its event horizon? -a 10MSun black hole -a 100MSun black hole -a 10^6MSun black hole
a 10^6Msun black hole
What occurs when fusion creates iron in the core of a star?
a massive star supernova
What occurs when fusion ignites on the surface of a white dwarf?
a nova
What occurs when hydrogen fusion ignites on the surface of a white dwarf in a binary system?
a nova
If we see a nova, we know we are observing what?
a white dwarf in a binary system
What can occur only in a binary system, and all such events are thought to have about the same luminosity?
a white dwarf supernova (Type Ia)
How precise did the length measurement have to be in order to make a successful detection?
about 4/10000 the size of a proton
If you were inside a 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 object of equal mass
What can form around a white dwarf, neutron star, or black hole in a binary system?
an accretion disk
What consists of hot, swirling gas captured by a white dwarf (or neutron star or black hole) from a binary companion star?
an accretion disk
If you were inside a 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
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 the diameter of a proton
According to the article, how were the gravitational waves generated?
by the merger of two massive black holes
The scientists in the article "Scientists Trace Gamma Rays to Collision of Dead Star" concluded that the short gamma ray bursts were caused by what?
collisions of two neutron stars or of a black hole and a neutron star
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 change at more than one location.
Why can a white dwarf remain stable in size?
electron degeneracy pressure
Where do gamma-ray bursts tend to come from?
extremely distant galaxies
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
What can be said of the size of the event horizon for a 10Msun black hole? -larger than that of a 1Msun black hole. -smaller than that of a 1Msun black hole. -the same size as for a 1Msun black hole (because the escape velocity for both is the speed of light).
larger than that of a 1Msun black hole.
What fraction of galaxies are believed to contain supermassive black holes at their center?
most of them
Why can a neutron star remain stable in size?
neutron degeneracy pressure
What type of light can escape from a black hole?
no light can escape
Consider three planets. All have the same mass as Earth, but with different radii (from largest to smallest: Planet 1, 2, 3). For which planet is the escape velocity from the surface the largest?
planet 3
What is a rapidly rotating neutron star?
pulsar
As a falling rocket plunges toward the event horizon, an observer in an orbiting rocket would see that the falling rocket __________.
slows down as it approaches the event horizon and never actually crosses the event horizon
When does degeneracy pressure arise?
subatomic particles are packed as tightly as the laws of quantum mechanics allow
The team led by Derek Fox used many telescopes to do their analysis. They argue that their detection of the afterglow of the explosion is exactly what you'd expect from the collision of two neutron stars. Which of the following telescopes were used to detect X-rays from the afterglow?
the Chandra X-ray Telescope and the High Energy Transient Explorer
What would happen if the Sun suddenly became a black hole without changing its mass?
the Earth's orbit would not change
What marks the boundary between the inside and outside of a black hole?
the event horizon
Gravitational waves were first detected directly in 2015. According to models, what was the source of these gravitational waves?
the merger of two black holes
Why are some x-ray binaries candidates for black holes?
the object in the center of the accretion disk is too massive to be a neutron star.
What is the place to which all black hole's mass is in principle located within the black hole?
the singularity
A white dwarf in a close binary system will explode as a supernova if it gains enough mass to exceed what?
the white dwarf limit (1.4 solar masses)
