ASTRO 101 CH. 14 HMW

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 GM2r where M is the mass of the neutron star, r is its radius, and G=6.67×10−11m3/kg×s2 is the gravitational constant. How does it compare with the amount of energy released by the Sun during its entire main-sequence lifetime?

(Esupernova explosion)/ (Esun total) ~ 10^2

Which of these objects has the smallest radius? -a 1.2Msun white dwarf -a 0.6Msun white dwarf -Jupiter

-a 1.2 Msun white dwarf

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 neutron star, Jupiter, the Moon, a typical black hole-formed in a supernova, a one solar mass white dwarf, main sequence star of spectral type M)

-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

Ranking Task: The Size of Planets, Stars, and Stellar Remnants 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.) (Jupiter, the Moon, the event horizon of a two solar mass black hole, a two solar mass neutron star, main sequence star of spectral type A, a one solar mass white dwarf)

-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

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

Listed following are several astronomical objects. Rank these objects based on their density, from highest to lowest. (a typical neutron star, a main sequence star, the singularity of a black hole, a one solar mass white dwarf)

-the singularity of a black hole -a typical neutron star -a one solar mass white dwarf -a main sequence star

For the white dwarf supernova, the luminosity 175 days after it reaches peak brightness is about __________ of the luminosity at peak brightness

1%

Calculate the Schwarzschild radius (in kilometers) for each of the following. A mini-black hole with the mass of the Moon.

1.10 x 10^-7 km

Which of these objects has the largest radius? -1.2 Msun white dwarf -1.5 Msun neutron star -3.0 Msun black hole

1.2 Msun white dwarf

Approximately how many days does it take for a massive star supernova to decline to 10% of its peak brightness?

100 days

Which of these black holes exerts the weakest tidal forces on an object near its event horizon? -10Msun black hole -100Msun black hole -10^6Msun black hole

10^6 Msun black hole

Calculate the Schwarzschild radius (in kilometers) for each of the following. A 5MSun black hole that formed in the supernova of a massive star.

15 km

At peak brightness, the white dwarf supernova is approximately __________ times as luminous as the massive star supernova at its peak brightness.

3

Calculate the Schwarzschild radius (in kilometers) for each of the following. A 108MSun black hole in the center of a quasar

3.00 x 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

Calculate the Schwarzschild radius (in kilometers) for each of the following. A miniblack hole formed when a superadvanced civilization decides to punish you (unfairly) by squeezing you until you become so small that you disappear inside your own event horizon. (Assume that your mass is 50 kg.)

7.40 x 10^-29 km

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.

if jupiter turned into a black hole:

Earth would continue orbiting the Sun, unaffected by this event

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

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

consider three planets. All have the same mass as Earth but with different radii. For which planet is the escape velocity from the surface the largest? Planet 1 = ___________________ Planet 2 = ______________ Planet 3 = _________

Planet 3

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.

From your point of view, time runs normally in your spaceship and gravity must accelerate you as you fall toward the black hole.

There is no physical barrier at the event horizon, so you cross it unhindered.

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.

Sorting Task: The Bizarre Stellar Graveyard Listed following are distinguishing characteristics of different end states of stars. Match these to the appropriate consequence of stellar death.

White dwarf: -has a mass no greater than 1.4 MSun -in a binary systen, it can explode as a supernova -typically about the size(diameter) of Earth -supported by electron degeneracy pressure Neutron Star: -usually has a very strong magnetic field -sometimes appears as a pulsar Black hole: -viewed from afar, time stops at its event horizon -size defined by its Schwarzschild radius

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 event horizon of a 3 solar mass black hole is roughly the same size as:

a small town

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

a white dwarf in a binary system

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

A ________ consists of hot, swirling gas captured by a white dwarf (or neutron star or black hole) from a binary companion star.

accretion disk

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 - a binary with an X-ray burster - an X-ray binary containing a G star and another object of equal mass

an X-ray binary containing an O star and another object of equal mass

Which of these isolated neutron stars must have had a binary companion?

an isolated pulsar that pulses 600 times per second

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

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.

What would happen if the Sun suddenly became a black hole without changing its mass?

earths orbit would not change

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

Where do gamma-ray bursts tend to come from?

extremely distant galaxies

The singularity of a black hole:

is a place where density approaches infinity, so it is clearly the most dense of the objects shown.

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

the event horizon for a 10 solar mass black hole is:

larger than that of a 1 solar mass black hole

a _______ occurs when fusion creates iron in the core of a star

massive star supernova

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 Xray bursts black hole only: is detectable only if it is accreting gas from other objects -can have a mass of 10 solar masses both neutron stars and black holes: -may be surrounded by a supernova remnant -may be located in an Xray binary

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: -a young(5 million years) star explodes as a white dwarf supernova -an isolated star like our Sun explodes as a white dwarf supernova

a ____ occurs when hydrogen fusion ignites on the surface of a white dwarf in a binary system

nova

if you could measure the orbital speeds of particles in an accretion disk around a black hole, you would notice that:

particles near the center are moving fastest

white dwarfs may be surrounded by:

planetary nebulae because they are the remains of low-mass stars, while neutron stars form only in supernovae.

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

some Xray binaries are candidates for black holes because:

the object in the center of the accretion disk is too massive to be a neutron star

which of the following is true about observational evidence for black holes?

we have inferred the presence of supermassive black holes in many galaxies

what makes us think that black holes really exist?

we have observed orbital motions around objects so compact that according to current understandings, they must be black holes

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)

a _______ can occur only in a binary system, and all such events are thought to have the same luminosity

white dwarf supernova

Sorting Task: Distinguishing Massive Star and White Dwarf Supernovae To distinguish between properties of the two major types of supernovae: massive star supernovae and white dwarf supernovae. All supernovae represent the explosions of stars, but current understanding suggests there are two basic types of supernovae: one that occurs when a massive star reaches the end of its life, and the other that occurs when a white dwarf star explodes because its mass has exceeded the white dwarf limit (also called the Chandrasekhar limit) of 1.4 solar masses.

white dwarf supernova: ---spectra always lack strong hydrogen lines -can only occur in a binary system -can occur in a very old star cluster -star explodes completely leaving no compact object behind -has a brighter peak luminosity massive star supernova: -can only occur in a galaxy with ongoing star formation -black hole or neutron star left behind

Process of Science: Identifying Stellar Corpses 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 Xray bursts -can have a mass of 1.5 solar masses -may repeatedly dim and brighten more than once per second -may be surround by a supernova remnant

Neutron stars are much more dense than:

white dwarfs, which in turn are much more dense than main-sequence stars.

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 GM2r where M is the mass of the neutron star, r is its radius, and G=6.67×10−11m3/kg×s2 is the gravitational constant. Using this formula, estimate the amount of gravitational potential energy released in a massive star supernova explosion.

~10^47 jouls