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Arny Chapter 14

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Chapter 14 - STELLAR REMNANTS: White Dwarfs, Neutron Stars, and Black Holes

Section 14.1 White Dwarfs
This is the fate of stars like our Sun, stars with less than 10 solar masses.
Main-sequence, Red Giant, Planetary Nebula; when the planetary nebula fades what is left behind is a white dwarf.

White dwarfs are very small, typically about the size of the Earth.
Yet they contain as much mass as a star.
The white dwarf is made primarily out of carbon.
It is the surviving core of the star where fusion turned H and He into Carbon.
[Smaller stars (<.5 solar masses?) may form into helium white dwarfs and never have a red giant or planetary nebula phase.]

While a star, fusion generated heat and pressure to withstand gravity.
What stops gravity now that fusion has stopped?
The answer is electron degeneracy, which we discussed before.
Electrons can only be pushed so close together and then no more.
Inside the white dwarf, the electrons have reached this degenerate limit and cannot be compressed any more, gravity is balanced.

Our Sun will collapse into one of these very hot, dense objects (in about 7 billion years).

White dwarfs do exist.
The first one was discovered in 1862 (but it was not recognized as something unusual until 1915).
Tremendous numbers of white dwarfs have been discovered, despite the fact that they have very low luminosities.
10% of all the "stars" in the universe may be white dwarfs, the text speculates that the number may be much higher, maybe 50% of all mass is in white dwarfs but that seems unlikely.

White dwarfs start out very hot - they are the revealed core of a star.
White dwarfs are small, they have little surface area (this fits in with them being at the lower-left of the H-R diagram).
They produce no new energy.

Because of their low surface area, white dwarfs have a low luminosity, they lose energy only very slowly.
They take forever to cool off.
Eventually they will cool until they emit no more visible light.
Then they are called Black Dwarfs.
It is not believed that the universe has been around long enough for there to be any black dwarfs!

Maybe the most famous white dwarf is Sirius B (also the first one discovered).
A companion star to the bright star Sirius, the Dog Star
(Sirius B has been given the nickname 'the Pup').
But if Sirius B is a white dwarf now, it must've been a real star in the past.
In fact, that it became a white dwarf first, Sirius B must have once been the bigger and brighter of the two stars!

White Dwarf weight limit
There is an upper limit to the mass a white dwarf can have.
The most mass a white dwarf can have is 1.4 solar masses.
This is called the Chandrasekhar Limit.
We'll discuss this more in just a minute.


Novas (or the more proper plural, Novae)
Imagine a binary star system.
Two stars, probably with unequal masses.
The larger star will evolve faster.
It will become a Red Giant then a White Dwarf (we assume it isn't so big that it will go supernova).

Now we have a binary system of a main sequence star and a white dwarf (like Sirius and Sirius B today).
Later the main sequence star will evolve into a Red Giant.
Its outer layers will swell and expand.
The gravity of the white dwarf pulls some material away from the Red Giant (this will only happen if the two stars are close enough).
The material swirls around the white dwarf in an accretion disk.
Material spirals in and lands on the white dwarf.
See figure 14.3 on page 423.

 

 

 

 

 

 



The falling material gains a lot of energy.
The white dwarf (which is made mostly of carbon) becomes covered with a layer of extremely hot hydrogen.
The white dwarf is not hot or dense enough for carbon fusion.
But even on the surface, conditions can be sufficient for hydrogen fusion.

The hydrogen that has accumulated on the surface ignites in a burst of nuclear fusion.
This explosive flash is called a nova.
This burst can cause the stars to appear 50,000 times brighter.
About 100 novas occur in our galaxy every year.


Type I Supernova:
This is a continuation of our nova discussion.
The same white dwarf may go nova many times.
Although the explosive nova event may blow material into space, overall the white dwarf is gaining mass from its companion.
But there is a limit to the amount of mass a white dwarf can have (the Chandrasekhar Limit, 1.4 solar masses).

What if the white dwarf accretes enough mass to go over the Chandra limit?
It becomes hot enough for carbon fusion to occur.
These fusion processes make the star hotter causing other fusion processes to occur.
Fusion reactions all the way up to iron can occur all at once.
This sudden chain reaction causes an incredible release of energy.

The white dwarf completely destroys itself in the supernova explosion.
There is no remaining object (just sheets of gas flying out into space).


There are two types of supernovas, called Type I and Type II.
Differences between type I and type II supernovas:
See figure 14.5 on page 420.

Type I:
White dwarfs in binary systems.
Energy from runaway fusion.
Entire object destroyed.

An alternate theory is that Type I Supernovae may be due to merging white dwarfs in binary systems.

Type II:
Supergiant stars at the end of their life.
Energy from huge gravitational collapse.
Outer layers exploded, inner neutron star left.
More common


Section 14.2 Neutron Stars
This is the fate of most supergiant stars, stars with at least 10 solar masses.
Just prior to the supernova explosion of these stars, the protons and electrons were merged into neutrons, leaving a core entirely of neutrons.
That core, with gravity stopped by neutron degeneracy, is left behind in the SN explosion and is called a neutron star.

Neutron stars have a diameter of about 15 or 20 km (size of Bakersfield).
Unimaginably dense, the mass of a star in a mountain-sized volume.

Astronomers talked about neutron stars for a long time before ever seeing one.
Ideally we know just where to look for neutron stars, wherever there has been a past type II supernova explosion.
But most supernova explosions occurred so long ago that there is no longer any noticeable surrounding nebula.
Besides, neutron stars should be so tiny and hence dim that it seems unlikely we can directly see one.

Pulsars
In 1967, a celestial radio source was found with a regular period of exactly 1.33733 seconds.
Was this some alien race trying to communicate with us?
At first, some scientists thought so!
It created quite a stir.
But real communication would involve a varying signal.

Soon other such radio beacons were found, each with its own period.
Over a thousand have been found since.
These pulsating radio sources were named pulsars.
As you've probably guessed, pulsars are neutrons stars.
But why would neutron stars generate radio pulses?


As spinning things collapse or contract, they spin faster
(conservation of angular momentum, ice-skater effect).
See figure 14.8 on page 423.
Neutron stars should be spinning very, very fast; maybe once a second.
Neutron stars should also have very powerful magnetic fields.
Because the magnetic field strength should get magnified because of the rotational magnification.

On the Earth, the Earth's magnetic field pulls charged particles around towards the poles of the Earth.
Those particles crash into the atmosphere and create the auroras.
The same sort of thing will happen with neutron stars.
Passing charged particles will be pulled in by gravity and directed towards the magnetic poles by the magnetic field.
These particles will emit what's called synchrotron radiation, radio waves in the case of neutron stars.

On the Earth, the magnetic
poles and the rotation poles
aren't the same.
The same will likely be true
of neutron stars.
As the neutron star rotates,
the radio waves are beamed
in various directions, like a lighthouse.
See figure 14.7 on page 422
See figure 14.9B on page 424.

The period with which a distant person
would see radio pulses is the rotational period of the neutron star.
So, neutron stars really would appear as pulsars.
The identification is complete with the discovery of pulsars within most supernova remnants (like the Crab nebula).
Note that not all pulsar/lighthouses are oriented so that they can be easily seen from the Earth.


Most pulsars have periods in the range from 1/4 to 13 seconds.
Some pulsars have been found which are much faster, like .001 seconds.
These are called millisecond pulsars.
They are neutron stars in binary systems which are accreting mass from their companion.
[Yes, it is believed that a binary star system can survive the supernova explosion of one of the members.]
The extra mass falling onto the neutron star can speed up the spin.



Section 14.3 Black Holes
The mass limit for white dwarfs is 1.4 solar masses. (Chandrasekhar limit)
The mass limit for neutron stars is 2.5 solar masses. (No name, should be called the "Oppenheimer limit"
Any more mass and neutron degeneracy does not hold off gravity.
It is not really that neutron degeneracy is overcome, but that the underlying space is ripped apart by gravity.

Stars that start their life above 20 solar masses (40?) will finish with cores in excess of 2.5 solar masses (3?).
[Error in first line of section 14.3, says >10 solar masses becomes black hole.]
Nothing can stop gravitational collapse of these cores.
And gravity rips apart time and space in the process.

Imagine a layer of pennies laid flat across this table.
The pennies can't be squeezed any closer together, like neutron degeneracy.
But gravity is the equivalent of warping the table.
Suddenly, the pennies can be closer together.
The black hole is like a tear or hole in the space (in the table).
See figure 14.12 on page 428.
Pennies can flow through the hole and out of our universe.


The "curvature" of space can be measured using the escape velocity.
Recall we covered escape velocity in section 2.9.
The escape velocity is the speed necessary to propel an object into deep space.
Heavy, more compact objects have higher escape velocities.

Einstein taught us that nothing can go faster than the speed of light.
What if the escape velocity is greater than the speed of light?
Then nothing could escape! (Could not even orbit in that region.)
A neutron star is already close to this situation.

When the remaining core of a giant star collapses, if the mass is too great then the escape velocity exceeds the speed of light.
This volume where the escape velocity exceeds the speed of light is called a black hole.
The outer boundary of the black hole is called the event horizon.
The event horizon represents a point-of-no-return.
Things can go in but can never get back out (getting out requires going faster than the speed of light).

A mass M will have an escape velocity equal to the speed of light (c) if contained within a radius R = 2 G M / c^2.
The size of the event horizon (R), the radius of the black hole, is called the Schwarzschild Radius.


The text doesn't discuss some of the more fascinating aspects of black holes, but I intend to so long as we have enough class time.

In some countries, black holes are called frozen stars.
But not because they are cold!
Einstein showed that strong gravitational fields will affect time.
The stronger gravity is, the slower time will run in that region.
Time actually stops at the event horizon (that's why they're called frozen stars).

Let's imagine that you decide to fly a spaceship into a black hole.
What would happen to you?
What would it look like to someone watching you from afar?
We'll consider this second case first.

From Earth, your cautious friend would see you zooming towards the black hole.
But as you got real close, they would see you and your ship go into slow motion.
Time can run at different rates in different places!
As you have moved into a region of very strong gravity, time has started to pass more slowly.

For as long as your friend watches, you would never quite make it into the black hole.
For all the rest of time, you will be forever frozen at the edge of the black hole.

That's what it looks like to someone outside.
Now let's consider what it will look like from your point-of-view.
It will be a very different story.

As you plunge inward, you would consider yourself normal.
But everything in the outside universe would seem to be moving faster than normal.
You've moved into a region where time runs slower.
You don't notice it, you feel normal, it's just that others are moving fast.

You could turn around and come back out (chicken out).
You might find that although you spent only 10 minutes traveling, a year went by for the rest of the universe.
This wouldn't be a big surprise since you probably watched their year go by in super-fast motion.
[This is sometimes called the twin paradox because twins could end up with different ages, but really not a paradox.]

You don't chicken out and turn around.
You continue into the black hole.
The closer you get to the event horizon the faster the outside world seems to move.
As you reach the event horizon, the whole future of the outside universe flashes by.
It's all consistent, for that entire future, they saw you frozen at the event horizon.

Everything you left behind would be gone.
You would've seen everything.
But to you, it all happened in just a few minutes.
You enter the black hole.

What will you find inside?
No one knows for sure.
Best guess: You'll be pulled into a "singularity" and killed instantly.
But maybe not, modern theories are unclear and don't work under these conditions.
Bizarre theories of space travel, alternate universes, and time travel have been seriously proposed.

You can go into a black hole and find out what's there, but you can never come back.


Observing Black Holes
If light cannot escape a black hole, how can we see one?
It would be just a black speck against the black background of space.
Almost, there are some indicators that have allowed us to discover some black holes.

Black holes in binary systems can give away their presence in two ways:

X-rays and gravity

Gas falling into a black hole will end up "frozen" at the event horizon.
But before that, the gas will gain gravitational energy and heat up to extreme temperatures.
A black hole can be surrounded by an accretion disk of hot gas emitting X-rays.
If a black hole has gas falling into it (which will not be the case for most black holes), it will be a source of X-rays.

Of X-ray sources discovered in space, some were in binary systems.
We could not directly see the object - it was not a normal star.
But we could deduce its mass from the binary orbit.
If the mass is above 3 solar masses, we know the object is not a neutron star and deduce that it must be a black hole.
[X-rays don't penetrate the Earth's atmosphere, so these discoveries are made by satellites in orbit.]


Stellar evolution handout.
End chapter 14.



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