WHITE DWARFS, NEUTRON STARS, AND BLACK HOLES

White Dwarfs are about the size of the Earth; their sizes have a mass dependence- as the mass increases their sizes get smaller.

Neutron Stars are about the size of a small city; their sizes are fairly constant; that is, the size does not depend upon the mass.

Black Hole sizes can vary greatly because black holes can have mass ranging from a solar mass to millions of times the solar mass. The more massive the black hole the larger the size. A solar mass black hole is small, about the size of a college campus.

White Dwarfs (WDs)

WDs are the hot core remnant of a low mass star (those with masses less than about 8 times the sun's mass). They are composed of the the carbon and oxygen, the products of helium fusion. WDs are found in the centers of Planetary Nebulae.

A young astronomer named Chandrashekar discovered that the size of a WD gets smaller as the mass increases. Usually, the larger the original star's mass, the larger the mass of its left over core (i.e. WD). Chandrashekar also discovered that there is an upper limit to the mass of WDs. When the star's core exceeds 1.4 times the solar masses, the WD must collapse under its own weight. This upper mass limit for the WD is called the Chandrashekar Limit.

Equation of State (EOS)

The EOS is a mathematical relationship between the size of a stellar remnant and its density. The typical density of a WD is about 106 grams per cubic centimeter (about 1 million time that of water; water has a density of 1 gram per cubic centimeter [g/cc], that is 106 = 1 million.)

For WDs with larger mass, the density goes up and the size decreases. But, when the density of a WD would exceed a few million g/cc, the compressed oxygen and carbon nuclei and free electrons cannot stand the pressure. The physics (electrical repulsion of particles) that supports the WD from its own weight breaks down. The WD must collapse.

The EOS has no solution in the density range above a few million g/cc! Not until all the matter becomes nucleons, does the EOS have a solution again. The meaning of the EOS having no solution is basically a way of saying that there is no physics that exists for a given density range.

Neutron Stars (and Pulsars)

A NS is really just a big ball of neutrons. The density of a NS is about 1014 g/cc (100 trillions time that of water!). At this density the EOS again has a solution; NS have a size given by the crushing compression of all the matter now in the form of neutron.

NS usually exist in the center of supernovae explosions. That is, stars that originally had masses greater than about 8 times that of the sun explode and their left over cores are greater than the Chandrashekar Limit.

Many NS can be found because they give of pulses of light. When the star collapses, its magentic field gets highly compressed and the star rotation becomes very very rapid (like when an ice skater pulls in her arms during a spin). The magnetic fields channel charged particles out the poles of the NS in a powerful beam. You can think of this as a light house beam that sweeps the sky, but very very rapidly. If NS pole is aligned such that the beam sweeps Earth, then we see the pulses (like a ship on the sea sees the light house beam, but an airplane in the sky would not). These NS are called Pulsars. We do not see all NS as pulsars.

In the Crab Nebula, which is a supernova remnant, we see a Pulsar in the center. This NS rotates 30 times per second(!) and we see its pulse every 0.033 times per second (1/30).

Black Holes

If the mass of a the stellar remnant is compressed enough in the supernovae explosion, the compression can be so fierce that even a the physics that supports a NS can fail. In this case, there is no physics that can stop all the mass from totally colaapsing into a point, called a singularity. We have no idea what this matter is like, only that it mathematically is a dimensionless point.

But what about the region around the singularity?

To answer this we must turn to Einstein's theories of gravity, which is called his General Theory of Relativity. Here is the key point: Eintein realized that mass was just one form of energy, and that this mass placed a stress on the fabric of space and time. If you think of space as a fabirc, then placing a mass in the space will cause the fabric to "warp" The larger the mass, the larger the warp. You can think of the warp as a funnel; the larger the mass, the deeper the funnel.

Now, this means that even light will appear to alter its path in the vacinity of a massive object. This is why we call warped space "curved" space. The light path can appear to curve.

Around most stars, for example, the funnel does not go very deep and the effect od curved space-time are not freaky to our everyday experience. But, the warp of space is such that the "funnel" goes infinitely deep!). This is called Black Hole (BH), because even if light goes too far down into this funnel, its path gets so curved that it cannot make its way back out of the funnel!

How deep does light go before it cannot make it back out? That is given by the equation

This "radius", which is just a mathematical location around the singularity, gets larger in proportion to the mass that collapsed into the singularity. It is called the "Event Horizon". Nothing, once it gets that close to the BH, can escape; it falls into the BH and its mass adds to the mass of the BH. Thus, BHs can grow in mass as they consume other matter and energy!

There are three parts to a BH:

The warping of space can lead to bending light so strongly that BHs can behave like optical lenses. However, we call these "gravitational lenses", becuase we still loosely think of it being gravity that bensd the light.

It is very importat to realize that far from the event horizon of a BH, the space time fabric is no different than what we would call normal. For example, if the Sun became a BH this instant, the planets wouod continue to orbit it just the same. The only difference would be that the solar system became dark when the sun when out. It is only when an object is deep in the funnel that things get strange or that you approach the event horizon.

What if You Fell into a Black Hole?

If you fell into a black hole, you would get stretched thin and squeezed as you approach the event horizon. Also, time slows down as you get closer and closer. If you looked back out to the universe, you would see the universe evolve to the end of time before you fell in. (This is because your time is so slow that the rest of time appears fast to you).

What if Your Friend Fell into a Black Hole?

If you watched another person fall into a BH, you would see them turn redder and redder because the light from them gets redshifted. This is called a gravitational redshift. Also, you would see their time slowing way down. In fact, as they approached the event horizon, their time wouls appear so slow that it would appear to stop just as they reach the event horizon. They would appear to freeze in time!

Where are Black Holes?

We see BHs that are busy consuming other matter. We cannot see an isolated BH. We see BH in two places. In binary stars, where the BH is consuming matter from its companion, and in the centers of galaxies, where the BH (usually very massive) is consuming stars. When the consumption rate is high, the BH sends off jets of material that has been heated and compressed. These jets are (again) due to beaming from magentic fields around the BH.

Wormholes and Time Travel

There is some speculation that space travel can be shortened by going through worm holes. That is, if you could survive the plunge into a BH, you might emerge somewhere (and somewhen!) else in the universe.