The final fate of a star depends very much upon its mass. Generally speaking, the higher the mass the more spectacular the funeral.
We have called attention several times to the Ring Nebula in Lyra. Many examples of such nebulae are known within our galaxy. What we are looking at here is a thin sphere of gas. It looks like a ring because we look through more material at the periphery. The material of the sphere is known by the Doppler shift to be expanding. It is believed by some astronomers that this gas was cast off by a dying star, which long ago was a nova. The gas shell will continue expanding until it becomes so diffuse that it can no longer be seen. Some of this material may one day contribute to the birth of new stars.
It is believed that such a gaseous shell is formed when the outer fringes of a red giant star get so cool that neutral atoms can form there. Such neutral atoms absorb light from the stellar core very readily. The absorption of energy by the shell causes it to expand, cool further, absorb even more efficiently, and so on.
When the envelope of the star is cast off, the white-hot core becomes visible through the ever more tenuous shell of gas. The star moves horizontally to the left from the red giant area of the H-R diagram. At this point the core consists of inert carbon surrounded by a hot layer of burning helium. Because the temperature of the carbon is not high enough to initiate carbon burning, the core shrinks and gravitational potential energy is converted into thermal energy.
The temperature of the carbon core never does reach the required temperature for carbon burning, because the Pauli exclusion principle for electrons eventually stops the shrinkage of the core. At this point the radius of the star is only several earth radii, and the density is about 10 tons per cubic inch. Because of its small size the overall luminosity is very low compared to when it was in the planetary nebula stage. It has become a "white dwarf."
Unable to shrink, unable to burn carbon, the white dwarf gradually burns off the helium shell, ever falling in temperature, until finally it becomes a dense cold lifeless object--dead.
Now, Chandrasekhar has demonstrated that a stable white dwarf state can only be achieved by a star of final mass less than about 1.4 MO. What happens to a star which fails to cast off sufficient mass to become a stable white dwarf?
When a heavier star with a carbon core collapses, the temperature reaches the carbon burning temperature before the Pauli principle stops the shrinkage. The star cycles through the red giant region of the H-R diagram again. Eventually a star with an iron core is evolved. No amount of shrinkage will cause the iron core to burn. Therefore, the collapse will continue until the Pauli principle for electrons stops it.
However, even here there is a new feature to contend with. The temperature gets so high, say 1012 oK, that inverse beta decay is initiated. The electrons are swallowed up by protons to form neutrons. The star consists almost entirely of neutrons! The Pauli principle for electrons becomes irrelevant.
There is also a Pauli principle for neutrons. This stops the collapse when the neutrons get so close that the star assumes the density of nuclear matter.
Actually it is believed that half the stellar material is lost as the collapsing star bounces from the Pauli principle radius. The resulting supernova may be as bright as an entire galaxy for a short period of time. The Crab nebula in Taurus is an example of the explosion of a supernova in 1054 A.D. Such supernovae have actually been photographed in other galaxies. It is in such supernova explosions that small amounts of elements heavier than iron are formed. This material ultimately may take part in the formation of new stars.
The neutron star itself, that is, the core left behind in a supernova explosion is identified with a pulsar. Although no one is sure why pulsars blink, it is reassuring that such a pulsar has indeed been discovered buried in the crab nebula.
The neutron star is very small, perhaps ten miles in diameter, but with a density of nuclear matter. There appears to be a Chandrasekhar-type limit to the mass that a stable neutron star can possess. What happens if a star fails to cast off enough mass to be stable neutron star? Prof. Chandrasekhar has cited evidence for the existence of an object whose size is not over 103 km but whose mass is 6 MO. This object cannot be a stable white dwarf or a stable neutron star. He feels it must be a "black hole."
The light from a white dwarf is known to undergo a significant red shift unrelated to the Doppler shift. It is fully understood on the basis of Einstein's 1916 general theory of relativity. For light emitted from the surface of a neutron star the red shift predicted by Einstein's theory would be even more extreme. If one considers a body which is too massive to be a stable neutron star, it will continue to collapse until it reaches a radius called the Schwarzschild radius. The red shift of light emitted at the Schwarzschild radius is infinite! To a distant observer all clocks located at the Schwarzschild radius appear to tick not at all. Thus, this radius is now regarded to be a "horizon," from beyond which no signal can reach us. If you had the misfortune to fall into such a black hole, you could never get out. The horizon behaves like a perfect one-way door.
If the general theory of relativity is correct, the destiny of one who falls into a black hole is not pleasant. He eventually encounters a "singularity" in spacetime, where the gravitational tidal forces are infinite. The general theory of relativity offers no escape--and you could not even relate the event to a distant observer, for to him it would appear that you never really made it into the black hole.