I. White Dwarfs -- Our Sun, after using up its nuclear fuel and expelling its envelope into space as a stellar wind, will become a ball of gas a little larger than Earth that will slowly cool and become less and less bright. It will be a white dwarf. -- The higher the mass, the stronger the gravity, and the smaller the white dwarf. Packing the mass of the Sun into the size of the Earth requires the density of a white dwarf be about 300,000 times more than that of rock! -- Solar type stars lose the majority of their mass in the planetary nebula stage, so to get a white dwarf with the mass of the Sun you need to start with a main-sequence star that is about 5 times more massive than the Sun. -- White dwarfs have little in the way of internal heat sources, so they basically just cool. The stars that evolve into WDs stay on the main sequence for a long time, and indeed solar-like stars have only had about enough time since the beginning of the universe to evolve into WDs (our Sun hasn't yet because it wasn't around for about the first 10 billion years of our universe). Thus there simply hasn't yet been enough time to evolve WDs from stars much smaller than our Sun. Thus there are not yet any WDs in the universe with masses less than about 0.6 times the Sun. -- White dwarfs are compressed by gravity, and this is balanced as usual by gas pressure, but the density is so high and so much heat has been lost in forming the white dwarf that the whole system is starting to approach its quantum mechanical ground state, making it more difficult for it to continue to lose heat. When the electrons start to approach their communal ground state, the very high pressure that results is called "degeneracy pressure." It is called that because the electrons are becoming "degenerate", a strange term used to mean that they are starting to pile up in their lowest possible energy states. At this point the electrons are ruled by the "Pauli exclusion principle", which means only one electron is allowed in each state, which is what inhibits their ability to continue losing heat-- to lose heat, some of them would need to occupy states already occupied by other electrons. -- degeneracy pressure increases as the density increases, but not as fast as regular ideal-gas pressure would, because degeneracy pressure is the minimum pressure possible at given density. Adding mass to a white dwarf increases the gravity more than it increases that minimum pressure, so causes the white dwarf to shrink further. Thus the radius of a white dwarf actually gets smaller as the mass increases. So you have to use caution when talking about how "big" a white dwarf is-- do you mean size or mass? -- If the radius gets smaller as the mass increases, what happens when the mass gets so big that the radius goes to zero? Chandrasekhar surmised that this would happen at a mass of about 1.4 solar masses, and the matter itself would then collapse into a totally new state: a "neutron star".
II. Neutron Stars -- What causes the collapse of a stellar core into a neutron star is when the electrons get so hot their speed approaches the universal speed limit, the speed of light. We then say the electrons are "relativistic." -- The electrons in the core of the more massive stars go relativistic before they go degenerate, i.e. they approach the speed of light before they reach their quantum mechanical ground state. Bumping into the universal speed limit means the electrons don't speed up as the core contracts further and gravity gets stronger, so the stronger gravity cannot be opposed by the motion of the electrons, and so the electrons can no longer prevent the rest of the core (and the electrons with it) from getting pulled in by gravity, causing a "core collapse." -- When the electrons are squished by the core collapse, they are actually swallowed up by the protons and together produce neutrons. There are already neutrons in all atomic nuclei except hydrogen, but in a neutron star, there is little else but neutrons. It is like the whole star is one giant atomic nucleus, but it is held together by gravity rather than the forces that hold together nuclei. -- It appears that any main sequence star with mass greater than about 8 times the Sun will not lose enough mass in its planetary nebula stage to be able to make a white dwarf. All these stars will end up with a core that gets squished into a neutron star, or even a black hole.
III. Supernovae -- in 1885, astronomical study took a bizarre turn. A star in the Andromeda galaxy became suddenly so bright that the entire brightness of Andromeda was increased about 10 percent. That means it had become about 10 billion times more luminous than our Sun! Of course, the event did not actually occur in 1885, that's just when we saw it. Andromeda is 2 million light years away (about 500,000 parsecs, or a hundred billion AU), so it really happened 2 million years ago, when life on Earth looked a lot different! -- the outburst only lasted about a week, and was called a super-nova, since it was so much brighter than the short-term brightenings called novae. -- Only 4 supernova have been seen in our galaxy in the last thousand years. The brightest was seen by Chinese astronomers in 1006. The last ones were over three centuries ago. It is unlikely there will be one in our galaxy in our lifetimes, but perhaps we are "due"! It would put on a great show. -- Supernova are classed into Type I and Type II, depending on how much hydrogen is present. Type I has hydrogen, Type II does not. -- Type II come from the collapse of the core of a massive star, by the time it has fused everything into iron in the core. The iron core collapses into a neutron star, and the gravitational energy released is ejected in the form of a huge mass outflow, an explosion of the envelope out into space. -- In 1987, supernova studies got a shot in the arm when a star in the Large Magellanic Cloud went supernova. It could be seen with the naked eye. -- for pics of supernova remnants, see here.
IV. Supernova Remnants and Pulsars -- the cloud of gas left behind by a supernova is called a remnant -- usually remnants look like a broken up shell, where fast gas from the supernova meets the interstellar medium. Sometimes, however, the shell appears filled in by luminous material, called a plerion -- the neutron star whose formation caused the supernova still remains at the center of the remnant. The neutron star continues to emit intense radio waves for a while, and during that time, it is called a pulsar. When the pulsar is active, it creates the plerion appearance. -- pulsars were discovered in 1967 by accident. At first it was thought they must be some man-made signal, but when that possibility was eliminated, it was considered that they could be extraterrestrial intelligence. They were then jokingly referred to as LGMs: little green men! -- it was later decided that pulsars were neutron stars whose strong magnetic fields collimated the radio emissions like the searchlight in a lighthouse, so as the star rotates, its beam can cross Earth and be observed as radio blips with a very regular period. -- pulsar periods range from a microsecond to a few seconds. Most are about a second. This range in periods were hard to accomplish, and were used to eliminate other possibilities like stellar pulsations. White dwarfs would pulsate in a few seconds, nuetron stars a few microseconds, but nothing could explain the intermediate periods except the rotation rate of a neutron star. -- pulsars are associated with supernova remnants: for example, there is one in the center of the Crab Nebula, which is a plerion.
V. Black Holes -- perhaps the most bizarre and amazing form of matter is a black hole. -- black holes form because neutron stars, like white dwarfs, actually get smaller as their mass increases. As they get small, the escape velocity increases, and can eventually reach the speed of light. This radius is called the Schwarzschild radius, R = 2*G*M/(c squared). -- when even light cannot escape the surface, Newtonian mechanics completely breaks down, and a Black Hole forms -- to understand black holes well, you actually need a whole new type of physics, called General Relativity, invented by Einstein