End States of Stars: Dwarfs, supernovae, pulsars, black holes, Nucleosynthesis in supernovae

The computer models (physics) show that if a star's mass is less than about 1.4 times the mass of the sun ( 1.4m_$\odot$) it will produce, by fusion, nuclei as heavy as carbon, but no heavier. Then it will contract in size until it is about 10,000 miles across (one one-hundredth of its main sequence size). This is exactly the size white dwarves have. So we have a consistent picture of evolution from diffuse cloud of atoms to white dwarf. And no white dwarf heavier than 1.4m_$\odot$ is known.

What of the heavier stars? The models 'blow up' mathematically: they lead to division by zero, which is mathematically meaningless. The physics behind the division by zero is gravitational collapse: the force which opposes gravity, and keeps the star from imploding, becomes too weak. (The nature of that force is a bit too technical for us; part of it is due to the effect of radiation pushing outward.) The blow up in the mathematics seems to occur in reality as well.

There are stars which, overnight or faster, become 20 magnitudes brighter. (That's 100,000,000 times brighter.) These are the objects called supernovae. Does anything remain after the explosion? Maybe. Physics allows an object about as heavy as the sun to be stable in only a very few sizes. One is 1,000,000 miles; one is 10,000 miles; and the only other one is about 10 miles. The first two have been discussed. The third, for nuclear physics reasons, is known as a neutron star. How might a 1 solar mass, 10 mile across object behave?

For a clue we return to Kepler's law of areas. If a spinning object becomes smaller (more precisely: draws its constituent material closer to the axis of rotation), it spins faster. That's true for ice skaters, professors in swivel chairs, orbiting planets, and spinning stars. Do main sequence stars spin? The only one which we can directly check is the sun. It does, about once a month. If it shrunk to 10 miles (100,000 times smaller), it would spin 10¹⁰ times as fast. That's about once in a thousandth of a second.

What should we look for (in the sky) that might be a star that spins a thousand times a second? Is there anything that happens, over and over and over, at that rate? In 1964 the first such thing in the sky was discovered and many more have been found since. Because its rate was so close to the human heart's it was called a pulsar. It radiates for a very short time, then stops radiating, then starts again, over and over and over, very regularly. The times between pulses are about one second. The first pulsars were radio objects but pulsars are now known which radiate in almost all parts of the spectrum.

Why would a spinning neutron star send radiation in our direction only once a second? The sun doesn't send us light only once a month. Something must make the object behave like a lighthouse. The conventional explanation invokes magnetism as the cause.

So the third stable configuration of a one solar mass object has been seen. Might a supernova end in another way? The only other way is indefinite collapse. That's a 'black hole.' Have these been seen? What would their observational signature be? They have probably been seen. The most likely candidates are x-ray sources.

(The 'black' in the name of the things called black holes is used because the gravitational force on the surface of such an object is so strong that no light can leave it; the 'hole' refers to the fact that anything that got close enough to it would fall irretreviably inside. A black hole may have any mass. The ones discussed here are single stars. They were once, briefly, known as 'collapsars'; 'black hole' has proven catchier. Another often-discussed class of black holes has as much matter as a galaxy-quite a different scale even if the same name is used.)

How were the heavy elements made? Only supernovae produce high enough temperatures. That leads us to the remarkable conclusion that (since there is gold and lead and uranium and all the other heavy atoms here on the earth, and these must have been produced in supernovae) that we are made from stuff that was made by the explosion of a star that lived a full life, died, spewed itself out into space, where that stuff formed a new star, which perhaps went through the process again, finally forming into our sun and solar system and us.