Technically speaking, a small star is a star with up to about twice the mass of our sun, a medium star is from 2-8 solar masses, and a large star is larger than 8 solar masses. By this criterion, our sun is is a small star. But for the sake of this section, I will describe stars of ~ 1 solar mass, stars much smaller, and stars much larger.
Our sun began as a nebula, condensing enough to ignite hydrogen fusion at its core. We saw previously that the sun is in a state of balance between the compression of gravity and the huge internal pressure from the fusion reactions. A star in this stable state is said to be in its main sequence. As long as it has enough hydrogen, it will remain stable in its main sequence state. Our sun has a main sequence lifetime of about 10 billion years.
When the hydrogen is mostly used up, the rate of fusion drops. The pressure in the core also drops, so there is less outward force, and gravity causes the core of the star to collapse. This creates more pressure and heat, igniting the fusion of helium into carbon, once again generating high heat and pressure in the core.
This high temperature is enough to generate fusion in hydrogen in the shell surrounding the core. This extra pressure causes the outer shell of the sun to puff up, producing a red giant star. The star is no longer in the main sequence.
The radius of a red giant is larger than 1 AU -- in other words, the earth would be inside the star!
This red giant star is unstable. The super-hot core will blow off the outer shell, until only a small white dwarf star remains. The outer gasses spread out, producing a glowing nebula, called a planetary nebula.
Over billions of years, the white dwarf will cool to a giant crystal of carbon -- a diamond!
The vast majority of stars are much smaller than ours. These are called red dwarfs and brown dwarfs.
If the star has a mass of less than about half of our sun, the hydrogen fusion occurs more slowly. As a result, it is small, glows only dimly red (hence the name red dwarf), but remains in the main sequence state for a very long time -- 10 to 100 times longer than our sun (100 billion years or more). When the hydrogen is exhausted, they may collapse to a white dwarf, or if they are too small, simply burn out.
A star that has insufficient mass (less than 8% of the mass of our sun, or 0.08 solar mass) to ignite hydrogen fusion simply glows from the heat of pressure, and is called a brown dwarf, or a failed star.
If the star is much larger than the sun, hydrogen fusion occurs very rapidly, producing a very large, hot star. These stars burn their hydrogen so rapidly they remain on the main sequence for only a few million years. When the hydrogen is used up and it leaves the main sequence, the core collapses to fuse helium, like our sun. The outer shell puffs up to produce a red supergiant. These stars may have a diameter over 600 times greater than our sun.
When a red supergiant core runs out of helium, it will begin fusing heavier elements. If it begins to fuse iron, it actually sucks up energy, causing a catastrophic core collapse.
The gravitational force is so great, that it actually squeezes all the atomic nuclei together, producing, essentially, a giant atomic nucleus more massive than our sun. This is a neutron star. The neutron star material is so incredibly dense that 1 cubic centimetre has a mass of about 100 billion kg. This means a teaspoon has a mass of 500 million tonnes.
The neutron star core is solid and uncompressible, so much of the outer material that collapses onto it will bounce back, producing an enormous explosion that blows away the outer shell. This is called a Type II Supernova. A type II supernova is so bright, it can outshine all the other stars in a galaxy put together. Also, a supernova explosion is the only way elements heavier than Iron can form naturally in the universe.
If the core is larger than about 3 solar masses, it will have enough gravity to compress even further. The entire core collapses to virtually nothing, a point of infinite density. The gravity near this point is so great that even light cannot escape, so it is called a black hole.
Even though the gravity near the black hole is very great, at a distance it is no stronger than a normal star, so it does not in fact suck in everything around it, as depicted in science fiction films.
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