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The Birth of a Star
A star forms when a massive, light-years-wide cloud of dust and gas clumps together under the pull of its own gravity. The clump gets larger and heavier as it collects and its gravity field compresses it, causing it to heat up. This hot, compact ball of gas is technically called a "protostar." When it reaches a critical level of mass and the temperature in its core is hot enough to cause spontaneous nuclear reactions, the protostar ignites and becomes a proper star. If this crucial level of mass isn't reached the protostar won't ignite and instead remains a giant ball of hot gas, like Jupiter.
The Main Sequence
Once a star has formed, ignited and stabilized, it enters its mature phase, which scientists call the "main sequence." The dense, blazing core of the star is a nuclear furnace, where fusion converts the core's store of hydrogen fuel into helium. This produces enough expansive energy to counterbalance the inward pull of the star's gravity, forming an equilibrium. A star can remain stable like this for billions of years; if it cools down, the gravity compresses it further, making it heat up and expand again. But eventually, its furnace runs out of hydrogen and the nuclear reactions stop, and gravity now crushes the core material to unprecedented pressures and temperatures. The main sequence is over.
Red Giant
Although nuclear fusion has ceased in the star's core, most of its hydrogen remains intact in the outer layers, where fusion continues. The shrinking and increasingly hot core forces the outer layers to expand and cool, which creates a red giant. In sufficiently massive stars, the core becomes so hot that new chain reactions start, this time fusing the leftover helium into heavier elements, all the way up to iron. Iron will not cause chain reactions under normal circumstances, so as the iron increases, the nuclear reactions become unstable, burning erratically, causing the outer layers to blow off.
White Dwarf
During the final stages of its red giant phase, the bloated star will continue blowing off its outer layers in puffs of gas and dust until only the bright, dense, fiery core remains, known as a "white dwarf." Although the core is still white hot, without any further source of fuel, it can only lose energy now. This is the ultimate end of our sun, as well as the vast majority of other stars in the universe. Hugely massive stars suffer a much different fate.
Supernovae and Neutron Stars
When the core of a hyper-massive star runs out of nuclear fuel, the gravitational collapse is so sudden and powerful that the core's atoms shatter. Under pressure, the protons and electrons combine to create a type of exotic matter consisting only of neutrons, which is quite possibly the hardest material in the universe. This "neutronium" is the only thing that can prevent the core from collapsing further. Meanwhile, the vastly expanded outer layers of the star which are still violently collapsing suddenly hit the hard shell of the core and release their implosive energy as an explosion. This explosion is a "supernova" which can make a star temporarily shine as bright as a galaxy. The supernova will eventually fade and so will the star, which is now a tiny, dim, nearly impossibly compact neutron star.
Black Holes
For the most massive stars, the final gravitational collapse is too much, even for a material made from solid neutrons. Once the neutronium breaks down, there is nothing in the universe to keep the star from collapsing to a point of zero volume and infinite density, a singularity, or more imaginatively, a black hole.