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The next step is for helium to fuse into carbon and the core will ignite in what is called a helium core flash. If the mass is bigger this is much gentler and not as obvious than if the star has a smaller mass. This whole process is also much shorter than any of the previous stages a star goes through.
If the star is less than 8 solar masses it will not reach a temperature hot enough to start burning the carbon. The carbon core continues to contract until it is supported by pressure from electrons instead of pressure of the burning gas and the star becomes a white dwarf. Eventually the outer layers of the star are ejected and it forms a nebula.
If the star is greater than 8 solar masses the temperature will get hot enough to form neon from the carbon and continue to form heavier and heavier elements until it forms iron. Iron cannot burn into any other elements and does not create any more energy for the star. This lack of energy result in the star collapsing until the pull of its own gravity. Here is where most stars will stop contraction of the core and create a shock wave that will blow the star apart and cause it to go supernova. However, if the star has a great enough mass the star will collapse even further as it can be held by only the pressure of the electrons, resulting in the creation of a black hole.

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