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The triple-alpha process is the means by which stars fuse helium nuclei into carbon and oxygen nuclei when they have exhausted their hydrogen fuel. Initiating the triple-alpha process requires sustained temperatures of over 100,000,000 K and a sufficient density of helium. This happens when a star begins to build up substantial amounts of helium "ash" in its core from hydrogen burning. The helium has nowhere to go and doesn't produce its own energy, so it aggregates in the core and contracts. The contraction increases the heat and pressure tremendously. At 100 megaKelvins, the triple-alpha process, also known as helium burning, initiates.
The triple-alpha process gets its name because the process is the fusion of three alpha particles. An alpha particle is two protons and two neutrons bound together, which is the same thing as a helium nucleus. Under the colossal pressures at the stellar core, two helium nuclei can be coaxed into combining into a beryllium nucleus, releasing a gamma ray in the process. The beryllium nucleus is unstable, Within 2.6×10-16 seconds, it collapses back into helium nuclei. But if enough beryllium nuclei are continuously being created, eventually one will merge with another energetic helium nuclei and create carbon, a nuclei with a total of six protons and six neutrons.
The triple-alpha process occurs in all low to intermediate mass stars (0.6-10 solar masses) late in their life. After the Red Giant stage, which features traditional hydrogen burning in a compressed shell around a helium core, the core collapses and starts burning helium, launching the star into the Asymptotic giant branch of the Hertzsprung-Russell diagram, which compares star luminosity to spectral type.
The speed of the triple-alpha reaction is strongly dependent on the temperature of the core — the reaction rate is the product of the temperature to the 30th power and the density squared. In small stars, the helium core gets so dense that it becomes a form of degenerate matter, where increases in temperature do not correspond to increases in volume. This can lead to a runaway triple-alpha reaction called a helium flash, where 60-80% of the helium in the core is incinerated in minutes. For larger stars, helium begins to fuse on a shell outside a carbon core, preventing it from reaching the degenerate matter state. In these larger stars, eventually carbon burning initiates.