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As the helium core continues to contract under the influence of gravity, it will eventually reach the temperatures and densities needed to fuse three helium nuclei into a carbon nucleus. Another nuclear reaction will compete for the available helium nuclei at the same temperature: the carbon can fuse with an additional helium nucleus to form oxygen. The amount of oxygen produced during this process is largely determined by the relative rates of these two competing reactions. Since the Sun is not very massive by stellar standards, it will never get hot enough in the center to produce nuclei much heavier than carbon and oxygen. These elements will collect in the center of the star, which will then shed most of its red giant envelope -- creating a planetary nebula -- and emerge as a hot white dwarf star.

Once a white dwarf star forms and the nuclear reactions have ceased, its structural and thermal evolution is dominated by cooling, and regulated by the opacity of its thin atmospheric outer layers. It will slowly fade as it radiates its residual thermal energy into space -- eventually cooling through a narrow range of temperatures that will cause it to vibrate in a periodic manner, sending gravity-driven seismic waves deep through the interior and bringing information to the surface in the form of brightness variations. This is fortunate, because a detailed record of the nuclear history of the star is locked inside, and pulsations provide the only known key to revealing it.