Editing Triple-alpha process (section)

==Reaction rate and stellar evolution==
The triple-alpha steps are strongly dependent on the temperature and density of the stellar material. The power released by the reaction is approximately proportional to the temperature to the 40th power, and the density squared.<ref name="Carroll and Ostlie 2006">{{cite book |last1=Carroll |first1=Bradley W. |last2=Ostlie |first2=Dale A.  |title=An Introduction to Modern Astrophysics |publisher=Addison-Wesley, San Francisco |date=2006 |edition=2nd | pages=312–313 |isbn=978-0-8053-0402-2 }}</ref> In contrast, the [[proton–proton chain reaction]] produces energy at a rate proportional to the fourth power of temperature, the [[CNO cycle]] at about the 17th power of the temperature, and both are linearly proportional to the density. This strong temperature dependence has consequences for the late stage of stellar evolution, the [[red giant|red-giant]] stage.

For lower mass stars on the [[red-giant branch]], the helium accumulating in the core is prevented from further collapse only by [[degenerate matter|electron degeneracy]] pressure.  The entire degenerate core is at the same temperature and pressure, so when its density becomes high enough, fusion via the triple-alpha process rate starts throughout the core.  The core is unable to expand in response to the increased energy production until the pressure is high enough to lift the degeneracy.  As a consequence, the temperature increases, causing an increased reaction rate in a positive feedback cycle that becomes a [[thermal runaway|runaway]] reaction. This process, known as the [[helium flash]], lasts a matter of seconds but burns 60–80% of the helium in the core.  During the core flash, the star's [[power (physics)|energy production]] can reach approximately 10<sup>11</sup> [[solar luminosity|solar luminosities]] which is comparable to the [[luminosity]] of a whole [[galaxy]],<ref name="Carroll and Ostlie 2006bis">{{cite book |last1=Prialnik |first1=Dina  |title=An Introduction to the Theory of Stellar Structure and Evolution |publisher=Addison-Wesley, San Francisco |date=2006 |edition=2nd | pages=461–462 |isbn=978-0-8053-0402-2 }}</ref> although no effects will be immediately observed at the surface, as the whole energy is used up to lift the core from the degenerate to normal, gaseous state. Since the core is no longer degenerate, [[hydrostatic equilibrium]] is once more established and the star begins to "burn" helium at its core and hydrogen in a spherical layer above the core. The star enters a steady helium-burning phase which lasts about 10% of the time it spent on the main sequence (the Sun is expected to burn helium at its core for about a billion years after the helium flash).<ref>{{Cite web|title=The End Of The Sun|url=https://faculty.wcas.northwestern.edu/~infocom/The%20Website/end.html|access-date=2020-07-29|website=faculty.wcas.northwestern.edu}}</ref>

In higher mass stars, which evolve along the [[asymptotic giant branch]], carbon and oxygen accumulate in the core as helium is burned, while hydrogen burning shifts to further-out layers, resulting in an intermediate helium shell. However, the boundaries of these shells do not shift outward at the same rate due to differing critical temperatures and temperature sensitivities for hydrogen and helium burning. When the temperature at the inner boundary of the helium shell is no longer high enough to sustain helium burning, the core contracts and heats up, while the hydrogen shell (and thus the star's radius) expand outward. Core contraction and shell expansion continue until the core becomes hot enough to reignite the surrounding helium. This process continues cyclically – with a period on the order of 1000 years – and stars undergoing this process have periodically variable luminosity. These stars also lose material from their outer layers in a [[stellar wind]] driven by [[radiation pressure]], which ultimately becomes a [[superwind]] as the star enters the [[planetary nebula]] phase.<ref name="Prialnik 9.6">{{cite book |last1=Carroll |first1=Bradley W. |last2=Ostlie |first2=Dale A. |title=An Introduction to Modern Astrophysics |publisher=Cambridge University Press |date=2010 |edition=2nd | pages=168–173 |chapter=Thermal pulses and the asymptotic giant branch |isbn=9780521866040 }}</ref>