The helium flash is a very brief stage of stellar evolution in stars less than about two and a half times the mass of the Sun.

As stars evolve along the main sequence, they slowly turn the hydrogen within their cores to helium via nuclear fusion. When a star exhausts all of the hydrogen in the core, nuclear fusion ceases, and the core shrinks. As it does so, the temperature in the layers above the core rise, and hydrogen starts burning in a shell around the core. When this happens, two more things happen: the outer layers of the star are pushed out by radiation from the shell which turns the star into a red giant, and the helium now generated from the shell settles onto the core, making the central mass of helium larger and larger. The star begins to move up the red giant branch. As the core gets more massive and continues to shrink, the helium becomes degenerate (quantum mechanically), which means the gas no longer behaves anything like an ideal gas, and the pressure and temperature become independent of one another.

At the most luminous tip of the red giant branch, eventually the core temperature and pressure become so high, that the helium at the very center of the star starts to fuse into carbon, via the triple-alpha process. This releases a lot of energy. Ordinarily, this increase in energy would increase the temperature and hence the pressure, readjusting the structure of the star. But since the gas is degenerate, the energy released by the fusion doesn't change the pressure or density. Therefore, the energy released by helium fusion goes into thermal energy of the gas, and the temperature starts to build rapidly in and around the core, starting fusion in the surrounding layers of helium which are themselves degenerate. The burning front propagates outwards, until the temperature rises to the point where the gas is no longer degenerate. When it does, the star settles down onto a helium-burning main sequence -- either the horizontal branch or the red clump, depending upon whether the star is metal-poor or metal-rich.

The helium flash is correctly named, because unlike most phases of stellar evolution, the flash itself occurs over a matter of minutes rather than millions of years. It is essentially a massive nuclear explosion in the center of the star releasing a huge amount of energy (Mihalas and Binney quote core luminosities of one hundred thousand million times the energy output of the Sun, but only for a few seconds). However, this energy doesn't make the star explode. What happens is that the temperature profile of the star becomes very steep, to the point where most of the star outside the core becomes convective. The luminosity drops to about 100 times the luminosity of the Sun, and the star settles down into a quiescent phase of helium burning on the horizontal branch.

One interesting point about the helium flash is that the highest temperature during the flash is not in the very center of the star, but is instead in a shell at a radius containing about three tenths of a solar mass. This is because the triple-alpha process releases a large number of neutrinos which serve to carry energy away from the star without generating thermal energy. Neutrino generation peaks in the very center, and decreases outwards. Thus neutrino cooling is most efficient in the very center, resulting in a lower temperature.

Stars more massive than two and a half times the mass of the sun have high enough central densities and temperatures that stable helium burning begins before the core becomes degenerate, and they do not undergo a helium flash. They instead proceed smoothly through the red giant branch into a core helium burning phase.

References: Galactic Astronomy by D. Mihalas and J. Binney; Stellar Structure and Evolution by R. Kippenhahn and A. Weigert

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