For a star with a mass above about 0.25 solar masses (M☉), once the core is depleted of hydrogen it contracts and heats up so that hydrogen starts to fuse in a shell around the core. The portion of the star outside the shell expands and cools, but with only a small increase in luminosity, and the star becomes a subgiant. The inert helium core continues to grow and increase in temperature as it accretes helium from the shell, but in stars up to about 10-12 M☉ it does not become hot enough to start helium burning (higher-mass stars are supergiants and evolve differently). Instead, after just a few million years the core reaches the Schönberg–Chandrasekhar limit, rapidly collapses, and may become degenerate. This causes the outer layers to expand even further and generates a strong convective zone that brings heavy elements to the surface in a process called the first dredge-up. This strong convection also increases the transport of energy to the surface, the luminosity increases dramatically, and the star moves onto the red-giant branch where it will stably burn hydrogen in a shell for a substantial fraction of its entire life (roughly 10% for a Sun-like star). The core continues to gain mass, contract, and increase in temperature, whereas there is some mass loss in the outer layers.[6], § 5.9.
If the star's mass, when on the main sequence, was below approximately 0.4 M☉, it will never reach the central temperatures necessary to fuse helium.[7], p. 169. It will therefore remain a hydrogen-fusing red giant until it runs out of hydrogen, at which point it will become a helium white dwarf.[6], § 4.1, 6.1. According to stellar evolution theory, no star of such low mass can have evolved to that stage within the age of the Universe.
In stars above about 0.4 M☉ the core temperature eventually reaches 108 K and helium will begin to fuse to carbon and oxygen in the core by the triple-alpha process.[6],§ 5.9, chapter 6. When the core is degenerate helium fusion begins explosively, but most of the energy goes into lifting the degeneracy and the core becomes convective. The energy generated by helium fusion reduces the pressure in the surrounding hydrogen-burning shell, which reduces its energy-generation rate. The overall luminosity of the star decreases, its outer envelope contracts again, and the star moves from the red-giant branch to the horizontal branch.[6][8], chapter 6.
When the core helium is exhausted, a star with up to about 8 M☉ has a carbon–oxygen core that becomes degenerate and starts helium burning in a shell. As with the earlier collapse of the helium core, this starts convection in the outer layers, triggers a second dredge-up, and causes a dramatic increase in size and luminosity. This is the asymptotic giant branch (AGB) analogous to the red-giant branch but more luminous, with a hydrogen-burning shell contributing most of the energy. Stars only remain on the AGB for around a million years, becoming increasingly unstable until they exhaust their fuel, go through a planetary nebula phase, and then become a carbon–oxygen white dwarf.[6], § 7.1–7.4.
High-mass stars
Main-sequence stars with masses above about 12 M☉ are already very luminous and they move horizontally across the HR diagram when they leave the main sequence, briefly becoming blue giants before they expand further into blue supergiants. They start core-helium burning before the core becomes degenerate and develop smoothly into red supergiants without a strong increase in luminosity. At this stage they have comparable luminosities to bright AGB stars although they have much higher masses, but will further increase in luminosity as they burn heavier elements and eventually become a supernova.
Stars in the 8~12 M☉ range have somewhat intermediate properties and have been called super-AGB stars.[9] They largely follow the tracks of lighter stars through RGB, HB, and AGB phases, but are massive enough to initiate core carbon burning and even some neon burning. They form oxygen–magnesium–neon cores, which may collapse in an electron-capture supernova, or they may leave behind an oxygen–neon white dwarf.
O class main sequence stars are already highly luminous. The giant phase for such stars is a brief phase of slightly increased size and luminosity before developing a supergiant spectral luminosity class. Type O giants may be more than a hundred thousand times as luminous as the sun, brighter than many supergiants. Classification is complex and difficult with small differences between luminosity classes and a continuous range of intermediate forms. The most massive stars develop giant or supergiant spectral features while still burning hydrogen in their cores, due to mixing of heavy elements to the surface and high luminosity which produces a powerful stellar wind and causes the star's atmosphere to expand.
Low-mass stars
A star whose initial mass is less than approximately 0.25 M☉ will not become a giant star at all. For most of their lifetimes, such stars have their interior thoroughly mixed by convection and so they can continue fusing hydrogen for a time in excess of 1012 years, much longer than the current age of the Universe. They steadily become hotter and more luminous throughout this time. Eventually they do develop a radiative core, subsequently exhausting hydrogen in the core and burning hydrogen in a shell surrounding the core. (Stars with a mass in excess of 0.16 M☉ may expand at this point, but will never become very large.) Shortly thereafter, the star's supply of hydrogen will be completely exhausted and it is expected to become a helium white dwarf,[10] although the universe is too young for any such star to exist yet, so no star with that history has ever been observed.
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