Life Cycle of Stars: Protostars to Supernovae

Stars form from collapsing clouds of gas and dust (protostars), spend most of their lives on the main sequence fusing hydrogen into helium, then expand into red giants as the fuel is exhausted, and end as white dwarfs (low-mass stars, below about 8 M_☉) or in supernova explosions that leave neutron stars or black holes (massive stars). In brief: the star is stable when the inward pull of gravity is balanced by the outward pressure of the hot gas and radiation (hydrostatic equilibrium). The mass determines the whole life: a star of 10 M_☉ lives about 30 million years, the Sun about 10 billion years, and a red dwarf trillions of years. Stars make all the elements heavier than helium (and are the origin of the carbon, oxygen and iron in our bodies).

The Sun is about halfway through its life of 10 billion years. This guide follows the evolution of stars from the interstellar cloud to their final state, for low-mass and massive stars, discusses nucleosynthesis and the role of supernovae, compares the paths in a table, works through numerical examples of lifetimes and energy, and corrects common mistakes.

How do stars form?

Stars form in cold, dense molecular clouds (such as the Orion Nebula). A region of the cloud that is massive and cool enough starts to collapse under its own gravity (the Jeans criterion), triggered by a shock wave, such as from a nearby supernova. As the gas contracts, the gravitational potential energy is converted into thermal energy, and the core heats up: a protostar forms, surrounded by a disc of gas in which planets may form, and often with jets. The contraction continues until the core temperature reaches about 10 million K, when the fusion of hydrogen starts (taking about 10 to 50 million years for a star like the Sun). Objects with less than about 0.08 M_☉ never reach this temperature and become brown dwarfs. The newborn star settles on the main sequence.

What happens on the main sequence?

On the main sequence, hydrogen is fused to helium in the core (by the proton-proton chain in stars of the mass of the Sun or lower, and by the CNO cycle in more massive stars). The star is in hydrostatic equilibrium, and self-regulating: if the core heated up, the fusion rate would increase, the star would expand and cool, reducing the fusion rate again. This stable phase lasts most of the life of the star: about 10 billion years for the Sun. As hydrogen is converted into helium, the core becomes denser and hotter, so the luminosity slowly increases (the Sun was about 30 percent less luminous when it formed 4.6 billion years ago than it is now, and will be about 10 percent brighter in 1 billion years).

What is the fate of low-mass stars?

When the hydrogen in the core is used up, the core contracts and heats up, and hydrogen fuses in a shell around it. The outer layers expand and cool, and the star becomes a red giant (the Sun will reach about 100 times its present radius, perhaps engulfing Mercury and Venus). When the core reaches about 10⁸ K, helium fuses into carbon and oxygen (the triple-alpha process: 3 ⁴He → ¹²C). When helium is exhausted, the star expands again (asymptotic giant branch) and loses its outer layers in winds and expels them as a glowing shell, a planetary nebula (unrelated to planets). The remaining core, a hot carbon-oxygen sphere about the size of the Earth, is a white dwarf, supported against gravity by the pressure of degenerate electrons (a quantum effect). It cools over billions of years. The maximum mass of a white dwarf is the Chandrasekhar limit, about 1.4 M_☉. Red dwarfs (below 0.5 M_☉) fuse hydrogen very slowly, are fully convective and live for trillions of years.

What is the fate of massive stars?

Stars of more than about 8 M_☉ continue the sequence of fusion after helium: carbon (at about 6 × 10⁸ K), neon, oxygen and silicon, producing an onion-like structure with iron at the center. Each stage is faster than the previous one: for a 25 M_☉ star, hydrogen burning lasts about 7 million years, helium 700,000 years, carbon about 600 years, oxygen about 6 months, and silicon about 1 day. Iron cannot release energy by fusion (it has the highest binding energy per nucleon), so when the iron core reaches the Chandrasekhar mass (about 1.4 M_☉), electron degeneracy pressure fails and the core collapses in less than a second to nuclear density. The infalling outer layers rebound on the stiff neutron core, and a huge flux of neutrinos (carrying about 99 percent of the energy of 3 × 10⁴⁶ J) helps to expel the star’s envelope in a core-collapse supernova (type II), which for a few weeks can outshine a whole galaxy. The remnant is a neutron star (core mass up to about 2 to 3 M_☉) or a black hole (higher mass). Supernovae and neutron star mergers produce the elements heavier than iron, and scatter heavy elements into space, from which new stars and planets form. A type Ia supernova is a different process: a white dwarf in a binary system accretes matter and explodes when it approaches the Chandrasekhar limit.

Stellar life cycles compared

Worked example: lifetimes and energy

1. Lifetime of the Sun. About 10 percent of the Sun’s mass (2.0 × 10³⁰ kg × 0.1) is hydrogen in the core that can be fused; 0.71 percent of this mass becomes energy. E = 0.1 × 1.989 × 10³⁰ × 0.0071 × (3.00 × 10⁸)² = 1.27 × 10⁴⁴ J. At L = 3.83 × 10²⁶ W: t = 1.27 × 10⁴⁴ ÷ 3.83 × 10²⁶ = 3.3 × 10¹⁷ s = 10.5 billion years.
2. Massive star. A star of 10 M_☉ has L ≈ 10^3.5 L_☉ = 3,160 L_☉ and 10 times the fuel: t = 10.5 × 10⁹ × 10 ÷ 3,160 = 3.3 × 10⁷ years.
3. Red dwarf. With the simple relation L ∝ M^3.5, a star of 0.2 M_☉ has L ≈ 0.2^3.5 = 0.0036 L_☉, and 0.2 times the fuel: t ≈ 10¹⁰ × 0.2 ÷ 0.0036 = 5.6 × 10¹¹ years. The relation is only approximate at low masses, and stellar models give lifetimes of the order of 10¹² years or more (red dwarfs can use most of their hydrogen because they are fully convective). In any case, this is much longer than the present age of the universe, 1.38 × 10¹⁰ years, so no red dwarf has yet died.
4. Energy of a supernova. The gravitational binding energy released in the collapse of a 1.4 M_☉ core to a radius of 12 km: E ≈ (3/5)GM²/R = 0.6 × 6.674 × 10⁻¹¹ × (2.78 × 10³⁰)² ÷ 1.2 × 10⁴ = 2.6 × 10⁴⁶ J, consistent with the quoted value of about 3 × 10⁴⁶ J, 99 percent carried by neutrinos. The visible light carries only about 10⁴² J, still comparable to the light of a whole galaxy.
5. Chandrasekhar limit. An iron core of 1.5 M_☉ exceeds the limit of about 1.4 M_☉ and collapses.

How was stellar evolution understood?

Arthur Eddington (1920) suggested that nuclear fusion powers the stars, and Hans Bethe worked out the reactions in 1938 to 1939. Subrahmanyan Chandrasekhar calculated the limiting mass of white dwarfs in 1930 and received the 1983 Nobel Prize in Physics. Fritz Zwicky and Walter Baade proposed neutron stars in 1934 as the products of supernovae. The theory of nucleosynthesis in stars was set out by Burbidge, Burbidge, Fowler and Hoyle in 1957. Supernova 1987A in the Large Magellanic Cloud confirmed the neutrino burst of core collapse (about 20 neutrinos were detected on Earth).

Which mistakes are common?

Mistake 1: Thinking that the Sun will explode as a supernova

The Sun is too small. It will become a red giant and then a white dwarf.

Mistake 2: Saying that stars burn fuel like fire

Stars shine by nuclear fusion, which needs no oxygen.

Mistake 3: Believing that a planetary nebula has anything to do with planets

The name comes from its round shape in early telescopes. It is the ejected envelope of a dying star.

Mistake 4: Thinking that all stars end as black holes

Most stars become white dwarfs. Only the most massive stars leave black holes.