Mass decides everything
A star is a ball of gas held together by its own gravity and kept from collapsing by the pressure of its hot interior. Its heat comes from nuclear fusion in the core. A star's mass when it forms, together with a small effect from its composition, sets how hot its core gets, how bright it shines, how long it lives and how it dies.
The Hertzsprung–Russell diagram
Around 1910 Ejnar Hertzsprung and Henry Norris Russell plotted stars by brightness against color. On today's version luminosity runs up the side, on a logarithmic scale with the Sun at 1, and surface temperature runs along the bottom, hottest on the left. A star's luminosity, radius and temperature are tied together by
L = 4πR²σT⁴, or L ÷ L☉ = (R ÷ R☉)² × (T ÷ 5,772 K)⁴
so stars at the top right are cool but bright, which means they are huge (giants and supergiants), and stars at the bottom left are hot but faint, which means they are tiny (white dwarfs). About 90% of stars lie on a diagonal band, the main sequence.
The main sequence
A star on the main sequence fuses hydrogen into helium in its core. This is the longest stage of its life, and where it sits on the band depends on its mass: massive stars are hot, blue and bright; small ones are cool, red and faint. Luminosity rises steeply with mass, roughly L ≈ M^3.5 for stars like the Sun and heavier. A star's fuel is proportional to its mass, so its lifetime goes roughly as
t ≈ 10¹⁰ years × M ÷ L
with M and L in solar units: heavy stars have more fuel but burn it far faster.
Stars like the Sun
- Subgiant and red giant: when the core runs out of hydrogen, fusion moves to a shell around it. The core contracts and heats, and the outer layers swell and cool. The star climbs the red giant branch, growing to a hundred or more times the Sun's radius and a few thousand times its luminosity.
- Helium burning: at about 100 million K the core starts fusing helium into carbon and oxygen, suddenly in stars below about 2 solar masses (the helium flash). The star shrinks to a smaller, steadier giant for roughly a hundred million years.
- Asymptotic giant branch: when core helium runs out, helium and hydrogen burn in two shells. The star swells larger still and loses mass in strong winds.
- Planetary nebula: the outer layers drift away as a glowing shell, lit by the exposed hot core, for a few tens of thousands of years.
- White dwarf: the core, about the size of Earth, with no fusion left, cools slowly for billions of years. No white dwarf can be heavier than the Chandrasekhar limit, about 1.4 solar masses.
Massive stars
Stars above about 8 solar masses go on fusing heavier elements, carbon, neon, oxygen and silicon, in shells like an onion, as red or blue supergiants. Each stage is shorter than the last: silicon burns in about a day. Fusion stops at iron, which gives no energy when fused. The iron core collapses in under a second to a neutron star, about 20 km across, and the rebound and flood of neutrinos blow the rest of the star apart in a core-collapse supernova, briefly as bright as a billion suns. Above roughly 20 to 25 solar masses the core may collapse further into a black hole. The most massive stars lose their outer layers in winds first, becoming hot Wolf–Rayet stars.
Small stars
Red dwarfs below about 0.35 solar masses are convective throughout, so they mix fresh hydrogen into the core and burn almost all of it. They live for trillions of years. None has had time to leave the main sequence in the 13.8 billion years since the Big Bang; models predict they will heat up into "blue dwarfs" and fade as helium white dwarfs.
Worked examples
- A star of 10 solar masses: L ≈ 10^3.5 ≈ 3,200 L☉, so t ≈ 10¹⁰ × 10 ÷ 3,200 ≈ 3 × 10⁷ years. Full stellar models give about 2 × 10⁷: the rough rule gets the size right.
- A red giant: a star with L = 2,500 L☉ and T = 4,200 K has R = √2,500 ÷ (4,200 ÷ 5,772)² = 50 ÷ 0.53 ≈ 94 R☉, close to the size of Earth's orbit, which is 215 R☉.
- A white dwarf: the Sun will leave a white dwarf of about 0.109 × 1 + 0.394 ≈ 0.5 solar masses, about 1.4% of its present radius, roughly one and a half times the size of Earth.
- The red dwarf rule fails: for 0.1 solar masses, L ≈ 0.0012 L☉ and the rule gives about 9 × 10¹¹ years; models give several trillion, because the rule assumes only the core's hydrogen is burned.
Using the simulation
In the Stellar Evolution and Hertzsprung–Russell Diagram Simulator, things to try:
- Follow the Sun: up the red giant branch, down to helium burning, up the asymptotic giant branch, across to a planetary nebula and down to a white dwarf.
- Compare the time on the main sequence for 0.5, 1, 2 and 10 solar masses.
- Choose 15 solar masses: a red supergiant, a supernova and a neutron star. Then 40: a Wolf–Rayet star and a black hole.
- Choose 0.1: the stats note that every star this small is still on the main sequence.
- Watch the white dwarf cool and fade down the diagram, and read its age.
What the model assumes
- Single stars of the Sun's composition, not rotating, with no companion.
- Tracks are simplified: each stage is a straight run on the diagram between points based on published models; the real tracks wiggle, loop and double back.
- Main-sequence lifetimes come from a table based on stellar models; the main-sequence luminosity follows a piecewise mass–luminosity law.
- White dwarf masses follow an empirical fit, 0.109M + 0.394 solar masses, and cool following Mestel's simple law.
- Fixed boundaries: below 0.5 solar masses a helium white dwarf, up to 8 a white dwarf, up to 25 a neutron star, above 25 a black hole.
- Neutron stars and black holes are not placed on the diagram: they are too small and, at first, too hot to fit.
Edge cases
- 0.1 solar masses: the star outlives the universe so far by hundreds of times; its later stages are predictions that no one has observed.
- Near 8 solar masses: stars may end as heavy oxygen-neon white dwarfs or in a weaker electron-capture supernova; the simulation switches at a sharp line.
- Around 20 to 25 solar masses: whether the core forms a neutron star or a black hole is uncertain, and some stars may collapse with little or no explosion.
- 40 solar masses: the black hole's mass depends on how much the star lost in winds, guessed here as a quarter of its starting mass.
- Supernova stage: the star is not shown; for a few weeks it is as bright as a billion suns.
Where the model stops being right
- Binary stars. About half of Sun-like stars, and most massive stars, have companions. Mass transfer strips some stars and feeds others, and a white dwarf gaining mass from a companion can explode as a type Ia supernova, a fate the single-star model cannot show.
- Mass loss and rotation. How much mass stars lose in winds, and how fast they spin, is uncertain and changes the tracks and fates of massive stars a great deal.
- Composition. Stars poor in heavier elements, like those of the early universe, are hotter, lose less mass, and leave larger black holes.
- Real tracks. The helium flash, the blue loops of intermediate-mass stars and the thermal pulses on the asymptotic giant branch are smoothed out here.
- Very massive stars. Stars of roughly 130 to 250 solar masses, if they keep most of their mass, may be torn apart completely by pair-instability supernovae, leaving nothing behind.
- White dwarf cooling slows further as the interior crystallizes; Mestel's law ignores this.
Related tools
A star's color comes from its temperature, as the Blackbody Radiation Simulator shows; How the Greenhouse Effect Works follows the Sun's light to Earth. The Orbit Simulator shows planets and stars moving under gravity, the Scientific Notation Converter handles the huge numbers, and the Temperature Converter converts kelvin.