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Stars — life and death

Every star is a tug-of-war between gravity and the pressure of hot gas. Pick a mass and watch the star swell into a giant and die: quietly as a white dwarf or with a bang as a supernova. At the end, find out which atoms in your body were made in stars.

Each dot is a star. Color: temperature (blackbody spectrum). Dashed diagonal lines: constant radius.

←→ mass Space start / pause 1–3 views Esc stop

Spectral classification

O B A F G K M — spectral classes

Split starlight with a prism and you'll see a rainbow crossed by dark lines. Which lines are strong depends mainly on the surface temperature. That's why astronomers sort stars into classes — from the hottest, O, to the coolest, M. Hover over a class and its band lights up on the H–R diagram above.

Brown dwarfs (too light to burn hydrogen for long):

Watch out for a common mistake

The letters sort stars by surface temperature and color, not by brightness. Luminosity also depends on size: Betelgeuse, a class M red supergiant, shines about 90,000 times brighter than the Sun (class G), even though it is cooler — because it is about 760 times larger. On the H–R diagram the classes are vertical bands: each band holds both dwarfs and giants.

Subclasses and luminosity classes

Each letter is split into subclasses 0–9: 0 is the hottest part of the class, 9 the coolest (G2 is hotter than G8). After it comes a Roman numeral — the luminosity class, i.e. the star's “size.” The Sun is G2 V: class G, subclass 2, a main-sequence dwarf.

Isupergiants (Ia, Ib) — e.g. Betelgeuse M1–2 Ia–ab, Rigel B8 Ia
IIbright giants
IIIgiants — e.g. Aldebaran K5 III
IVsubgiants — e.g. Procyon F5 IV–V
Vmain sequence (dwarfs) — e.g. the Sun G2 V, Sirius A A1 V

How to remember the order?

  • Oh Be A Fine Girl/Guy, Kiss Methe classic English mnemonic
  • Old Blue Albatrosses Fly Gracefully, Kissing Moonlighta playful mnemonic (made up for this page)
  • Observe Boldly, Astronomers — Fascinating Giants Keep Mesmerizinganother one, just as silly

Stars and planets

The habitable zone — where can there be liquid water?

Around every star there is a band of distances where an Earth-like planet could have liquid water on its surface — not too hot, not too cold. Where that band lies and how long it lasts depends on the star. The star choice and the age slider are linked to the experiment above.

Star:
Examples (approximate):

Darker green band: conservative zone; lighter: optimistic. Limits after Kopparapu et al. (2013), simplified. The star and planets are not drawn to scale unless the star is bigger than its icon (e.g. a red giant).

Caveats

The habitable zone is only about liquid water on the surface. Life could also exist outside it — e.g. in the subsurface oceans of Europa and Enceladus, heated by tides from their giant planets.

The atmosphere (greenhouse effect), a magnetic field shielding against the stellar wind, and the planet's size also matter. Venus sits at the edge of the zone and is a hellscape; Mars is in the optimistic zone and frozen solid.

The “Rare Earth” hypothesis is still debated: some think complex life needs an exceptional coincidence, others that it may be common. So far we know of no life beyond Earth.

Mass limits for remnants

The Chandrasekhar limit — when a star can no longer resist gravity

The dead core of a star has no fuel left, so it doesn't heat up and can't hold itself up with heat. Quantum physics saves it — but only up to a certain mass. Move the slider and see what can support a remnant of a given mass.

0.6M☉

Object—
Size—

What holds up a white dwarf?

The Pauli exclusion principle: no two electrons can occupy the same state. Squeezed electrons are forced into ever higher momenta — and they push outward. This is electron degeneracy pressure; it doesn't depend on temperature, so it works even in a cooling dwarf.

The greater the mass, the harder gravity squeezes the dwarf and the faster the electrons move. As they approach the speed of light, their resistance grows more slowly than gravity. So there is a mass that no white dwarf can support:

MCh ≈ 5.83μe² M☉

μe is the number of nucleons per electron — it depends on the composition. For helium, carbon and oxygen μe = 2, so the formula gives about 1.46 M☉. Small corrections lower this to about 1.4 M☉ (textbooks often say 1.44 M☉). For iron (μe ≈ 2.15) the limit is lower: about 1.26 M☉ by this formula.

This is the limit for the remnant, not for the whole star. Stars of up to about 8 M☉ shed their envelopes, so their white dwarfs have less than 1.4 M☉ — usually about 0.6 M☉.

The next limit: a neutron star

Above the Chandrasekhar limit, electrons are pressed into protons and neutrons form. A neutron star is held up by neutron degeneracy pressure and nuclear forces — up to the Tolman–Oppenheimer–Volkoff limit, about 2–2.3 M☉. The exact value is uncertain because we don't understand matter at nuclear density well. The heaviest precisely measured neutron stars have about 2 M☉. Above this limit nothing can stop the collapse: a black hole forms.

History: a 19-year-old vs. Eddington

Subrahmanyan Chandrasekhar calculated this limit in 1930, at age 19, on a voyage from India to England. In 1935, at a meeting of the Royal Astronomical Society, Arthur Eddington, the most famous astrophysicist of the era, publicly ridiculed the result. Chandrasekhar was right, though — in 1983 he received the Nobel Prize (shared with William Fowler).

Type Ia supernovae and the accelerating Universe

A white dwarf in a binary system can pull gas from its companion. When it nears the limit (about 1.38 M☉), carbon ignites inside it and the whole dwarf explodes thermonuclearly. Such explosions have similar peak brightness and, after a small correction, serve as “standard candles” for measuring distances. In 1998 they revealed that the expansion of the Universe is accelerating — the 2011 Nobel Prize went to Saul Perlmutter, Brian Schmidt and Adam Riess.

Dwarf mass: 1.20 M☉

Some type Ia supernovae also come from collisions of two white dwarfs.

Origin of the elements

We are made of stardust

The hydrogen in the water you drink was made in the Big Bang. The carbon in your DNA, the oxygen in the air, the calcium in your bones and the iron in your blood were forged by stars. And the gold in a wedding ring — most likely by colliding neutron stars. Each tile shows where a given element in the Solar System comes from.

Where they come from (click to highlight)
Explore all the elements in the periodic table

The shares are approximate and still uncertain for many elements. We attribute r-process elements to neutron star collisions, although some may also come from rare types of supernovae.

How does it work?

A star is a huge ball of hot plasma. Gravity squeezes it inward, while the pressure of the gas, heated by nuclear reactions in the core, pushes outward. As long as these forces are in balance, the star shines steadily.

Hertzsprung–Russell diagram

The horizontal axis shows surface temperature — reversed: hot stars are on the left. The vertical axis shows luminosity in units of the Sun's luminosity (L☉) on a logarithmic scale: each grid line means 10 times more. About 90% of stars lie on a diagonal band — the main sequence, because that's where stars spend most of their lives, burning hydrogen.

Luminosity, radius and temperature

L = 4π R² σ T⁴Stefan–Boltzmann law

σ = 5.670·10⁻⁸ W/(m²·K⁴). For the Sun (R = 6.957·10⁸ m, T = 5,772 K):

L☉ = 4π · (6.957·10⁸ m)² · 5.670·10⁻⁸ · (5,772 K)⁴ ≈ 3.83·10²⁶ W

So a cool but very bright star must be huge, and a hot but faint one must be tiny. That's why red giants sit in the upper right of the diagram and white dwarfs at the lower left.

Color is a thermometer

λmax = bT,   b ≈ 2.898·10⁻³ m·KWien's law

The Sun emits the most light at about 502 nm. Stars at 3,000 K glow orange, and those at 20,000 K blue-white. The colors of the dots on this page are computed from the blackbody spectrum.

Mass decides everything

The greater the mass, the harder gravity squeezes the core, the hotter it gets and the faster it burns its fuel. For stars of about 1 to 20 solar masses, luminosity grows roughly as

L ∝ M3.5

The fuel supply is proportional to mass and it is used up in proportion to luminosity, so t ∝ M / L ∝ M−2.5:

t ≈ 10¹⁰ years · (MM☉)−2.5

A star 10 times more massive than the Sun shines about 3,000 times brighter but lives about 300 times shorter: about 30 million years.

Where does the energy come from?

4 ¹H → ⁴He + 2 e⁺ + 2 νe  ·  Δm ≈ 0.7%  ·  E = Δm c²

Every second the Sun turns about 600 million tonnes of hydrogen into helium, and about 4.3 million tonnes of mass are converted into energy. When the hydrogen in the core runs out, the star contracts its core, heats it up and ignites the next fuels: helium, carbon, neon, oxygen, silicon. Iron is where it all ends — fusing it no longer releases energy, it absorbs it.

How stars end

Simplifications. The evolutionary tracks are simplified: smooth curves roughly fitted to models of stars with a composition similar to the Sun's. We ignore rotation, binary stars, pulsations and the details of mass loss. The mass limits are approximate — they depend on chemical composition and on how much mass the star loses. The lifetime formula is a rough guide: the most massive stars actually live 3–5 million years, longer than it predicts, and the durations of post-main-sequence stages are rough estimates. The population on the diagram is randomly generated, and the data for known stars are approximate (measurements differ between sources).

Challenges 0 / 7

  1. Place the Sun on the diagram

    The Sun will vanish from the H–R diagram — point to where it belongs. Hint: the Sun's luminosity is by definition 1 L☉.

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  2. Calculate the lifetime of a 0.5 M☉ star

    Using the formula t ≈ 10¹⁰ years · (M/M☉)−2.5, work out how long a star of 0.5 M☉ will shine on the main sequence.

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  3. Find a mass that ends as a black hole

    Choose an initial mass and watch the star's life to the very end — in view 2, or as an explosion in view 3.

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  4. An element from neutron star collisions

    In the “We are made of stardust” table, find an element that is made at least 90% in neutron star collisions.

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  5. A habitable zone closer than Mercury

    Find a type of main-sequence star whose whole (conservative) habitable zone lies closer than Mercury's orbit (0.39 au).

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  6. Find the mass at which a white dwarf is no longer possible

    In the section on the Chandrasekhar limit, move the remnant mass until a white dwarf can no longer hold itself up.

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  7. Arrange the spectral classes from hottest to coolest

    Drag the tiles into the right places. With the keyboard: select a tile and move it with the ← → arrows.

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