Main-Sequence Simulator: Hydrogen Fusion in Stars

simulator intermediate ~10 min
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L = 1.0 L☉ — pp-chain dominated, 10 Gyr lifetime

A 1 solar-mass star burns hydrogen via the pp-chain at a core temperature of 15.7 MK, producing luminosity 1 L☉ with a main-sequence lifetime of about 10 billion years.

Formula

L = L☉ × (M/M☉)^3.5
ε_pp ∝ ρ X² T^4 (pp-chain energy generation)
ε_CNO ∝ ρ X Z_CNO T^16 (CNO cycle energy generation)

The Stellar Furnace

Deep within every main-sequence star, temperatures and densities are extreme enough to overcome the electrostatic repulsion between protons, enabling nuclear fusion. In the Sun's core — 15.7 million Kelvin and 150 times the density of water — hydrogen nuclei fuse into helium through the proton-proton chain, releasing 3.8 × 10²⁶ watts. This simulation lets you explore how mass and core conditions control the fusion process.

Two Paths to Helium

Nature provides two hydrogen-burning pathways. The pp-chain, dominant in stars below ~1.3 M☉, fuses protons directly through deuterium and helium-3 intermediates. The CNO cycle, dominant in more massive stars, uses pre-existing carbon, nitrogen, and oxygen as catalysts in a cyclic reaction sequence. The CNO cycle's extreme temperature sensitivity (ε ∝ T¹⁶) produces convective cores in massive stars, thoroughly mixing the nuclear fuel.

Mass Controls Everything

The mass-luminosity relation L ∝ M^3.5 is the most consequential relationship in stellar astrophysics. It means that doubling a star's mass increases its luminosity eleven-fold but only doubles its fuel supply, cutting its lifetime by a factor of six. The most massive O-stars exhaust their hydrogen in a few million years, while the smallest M-dwarfs can shine for trillions — outlasting the current age of the universe many times over.

The Hydrogen Clock

As hydrogen depletes in the core, the mean molecular weight increases, reducing pressure support. The core contracts slightly and heats up, paradoxically increasing the fusion rate and luminosity. The Sun today is about 30% more luminous than when it formed 4.6 billion years ago. When core hydrogen fraction drops below ~1%, the star leaves the main sequence — a transition this simulation tracks through the core hydrogen fraction parameter.

FAQ

What is the main sequence?

The main sequence is the evolutionary stage where stars fuse hydrogen into helium in their cores. It is the longest phase of a star's life, during which the star is in hydrostatic equilibrium — gravity balanced by radiation and gas pressure from nuclear fusion.

What is the difference between the pp-chain and CNO cycle?

Both convert hydrogen to helium, but the pp-chain (proton-proton) dominates below ~17 MK and depends on temperature as T^4. The CNO cycle uses carbon, nitrogen, and oxygen as catalysts and dominates above 17 MK with a much steeper T^16 dependence.

Why do massive stars live shorter lives?

Luminosity scales as M^3.5 while fuel supply scales as M, so lifetime scales as M^(−2.5). A 10 M☉ star is ~3000× more luminous than the Sun but has only 10× the fuel, giving it a lifetime of ~30 million years vs the Sun's 10 billion.

What happens when hydrogen runs out?

When core hydrogen is exhausted, fusion ceases in the core and shifts to a hydrogen-burning shell. The core contracts and heats while the envelope expands, turning the star into a red giant as it ascends the giant branch on the HR diagram.

Sources

Embed

<iframe src="https://homo-deus.com/lab/stellar-evolution/main-sequence/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub