Life on the Main Sequence: How Stars Burn Hydrogen

## Life on the Main Sequence

A star spends roughly 90% of its life on the main sequence, fusing hydrogen into helium in its core. The main sequence is not a place but a state — hydrostatic equilibrium, where the outward pressure from fusion exactly balances the inward pull of gravity.

### The Proton-Proton Chain

In stars like the Sun and smaller, hydrogen fusion proceeds via the proton-proton (pp) chain:
1. Two protons fuse to form deuterium, releasing a positron and a neutrino
2. Deuterium captures another proton to form helium-3
3. Two helium-3 nuclei combine to form helium-4 and release two protons

Net result: 4 hydrogen nuclei become 1 helium nucleus, with 0.7% of the mass converted to energy via E=mc².

### The CNO Cycle

In stars more massive than about 1.3 solar masses, the CNO (carbon-nitrogen-oxygen) cycle dominates. Carbon acts as a catalyst: it is consumed and regenerated while hydrogen is converted to helium. The CNO cycle is extremely temperature-sensitive (rate proportional to T¹⁶), making massive stars far more luminous.

### The Mass-Luminosity Relation

Main-sequence luminosity scales roughly as mass to the 3.5 power:

L ∝ M^3.5

This means a star twice the Sun's mass is about 11 times more luminous — and burns through its fuel 5.5 times faster. This is why massive stars live millions of years while red dwarfs can burn for trillions.

### Lifetimes on the Main Sequence

| Spectral Class | Mass (M☉) | Main Sequence Lifetime |
|---|---|---|
| O5V | 60 | 3 million years |
| B0V | 18 | 11 million years |
| A0V | 3 | 440 million years |
| G2V (Sun) | 1 | 10 billion years |
| K5V | 0.7 | 24 billion years |
| M5V | 0.2 | >1 trillion years |