Stellar Equilibrium: How Radiation Pressure Balances Gravity in Stars

Stars maintain hydrostatic equilibrium: the outward force of radiation pressure (and gas pressure) balances the inward pull of gravity, preventing collapse.

The Balance

• Gravity: Compresses stellar material inward; depends on mass.
• Pressure: Thermal (gas) pressure + radiation pressure (photon momentum). In massive stars (>10 M☉), radiation pressure dominates.
• Energy source: Nuclear fusion (H → He in core) releases photons → radiation pressure.

Hydrostatic Equilibrium Equation

dP/dr = -G m(r) ρ(r) / r²

Pressure gradient supports weight of overlying layers.

Stability

• Self-regulating: If core contracts → T increases → fusion rate ↑ → pressure ↑ → expansion → cooling → fusion slows.
• This negative feedback loop maintains stability for millions/billions of years (main sequence).

When Equilibrium Fails

• Fuel exhaustion → core contracts → new burning stages (He, C, O, Si) → eventual iron core.
• Iron cannot fuse exothermically → core collapse → supernova (massive stars) or white dwarf formation (low-mass).

Eddington Limit

Maximum luminosity where radiation pressure equals gravity. Above it, radiation drives mass loss (stellar winds). Relevant for massive stars, accretion disks.

Equilibrium is not static—it's a dynamic, self-correcting balance that defines a star's life.