Stellar structure

Stars are not uniform blobs of gas; their internal structure varies dramatically depending on their mass, age, and chemical composition. Models of stellar structure break down a star’s interior to predict its brightness, color, and how it will change over time. These models rely on understanding how energy moves from the core outward.

Energy moves through a star’s layers in different ways. The two main mechanisms are convection and radiative transfer, though thermal conduction becomes important in white dwarfs. Convection dominates where the temperature changes steeply: a pocket of hot gas becomes buoyant and rises, while a cooler pocket sinks. Radiative transfer takes over in regions where the temperature gradient is gentle and the gas is transparent enough for photons to carry energy efficiently.

A star’s internal layout depends heavily on its mass. For stars between 0.3 and 1.5 times the Sun’s mass—including the Sun itself—hydrogen fusion runs mainly via the proton-proton chain. This process produces a shallow temperature gradient, so the inner region is radiative. However, the outer layers are cool enough that hydrogen is neutral and blocks ultraviolet light, making those layers convective. These stars therefore have a radiative core and a convective envelope.

In more massive stars (above about 1.5 solar masses), the core exceeds roughly 18 million Kelvin, and fusion shifts to the CNO cycle. This cycle is extremely sensitive to temperature—energy generation scales as temperature to the 15th power, compared to the 4th power for proton-proton chains. The resulting steep temperature gradient makes the core convective. The outer layers, though having a shallower gradient, are hot enough to keep hydrogen ionized and transparent, so they are radiative. The least massive main-sequence stars lack a radiative zone entirely; convection carries energy throughout the whole star.

The simplest useful model assumes a star is spherical, steady, and in local thermodynamic equilibrium (meaning matter and photons share the same temperature, an excellent approximation because the photon mean free path is tiny compared to temperature changes). This model uses four linked differential equations describing how density, temperature, pressure, luminosity, and energy generation rate change with radius.

The first equation states hydrostatic equilibrium: the outward push from the pressure gradient exactly balances the inward pull of gravity. Mathematically, dP/dr = –G m ρ / r², where m(r) is the mass enclosed within radius r. The mass itself grows with radius according to the mass continuity equation.