A star like the Sun is built inside out compared with a heavier one
In the Sun, energy crawls outward from the core as radiation and then boils to the surface in convection currents. In stars more than one and a half times heavier, the arrangement flips: a churning core sits beneath a calm, radiating envelope. The difference comes down to how fiercely each star burns.
Stars move heat outward mainly in two ways. Convection wins where temperature falls steeply with height, so a slightly lifted parcel of gas stays warmer than its surroundings and keeps rising. Radiation wins where the temperature gradient is gentle and the gas is transparent enough to let light through. In white dwarfs, plain conduction matters as well.
For stars between about 0.3 and 1.5 solar masses, including the Sun, hydrogen fuses through proton-proton chains, whose output rises with roughly the fourth power of temperature. That gentle dependence keeps the core gradient shallow, so the inner star radiates. Near the surface, cooler neutral hydrogen blocks ultraviolet light, so convection takes over. Heavier stars have cores above about 18 million kelvin and fuse through the CNO cycle, whose rate climbs with the fifteenth power of temperature. That extreme sensitivity steepens the core gradient and makes it convect, while the hot, ionised outer layers let radiation escape. The smallest stars convect all the way through.
The standard model treats a star as a static, perfectly round ball and describes it with four linked equations for how mass, pressure, temperature and brightness change with distance from the centre. One expresses hydrostatic balance, with outward pressure exactly matching gravity's pull. Solving them needs more ingredients: equations of state for the gas, including radiation pressure and degenerate electrons, opacity tables rather than any single formula, and nuclear reaction rates, plus boundary conditions such as zero pressure at the surface and the star's total mass.
Convection is the weak link. It has no rigorous mathematical description and is usually handled with mixing length theory, which imagines gas blobs travelling a set distance before blending in and relies on two adjustable parameters. Turbulence remains the toughest problem, and some teams now attempt simplified three-dimensional models. Rapidly pulsating or collapsing stars need extra terms the simple model lacks.
Source: Stellar structure
