Stellar structure

Stellar structure follows from mass conservation, hydrostatic equilibrium, energy generation, and energy transport together with an equation of state and opacity law.

A stellar polytrope obeys $P=K{\rho }^{1+1/n}$ for constant $K$ and polytropic index $n$. Its dimensionless density profile satisfies the Lane-Emden equation.

Homologous stellar models have the same dimensionless radial profiles after mass, radius, density, pressure, and temperature are scaled by characteristic values.

In a radiative stellar region, photons carry luminosity down the temperature gradient. Dimensional scaling of the radiative-diffusion equation gives $L\sim R{T}_c^4/({\kappa }_c{\rho }_c)$.

The mass-luminosity relation connects a star's mass to its luminosity. Its slope depends on opacity, nuclear burning, pressure support, composition, and evolutionary state.

Balancing outward radiative acceleration against gravity givesIt is an approximate upper luminosity for a hydrostatic star of opacity $\kappa$.