There is a general model of Large mass stars have CNO Cycle fusion in the core, with a region surrounding it conveying energy via radiative transfer, the inner part of which also has some Proton-Proton Chain fusion, which can be triggered by somewhat lower temperatures. Small mass stars such as Red Dwarves have only Proton-Proton Chain fusion in the core, and transfer energy through convection. Between are stars like the Sun, which have an inner portion much like a large star, with a convection layer surrounding it. The most basic mathematical model includes four differential equations relating changes in mass, Temperature, Luminosity (L), and pressure to the distance from the center of the star. They presume Local Thermodynamic Equilibrium (LTE) and Hydrostatic Equilibrium. dm —— = 4πr²ρ dr (density is assumed constant at distance r from the center) dP Gmρ —— = - ——— dr r² (pressure counteracts Gravity at distance r from the center) dL —— = 4πr²ε dr (energy is conserved, any addition is from fusion at that level) dT 3κρL —— = ———————— dr 64πr²σT³ (Opacity directly affects the rate at which temperature changes with radius. This is the equation for radiative transfer, i.e., energy transfer via EMR; Other equations are needed if heat conduction is significant or if there is convection.) - r - distance from the center of the star, i.e., radius of a spherical portion of the star centered at the star's center.
- m - mass of the star within distance r from the center.
`ρ`- density, a function of r, i.e., the same at all points equidistant from the center.- L - luminosity, the rate at which energy is flowing from inside r to outside r.
- T - temperature at r, also modeled as being the same at all points equidistant from the center.
- P - pressure at r, also modeled as being the same at all points equidistant from the center.
- ε - the amount of energy generated by fusion per unit of volume at r.
`κ`- Opacity at r.- G - gravitational constant.
- σ - Stefan-Boltzmann Constant (σ).
Opacity, density, and energy generation are functions of temperature and pressure and it is key that simple-but-effective approximate models have been developed (Equations of State (EoS)).
To model a star with these equations, a set of consistent
stars,models)Referenced by:
Binary Star Binding Energy Boltzmann Equation Quantum Tunneling RT Instability Stellar Temperature Determination |