Astrophysics (index) | about |

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
( dm —— = 4πr²ρ dr
(The dP Gmρ —— = - ——— dr r² (pressure counteracts Gravity at distance r from the center) dL —— = 4πr²ε dr
(The 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.
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).
Among approximations used to make the behavior of a star's Atmosphere
more tractable are the
To model a star,
these are generally solved using
Codes using this approach are called stars,models)http://personal.psu.edu/rbc3/A534/lec2.pdf http://www.jb.man.ac.uk/~smao/starHtml/stellarEquation.pdf Referenced by:
Binary Star Binding Energy Boltzmann Equation Eddington Approximation Giant Planet Mass Shell Mixing Length Theory Quantum Tunneling Equation of Radiative Transfer (RTE) RT Instability Stellar Temperature Determination Subgrid-Scale Physics Sun |