star is zero; , there is no mass inside the center of the star, as required if the mass density remains finite; , the total mass of the star is the star's mass; and , the temperature at the surface is the effective temperature of the star. Although nowadays stellar evolution models describe the main features of color–magnitude diagrams, important improvements have to be made in order to remove uncertainties which are linked to the limited knowledge of transport phenomena. The most difficult challenge remains the numerical treatment of turbulence. Some research teams are developing simplified modelling of turbulence in 3D calculations. Rapid evolution The above simplified model is not adequate without modification in situations when the composition changes are sufficiently rapid. The equation of hydrostatic equilibrium may need to be modified by adding a radial acceleration term if the radius of the star is changing very quickly, for example if the star is radially pulsating. Also, if the nuclear burning is not stable, or the star's core is rapidly collapsing, an entropy term must be added to the energy equation. See also Scale height Standard solar model References Sources External links opacity code retrieved November 2009 The Yellow CESAM code, stellar evolution and structure Fortran source code EZ to Evolve ZAMS Stars a FORTRAN 90 software derived from Eggleton's Stellar Evolution Code, a web-based interface can be found here . Geneva Grids of Stellar Evolution Models (some of them including rotational induced mixing) The BaSTI database of stellar evolution tracks Structure