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Stellar structure codes (meaning computer programs calculating the model's variables) either interpolate in a density-temperature grid to obtain the opacity needed, or use a fitting function based on the tabulated values. A similar situation occurs for accurate calculations of the pressure equation of state.
This stellar model, technically the spherically symmetric quasi-static model of a star, has stellar structure described by several differential equations derived from basic physical principles. The model is constrained by boundary conditions , namely the luminosity , radius, age and composition of the Sun, which are well determined.
Theoretical calculations of stellar structure and the evolution of stars produce plots that match those from observations. This type of diagram could be called temperature-luminosity diagram , but this term is hardly ever used; when the distinction is made, this form is called the theoretical Hertzsprung–Russell diagram instead.
A similar structure of singularities appears in other non-linear equations that result from the reduction of the Laplace operator in spherical symmetry, e.g., Isothermal Sphere equation. [7] Analytic solutions can be extended along the real line by analytic continuation procedure resulting in the full profile of the star or molecular cloud cores.
The horizontal branch (HB) is a stage of stellar evolution that immediately follows the red-giant branch in stars whose masses are similar to the Sun's. Horizontal-branch stars are powered by helium fusion in the core (via the triple-alpha process) and by hydrogen fusion (via the CNO cycle) in a shell surrounding the core.
In stellar evolution, an isochrone is a curve on the Hertzsprung-Russell diagram, representing a population of stars of the same age but with different mass. [1] The Hertzsprung-Russell diagram plots a star's luminosity against its temperature, or equivalently, its color. Stars change their positions on the HR diagram throughout their life.
The stellar structure is usually assumed to be spherically symmetric, so the horizontal (i.e. non-radial) component of the oscillations is described by spherical harmonics, indexed by an angular degree and azimuthal order . In non-rotating stars, modes with the same angular degree must all have the same frequency because there is no preferred axis.
IMF and PDMF can be linked through the "stellar creation function". [2] Stellar creation function is defined as the number of stars per unit volume of space in a mass range and a time interval. In the case that all the main sequence stars have greater lifetimes than the galaxy, IMF and PDMF are equivalent.