The interior of stars (part VI)
7 Abril 2020, 13:00 • Israel Matute
The equations of stellar structure are coupled differential equations that need to be solved numerically. Useful insight can be gained, however, using analytical methods involving simple assumptions. This lecture started the discussion on the first of the assumptions, the -polytropic model-:
- This model supposes that at some distance r from the stellar centre, the pressure and density are related by P(r) = K ρ γ where K is a constant and γ is related to some polytropic index n through γ = (n + 1)/n.
Substituting in the equations of hydrostatic equilibrium and mass conservation then leads to the "Lane-Emden" equation which can be solved for a specific polytropic index n.
- We detailed how the solution of the Lane-Emden equation can approximate very well different types of stellar interiors: from solar-type stars to degenerated cores.