Sumários

The interior of stars (part VII)

16 Abril 2020, 14:00 • Israel Matute

During this lecture, we continued discussing how some approximations can be used for stellar models so that costly numerical solutions do not have to be computed for every single model. We saw

  • The advantage of parameterizing the eq. of stellar structure as a function of mass and not as a function of radius: the Vogt-Russell theorem;

  • We discussed the advantage of normalizing the equations as a function of mass and how this leads to the concept of homologous stars:

  • The homologous relations for stars under the approximation of ideal gas are introduced and discussed. The form that many of these relations (especially the one link L and effective temperature)  allow a better understanding of the HR diagram;

  • Approximations to the computation of opacities: Kramers opacity, etc.

  • Stellar-mass limits in the Main-Sequence: the Eddington luminosity

  • Example of an extreme stellar system: Eta-Carinae

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.

The interior of the stars (part V)

6 Abril 2020, 13:00 • Israel Matute

Solving the equations for Stellar Structure:

  • The importance of boundary conditions to solve 4 diff Eqs + 3 constitute relations for stellar structure

  • Voight-Russell Theorem

  • Relations between Stellar Quantities

  • Integration of the structural equations

Exercises Series #3 - Stellar atmospheres (part II)

2 Abril 2020, 15:00 • Israel Matute

Lab lecture dedicated to the discussion and the solving of the second part of exercises posted in the third series of exercises and dedicated to the concepts introduced for stellar atmospheres.

The interior of stars (part IV)

2 Abril 2020, 14:00 • Israel Matute

Energy transport:

  • Sources of Stellar Energy

    • H/He burning, Fusion processes up to 56Fe

  • Energy transfer

    • Equation of radiative energy transfer

    • Radiative vs convective. Conditions for convection to dominate the energy transport. 

    • Simplification for the treatment of convection: theory of mixing length