1. Radiative Equilibrium

2. Radaitive Equilibrium2 The Condition of Radiative Equilibrium Modes of Energy Transport Modes of Energy Transport Radiative Radiative Convective Convective Conduction - Not important except in WD’s etc Conduction - Not important except in WD’s etc When all energy is transported by radiation the condition of radiative equilibrium applies. When all energy is transported by radiation the condition of radiative equilibrium applies. Schwarzschild: τ  1 : Radiative τ > 1 : Convective Schwarzschild: τ  1 : Radiative τ > 1 : Convective Convection is driven by Hydrogen ionization. Convection is driven by Hydrogen ionization.

3. Radaitive Equilibrium3 Radiative Equilibrium The Energy Removed from the Beam: The Energy Removed from the Beam: Κ ν - total absorption coefficient Κ ν - total absorption coefficient Total Energy Replaced In Beam: Total Energy Replaced In Beam: Radiative Equilibrium Demands: Radiative Equilibrium Demands:

4. Radaitive Equilibrium4 Flux Constancy Take the Equation of Transfer and Integrate over all Frequencies and Solid Angles Take the Equation of Transfer and Integrate over all Frequencies and Solid Angles But Under Radiative Equilibrium the Right Side = 0! But Under Radiative Equilibrium the Right Side = 0! Therefore the Flux is constant with depth! Therefore the Flux is constant with depth! Total Flux uniquely specified for each atmosphere Total Flux uniquely specified for each atmosphere

5. Radaitive Equilibrium5 Consider A Blackbody A Small Opening in A TE Cavity A Small Opening in A TE Cavity Total Flux is the Integral over Frequency: Total Flux is the Integral over Frequency: Define Teff: Define Teff:

6. Radaitive Equilibrium6 One Last Consideration Look at (*) Again Scattering has cancelled out as it puts as much energy into the beam as it takes out!

7. Radaitive Equilibrium7 HR Diagram Chapter 13 – “Stellar Rotation” Böhm-Vitense – Introduction to Stellar Astrophysics Vol 1 Landolt-Börnstein