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Radiative Equilibrium in Astrophysics

Explore the essence of radiative equilibrium in stellar astrophysics, covering modes of energy transport, Schwarzschild criterion, flux constancy, Blackbody consideration, and HR Diagram analysis. This essential concept sheds light on energy balance in celestial bodies.

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Radiative Equilibrium in Astrophysics

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  1. Radiative Equilibrium

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

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

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

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

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

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

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