Absorption Cross Sections (Hubeny & Mihalas Chapter 5) Bound-bound transitions (Einstein relations) Bound-free transitions (Einstein-Milne relations)

Bound-Bound Transitions Balance transitions between two levels Upwards absorption Downwards by spontaneous or stimulated emission j hνij i

Energy Absorption Rate: Bij = Einstein coefficient for absorption

Return Rates: Aji=Einstein coeff. spontaneous em. Bji=Einstein coeff Return Rates: Aji=Einstein coeff. spontaneous em. Bji=Einstein coeff. stimulated em. (isotropic) (same direction as Iν)

*Thermodynamic Equilibrium: Iν=Bν

b-b Transfer Equation

b-b Transfer Equation

Transition Rates Calculate or measure cross section

Transition Rates: Hydrogen H transitions n'→n

Einstein-Milne Relations for Bound-Free Transitions

Einstein-Milne Relations: energy and velocity Replace v dv increment in recombination term with this.

Einstein-Milne Relations: #photoionizations=#recombinations

Denominator Term: Maxwell dist. ne(v); Saha eq. n0/n1 …….=1. ……

T.E.: αν=pνhν , ne=Maxwellian, n0*/n1*=Saha, G(v)/pν above … b-f Transfer Equation T.E.: αν=pνhν , ne=Maxwellian, n0*/n1*=Saha, G(v)/pν above …