Chapter 8 – Continuous Absorption Physical Processes Definitions Sources of Opacity Hydrogen bf and ff H- He Scattering

Physical Processes Bound-Bound Transitions – absorption or emission of radiation from electrons moving between bound energy levels. Bound-Free Transitions – the energy of the higher level electron state lies in the continuum or is unbound. Free-Free Transitions – change the motion of an electron from one free state to another. Scattering – deflection of a photon from its original path by a particle, without changing wavelength Rayleigh scattering if the photon’s wavelength is greater than the particle’s resonant wavelength. (Varies as l-4) Thomson scattering if the photon’s wavelength is much less than the particle’s resonant wavelength. (Independent of wavelength) Electron scattering is Thomson scattering off an electron Photodissociation may occur for molecules

Electron Scattering vs. Free-Free Transition Electron scattering – the path of the photon is altered, but not the energy Free-Free transition – the electron emits or absorbs a photon. A free-free transition can only occur in the presence of an associated nucleus. An electron in free space cannot gain the energy of a photon.

Why Can’t an Electron Absorb a Photon? Consider an electron at rest that is encountered by a photon, and let it absorb the photon…. Conservation of momentum says Conservation of energy says Combining these equations gives So v=0 (the photon isn’t absorbed) or v=c (not allowed)

What can various particles do? Free electrons – Thomson scattering Atoms and Ions – Bound-bound transitions Bound-free transitions Free-free transitions Molecules – BB, BF, FF transitions Photodissociation Most continuous opacity is due to hydrogen in one form or another

Monochromatic Absorption Coefficient Recall dtn = knrdx. We need to calculate kn, the absorption coefficient per gram of material First calculate the atomic absorption coefficient an (per absorbing atom or ion) Multiply by number of absorbing atoms or ions per gram of stellar material (this depends on temperature and pressure)

Bound-Bound Transitions These produce spectral lines At high temperatures (as in a stellar interior) these may often be neglected. But even at T~106K, the line absorption coefficient can exceed the continuous absorption coefficient at some densities

Bound Free Transitions An expression for the bound-free coefficient was derived by Kramers (1923) using classical physics. A quantum mechanical correction was introduced by Gaunt (1930), known as the Gaunt factor (gbf – not the statistical weight!) For the nth bound level below the continuum and l < ln where a0 = 1.044 x 10–26 for l in Angstroms

Converting to the MASS Absorption Coefficient Multiply by the number of neutral hydrogen atoms per gram in each excitation state n Back to Boltzman and Saha! gn=2n2 is the statistical weight u0(T)=2 is the partition function

H I H II

Class Investigation Compare kbf at l=5000A and level T=Teff for the two models provided Recall that and k=1.38x10-16, a0 =1x10-26 And Use the hydrogen ionization chart provided