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Chapter 8 – Continuous Absorption

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.

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Chapter 8 – Continuous Absorption

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

  2. 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

  3. 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.

  4. 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)

  5. 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

  6. 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)

  7. 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

  8. 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

  9. 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

  10. 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 from your homework.

  11. Free-Free Absorption from H I • Much less than bf absorption • Kramers (1923) + Gaunt (1930) again • Absorption coefficient depends on the speed of the electron (slower electrons are more likely to absorb a photon because their encounters with H atoms take longer) • Adopt a Maxwell-Boltzman distribution for the speed of electrons • Again multiply by the number of neutral hydrogen atoms:

  12. Opacity from Neutral Hydrogen • Neutral hydrogen (bf and ff) is the dominant source of opacity in stars of B, A, and F spectral type • Discussion Questions: • Why is neutral hydrogen not a dominant source of opacity in O stars: • Why not in G, K, and M stars?

  13. Opacity from the H- Ion • Only one known bound state for bound-free absorption • 0.754 eV binding energy • So l < hc/hn = 16,500A • Requires a source of free electrons (ionized metals) • Major source of opacity in the Sun’s photosphere • Not a source of opacity at higher temperatures because H- becomes too ionized (average e- energy too high)

  14. More H- Bound-Free Opacity • Per atom absorption coefficient for H- can be parameterized as a polynomial in l: • Peaks at 8500A

  15. H- Free-Free Absorption Coefficient • The free-free H- absorption coefficient depends on the speed of the electron • Possible because of the imperfect shielding of the hydrogen nucleus by one electron • Proportional to l3 • Small at optical wavelengths • Comparable to H- bf at 1.6 microns • Increases to the infrared

  16. He absorption • Bound-free He- absorption is negligible (excitation potential of 19 eV!) • Free-free He- can be important in cool stars in the IR • BF and FF absorption by He is important in the hottest stars (O and early B)

  17. Electron Scattering • Thomson scattering: • Independent of wavelength • In hot stars (O and early B) where hydrogen dominates, then Pe~0.5Pg, and k(e) is independent of pressure • In cool stars, e- scattering is small compared to other absorbers for main sequence star but is more important for higher luminosity stars

  18. Rayleigh Scattering • Generally can be neglected • But – since it depends on l-4 it is important as a UV opacity source in cool stars with molecules in their atmospheres. • H2 can be an important scattering agent

  19. Other Sources • Metals: C, Si, Al, Mg, Fe produce bound-free opacity in the UV • Line Opacity: Combined effect of millions of weak lines • Detailed tabulation of lines • Opacity distribution functions • Statistical sampling of the absorption • Molecules: CN-, C2-, H20- , CH3, TiO are important in late and/or very late stars

  20. Molecular Hydrogen Opacity • H2 is more common than H in stars cooler than mid-M spectral type (think brown dwarfs!!) • H2 does not absorb in the visible spectrum • H2+ does, but is less than 10% of H- in the optical • H2+ is a significant absorber in the UV • H2- ff absorption in the IR

  21. Opacity vs. Spectral Type Main Sequence Supergiants

  22. Dominant Opacity vs. Spectra Type Low Electron scattering (H and He are too highly ionized) Low pressure – less H- Electron Pressure He+ He Neutral H H- H- High (high pressure forces more H-) O B A F G K M

  23. Sources of Opacity for Teff=4500 Log g = 1.5

  24. Class Exercise – Electron Scattering • Estimate the absorption coefficient for electron scattering for the models provided at a level where T=Teff • Recall that • and • with m in AMU and k=1.38x10-16 • How does ke compare to kRosseland

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