Free-Free Absorption from H I

1. 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:

2. 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?

3. 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)

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

5. 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

6. He absorption • Bound-free He- absorption is negligible (excitation potential if 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)

7. 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

8. 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

9. 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

10. 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

11. Opacity vs. Spectral Type Main Sequence Supergiants

12. 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

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

14. 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