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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: log e I 3 ( H ff ) 0 g f 2I 10 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? Opacity from the H- Ion • Only one known bound state for bound-free absorption • 0.754 eV binding energy • So < 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) More H- Bound-Free Opacity • Per atom absorption coefficient for H- can be parameterized as a polynomial in : bf a0 a1 a2 ... 2 N (H ) 5040 log log Pe I 2.5 log T 0.1248 N (H ) T 5 2 ( H bf ) 4.158 x10 10 bf Pe 100.754 • Peaks at 8500A 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 3 • Small at optical wavelengths • Comparable to H- bf at 1.6 microns • Increases to the infrared 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) Electron Scattering • Thomson scattering: 8 e2 2 e ( 2 ) 6.654 x1025 cm2 3 mc (e) e Ne • Independent of wavelength • In hot stars (O and early B) where hydrogen dominates, then Pe~0.5Pg, and (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 Rayleigh Scattering • Generally can be neglected • But – since it depends on 4 it is important as a UV opacity source in cool stars with molecules in their atmospheres. • H2 can be an important scattering agent 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 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 40 30 Main Sequence 20 10 Temperature 25000 8000 6500 0 12000 Supergiants 5500 Kappa Rosseland Opacity vs. Spectral Type Dominant Opacity vs. Spectra Type Low Electron scattering (H and He are too highly ionized) He+ He Low pressure – less H- Neutral H H- H- High (high pressure forces more H-) O B A F G K M 100% 80% H(BF) 60% H2+ 40% Mg+Al+Si 20% H- Optical Depth 10 1 0.1 0.01 0% 0 Fraction of Opacity Sources of Opacity for Teff=4500 Log g = 1.5 Class Exercise – Electron Scattering • Estimate the absorption coefficient for electron scattering for the models provided at a level where T=Teff 25 N e • Recall that e 6.6 x10 • and P kT m • with m in AMU and k=1.38x10-16 • How does e compare to Rosseland