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:

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 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)

More H- Bound-Free Opacity Per atom absorption coefficient for H- can be parameterized as a polynomial in l: 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 l3 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: 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

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

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

Opacity vs. Spectral Type Main Sequence Supergiants

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

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 Recall that and with m in AMU and k=1.38x10-16 How does ke compare to kRosseland