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