Download Chapter 8 – Continuous Absorption

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
2I
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 x1025 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