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A540 – Stellar Atmospheres
Organizational Details
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Meeting times
Textbook
Syllabus
Projects
Homework
• Topical
Presentations
• Exams
• Grading
• Notes
Basic Outline
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Textbook Topics
– Chapter 1 – Review of relevant
basic physics
– Chapter 5 – Radiation
– Chapter 6 – Black bodies
– Chapter 7 – Energy transport
– Chapter 8 – Continuous Opacity
– Chapter 9 – Model Photospheres
– Chapter 10 – Stellar Continua
– Chapter 11 – Line Absorption
– Chapter 13 – Spectral Lines
– Chapter 14 – Chemical Analysis
– Chapter 15 – Radii and
Temperatures
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Additional Topics
– Stars in the astrophysical
zoo
– Stellar rotation
– Stellar activity
– Winds and mass loss
– White dwarf spectra and
atmospheres
– M, L and T dwarfs
– Non LTE
– Metal poor stars
– Pulsating stars
– Asteroseismology
– Supergiants
– Wolf-Rayet stars
– AGB stars
– Post-AGB stars
– Peculiar A stars
– Pre main sequence stars
– Other ideas…
Goals
• Familiarity with basic terms and definitions
• Physical insight for conditions, parameters,
phenomena in stellar atmospheres
• Appreciation of historical and current problems
and future directions in stellar atmospheres
History of Stellar Atmospheres
• Cecelia Payne Gaposchkin wrote the first PhD
thesis in astronomy at Harvard
• She performed the first analysis of the
composition of the Sun (she was mostly right,
except for hydrogen).
• What method did she use?
• Note limited availability of atomic data in the
1920’s
Useful References
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Astrophysical Quantities
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Holweger & Mueller 1974, Solar Physics, 39, 19 – Standard Model
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MARCS model grid (Bell et al., A&AS, 1976, 23, 37)
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Kurucz (1979) models – ApJ Suppl., 40, 1
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Solar composition – "THE SOLAR CHEMICAL COMPOSITION " by
Asplund, Grevesse & Sauval in "Cosmic abundances as records of
stellar evolution and nucleosynthesis", eds. F. N. Bash & T. G.
Barnes, ASP conf. series, in press: see also Grevesse & Sauval 1998,
Space Science Reviews, 85, 161 or Anders & Grevesse 1989,
Geochem. & Cosmochim. Acta, 53, 197
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Solar gf values – Thevenin 1989 (A&AS, 77, 137) and 1990 (A&AS,
82, 179)
What Is a Stellar Atmosphere?
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Basic Definition: The transition between the inside and the outside of
a star
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Characterized by two parameters
– Effective temperature – NOT a real temperature, but rather the
“temperature” needed in 4pR2T4 to match the observed flux at a
given radius
– Surface gravity – log g (note that g is not a dimensionless number!)
• Log g for the Earth is 3.0 (103 cm/s2)
• Log g for the Sun is 4.4
• Log g for a white dwarf is 8
• Log g for a supergiant is ~0
Basic Assumptions in
Stellar Atmospheres
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Local Thermodynamic Equilibrium
– Ionization and excitation correctly described
by the Saha and Boltzman equations, and
photon distribution is black body
Hydrostatic Equilibrium
– No dynamically significant mass loss
– The photosphere is not undergoing large
scale accelerations comparable to surface
gravity
– No pulsations or large scale flows
Plane Parallel Atmosphere
– Only one spatial coordinate (depth)
– Departure from plane parallel much larger
than photon mean free path
– Fine structure is negligible (but see the Sun!)
Basic Physics – Ideal Gas Law
PV=nRT or P=NkT where N=r/m
P= pressure (dynes cm-2)
V = volume (cm3)
N = number of particles per unit volume
r = density of gm cm-3
n = number of moles of gas
R = Rydberg constant (8.314 x 107 erg/mole/K)
T = temperature in Kelvin
k = Boltzman’s constant
1.38 x 10–16 erg K-1
8.6x10-5 eV K-1
m = mean molecular weight in AMU (1 AMU = 1.66 x 10-24 gm)
Basic Physics – Thermal
Velocity Distributions
• RMS Velocity = (3kT/m)1/2
• What are the RMS velocities of 7Li, 16O, 56Fe, and
137Ba in the solar photosphere (assume T=5000K).
• How would you expect the width of the Li
resonance line to compare to a Ba line?
Basic Physics – the Boltzman Equation
N n g n   / kT

e
Nm gm
Where u(T) is the partition function, gn is the statistical
weight, and Xn is the excitation potential. For back-ofthe-envelope calculations, this equation is written as:
Nn
gn
q n

10
N u (T )
Note here also the definition of q = 5040/T = (log e)/kT
with k in units of electron volts per degree, since X is in
electron volts. Partition functions can be found in an appendix
in the text.
Basic Physics – The Saha Equation
The Saha equation describes the ionization of atoms (see the text
for the full equation). For hand calculation purposes, a shortened
form of the equation can be written as follows
N1/ N0 = (1/Pe) x 1.202 x 109 (u1/u0) x T5/2 x 10–qI
Pe is the electron pressure and I is the ionization potential in ev.
Again, u0 and u1 are the partition functions for the ground and first
excited states. Note that the amount of ionization depends inversely
on the electron pressure – the more loose electrons there are, the
less ionization there will be.
N1
 5040
u1
log
Pe 
I  2.5 log T  log  0.1762
N0
T
u0
Problems YOU should
be able to solve…
• Using the ideal gas law, estimate the number
density of atoms in the Sun’s photosphere and in
the Earth’s atmosphere at sea level. For the Sun,
assume T=5000K, P=105 dyne cm-2. How do the
densities compare?
More Problems
• During the course of its evolution, the Sun will
pass from the main sequence to become a red
giant, and then a white dwarf.
• Estimate the radius of the Sun in both phases,
assuming log g = 1.0 when the Sun is a red giant,
and log g=8 when the Sun is a white dwarf.
Assume no mass loss.
• Give the answer in both units of the current solar
radius and in cgs or MKS units.
More Problems
• At (approximately) what Teff is Fe
50% ionized in a main sequence star?
In a supergiant?
• What is the dominant ionization state
of Li in a K giant at 4000K? In the
Sun? In an A star at 8000K?