Class Goals

1
Class 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

2
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
  1920s

3
Useful References

• Astrophysical Quantities
• Holweger Mueller 1974, Solar Physics, 39, 19
  Standard Model
• MARCS model grid (Bell et al., AAS, 1976, 23,
  37)
• Kurucz (1979) models ApJ Suppl., 40, 1
• Stellar Abundances Grevesse Sauval 1998,
  Space Science Reviews, 85, 161 or Anders
  Grevesse 1989, Geochem. Cosmochim. Acta, 53,
  197
• Solar gf values Thevenin 1989 (AAS, 77, 137)
  and 1990 (AAS, 82, 179)

4
What Is a Stellar Atmosphere?

• Basic Definition The transition between the
  inside and the outside of a star
• 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

5
Class Problem

• 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 g8 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.
•  

6
Basic Assumptions in Stellar Atmospheres

• 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!)

7
Solar granulation
8
Basic Physics Ideal Gas Law

• PVnRT or PNkT where Nr/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 Boltzmans constant (1.38 x 1016 erg/K)
• m mean molecular weight in AMU (1 AMU 1.66 x
  10-24 gm)

9
Class Problem

• Using the ideal gas law, estimate the number
  density of atoms in the Suns photosphere and in
  the Earths atmosphere at sea level. For the
  Sun, assume T5000K, P105 dyne cm-2. How do the
  densities compare?

10
Basic Physics Thermal Velocity Distributions

• RMS Velocity (3kT/m)1/2
• Class Problem What are the RMS velocities of
  7Li, 16O, 56Fe, and 137Ba in the solar
  photosphere (assume T5000K).
• How would you expect the width of the Li
  resonance line to compare to a Ba line?

11
Basic Physics the Boltzman Equation

• Nn (gn/u(T))e-Xn/kT
• Where u(T) is the partition function, gn is
  the statistical weight, and Xn is the excitation
  potential. For back-of-the-envelope
  calculations, this equation is written as
• Nn/N (gn/u(T)) x 10 QXn
• 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.

12
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
  10QI
• 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.

13
Class 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?