Class GoalsClass 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 AtmospheresHistory 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 ReferencesUseful References

• Astrophysical Quantities

• Holweger & Mueller 1974, Solar Physics, 39, 19 – Standard Model

• MARCS model grid (Bell et al., A&AS, 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 (A&AS, 77, 137) and 1990 (A&AS, 82, 179)

What Is a Stellar Atmosphere?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 4R2T4 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

Class ProblemClass 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 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.

 

Basic Assumptions in Stellar AtmospheresBasic 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!)

Solar granulationSolar granulation

Basic Physics – Ideal Gas LawBasic Physics – Ideal Gas Law

PV=nRT or P=NkT where N=/P= pressure (dynes cm-2)V = volume (cm3)N = number of particles per unit volume = density of gm cm-3

n = number of moles of gasR = Rydberg constant (8.314 x 107 erg/mole/K)T = temperature in Kelvink = Boltzman’s constant (1.38 x 10–16 erg/K) = mean molecular weight in AMU (1 AMU =

1.66 x 10-24 gm)

Class ProblemClass Problem

• 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?

Basic Physics – Thermal Basic Physics – Thermal Velocity DistributionsVelocity 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 T=5000K).

• How would you expect the width of the Li resonance line to compare to a Ba line?

Basic Physics – the Boltzman Basic Physics – the Boltzman EquationEquation

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 –Xn

Note here also the definition of = 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 Basic Physics – The Saha EquationEquation

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–I

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.

Class ProblemsClass 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?