A 540 Stellar Atmospheres Organizational Details Meeting times

A 540 – Stellar Atmospheres Organizational Details • • • Meeting times Textbook Syllabus Projects Homework • Topical Presentations • Exams • Grading • Notes

Basic Outline • 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 • 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 Ph. D 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 • 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 – Ap. J Suppl. , 40, 1 • 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 • Solar gf values – Thevenin 1989 (A&AS, 77, 137) and 1990 (A&AS, 82, 179)

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 4 p. R 2 T 4 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/s 2) • 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 • • • 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=n. RT or P=Nk. T where N=r/m P= pressure (dynes cm-2) V = volume (cm 3) 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. 6 x 10 -5 e. V K-1 m = mean molecular weight in AMU (1 AMU = 1. 66 x 10 -24 gm)

Basic Physics – Thermal Velocity Distributions • RMS Velocity = (3 k. T/m)1/2 • What are the RMS velocities of 7 Li, 16 O, 56 Fe, and 137 Ba in the solar photosphere (assume T=5000 K). • How would you expect the width of the Li resonance line to compare to a Ba line?

Basic Physics – the Boltzman Equation 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: Note here also the definition of q = 5040/T = (log e)/k. T 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 N 1/ N 0 = (1/Pe) x 1. 202 x 109 (u 1/u 0) x T 5/2 x 10–q. I Pe is the electron pressure and I is the ionization potential in ev. Again, u 0 and u 1 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.

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=5000 K, 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 4000 K? In the Sun? In an A star at 8000 K?