Transcript Basic Physics

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
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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Stellar Abundances – 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
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 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 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!)
Solar granulation
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)
m = mean molecular weight in AMU (1 AMU = 1.66 x
10-24 gm)
Class 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
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 T=5000K).
• How would you expect the width of the Li
resonance line to compare to a Ba line?
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.
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.
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?