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 3 – Spectrographs
– Chapter 4 - Detectors
– Chapter 5 – Radiation
– Chapter 6 – Black bodies
– Chapter 7 – Energy transport
– Chapter 8 – Continuous Absorption
– Chapter 9 – Model Photospheres
– Chapter 10 – Stellar Continua
– Chapter 11 – Line Absorption
– Chapter 12,13 – Spectral Lines
– Chapter 14 – Radii and Temperatures
– Chapter 15 - Pressure
– Chapter 16 - Chemical Analysis
– Chapter 17 – Velocity Fields
– Chapter 18 - Rotation
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Integrating Stars
– Stars in the astrophysical
zoo
– 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
– Chemically Peculiar Stars
– Pre-main sequence stars
– Binary star evolution
– 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 4pR2sT4 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 (2.7 x 104 cm/s2)
• Log g for a white dwarf is 8
• Log g for a supergiant is ~0
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Mostly CGS units…
Make it real…
• 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 units of the
current solar radius) 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.
• What assumptions are useful to simplify the
problem?
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
Densities, pressures in
stellar atmospheres are
low, so the ideal gas law
generally applies.
P= pressure (dynes cm-2)
V = volume (cm3)
N = number of particles per unit volume
r = density (gm cm-3)
n = number of moles of gas (Avogadro’s # = 6.02x1023)
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)
Don’t forget the electron pressure: Pe = NekT
Make it real…
• 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 P=105 dyne cm-2.
• For the Earth, assume P=106 dyne cm-2.
• How do the densities compare?
Thermal Velocity Distributions
• RMS velocity = (3kT/m)1/2
• Most probable velocity = (2kT/m)1/2
• Average velocity = (8kT/pm)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?
Excitation – the Boltzman Equation
N n g n  Dc / kT

e
Nm gm
g is the statistical weight and Dc is the difference in
excitation potential. For calculating the population of a
level the equation is written as:
Nn
gn
qc n

10
N u (T )
u(T) is the partition function (see def in text). Partition
functions can be found in an appendix in the text.
Note here also the definition of q = 5040/T = (log e)/kT
with k in units of electron volts per degree (k= 8.6x10-5 eV K-1)
since c is normally given in electron volts.
Ionization – The Saha Equation
The Saha equation describes the ionization of atoms (see the text
for the full equation).
(2pme ) 2 / 3 (kT )5 / 2 2u1 (T )  I / kT
N1
Pe 
e
3
N0
h
u0 (T )
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. For hand calculation purposes, a shortened form of
the equation can be written as follows
N1
 5040
u1
log
Pe 
I  2.5 log T  log  0.1762
N0
T
u0
Make it real…
• 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?
The Stellar Zoo
Across the HR diagram:
What causes an ordinary
star to become weird?
•basic stellar evolution
•mass loss & winds
•diffusion & radiative levitation
•pulsation (radial and non-radial)
•rotation
•mixing
•magnetic fields
•binary evolution & mass transfer
•coalescence
The Upper Upper Main Sequence
• 100 (or so) solar masses, T~20,000 – 50,000 K
• Luminosities of 106 LSun
• Generally cluster in groups (Trapezium, Galactic Center, Eta
Carinae, LMC’s R136 cluster)
• Always variable – unstable.
(Some of) The Brightest Stars in the Galaxy
Star
mV
MV
Mbol
Sp. T.
Dist.
Pistol Star
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-11.8
HD 93129A
7.0
-7.0
-12
O3If
Eta Carina
6.2
-10
-11.9
B0 0
2.5 kpc
Cyg OB2#12
11.5
-10
-10.9
B5 Ia+e
1.7 kpc
Zeta-1 Sco
4.7
-8.7
-10.8
B1.5 Ia+
1.9 kpc
7 kpc
3.4 kpc
Wolf-Rayet Stars
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Luminous, hot supergiants
Spectra with emission lines
Little or no hydrogen
105-106 Lsun
Maybe 1000 in the Milky Way
Losing mass at high rates, 10-4 to 10-5 Msun per year
T from 50,000 to 100,000 K
•WN stars (nitrogen rich)
•Some hydrogen (1/3 to 1/10 He)
•No carbon or oxygen
WC stars (carbon rich)
NO hydrogen
C/He = 100 x solar or more
Also high oxygen
•Outer hydrogen envelopes stripped by mass loss
•WN stars show results of the CNO cycle
•WC stars show results of helium burning
•Do WN stars turn into WC stars?
More Massive Stars
• Luminous Blue Variables (LBVs)
– Large variations in brightness (9-10 magnitudes)
– Mass loss rates ~10-3 Msun per year, transient rates of 10-1
Msun per year
– Episodes of extreme mass loss with century-length periods of
“quiescence”
– Stars’ brightness relatively constant but circumstellar
material absorbs and blocks starlight
– UV absorbed and reradiated in the optical may make the star
look brighter
– Or dimmer if light reradiated in the IR
– Hubble-Sandage variables are also LBVs, more frequent
events
– Possibly double stars?
– Radiation pressure driven mass loss?
– Near Eddington Limit?
Chemically Peculiar Stars of
the Upper Main Sequence
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Ap stars (magnetic, slow
rotators, not binaries,
spots)
– SrCrEu stars
– Silicon Stars
– Magnetic fields
– Oblique rotators
Am-Fm stars (metalliclined, binaries, slow
rotators)
– Ca, Sc deficient
– Fe group, heavies
enhanced
– diffusion?
HgMn stars
The l Boo stars
Binaries?
Solar Type Stars (F, G, K)
• Pulsators
– The delta Scuti stars, etc.
– SX Phe stars
• Binaries
– FK Comae Stars
– RS CVn stars
– W UMa stars
– Blue Stragglers
Boesgaard & Tripicco 1986: Fig 2
The famous lithium dip!
The Lower Main Sequence – UV Ceti Stars
• M dwarf flare stars
• About half of M dwarfs are flare stars (and a few K dwarfs, too)
• A flare star brightens by a few tenths up to a magnitude in V
(more in the UV) in a few seconds, returning to its normal
luminosity within a few hours
• Flare temperatures may be a million degrees or more
• Some are spotted (BY Dra variables)
• Emission line spectra, chromospheres and coronae; x-ray sources
• Younger=more active
• Activity related to magnetic fields (dynamos)
• But, even stars later than M3 (fully convective) are active –
where does the magnetic field come from in a fully convective
star?
• These fully convective stars have higher rotation rates (no
magnetic braking?)
On to the Giant Branch…
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Convection
1st dredge-up
LF Bump
Proton-capture
reactions
• CNO, Carbon Isotopes
• Lithium
Gilliland et al 1998 (47 Tuc)
Real Red Giants
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Miras (long period variables)
– Periods of a few x 100 to 1000 days
– Amplitudes of several magnitudes in V (less in K near flux
maximum)
– Periods variable
– “diameter” depends greatly on wavelength
– Optical max precedes IR max by up to 2 months
– Fundamental or first overtone oscillators
– Stars not round – image of Mira
– Pulsations produce shock waves, heating photosphere, emission
lines
– Mass loss rates ~ 10-7 Msun per year, 10-20 km/sec
– Dust, gas cocoons (IRC +10 216) some 10,000 AU in diameter
Semi-regular and irregular variables (SRa, SRb, SRc)
– Smaller amplitudes
– Less regular periods, or no periods
Pulsators
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Found in many regions of the
HR diagram
Classical “Cepheid Instability
Strip”
– Cepheids
– RR Lyrae Stars
– ZZ Ceti Stars
“Other” pulsators
– Beta Cephei Stars
– RV Tauri
– LPVs
– Semi-Regulars
– PG 1159 Stars
– Ordinary red giants
– …
Amplitude of Mira Light Curve
More Red Giants
• Normal red giants are oxygen rich – TiO dominates the spectrum
• When carbon dominates, we get carbon stars (old R and N
spectral types)
• Instead of TiO: CN, CH, C2, CO, CO2
• Also s-process elements enhanced (technicium)
• Double-shell AGB stars
Peery 1971
Weirder Red Giants
• S, SC, CS stars
– C/O near unity – drives molecular equilibrium to weird
oxides
• Ba II stars
– G, K giants
– Carbon rich
– S-process elements enhanced
– No technicium
– All binaries!
• R stars are warm carbon stars – origin still a mystery
– Carbon rich K giants
– No s-process enhancements
– NOT binaries
– Not luminous for AGB double-shell burning
• RV Tauri Stars
Mass Transfer Binaries
The more massive star in a binary evolves
to the AGB, becomes a peculiar red giant,
and dumps its envelope onto the lower mass
companion
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Ba II stars (strong, mild, dwarf)
CH stars (Pop II giant and subgiant)
Dwarf carbon stars
Nitrogen-rich halo dwarfs
Li-depleted Pop II turn-off stars
After the AGB
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Superwind at the end of the AGB phase strips most of the
remaining hydrogen envelope
Degenerate carbon-oxygen core, He- and H-burning shells, thin H
layer, shrouded in dust from superwind (proto-planetary nebula)
Mass loss rate decreases but wind speed increases
Hydrogen layer thins further from mass loss and He burning shell
Star evolves at constant luminosity (~104LSun), shrinking and heating
up, until nuclear burning ceases
Masses between 0.55 and 1+ solar masses (more massive are
brighter)
Outflowing winds seen in “P Cygni” profiles
Hydrogen abundance low, carbon abundance high (WC stars)
If the stars reach T>25,000 before the gas/dust shell from the
superwind dissipates, it will light up a planetary nebulae
Temperatures from 25,000 K on up (to 300,000 K or even higher)
Zanstra temperature - Measure brightness of star compared to
brightness of nebula in optical hydrogen emission lines to estimate
the uv/optical flux ratio to get temperature
R Corona Borealis Stars
• A-G type Supergiants
• Suddenly become much
fainter (8 mag)
• He, Carbon rich, H poor
• “Dust puff theory” Mass loss and dust
obscuration?
• Origin - Double
degenerate (He + CO
with mass transfer)?
• about 100 known
White Dwarf Merger Scenario
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The camera aspect remains the same, but moves back to keep the star in
shot as it expands. After the star reaches 0.1 solar radii, an octal is cut
away to reveal the surviving disk and white dwarf core. The red caption
(x) is a nominal time counter since merger. A rod of length initially 0.1
and later 1 solar radius is shown just in front of the star. (Saio &
Jeffrey - http://star.arm.ac.uk/~csj/movies/merger.html)
White Dwarf Soup
• Single Stars
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– DO (continuous)
– DB (helium)
– DA (hydrogen)
– DZ (metals)
– DC (carbon)
• Evolutionary sequence
still unclear
Cataclysmic
Variables
– WD + low mass
companion
– Neutron star +
companion
– Accretion disk