A540 – Stellar AtmospheresA540 – Stellar AtmospheresOrganizational DetailsOrganizational Details

• Meeting times• Textbook• Syllabus• Projects• Homework

• Topical Presentations

• Exams• Grading• Notes

Basic OutlineBasic Outline• 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

• 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…

GoalsGoals

• 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

• 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?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 (2.7 x 104 cm/s2)• Log g for a white dwarf is 8• Log g for a supergiant is ~0

• Mostly CGS units…

Make it real…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 Basic Assumptions in in Stellar Stellar AtmospheresAtmospheres• 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 LawBasic Physics – Ideal Gas LawPV=nRT or P=NkT where N=/

P= pressure (dynes cm-2)V = volume (cm3)N = number of particles per unit volume = 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 Kelvink = Boltzman’s constant

1.38 x 10–16 erg K-1 (8.6x10-5 eV K-1) = mean molecular weight in AMU (1 AMU = 1.66 x 10-24

gm)

Don’t forget the electron pressure: Pe = NekT

Densities, pressures in stellar atmospheres are low, so the ideal gas law generally applies.

Make it real…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 Thermal Velocity DistributionsDistributions

• RMS velocity = (3kT/m)1/2

• Most probable velocity = (2kT/m)1/2

• Average velocity = (8kT/m)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 EquationExcitation – the Boltzman Equation

g is the statistical weight and is the difference in excitation potential. For calculating the population of a level the equation is written as:

kT

m

n

m

n eg

g

N

N /

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 = 5040/T = (log e)/kT with k in units of electron volts per degree (k= 8.6x10-5 eV K-1) ) since is normally given in electron volts.

n

Tu

g

N

N nn 10)(

Ionization – The Saha Ionization – The Saha EquationEquation

The Saha equation describes the ionization of atoms (see the text for the full equation).

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

1762.0loglog5.25040

log0

1

0

1

u

uTI

TPe

N

N

kTIee e

Tu

Tu

h

kTmP

N

N /

0

13

2/53/2

0

1

)(

)(2)()2(

Make it real…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 ZooThe Stellar ZooAcross the HR diagram:

What causes an ordinary star to become weird?

•basic stellar evolutionbasic stellar evolution•mass loss & winds mass loss & winds •diffusion & radiative levitationdiffusion & radiative levitation•pulsation (radial and non-pulsation (radial and non-radial)radial)•rotationrotation•mixingmixing•magnetic fieldsmagnetic fields•binary evolution & mass binary evolution & mass transfertransfer•coalescencecoalescence

The Upper Upper Main SequenceThe 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 … … -11.87 kpc

HD 93129A 7.0 -7.0 -12 O3If3.4 kpc

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

Wolf-Rayet StarsWolf-Rayet Stars• 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 hydrogenC/He = 100 x solar or moreAlso 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 StarsMore 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 Chemically Peculiar Stars of the Upper Main Sequencethe Upper Main Sequence

• Ap stars (magnetic, slow rotators, not binaries, spots)– SrCrEu stars– Silicon Stars– Magnetic fields– Oblique rotators

• Am-Fm stars (metallic-lined, binaries, slow rotators)– Ca, Sc deficient– Fe group, heavies

enhanced– diffusion?

• HgMn stars• The Boo stars• Binaries?

Solar Type Stars (F, G, K)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 Boesgaard & Tripicco 1986: Fig 22

The famous lithium dip!

The Lower Main Sequence – UV Ceti StarsThe 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…On to the Giant Branch…• Convection• 1st dredge-up• LF Bump• Proton-capture

reactions

• CNO, Carbon Isotopes• Lithium

Gilliland et al 1998 (47 Tuc)

Real Red GiantsReal Red Giants• 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

PulsatorsPulsators• 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 Amplitude of Mira Light CurveCurve

More Red GiantsMore 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 GiantsWeirder 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 BinariesMass 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

• 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 AGBAfter the AGB• 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 StarsR 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 ScenarioWhite Dwarf Merger Scenario

• 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 SoupWhite Dwarf Soup

• Single Stars– 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