RADIATIVE TRANSFER AND STELLAR ATMOSPHERES
Institute for AstronomyFall Semester 2007
Rolf Kudritzki
Fall
2007 Outline
Introduction: Modern astronomy and the power of quantitative spectroscopyBasic assumptions for “classic” stellar atmospheres: geometry, hydrostatic equilibrium, conservation of momentum-mass-energy, LTE (Planck, Maxwell)Radiative transfer: definitions, opacity, emissivity, optical depth, exact and approximate solutions, moments of intensity, Lambda operator, diffusion (Eddington) approximation, limb darkening, grey atmosphere, solar modelsEnergy transport: Radiative equilibrium and convection, grey atmospheres,numerical solutions for model atmospheresAtomic radiation processes: Einstein coefficients, line broadening, continuous processes and scattering (Thomson, Rayleigh)Excitation and ionization (Boltzmann, Saha), partition functionExample: Stellar spectral typesNon-LTE: basic concept and examples2-level atom, formation of spectral lines, curves growthRecombination theory in stellar envelopes and gaseous nebulaeStellar winds: introduction to line transfer with velocity fields, hydrodynamics of radiation driven winds
1. Introduction
Astrophysics is based on the collection of photons from cosmic objects from the whole electromagnetic spectrum.
The majority of these photons originates in stellar objects (photospheres or envelopes), constituents of galaxies.
The quantitative analysis of spectra is necessary for the physical understanding of most astronomical objects in the universe.
Munich University Observatory
1820
The birthplace of stellar spectroscopy
Joseph von Frauenhofer1820
Spectrum of the sun
Spectrum of Arcturus, α CrB
Lamont, 1836
Munich solar eclipse, 1999
Munich University Observatory solar eclipse, 1999
Fall
2007 Examples of spectra
The visible solar spectrum NOAO/AURA/NSF
Fall
2007 Examples of spectra
Fall
2007 Examples of spectra
O4 supergiant ζ PuppisPauldrach, Puls, Kudritzki et al. 1994,
SSRev, 66, 105
UV spectrum
Stellar winds
Spectral diagnostics of massive stars
diagnostic problem:high luminosity enormous energy and momentum
density of radiation field
NLTE stellar winds
Model atmospheres and radiative transfer
• detailed NLTE treatment
• radiation-hydrodynamics of line-driven winds
• spherical extension
Fall
2007 LTE vs NLTE
LTEeach volume element separately in thermodynamic equilibrium at temperature T(r)
1. f(v) dv = Maxwellian with T = T(r)
2. Saha: (np ne)/n1 / T3/2 exp(-hν1/kT)3. Boltzmann: ni / n1 = gi / g1 exp(-hν1i/kT)
However:
volume elements not closed systems, interactions by photons
LTE non-valid if absorption of photons disrupts equilibrium
Fall
2007
NLTE1. f(v) dv remains Maxwellian
2. Boltzmann – Saha replaced by dni / dt = 0 (statistical equilibrium)
for a given level i the rate of transitions out = rate of transitions in
niXj 6=i
Pij =Xj 6=i
njPji
rate out = rate in
rate equations
Pi,j transition probabilities
i
Fall
2007 complex atomic models for O-stars (Pauldrach et al., 2001)
AWAP 05/19/05
NLTENLTE AtomicAtomic ModelsModels in modern model atmosphere codesin modern model atmosphere codeslines, collisions, ionization, recombination
Essential for occupation numbers, line blocking, line forceAccurate atomic models have been includedAccurate atomic models have been included
26 elements149 ionization stages5,000 levels ( + 100,000 )20,000diel. rec. transitions4 106 b-b line transitions
Auger-ionizationrecently improved models are based onrecently improved models are based on SuperstructureSuperstructure
Eisner et al., 1974, CPC 8,270
Basic equations
v dvdr= −dp
dr1ρ + grad − gM = 4πr2ρv
)grad = gcont +constρ
Plines
flugl(nlgl −
nugu )
R∞0
R +1−1 Iν(μ)φ(ν)μdμdν
niP
j 6= i(Rij + Cij) + ni(RiK + CiK ) =P
j 6= inj(Rji + Cji) + n
+1 (RKi + CKi)
(Sν − Iν)κν = μ∂Iν∂r
+1− μ2r
∂Iν∂μ
v dedr+ pv d
dr(1ρ) =
1ρ ·R∞04πκν(Jν − Sν)dν
Teff g
R? [Z] Input
Hydrodyn.
Rateequations
Radiative transfer
energy equation
Non-linear coupling complex iteration !!!
Fall
2007 HD 93129A O3Ia
Taresch, Kudritzki et al. 1997, A&A, 321, 531
Fall
2007
consistent treatment of expanding atmospheres along withspectrum synthesis techniquesspectrum synthesis techniques allow the determination of
stellar parameters, wind parameters, andstellar parameters, wind parameters, and abundancesabundancesPauldrach, 2003, Reviews in Modern Astronomy, Vol. 16
Fall
2007 Crowther et al. 2002,
ApJ, 579, 774AV 232 - SMC
Fall
2007 Examples of spectra
Supernovae (photospheric phase)
Filippenko 1997, ARA&A, 35, 309
Fall
2007 Examples of spectra Quasar
composite
Vanden Berk et al. 2001, AJ, 122, 549
(Sloan)
Fall
2007 Examples of spectra Quasar + Damped
Lyman a system
Carlton & Churchill 2000
Fall
2007 Examples of spectra
Seyfert 1 & 2
Osterbrock 1978, Physica Scripta, 17, 137
Fall
2007 Examples of spectra
HII regions in M83HII regions in M83
disk
Hot spot
Bresolin & Kennicutt 2002, ApJ, 572, 838
element abundancesstellar contentionizing flux, stellar atmospheres
Fall
2007 PN
Fall
2007 Examples of spectra Zhang & Liu 2002,
MNRAS, 337, 499
Planetary Nebula
Fall
2007 Examples of spectra Stephens & Boesgaard
2002, AJ, 123, 1647
Galactic halo star
Fall
2007 Spectral Analysis
SEDs of massive stars in star forming regions heavy extinctionIR spectroscopy
O-star SED(intrinsic)
IR-excessstellar wind
AV = 30 mag
Arches cluster in GC
Fall
2007 Galactic Center Arches cluster:
quantitative IR spectroscopy
NIII
NIII
NIII
Najarro, Figer, Hillier, Kudritzki,2004, ApJ Letters
Extragalactic stellar astronomywith
the brightest stars in the universe
Rolf Kudritzki, Fabio Bresolin, Miguel Urbaneja
Extragalactic stellar astronomy
Properties of stellar populationsEvolution of galaxiesChemical abundance and abundance pattern gradientsInterstellar extinctionDistancesDark matter content
Quantitative stellar spectroscopy of individual starsin galaxies beyond the Local Group
TMT
2007 A supergiants – objects in transition
B8–A4
Brightest normal stars at visual light: -7 ≥ MV ≥ -10 mag
tev ~ 103 yrsL, M ~ const.
ideal to determine• chemical compos.• abundance grad.• SF history• extinction• extinction laws• distances
of galaxies
TMT
2007
pilot study W. Gieren, G. Pietrzynski,Araucaria Project: F. Bresolin, M. Urbaneja, RPK
NGC 300NGC 300 – Sculptor Group (2 Mpc)
117 cepheids
70 blue supergiantspectra
Kudritzki, Urbaneja, Bresolin,2007, ApJ, in prep.
TMT
2007
Bresolin, Gieren,
Kudritzki et al. 2002
ApJ 567, 277
TMT
2007 NGC 300: spectral classification
V = 19.0
Galactic template
Galactic template
NGC 300 A2 supergiant
Bresolin, Gieren, Kudritzki et al. 2002, ApJ 567, 277
Study of metallicitiesA supergiants
TMT
2007 Metallicity: spectral window
TMT
2007 Spectral window 4497-4607Å
TMT
2007 Spectral window 4497-4607Å
χ2i =SN
2 1npix
npixj=1 (Oj − Cj)2
TMT
2007 χi spectral window 4497-4607Å
TMT
2007 another spectral window
TMT
2007 Spectral window 4438-4497Å
TMT
2007 χi spectral window 4438-4497Å
TMT
2007 Χi all windows [Z] = -0.4±0.1
TMT
2007
WN 11 star
TMT
2007 Wolf-Rayet star in NGC 300
WN11 star
Bresolin, Kudritzki, Najarro et al. 2002, ApJ Letters 577, L107
emission line diagnostics:first detailed abundance pattern outside Local Group
TMT
2007 NGC 300 WN11 star
non-LTE line-blanketed
hydrodynamic model atmospheres
with stellar winds
stellar parameters
wind parameters
H, He, CNO, Al, Si, Fe abundances
Bresolin, Kudritzki, Najarro et al. 2002, ApJ Letters 577, L107
TMT
2007 NGC 300 WN11 star
Rom
e 200
5Stellar metallicity gradient in NGC300
■ B0 – B3 supergiants
● B8 – A4 supergiants
--- [Z] = -0.03 – 0.45•ρ/ρ0
= -0.03 – 0.08•d/kpc
ρ0 = 9.75 arcmin ≈ 5.7kpc
[Z] = log(Z/Z_sun)
Kudritzki, Urbaneja, Bresolin, Przybilla, Gieren, Pietrzynski, 2007, in prep.
AA
S 20
07
NGC 3621NGC 3621: 7 Mpc HST/ACS
Bresolin, Kudritzki, Mendez & Przybilla 2001~19 blue supergiant candidates (VLT/FORS)
4 analyzed
AA
S 20
07
NGC 3621NGC 3621:
Bresolin, Kudritzki, Mendez & Przybilla 2001~19 blue supergiant candidates (VLT/FORS)
4 analyzedBresolin, Kudritzki, Mendez, Przybilla
2001, ApJ Letters 548, L159
Galactic template
Galactic template
NGC 3621 A0 supergiant
AA
S 20
07
Bresolin, Kudritzki, Mendez, Przybilla2001, ApJ Letters 548, L159
0.2 & 0.5 solar metallicity models
A0 Ia starV = 20.5 MV = -9
TMT
2007
Blue supergiants asdistance indicators
TMT
2007
Flux weighted Gravity – Luminosity Relationship (FGLR)
Kudritzki, Bresolin, Przybilla, ApJ Letters, 582, L83 (2003)
M ~ g×R2 ~ L×(g/T4) = const.
const.
with L ~ Mx ~ Lx(g/T4)x, x ~ 3
L1-x ~ (g/T4)x
or with Mbol ~ -2.5log L
Mbol = a log(g/T4) + b FGLR
a =2.5 x/(1-x) ~ 3.75
B1-A4
L,M ~ const.
TMT
2007
FGLR Local Group, NGC300 & NGC3621Kudritzki, Bresolin & Przybilla, 2003,ApJL, 582, L83 Kudritzki, Urbaneja, Bresolin et al., ApJ, 2007, in prep.
Mbol = 3.75 log(g/T4eff,4) – 13.73
σ= 0.24
TMT
2007
• WFOS quantitative spectroscopy possible down to mV ~ 24.5 mag
with objects MV ≤ - 8 mag
m – M ~ 32.5 mag ~ 30 Mpc possible
chemical evolution studiesSFISM, extinction, extinction lawsdistances
10 objects per galaxy Δ(m-M) ~ 0.1 mag
Application to TMT (30m telescope)
Mauna KeaMauna Kea
$ 1 billion science endeavor$ 1 billion science endeavor
Mauna Kea ObservatoriesMauna Kea Observatories
The best in the worldThe best in the world
Operating at 14,200 ft.Operating at 14,200 ft.
Adaptive Optics Adaptive Optics
TMT
TMT.PMO.PRE.07.009.REL03
TMT Design
Site on Mauna Kea
Northern Plateau
- below summit
- less visibility
- less cultural and
economic impact
- foreseen in year
2000 Master Plan
of UH
TMT- 13 North test site
Planets around other stars
“Brown Dwarf”orbiting a star
Gemini/Keck AO detectionby Michael Liu (IfA)
Problem: Planets much fainter than Brown Dwarfs
30m telescope needed !!
TMT !!
The power of TMTTMT will allow
for the first time
● To image giant planetssurrounding many hundred stars
● To determine masses and radii
● To analyzeatmospheric structure
and chemical composition
Exploring other solar systems
Artist conception of planetary system orbiting around 55 Cancri using results of radial velocity Keck observations
Sudarsky, Burrows& Lunine, 2003
55 Cancri – physical characterization byspectroscopy
Predicted spectra of a 5 Gyr Jupiter-like planet
Hubeny, 2007, priv. comm.
Predicted spectra of some interesting planets
Hubeny, 2007, priv. comm.
Stellar atmospheres: an overview
M = 2x1033 g 50 Mo
R = 7x1010 cm 20 RoL = 4x1033 erg/s 106 Lo 104 (PN) 106 (HII) 1012 (QSO) Lo
ΔR = 200 km ~ 3x10‐4 Ro 0.1 Ron = 1015 cm‐3 1014 cm‐3
T = 6000 K 40,000 K
ΔR = 1000 km/1 Ro 100 Ro 105 Ro 0.1 (PN) 10 (HII) 1,000 (QSO) pcn = 1012/106 cm‐3 1011…108 cm‐3
T = 20,000/2x106 K 40,000…15,000 K
Core
Photosphere
Envelope Chromosphere/Corona
Spectral Analysis
Plasma phyics: diagnostics, line broadeningAtomic physics + quantum mechanics: light-matter interaction (micro)Thermodynamics: TE, LTE, non-LTEHydrodynamics: atmospheric structure, velocity fieldsRadiative transfer (macro)
Stellar properties: mass, radius, luminosity, temperature, chemical composition
Galactic structureStellar and galactic evolutionDistance scale
Spectral Analysis
Observed spectrum Synthetic spectrumcomparison
Theory of stellar atmospheres
•Geometry•Hydrodynamics•Thermodynamics•Radiative transfer•Atomic physics
ModelNumerical solution of theoretical
Equations
L, R, M, chemical composition
Basic equations
v dvdr= −dp
dr1ρ + grad − gM = 4πr2ρv
)grad = gcont +constρ
Plines
flugl(nlgl −
nugu )
R∞0
R +1−1 Iν(μ)φ(ν)μdμdν
niP
j 6= i(Rij + Cij) + ni(RiK + CiK ) =P
j 6= inj(Rji + Cji) + n
+1 (RKi + CKi)
(Sν − Iν)κν = μ∂Iν∂r
+1− μ2r
∂Iν∂μ
v dedr+ pv d
dr(1ρ) =
1ρ ·R∞04πκν(Jν − Sν)dν
Teff g
R? [Z] Input
Hydrodyn.
Rateequations
Radiative transfer
energy equation
Non-linear coupling complex iteration !!!
Fall
2007 complex atomic models for O-stars (Pauldrach et al., 2001)
Fall
2007 HD 93129A O3Ia
Taresch, Kudritzki et al. 1997, A&A, 321, 531
consistent treatment of expanding atmospheres along withspectrum synthesis techniquesspectrum synthesis techniques allow the determination of
stellar parameters, wind parameters, andstellar parameters, wind parameters, and abundancesabundancesPauldrach, 2003, Reviews in Modern Astronomy, Vol. 16
non-LTE atmospheres with windsplus stellar evolution models
Synthetic spectra of galxies at high zas a function of Z, IMF, SFR
Population synthesis of highPopulation synthesis of high--z galaxiesz galaxies
Galaxy spectra
Stellar spectra
Stellar Population
Initial Mass Function
Star Formation History MetallicityStellar Evolution
Fall
2007
Spectral diagnostics of high-z starburstsStarburst models - fully synthetic spectra based on model atmospheres
Rix, Pettini, Leitherer, Bresolin, Kudritzki, Steidel, 2004, ApJ 615, 98
Fall
2007
Spectral diagnostics of high-z starbursts
Rix, Pettini, Leitherer,Bresolin, Kudritzki, Steidel2004, ApJ 615, 98
cB58 @ z=2.7
fully synthetic spectravs. observation
Fall
2007
NGC 5253
Leitherer et al. 2001, ApJ, 550, 724
Starburst99 population synthesis models
+
UV stellar libraries at ~solar and ~0.25 solar (LMC,
SMC) abundance
Fall
2007 Outline
Introduction: Modern astronomy and the power of quantitative spectroscopyBasic assumptions for “classic” stellar atmospheres: geometry, hydrostatic equilibrium, conservation of momentum-mass-energy, LTE (Planck, Maxwell)Radiative transfer: definitions, opacity, emissivity, optical depth, exact and approximate solutions, moments of intensity, Lambda operator, diffusion (Eddington) approximation, limb darkening, grey atmosphere, solar modelsEnergy transport: Radiative equilibrium and convection, grey atmospheres,numerical solutions for model atmospheresAtomic radiation processes: Einstein coefficients, line broadening, continuous processes and scattering (Thomson, Rayleigh)Excitation and ionization (Boltzmann, Saha), partition functionExample: Stellar spectral typesNon-LTE: basic concept and examples2-level atom, formation of spectral lines, curves growthRecombination theory in stellar envelopes and gaseous nebulaeStellar winds: introduction to line transfer with velocity fields, hydrodynamics of radiation driven winds
Fall
2007 Readings
Mihalas, D., “Stellar Atmospheres”, 2nd ed., Freeman & Co., San Francisco, 1978Gray, D.F., “The Observation and Analysis of Stellar Photospheres”, 2nd ed., Cambridge University Press, Cambridge, 1992Rutten, R.J., “Radiative Transfer in Stellar Atmospheres”, 7th
ed., 2000 (http://www.astro.uu.nl/~rutten/tmr/)Rybicki, G.B. & Lightman, A., “Radiative Processes in Astrophysics”, New York, Wiley, 1979Osterbrock, D.E., “Astrophysics of Gaseous Nebulae and Active Galactic Nuclei”, University Science Books, Mill Valley, 1989these notes