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