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Model Atmosphere Results(Kurucz 1979, ApJS, 40, 1)

Kurucz ATLAS LTE codeLine BlanketingModels, Spectra

Observational Diagnostics

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ATLAS by Robert Kurucz (SAO)

• Original paper and updated materials (kurucz.cfa.harvard.edu) have had huge impact on stellar astrophysics

• LTE code that includes important continuum opacity sources plus a statistical method to deal with cumulative effects of line opacity (“line blanketing”)

• Other codes summarized in Gray

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ATLAS Grid

• Teff = 5500 to 50000 KNo cooler models since molecular opacities largely ignored.Models for Teff > 30000 K need non-LTE treatment (also in supergiants)

• log g from main sequence to lower limit set by radiation pressure (see Fitzpatrick 1987, ApJ, 312, 596 for extensions)

• Abundances 1, 1/10, 1/100 solar

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Line Blanketing and Opacity Distribution Functions

• Radiative terms depend on integrals

• Rearrange opacity over interval:DF = fraction of interval with line opacity < ℓν

• Same form even with many lines in the interval

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ODF Assumptions

• Line absorption coefficient has same shape with depth (probably OK)

• Lines of different strength uniform over interval with near constant continuum opacity (select freq. regions carefully)

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ODF Representation

• DF as step functions

• Pre-computed for grid over range in: temperatureelectron densityabundancemicroturbulent velocity(range in line opacity)

T = 9120 K

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Line Opacity in Radiation Moments

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Atmospheric Model Listings

• Tables of physical and radiation quantities as a function of depth

• All logarithms except T and 0 (c.g.s.)

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Emergent Fluxes (+ Intensities)

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Temperature Relation with Line Blanketing

• With increased line opacity, emergent flux comes from higher in the atmosphere where gas is cooler in general; lower Iν, Jν

• Radiative equilibrium: lower Jν → lower T

• Result: surface cooling relative to models without line blanketing

J d S d B d

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Temperature Relation with Line Blanketing

• To maintain total flux need to increase T in optically thick part to get same as gray case

•

• Result: backwarming

HB

T

dT

dz

T

1

3

1

3

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Flux Redistribution (UV→optical):opt. Fν ~ hotter unblanketed model

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Temperature Relation with Convection

• Convection:

• Reduces T gradient in deeper layers of cool stars

•

Rrad ia tive

ad iaba tic A

d T

d P

ln

ln

F F Frad conv

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Geometric Depth Scale

•

• Physical extent large in low density cases (supergiants)

d xd

xd

i

i

0

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Observational Parameters

• Colors: Johnson UBVRI, Strömgren ubvy (Lester et al. 1986, ApJS, 61, 509)

• Balmer line profiles (Hα through Hδ)

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Flux Distributions

• Wien peak

• Slope of Paschen continuum (3650-8205)

• Lyman jump at 912 (n=1)Balmer jump at 3650 (n=2)Paschen jump at 8205 (n=3)

• Strength of Balmer lines

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H 912 He I 504 He II 227

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Comparison to Vega

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IDL Quick Look

• IDL> kurucz,teff,logg,logab,wave,flam,fcont

INPUT:• teff = effective temperature (K, grid value)• logg = log gravity (c.g.s, grid value)• logab = log abundance (0,-1,-2)

OUTPUT:• wave = wavelength grid (Angstroms)• flam = flux with lines (erg cm-2 s-1 Angstrom-1)• fcont = flux without lines

• IDL> plot,wave,flam,xrange=[3300,8000],xstyle=1

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Limb DarkeningEddington-Barbier Relationship

S=B(τ=1)

S=B(τ=0)

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How Deep Do We See At μ=1? Answer Depends on Opacity

T(τ=0)

T(τ=1)low opacity

T(τ=1)high opacity

Limb darkening depends on the contrast between B(T(τ=0)) and B(T(τ=1))

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Limb Darkening versus Teff and λ

• Heyrovský 2007, ApJ, 656, 483, Fig.2

• u increases with lower λ, lower Teff

• Both cases have lower opacity → see deeper, greater contrast between T at τ=0 and τ=1

Linear limb-darkening coefficient vs Teff for bands B (crosses), V (circles), R (plus signs), and I (triangles)