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