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

Model Atmosphere Results
(Kurucz 1979, ApJS, 40, 1)
Kurucz ATLAS LTE code
Line Blanketing
Models, 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 K
No 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:
temperature
electron density
abundance
microturbulent 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
   J d     S d     B d
• Result: surface cooling relative to models
without line blanketing
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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
• H   1  1  B   dT 
3    T   dz 
 T3
• Result: backwarming
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Flux Redistribution (UV→optical):
opt. Fν ~ hotter unblanketed model
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Temperature Relation
with Convection
• Convection:
 d ln T 
R  
  adiabatic   A

 d ln P  radiative
• Reduces T
gradient in
deeper layers
of cool stars
• F  Frad  Fconv
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Geometric Depth Scale
•
dx 
d 
 
 x i  

i
0
d
     
• Physical extent
large in low
density cases
(supergiants)
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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 Darkening
Eddington-Barbier Relationship
S=B(τ=0)
S=B(τ=1)
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How Deep Do We See At μ=1?
Answer Depends on Opacity
T(τ=1)
low opacity
T(τ=1)
high opacity
T(τ=0)
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)
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