J/A+A/405/1095 Limb-darkening coefficients from ATLAS9 models (Barban+, 2003)
New grids of ATLAS9 atmospheres. II.
Limb-darkening coefficients for the Stroemgren photometric system for A-F stars.
Barban C., Goupil M.J., Van't Veer-Menneret C., Garrido R., Kupka F.,
Heiter U.
<Astron. Astrophys. 405, 1095 (2003)>
=2003A&A...405.1095B 2003A&A...405.1095B
ADC_Keywords: Models, atmosphere ; Photometry, uvby
Keywords: stars: atmospheres - photometry, uvby - stars: oscillations -
convection
Description:
Using up-to-date model atmospheres (Heiter et al. 2002A&A...392..619H 2002A&A...392..619H)
with the turbulent convection approach developed by Canuto, Goldman &
Mazzitelli (1996ApJ...473..550C 1996ApJ...473..550C, CGM), quadratic, cubic and square
root limb darkening coefficients (LDC) are calculated with a least
square fit method for the Stroemgren photometric system. This is done
for a sample of solar metallicity models with effective temperatures
between 6000 and 8500K and with logg between 2.5 and 4.5. A comparison
is made between these LDC and the ones computed from model atmospheres
using the classical mixing length prescription with a mixing length
parameter α=1.25 and α=0.5. For CGM model atmospheres, the
law which reproduces better the model intensity is found to be the
square root one for the u band and the cubic law for the v band. The
results are more complex for the b and y bands depending on the
temperature and gravity of the model. Similar conclusions are reached
for Mixing Length Theory (MLT) α=0.5 models. As expected much
larger differences are found between CGM and MLT with α=1.25. In
a second part, the weighted limb-darkening integrals, bell, and
their derivatives with respect to temperature and gravity, are then
computed using the best limb-darkening law. These integrals are known
to be very important in the context of photometric mode identification
of non-radial pulsating stars. The effect of convection treatment on
these quantities is discussed and as expected differences in the
bell coefficients and derivatives computed with CGM and MLT
α=0.5 are much smaller than differences obtained between
computations with CGM and MLT α=1.25.
The limb darkening coefficients are given here for the u, v, b and y
bands and for CGM models, MLT α=0.5 models and MLT α=1.25
models.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
cgm.dat 78 924 Quadratic (a,b), cubic (c,d,e), square root (f,g)
limb darkening coefficients and σ (sd)
corresponding to the law for uvby bands and for
CGM (1996ApJ...473..550C 1996ApJ...473..550C) models. (tables 1-4)
mlt050.dat 78 924 Quadratic (a,b), cubic (c,d,e), square root (f,g)
limb darkening coefficients and σ (sd)
corresponding to the law for uvby bands and for
Mixing Length Theory (MLT) α=0.5 models.
(tables 5-8)
mlt125.dat 78 924 Quadratic (a,b), cubic (c,d,e), square root (f,g)
limb darkening coefficients and σ (sd)
corresponding to the law for uvby band and for
Mixing Length Theory (MLT) α=1.25 models.
(tables 9-12)
tables.tex 173 2933 LaTeX version of the tables
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See also:
J/A+A/401/657 : Non-linear limb-darkening law for LTE models II (Claret, 2003)
J/A+A/363/1081 : Non-linear limb-darkening law for LTE models (Claret, 2000)
J/A+A/335/647 : Limb-darkening coefficients for ubvyUBVRIJHK (Claret 1998)
J/A+AS/110/329 : LTE model atmospheres coeff. (Diaz-cordoves+, 1995)
J/A+AS/114/247 : Limb-darkening coefficients for RIJHK (Claret+, 1995)
Byte-by-byte Description of file: *.dat
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Bytes Format Units Label Explanations
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1 A1 --- Band [uvby] Band (Stroemgren photometry)
3- 5 F3.1 [cm/s+2] logg Surface gravity
7- 10 I4 K Teff Effective temperature
12- 16 F5.3 --- a Quadratic limb-darkening coefficient (1)
18- 23 F6.3 --- b Quadratic limb-darkening coefficient (1)
25- 30 F6.4 --- sigmaq Standard deviation for the quadratic law (2)
32- 36 F5.3 --- c Cubic limb-darkening coefficient (1)
38- 43 F6.3 --- d Cubic limb-darkening coefficient (1)
45- 51 F7.4 --- e Cubic limb-darkening coefficient (1)
53- 58 F6.4 --- sigmac Standard deviation for the cubic law (2)
60- 64 F5.3 --- f Square root limb-darkening coefficient (1)
66- 71 F6.3 --- g Square root limb-darkening coefficient (1)
73- 78 F6.4 --- sigmasr Standard deviation for the square root law (2)
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Note (1): Limb-darkening coefficients:
a, b (quadratic):
I(µ)/I(1) = 1 - a(1-µ) - b(1-µ)2
c, d, e (cubic):
I(µ)/I(1) = 1 - c(1-µ) - d(1-µ)2 -e(1-µ)3
f, g (square root):
I(µ)/I(1) = 1 - f(1-µ) - g(1-sqrt(µ))
where I(1) is the specific intensity at the center of the disk, a, b,
c, d, e, f, g are the corresponding limb-darkening coefficients and
µ=cos(γ), γ being the angle between the line of sight
and the emergent intensity
Note (2): Same definition of the standard deviation as in
Diaz-Cordoves Gimenez (1992A&A...259..227D 1992A&A...259..227D).
sigma2=1/20 {sum(i=1to20)}{[I(mu)/I(1)th - I(mu)/I(1)ap]i}2,
where the subindex th denotes the values derived from the models and
ap corresponds to those derived from the corresponding approximation.
We consider sigma as a measure of the quality of the actual fit.
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Acknowledgements: Caroline Barban
References:
Heiter et al., Paper I 2002A&A...392..619H 2002A&A...392..619H
(End) Patricia Bauer [CDS] 22-May-2003