J/A+A/529/A75 Limb-darkening coefficients (Claret+, 2011)
Gravity and limb-darkening coefficients for Kepler, CoRoT, Spitzer,
uvbyUBVRIJHK, and Sloan photometric systems.
Claret A., Bloemen S.
<Astron. Astrophys. 529, A75 (2011)>
=2011A&A...529A..75C 2011A&A...529A..75C
ADC_Keywords: Models, atmosphere ; Photometry, infrared ; Photometry, SDSS ;
Photometry, uvby ; Photometry, UBVRI
Keywords: binaries: eclipsing - stars: interiors - stars: rotation -
stars: atmospheres - planetary systems
Abstract:
The degree of complexity of physics due to proximity effects in close
binary stars is one of the most important challenges in theoretical
stellar physics. The knowledge of how the specific intensity is
distributed over the stellar disk is primordial to model the light
curves of eclipsing binaries and planetary transits correctly. In
order to provide theoretical input for light curve modelling codes, we
present new calculations of gravity- and limb darkening coefficients
for a wide range of effective temperatures, gravities, metallicities
and microturbulent velocities.
We have computed limb darkening coefficients for several atmosphere
models, covering the transmission curves of the Kepler, CoRoT and
Spitzer space missions as well as more widely used passbands
(Stroemgren, Johnson-Cousins, Sloan). In addition to these
computations, which were computed by adopting the Least-Square Method,
we also performed calculations for the bi-parametric approximations by
adopting the Flux Conservation Method to provide users with an
additional tool to estimate the theoretical error bars. To facilitate
the modelling of the effects of tidal and rotational distortions, we
computed the GDCs y(λ) using the same models of stellar
atmospheres as in the case of limb-darkening. Compared to previous
work, a more general differential equation was used which now takes
into account local gravity variations and the effects of convection.
The limb darkening coefficients were computed with a larger numerical
resolution (100um points instead of 15 or 17 as is often used in the
ATLAS models) and five equations were used to describe the specific
intensities (linear, quadratic, root-square, logarithmic and a
4-coefficient law (Equation 5)). Concerning the GDCs, the influence of
the local gravity on y(λ) is shown as well as the effects of
convection, which turn out to be very significant for cool stars. The
results are tabulated for log(g)'s ranging from 0.0 to
5.0,-5.0≤log[M/H]≤+1, 2000K≤Teff≤50000K and for 5 values of the
microturbulent velocity (0, 2, 4, 6, 8). ATLAS and PHOENIX
plane-parallel atmosphere models were used for all the computations.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
tableu.dat 44 540736 u linear limb darkening coefficients
tableab.dat 51 446276 a, b quadratic limb darkening coefficients
tablecd.dat 51 446276 c, d root-square limb darkening coefficients
tableef.dat 51 446276 e, f logarithmic limb darkening coefficients
tableeq5.dat 67 223138 a1, a2, a3, a4 limb darkening coefficients
from equation 5
tabley.dat 45 200851 y gravity darkening coefficients
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See also:
J/A+AS/110/329 : LTE model atmospheres coeff. (Diaz-cordoves+, 1995)
J/A+AS/114/247 : Limb-darkening coeff. for RIJHK (Claret+, 1995)
J/A+A/335/647 : Limb-darkening coeff. for ubvyUBVRIJHK (Claret 1998)
J/A+A/405/1095 : Limb-darkening coeff. from ATLAS9 models (Barban+, 2003)
J/A+A/510/A21 : Stellar limb-darkening coeff. (Sing, 2010)
Byte-by-byte Description of file: tableu.dat
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Bytes Format Units Label Explanations
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1- 5 F5.2 [cm/s2] logg [0/5] Surface gravity
7- 12 F6.0 K Teff [2000/50000] Effective temperature
14- 17 F4.1 [Sun] Z [-5/1] Metallicity (log[M/H])
19- 22 F4.1 km/s xi [0/8] Microturbulent velocity
24- 30 F7.4 --- u Linear limb darkening coefficient u (G2)
32- 33 A2 --- Filt Filter (G1)
35 A1 --- Met [LF] Method (Least-Square or Flux Conservation)
38- 44 A7 --- Mod Model (ATLAS or PHOENIX)
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Byte-by-byte Description of file: tableab.dat
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Bytes Format Units Label Explanations
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1- 5 F5.2 [cm/s2] logg [0/5] Surface gravity
7- 12 F6.0 K Teff [2000/50000] Effective temperature
14- 17 F4.1 [Sun] Z [-5/1] Metallicity (log[M/H])
19- 22 F4.1 km/s xi [0/8] Microturbulent velocity
24- 30 F7.4 --- a Quadratic limb darkening coefficient a (G2)
32- 38 F7.4 --- b Quadratic limb darkening coefficient b (G2)
40- 41 A2 --- Filt Filter (G1)
43 A1 --- Met [LF] Method (Least-Square or Flux Conservation)
45- 51 A7 --- Mod Model (ATLAS or PHOENIX)
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Byte-by-byte Description of file: tablecd.dat
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Bytes Format Units Label Explanations
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1- 5 F5.2 [cm/s2] logg [0/5] Surface gravity
7- 12 F6.0 K Teff [2000/50000] Effective temperature
14- 17 F4.1 [Sun] Z [-5/1] Metallicity (log[M/H])
19- 22 F4.1 km/s xi [0/8] Microturbulent velocity
24- 30 F7.4 --- c Root-square limb darkening coefficient c (G2)
32- 38 F7.4 --- d Root-square limb darkening coefficient d (G2)
40- 41 A2 --- Filt Filter (G1)
43 A1 --- Met [LF] Method (Least-Square or Flux Conservation)
45- 51 A7 --- Mod Model (ATLAS or PHOENIX)
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Byte-by-byte Description of file: tableef.dat
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Bytes Format Units Label Explanations
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1- 5 F5.2 [cm/s2] logg [0/5] Surface gravity
7- 12 F6.0 K Teff [2000/50000] Effective temperature
14- 17 F4.1 [Sun] Z [-5/1] Metallicity (log[M/H])
19- 22 F4.1 km/s xi [0/8] Microturbulent velocity
24- 30 F7.4 --- e Logarithmic limb darkening coefficient e (G2)
32- 38 F7.4 --- f Logarithmic limb darkening coefficient f (G2)
40- 41 A2 --- Filt Filter (G1)
43 A1 --- Met [LF] Method (Least-Square or Flux Conservation)
45- 51 A7 --- Mod Model (ATLAS or PHOENIX)
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Byte-by-byte Description of file: tableeq5.dat
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Bytes Format Units Label Explanations
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1- 5 F5.2 [cm/s2] logg [0/5] Surface gravity
7- 12 F6.0 K Teff [2000/50000] Effective temperature
14- 17 F4.1 [Sun] Z [-5/1] Metallicity (log[M/H])
19- 22 F4.1 km/s xi [0/8] Microturbulent velocity
24- 30 F7.4 --- a1 Equation 5 limb darkening coefficient a1 (G2)
32- 38 F7.4 --- a2 Equation 5 limb darkening coefficient a2 (G2)
40- 46 F7.4 --- a3 Equation 5 limb darkening coefficient a3 (G2)
48- 54 F7.4 --- a4 Equation 5 limb darkening coefficient a4 (G2)
56- 57 A2 --- Filt Filter (G1)
59 A1 --- Met [LF] Method (Least-Square or Flux Conservation)
61- 67 A7 --- Mod Model (ATLAS or PHOENIX)
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Byte-by-byte Description of file: tabley.dat
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Bytes Format Units Label Explanations
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1- 5 F5.2 [cm/s2] logg [0/5] Surface gravity
7- 13 F7.4 [K] logTeff [3.3/4.7] Effective temperature
15- 19 F5.2 [Sun] Z [-5/1] Metallicity (log[M/H])
21- 26 F6.3 km/s xi [2/8] Microturbulent velocity
28- 34 F7.4 --- y Gravity darkening coefficient y (1)
36- 37 A2 --- Filt Filter (G1)
39- 45 A7 --- Mod Model (ATLAS or PHOENIX)
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Note (1): the gravity darkening coefficient represents the variation of
ln(I) vs ln(g), see Eq. (7) and section 3 of the paper.
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Global notes:
Note (G1): Phorometry system used:
Kp = Kepler
C = CoRoT
S1 = Spitzer filter 1, 3.6um
S2 = Spitzer filter 2, 4.5um
S3 = Spitzer filter 3, 5.8um
S4 = Spitzer filter 4, 8.0um
uvby = Stroemgren uvby filters
UVBRIJHK = Johnson-Cousins UVBRIJHK filters
u'g'r'i'z' = SDSS u'g'r'i'z' filters
Note (G2): fitting coefficients:
-------------------------------------------------------------------------
(1) Linear I(µ)/I(1) = 1-u(1-µ)
(2) Quadratic I(µ)/I(1) = 1-a(1-µ)-b(1-µ)2
(3) Square root I(µ)/I(1) = 1-c(1-µ)-d(1-sqrt(µ))
(4) Logarithmic I(µ)/I(1) = 1-e(1-µ)-fµln(µ)
(5) Non-linear law I(µ)/I(1) = 1 - a1*(1-µ0.5) - a2*(1-µ)
- a3*(1-µ1.5) - a4*(1-µ2)
-------------------------------------------------------------------------
where I(1) is the specific intensity at the center of the disk, u, a,
b, c, d, e, f, ai are the corresponding limb-darkening coefficients
and µ=cos(γ), γ being the angle between the line of
sight and the emergent intensity
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Acknowledgements:
Antonio Claret, claret(at)iaa.es
History:
* 05-Apr-2011: First version
* 17-Jun-2011: Corrected version (from author)
(End) Patricia Vannier [CDS] 03-Mar-2011