J/A+A/546/A14 Limb-darkening for CoRoT, Kepler, Spitzer (Claret+, 2012)
New limb-darkening coefficients for PHOENIX/1D model atmospheres.
I. Calculations for 1500K ≤ Teff ≤ 4800 K Kepler, CoRot, Spitzer, uvby,
UBVRIJHK, Sloan, and 2MASS photometric systems.
Claret A., Hauschildt P.H., Witte S.
<Astron. Astrophys. 546, A14 (2012)>
=2012A&A...546A..14C 2012A&A...546A..14C
ADC_Keywords: Models, atmosphere ; Photometry, infrared ; Photometry, SDSS ;
Photometry, uvby ; Photometry, UBVRI
Keywords: stars: atmospheres - binaries: eclipsing - brown dwarfs -
planetary systems - stars: late-type
Abstract:
The knowledge of how the specific intensity is distributed over the
stellar disk is crucial for interpreting the light curves of
extrasolar transiting planets, double-lined eclipsing binaries, and
other astrophysical phenomena. To provide theoretical inputs for light
curve modelling codes, we present new calculations of limb-darkening
coefficients for the spherically symmetric PHOENIX models.
The limb-darkening coefficients were computed by covering the
transmission curves of Kepler, CoRoT, and Spitzer space missions, as
well as the passbands of the Stromgren, Johnson-Cousins, Sloan, and
2MASS. These computations adopted the least-square method. In
addition, we also calculated the linear and bi-parametric
approximations by adopting the flux conservation method as an
additional tool for estimating the theoretical error bars in the
limb-darkening coefficients.
Six laws were used to describe the specific intensity distribution:
linear, quadratic, square root, logarithmic, exponential, and a more
general one with 4 terms. The computations are presented for the solar
chemical composition, with logg varying between 2.5 and 5.5 and
effective temperatures between 1500K-4800K. The adopted
Microturbulent velocity and the mixing-length parameters are 2.0km/s
and 2.0, respectively. Model are for solar metallicity.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
tableu.dat 39 10972 u linear limb darkening coefficients,
quasi-spherical PHOENIX models
mu.dat 40 5486 Merit function for u linear limb darkening
coefficients
tableab.dat 48 10972 a, b quadratic limb darkening coefficients,
quasi-spherical PHOENIX models
mab.dat 40 5486 Merit function for a, b quadratic limb darkening
coefficients
tablecd.dat 48 10972 c, d root-square limb darkening coefficients,
quasi-spherical PHOENIX models
mcd.dat 40 5486 Merit function for c, d root-square limb
darkening coefficients
tableef.dat 48 10972 e, f logarithmic limb darkening coefficients,
quasi-spherical PHOENIX models
mef.dat 40 5486 Merit function for e, f logarithmic limb
darkening coefficients
tablegh.dat 48 5486 g, h exponential limb darkening coefficients,
quasi-spherical PHOENIX models
mgh.dat 40 5486 Merit function for g, h logarithmic limb
darkening coefficients,
quasi-spherical PHOENIX models
tableghs.dat 48 5486 g, h exponential limb darkening coefficients,
spherical PHOENIX models
mghs.dat 40 5486 Merit function for g, h logarithmic limb
darkening coefficients, spherical PHOENIX models
tablee6.dat 70 5486 a1, a2, a3, a4 limb darkening coefficients,
from equation 6, quasi-spherical PHOENIX models
meq6.dat 40 5486 Merit function for a1, a2, a3, a4 limb darkening
coefficients, from equation 6, quasi-spherical
PHOENIX models
tablee6s.dat 70 5486 a1, a2, a3, a4 limb darkening coefficients
from equation 6, spherical PHOENIX models
meq6s.dat 40 5486 Merit function for a1, a2, a3, a4 limb darkening
coefficients, from equation 6, spherical
PHOENIX models
ori/* . 26 Original files
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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/363/1081 : Non-linear limb-darkening law for LTE models (Claret, 2000)
J/A+A/405/1095 : Limb-darkening coeff. from ATLAS9 models (Barban+, 2003)
J/A+A/510/A21 : Stellar limb-darkening coeff. (Sing, 2010)
J/A+A/529/A75 : Limb-darkening coefficients (Claret+, 2011)
J/A+A/552/A16 : Limb-darkening for CoRoT, Kepler, Spitzer. II. (Claret+, 2013)
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 [2.5/5.5] Surface gravity
7- 12 F6.0 K Teff [1500/4800] Effective temperature
14- 17 F4.1 [Sun] Z [0] Metallicity (log[M/H])
19- 22 F4.1 km/s xi [2] Microturbulent velocity ξ
24- 31 F8.4 --- u Linear limb darkening coefficient u (G2)
33- 34 A2 --- Filt Filter (G1)
36 A1 --- Met [LF] Method (Least-Square or Flux Conservation)
38- 39 A2 --- Mod [qs] quasi-spherical PHOENIX model
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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 [2.5/5.5] Surface gravity
7- 12 F6.0 K Teff [1500/4800] Effective temperature
14- 17 F4.1 [Sun] Z [0] Metallicity (log[M/H])
19- 22 F4.1 km/s xi [2] Microturbulent velocity ξ
24- 31 F8.4 --- a Quadratic limb darkening coefficient a (G2)
33- 40 F8.4 --- b Quadratic limb darkening coefficient b (G2)
42- 43 A2 --- Filt Filter (G1)
45 A1 --- Met [LF] Method (Least-Square or Flux Conservation)
47- 48 A2 --- Mod [qs] quasi-spherical PHOENIX model
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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 [2.5/5.5] Surface gravity
7- 12 F6.0 K Teff [1500/4800] Effective temperature
14- 17 F4.1 [Sun] Z [0] Metallicity (log[M/H])
19- 22 F4.1 km/s xi [2] Microturbulent velocity ξ
24- 31 F8.4 --- c Root-square limb darkening coefficient c (G2)
33- 40 F8.4 --- d Root-square limb darkening coefficient d (G2)
42- 43 A2 --- Filt Filter (G1)
45 A1 --- Met [LF] Method (Least-Square or Flux Conservation)
47- 48 A2 --- Mod [qs] quasi-spherical PHOENIX model
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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 [2.5/5.5] Surface gravity
7- 12 F6.0 K Teff [1500/4800] Effective temperature
14- 17 F4.1 [Sun] Z [0] Metallicity (log[M/H])
19- 22 F4.1 km/s xi [2] Microturbulent velocity ξ
24- 31 F8.4 --- e Logarithmic limb darkening coefficient e (G2)
33- 40 F8.4 --- f Logarithmic limb darkening coefficient f (G2)
42- 43 A2 --- Filt Filter (G1)
45 A1 --- Met [LF] Method (Least-Square or Flux Conservation)
47- 48 A2 --- Mod [qs] quasi-spherical PHOENIX model
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Byte-by-byte Description of file: tablegh.dat tableghs.dat
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Bytes Format Units Label Explanations
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1- 5 F5.2 [cm/s2] logg [2.5/5.5] Surface gravity
7- 12 F6.0 K Teff [1500/4800] Effective temperature
14- 17 F4.1 [Sun] Z [0] Metallicity (log[M/H])
19- 22 F4.1 km/s xi [2] Microturbulent velocity ξ
24- 31 F8.4 --- g Exponential limb darkening coefficient g (G2)
33- 40 F8.4 --- h Exponential limb darkening coefficient h (G2)
42- 43 A2 --- Filt Filter (G1)
45 A1 --- Met [L] Method (Least-Square)
47- 48 A2 --- Mod [qs s] quasi-spherical/spherical PHOENIX model
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Byte-by-byte Description of file: tablee6.dat tablee6s.dat
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Bytes Format Units Label Explanations
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1- 5 F5.2 [cm/s2] logg [2.5/5.5] Surface gravity
7- 12 F6.0 K Teff [1500/4800] Effective temperature
14- 17 F4.1 [Sun] Z [0] Metallicity (log[M/H])
19- 22 F4.1 km/s xi [2] Microturbulent velocity ξ
24- 32 F9.4 --- a1 Equation 6 limb darkening coefficient a1 (G2)
34- 42 F9.4 --- a2 Equation 6 limb darkening coefficient a2 (G2)
44- 52 F9.4 --- a3 Equation 6 limb darkening coefficient a3 (G2)
54- 62 F9.4 --- a4 Equation 6 limb darkening coefficient a4 (G2)
64- 65 A2 --- Filt Filter (G1)
67 A1 --- Met [L] Method (Least-Square)
69- 70 A2 --- Mod [qs s] quasi-spherical/spherical PHOENIX model
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Byte-by-byte Description of file: m*.dat
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Bytes Format Units Label Explanations
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1- 5 F5.2 cm/s2 logg [2.5/5.5] Surface gravity
7- 12 F6.0 K Teff [1500/4800] Effective temperature
14- 17 F4.1 [Sun] Z [0] Metallicity (log[M/H])
19- 22 F4.1 km/s xi [2] Microturbulent velocity ξ
25- 32 F8.4 --- m merit function
34- 35 A2 --- Filt Filter (G1)
37 A1 --- Met [m] m for merit function
39- 40 A2 --- Mod [qs s] quasi-spherical/spherical PHOENIX model
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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
UBVRIJHK = Johnson-Cousins UBVRIJHK filters
u'g'r'i'z' = SDSS u'g'r'i'z' filters
Note (G2): fitting coefficients:
-------------------------------------------------------------------------
(1) Linear law I(µ)/I(1) = 1-u(1-µ)
(2) Quadratic law I(µ)/I(1) = 1-a(1-µ)-b(1-µ)2
(3) Square root law I(µ)/I(1) = 1-c(1-µ)-d(1-sqrt(µ))
(4) Logarithmic law I(µ)/I(1) = 1-e(1-µ)-fµln(µ)
(5) Exponential law I(µ)/I(1) = 1-g(1-µ)-h/[1-exp(µ)]
(6) 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
References:
Claret & Hauschildt, 2003A&A...412..241C 2003A&A...412..241C,
Limb-darkening for spherically symmetric NextGen model atmospheres
(End) Patricia Vannier [CDS] 10-Sep-2012