J/A+A/546/A14Limb-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..14CADC_Keywords: Models, atmosphere ; Photometry, infrared ; Photometry, SDSS ; Photometry, uvby ; Photometry, UBVRIKeywords: stars: atmospheres - binaries: eclipsing - brown dwarfs - planetary systems - stars: late-typeAbstract: 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:

FileName Lrecl Records Explanations

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/* 0 26 Original files

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

Bytes Format Units Label Explanations

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

Byte-by-byte Description of file: tableab.dat

Bytes Format Units Label Explanations

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

Byte-by-byte Description of file: tablecd.dat

Bytes Format Units Label Explanations

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

Byte-by-byte Description of file: tableef.dat

Bytes Format Units Label Explanations

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] quasm-sphgrycal PHOENIX model

Byte-by-byte Description of file: tablegh.dat tableghs.dat

Bytes Format Units Label Explanations

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

Byte-by-byte Description of file: tablee6.dat tablee6s.dat

Bytes Format Units Label Explanations

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

Byte-by-byte Description of file: m*.dat

Bytes Format Units Label Explanations

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

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' filtersNote (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-µ^{0.5}) - a2*(1-µ) - a3*(1-µ^{1.5}) - a4*(1-µ^{2}) ------------------------------------------------------------------------- where I(1) is the specific intensity at the center of the disk, u, a, b, c, d, e, f, a_{i}are the corresponding limb-darkening coefficients and µ=cos(γ), γ being the angle between the line of sight and the emergent intensity

Acknowledgements: Antonio Claret, claret(at)iaa.esReferences: Claret & Hauschildt, 2003A&A...412..241C, Limb-darkening for spherically symmetric NextGen model atmospheres(End)Patricia Vannier [CDS] 10-Sep-2012

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