J/A+AS/131/395 Eclipsing binaries light curves models (Claret 1998) ================================================================================ Comprehensive tables for the interpretation and modeling of the light curves of eclipsing binaries Claret A. =1998A&AS..131..395C (SIMBAD/NED BibCode) ================================================================================ ADC_Keywords: Binaries, eclipsing ; Models, evolutionary Keywords: stars: binaries: eclipsing - stars: evolution; interiors; fundamental parameters Abstract: We present parameters used in the investigation of the light curves of eclipsing binaries together with other data needed for the interpretation of their stellar and dynamical evolution. Parameters include limb-darkening coefficients and gravity darkening exponents, while data include the apsidal motion constants, the moment of inertia, and the potential energy. The adopted stellar models are those computed by Claret (1995, Cat. ) for a representative chemical composition of X=0.70 and Z=0.02. In addition to the parameters needed for the study of the dynamical behavior and tidal evolution of binary systems, we supply the linear limb-darkening coefficients computed in 12 different photometric bands, as well as the gravity darkening exponent for each point along the evolutionary track. We have developed a method, based on the triangles strategy by Kippenhahn et al. 1967 to compute the gravity-darkening exponent using interior models. For the first time, the gravity-darkening exponents are presented as a function of mass and age. The old values of {beta}_1_ (0.32 and 1.0 for convective and radiative envelopes) are thus superseded by the present calculations and a smooth transition is achieved between both energy transport mechanisms. The tables presented here assist modeling of the light curves of close binaries using limb-darkening and gravity darkening coefficients which are consistent with the observed masses, radii and effective temperatures. In order to facilitate the use of the grid of models presented here in a variety of different research fields other than binary stars, synthetic colors (U-B, B-V, u-b, b-y) and M_v_ are also given. Decription: The results of the models are available, either as the set of 24 tables (table01 to table24) corresponding to the 24 different initial mass and composition, or as the set of tabulated parameters as a function of model and age. In the set of 24 tables, the parameters are described as sets of 7 lines, containing respectively: 1: Parameters from the model, as detailed in the bytes 1-96 of the "Byte-by-byte Decription of file: models.dat" section 2: Linear limb-darkening coefficients, as detailed in the "Byte-by-byte Decription of file: ld1.dat" section 3-6: Quadratic limb-darkening coefficients, as detailed in the "Byte-by-byte Decription of file: ld2*.dat" section 7: Photometric parameters from the models, as in bytes 98-144 of the "Byte-by-byte Decription of file: models.dat" section In tables 1 to 24, the parameters are described as follow: ------------------------------------------------------------------------------ Line one: ------------------------------------------------------------------------------ 1- 5 I5 -- N Number of the model in the track 6- 18 D12.6 yr Age Age of models 19- 26 F8.4 [solLum] log(L) Total luminosity 27- 34 F8.4 [cm/s2] log(g) Surface gravity 35- 42 F8.4 [K] log(Teff) Effective temperature 43- 50 F6.4 [solMass] Mass Mass of the model 51- 57 F6.3 --- log(k2) Apsidal motion constant (j=2) 58- 64 F6.3 --- log(k3) Apsidal motion constant (j=3) 65- 71 F6.3 --- log(k4) Apsidal motion constant (j=4) 72- 80 D8.3 --- alpha alpha = -Ep x R/GM^2 81- 87 F6.3 ---- beta Fractional gyration radius 88- 96 F6.4 ---- beta_1 Gravity-Darkening exponent ------------------------------------------------------------------------------ Line two: ------------------------------------------------------------------------------ 1- 8 F8.4 --- u(u) Linear Limb-darkening coef. (Stroemgren u) 9- 16 F8.4 --- u(v) Linear Limb-darkening coef. (Stroemgren v) 17- 24 F8.4 --- u(b) Linear Limb-darkening coef. (Stroemgren b) 25- 32 F8.4 --- u(y) Linear Limb-darkening coef. (Stroemgren y) 33- 40 F8.4 --- u(U) Linear Limb-darkening coef. (Johnson U) 41- 48 F8.4 --- u(B) Linear Limb-darkening coef. (Johnson B) 49- 56 F8.4 --- u(V) Linear Limb-darkening coef. (Johnson V) 57- 64 F8.4 --- u(R) Linear Limb-darkening coef. (R) 65- 72 F8.4 --- u(I) Linear Limb-darkening coef. (I) 73- 80 F8.4 --- u(J) Linear Limb-darkening coef. (J) 81- 88 F8.4 --- u(H) Linear Limb-darkening coef. (H) 89 96 F8.4 --- u(K) Linear Limb-darkening coef. (K) ------------------------------------------------------------------------------ Line three: ------------------------------------------------------------------------------ 1- 8 F8.4 --- a(u) Quadratic Limb-darkening coef. (Stroemgren u) 9- 16 F8.4 --- a(v) Quadratic Limb-darkening coef. (Stroemgren v) 17- 24 F8.4 --- a(b) Quadratic Limb-darkening coef. (Stroemgren b) 25- 32 F8.4 --- a(y) Quadratic Limb-darkening coef. (Stroemgren y) 33- 40 F8.4 --- a(U) Quadratic Limb-darkening coef. (Johnson U) 41- 48 F8.4 --- a(B) Quadratic Limb-darkening coef. (Johnson B) 49- 56 F8.4 --- a(V) Quadratic Limb-darkening coef. (Johnson V) 57- 64 F8.4 --- a(R) Quadratic Limb-darkening coef. (R) 65- 72 F8.4 --- a(I) Quadratic Limb-darkening coef. (I) 73- 80 F8.4 --- a(J) Quadratic Limb-darkening coef. (J) 81- 88 F8.4 --- a(H) Quadratic Limb-darkening coef. (H) 89 96 F8.4 --- a(K) Quadratic Limb-darkening coef. (K) ------------------------------------------------------------------------------ Line four: ------------------------------------------------------------------------------ 1- 8 F8.4 --- b(u) Quadratic Limb-darkening coef. (Stroemgren u) 9- 16 F8.4 --- b(v) Quadratic Limb-darkening coef. (Stroemgren v) 17- 24 F8.4 --- b(b) Quadratic Limb-darkening coef. (Stroemgren b) 25- 32 F8.4 --- b(y) Quadratic Limb-darkening coef. (Stroemgren y) 33- 40 F8.4 --- b(U) Quadratic Limb-darkening coef. (Johnson U) 41- 48 F8.4 --- b(B) Quadratic Limb-darkening coef. (Johnson B) 49- 56 F8.4 --- b(V) Quadratic Limb-darkening coef. (Johnson V) 57- 64 F8.4 --- b(R) Quadratic Limb-darkening coef. (R) 65- 72 F8.4 --- b(I) Quadratic Limb-darkening coef. (I) 73- 80 F8.4 --- b(J) Quadratic Limb-darkening coef. (J) 81- 88 F8.4 --- b(H) Quadratic Limb-darkening coef. (H) 89 96 F8.4 --- b(K) Quadratic Limb-darkening coef. (K) ------------------------------------------------------------------------------ Line five: ------------------------------------------------------------------------------ 1- 8 F8.4 --- c(u) Square root Limb-darkening coef. (Stroemgren u) 9- 16 F8.4 --- c(v) Square root Limb-darkening coef. (Stroemgren v) 17- 24 F8.4 --- c(b) Square root Limb-darkening coef. (Stroemgren b) 25- 32 F8.4 --- c(y) Square root Limb-darkening coef. (Stroemgren y) 33- 40 F8.4 --- c(U) Square root Limb-darkening coef. (Johnson U) 41- 48 F8.4 --- c(B) Square root Limb-darkening coef. (Johnson B) 49- 56 F8.4 --- c(V) Square root Limb-darkening coef. (Johnson V) 57- 64 F8.4 --- c(R) Square root Limb-darkening coef. (R) 65- 72 F8.4 --- c(I) Square root Limb-darkening coef. (I) 73- 80 F8.4 --- c(J) Square root Limb-darkening coef. (J) 81- 88 F8.4 --- c(H) Square root Limb-darkening coef. (H) 89 96 F8.4 --- c(K) Square root Limb-darkening coef. (K) ------------------------------------------------------------------------------ Line six: ------------------------------------------------------------------------------ 1- 8 F8.4 --- d(u) Square root Limb-darkening coef. (Stroemgren u) 9- 16 F8.4 --- d(v) Square root Limb-darkening coef. (Stroemgren v) 17- 24 F8.4 --- d(b) Square root Limb-darkening coef. (Stroemgren b) 25- 32 F8.4 --- d(y) Square root Limb-darkening coef. (Stroemgren y) 33- 40 F8.4 --- d(U) Square root Limb-darkening coef. (Johnson U) 41- 48 F8.4 --- d(B) Square root Limb-darkening coef. (Johnson B) 49- 56 F8.4 --- d(V) Square root Limb-darkening coef. (Johnson V) 57- 64 F8.4 --- d(R) Square root Limb-darkening coef. (R) 65- 72 F8.4 --- d(I) Square root Limb-darkening coef. (I) 73- 80 F8.4 --- d(J) Square root Limb-darkening coef. (J) 81- 88 F8.4 --- d(H) Square root Limb-darkening coef. (H) 89 96 F8.4 --- d(K) Square root Limb-darkening coef. (K) ------------------------------------------------------------------------------ Line seven: ------------------------------------------------------------------------------ 1- 8 F8.4 --- M_v Absolute Visual Magnitude 9- 16 F8.4 --- M_bol Absolute Bolometric Magnitude 17- 24 F8.4 --- U-B Color Index U-B (Johnson) 25- 32 F8.4 --- B-V Color Index B-V (Johnson) 33- 40 F8.4 --- u-b Color Index u-b (Stroemgren) 41- 48 F8.4 --- b-y Color Index b-y (Stroemgren) ------------------------------------------------------------------------------ File Summary: -------------------------------------------------------------------------------- FileName Lrecl Records Explanations -------------------------------------------------------------------------------- ReadMe 80 . This file init.dat 21 24 Initial parameters ld1.dat 101 720 Linear limb-darkening coeff. ld2a.dat 101 720 Quadratic limb-darkening coeff., a ld2b.dat 101 720 Quadratic limb-darkening coeff., b ld2c.dat 101 720 Square root limb-darkening coefficients, c ld2d.dat 101 720 Square root limb-darkening coefficients, d models.dat 144 720 Parameters from models table01.txt 96 213 logM= 0.0000 ,X=0.70, Z=0.02, without overshooting table02.txt 96 213 logM= 0.0212 ,X=0.70, Z=0.02, without overshooting table03.txt 96 213 logM= 0.0492 ,X=0.70, Z=0.02, without overshooting table04.txt 96 213 logM= 0.0719 ,X=0.70, Z=0.02, without overshooting table05.txt 96 213 logM= 0.0969 ,X=0.70, Z=0.02, with overshooting table06.txt 96 213 logM= 0.1239 ,X=0.70, Z=0.02, with overshooting table07.txt 96 213 logM= 0.1492 ,X=0.70, Z=0.02, with overshooting table08.txt 96 213 logM= 0.1761 ,X=0.70, Z=0.02, with overshooting table09.txt 96 213 logM= 0.1987 ,X=0.70, Z=0.02, with overshooting table10.txt 96 213 logM= 0.2504 ,X=0.70, Z=0.02, with overshooting table11.txt 96 213 logM= 0.2101 ,X=0.70, Z=0.02, with overshooting table12.txt 96 213 logM= 0.3997 ,X=0.70, Z=0.02, with overshooting table13.txt 96 213 logM= 0.4997 ,X=0.70, Z=0.02, with overshooting table14.txt 96 213 logM= 0.5997 ,X=0.70, Z=0.02, with overshooting table15.txt 96 213 logM= 0.6998 ,X=0.70, Z=0.02, with overshooting table16.txt 96 213 logM= 0.8000 ,X=0.70, Z=0.02, with overshooting table17.txt 96 213 logM= 0.8998 ,X=0.70, Z=0.02, with overshooting table18.txt 96 213 logM= 1.0000 ,X=0.70, Z=0.02, with overshooting table19.txt 96 213 logM= 1.1089 ,X=0.70, Z=0.02, with overshooting table20.txt 96 213 logM= 1.1998 ,X=0.70, Z=0.02, with overshooting table21.txt 96 213 logM= 1.2999 ,X=0.70, Z=0.02, with overshooting table22.txt 96 213 logM= 1.3998 ,X=0.70, Z=0.02, with overshooting table23.txt 96 213 logM= 1.5000 ,X=0.70, Z=0.02, with overshooting table24.txt 96 213 logM= 1.6000 ,X=0.70, Z=0.02, with overshooting -------------------------------------------------------------------------------- See also: J/A+AS/109/441 : Stellar models until He burning - I. (Claret, 1995) J/A+AS/114/549 : Stellar models until He burning - II. (Claret+, 1995) J/A+AS/125/439 : Stellar models until He burning - III. (Claret+, 1997) J/A+AS/110/329 : LTE model atmospheres coeff. (Diaz-cordoves+, 1995) J/A+AS/114/247 : Limb-darkening coefficients for RIJHK (Claret+, 1995) J/A+A/335/647 : Limb-darkening coefficients for ubvyUBVRIJHK (Claret 1998) Byte-by-byte Description of file: init.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 2 I2 --- Table [1/24] Table number 4- 9 F6.4 [solMass] logM Initial mass 11- 14 F4.2 --- X X initial composition (H) 16- 19 F4.2 --- Y Y initial composition 21 A1 --- Overshoot [y/n] without (n) or with (y) overshooting -------------------------------------------------------------------------------- Byte-by-byte Description of file: models.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 2 I2 --- Table [1/24] Table number 4- 5 I2 -- N Number of the model in the track 7- 18 D12.6 yr Age Age of models 20- 26 F7.4 [solLum] log(L) Total luminosity 28- 34 F7.4 [cm/s2] log(g) Surface gravity 36- 42 F7.4 [K] log(Teff) Effective temperature 44- 50 F7.4 solMass M Mass of the model 52- 57 F6.3 --- log(k2) Apsidal motion constant (j=2) 59- 64 F6.3 --- log(k3) Apsidal motion constant (j=3) 66- 71 F6.3 --- log(k4) Apsidal motion constant (j=4) 73- 80 E8.3 --- alpha alpha = -Ep x R/GM^2^ 82- 87 F6.3 ---- beta Fractional gyration radius 91- 96 F6.4 ---- beta_1 Gravity-Darkening exponent 98-104 F7.4 mag Mvis Absolute visual magnitude 106-112 F7.4 mag Mbol Absolute bolometric magnitude 114-120 F7.4 mag U-B Color index U-B (Johnson) 122-128 F7.4 mag B-V Color index B-V (Johnson) 130-136 F7.4 mag u-b Color index u-b (Stroemgren) 138-144 F7.4 mag b-y Color index b-y (Stroemgren) -------------------------------------------------------------------------------- Byte-by-byte Description of file: ld1.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 2 I2 --- Table [1/24] Table number 4- 5 I2 -- N Number of the model in the track 8- 13 F6.4 --- u(u) Linear Limb-darkening coeff. (Stroemgren u) 16- 21 F6.4 --- u(v) Linear Limb-darkening coeff. (Stroemgren v) 24- 29 F6.4 --- u(b) Linear Limb-darkening coeff. (Stroemgren b) 32- 37 F6.4 --- u(y) Linear Limb-darkening coeff. (Stroemgren y) 40- 45 F6.4 --- u(U) Linear Limb-darkening coeff. (Johnson U) 48- 53 F6.4 --- u(B) Linear Limb-darkening coeff. (Johnson B) 56- 61 F6.4 --- u(V) Linear Limb-darkening coeff. (Johnson V) 64- 69 F6.4 --- u(R) Linear Limb-darkening coeff. (R) 72- 77 F6.4 --- u(I) Linear Limb-darkening coeff. (I) 80- 85 F6.4 --- u(J) Linear Limb-darkening coeff. (J) 88- 93 F6.4 --- u(H) Linear Limb-darkening coeff. (H) 96-101 F6.4 --- u(K) Linear Limb-darkening coeff. (K) -------------------------------------------------------------------------------- Byte-by-byte Description of file: ld2*.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 2 I2 --- Table [1/24] Table number 4- 5 I2 -- N Number of the model in the track 7- 13 F7.4 --- u Quadratic Limb-darkening coeff. (Stroemgren u) 15- 21 F7.4 --- v Quadratic Limb-darkening coeff. (Stroemgren v) 23- 29 F7.4 --- b Quadratic Limb-darkening coeff. (Stroemgren b) 31- 37 F7.4 --- y Quadratic Limb-darkening coeff. (Stroemgren y) 39- 45 F7.4 --- U Quadratic Limb-darkening coeff. (Johnson U) 47- 53 F7.4 --- B Quadratic Limb-darkening coeff. (Johnson B) 55- 61 F7.4 --- V Quadratic Limb-darkening coeff. (Johnson V) 63- 69 F7.4 --- R Quadratic Limb-darkening coeff. (R) 71- 77 F7.4 --- I Quadratic Limb-darkening coeff. (I) 79- 85 F7.4 --- J Quadratic Limb-darkening coeff. (J) 87- 93 F7.4 --- H Quadratic Limb-darkening coeff. (H) 95-101 F7.4 --- K Quadratic Limb-darkening coeff. (K) -------------------------------------------------------------------------------- History: Photometric data have been corrected on 03-Jul-2000 in models.dat and tables 01 to 24 (from authors). Acknowledgements: Antonio Claret ================================================================================ (End) Patricia Bauer [CDS] 03-Jul-2000