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.
<Astron. Astrophys. Suppl. Ser. 131, 395 (1998)>
=1998A&AS..131..395C 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. J/A+AS/109/441) 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
β1 (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thus superseded by the present calculations and a smooth transition is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 Mv 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
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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
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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/GM2
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