CDROM/AJ/V106/P2096 Limb-Darkening Coefficients (Van Hamme 1993) ================================================================================ New Limb-Darkening Coefficients for Modeling Binary Star Light Curves W. Van Hamme <1993, AJ, 106, 2096> =1993AJ....106.2096V ================================================================================ Abstract: We present monochromatic, passband-specific, and bolometric limb-darkening coefficients for a linear as well as nonlinear logarithmic and square root limb-darkening laws. These coefficients, including the bolometric ones, are needed when modeling binary star light curves with the latest version of the Wilson-Devinney light curve program. We base our calculations on the most recent ATLAS stellar atmosphere models for solar chemical composition stars with a wide range of effective temperatures and surface gravities. We examine how well various limb-darkening approximations represent the variation of the emerging specific intensity across a stellar surface as computed according to the model. For binary star light curve modeling purposes, we propose the use of a logarithmic or a square root law. We design our tables in such a manner that the relative quality of either law with respect to another can be easily compared. Since the computation of bolometric limb-darkening coefficients first requires monochromatic coefficients, we also offer tables of these coefficients (at 1221 wavelength values between 0.09 nm and 160 kmicrons) and tables of passband-specific coefficients for commonly used photometric filters. File Summary: -------------------------------------------------------------------------------- File Name Lrecl Records Explanations -------------------------------------------------------------------------------- table1.dat 79 410 Bolometric limb-darkening coefficients table2.dat 72 8610 Passband-specific limb-darkening coefficients model.001 95 . Monochromatic limb-darkening coefficients ... . . Monochromatic limb-darkening coefficients model.410 95 . Monochromatic limb-darkening coefficients -------------------------------------------------------------------------------- Comments for file: table1.dat -------------------------------------------------------------------------------- Table 1 contains the bolometric limb-darkening coefficients for each of the 410 Kurucz (1991) stellar atmosphere models with solar chemical abundances. -------------------------------------------------------------------------------- Byte-by-byte Description of file: table1.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 3 I3 --- Model Model number 4- 9 I6 K Teff Effective temperature, Teff 10-14 F5.1 --- log_g Logarithm of the surface gravity, log g 15-22 F8.3 --- lin_x Bolometric linear limb-darkening coeff., x 23-24 2X --- --- ' (' 25-30 F6.4 --- lin_Q *Quality factor, Q 31 1X --- --- ')' 32-39 F8.3 --- log_x Logarithmic law x coefficient 40-46 F7.3 --- log_y Logarithmic law y coefficient 47-48 2X --- --- ' (' 49-54 F6.4 --- log_Q Quality factor, Q, for log. law coefficients 55 1X --- --- ')' 56-63 F8.3 --- sqr_x Square root law x coefficient 64-70 F7.3 --- sqr_y Square root law y coefficient 71-72 2X --- --- ' (' 73-78 F6.4 --- sqr_Q Quality factor, Q, for sq. root law coeff. 79 1X --- --- ')' -------------------------------------------------------------------------------- Notes for file: table1.dat -------------------------------------------------------------------------------- lin_Q: Quality factor, Q, as defined in section 3 of the printed paper. This number may help in choosing which limb-darkening law to use in any particular case. -------------------------------------------------------------------------------- Comments for file: table2.dat -------------------------------------------------------------------------------- The table is formatted as a repeating sequence of passband-specific limb-darkening coefficients for each of the 410 Kurucz (1991) stellar atmosphere models with solar chemical abundances. The first record lists the effective temperature, the logarithm of the surface gravity, and a multiple of the solar abundance (always 1.00). A blank record follows, and then records containing the coefficients of the linear law, logarithmic law and square root law for each of the following passbands: bolometric, Stromgren uvby, Johnson UVBRN and Cousins R(c) and I(c). See section 4 of the printed paper for references to the transmission and response curves used in producing Table 2. Following each set of coefficients are two blank records and then the sequence repeats for the next set. Note that this format is not compatible with formatting in FITS ASCII tables format. -------------------------------------------------------------------------------- Byte-by-byte Description of file: table2.dat, Header Record -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1-16 16X --- --- ' Teff =' 17-22 I6 K Teff Effective temperature 23-34 12X --- --- ' K, log g =' 35-38 F4.1 --- log_g Logarithm of the surface gravity 39-63 25X --- --- ', 1.00 x Solar Abundance' -------------------------------------------------------------------------------- Byte-by-byte Description of file: table2.dat, Passband-specific record -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 5 A5 --- Band Passband 6- 8 3X --- --- Blank 9-13 F5.3 --- lin_x Linear limb-darkening coefficient, x 14-15 2X --- --- ' (' 16-21 F6.4 --- lin_Q *Quality factor, Q 22 1X --- --- ')' 23-31 F9.3 --- log_x Logarithmic law x coefficient 32-38 F7.3 --- log_y Logarithmic law y coefficient 39-40 2X --- --- ' (' 41-46 F6.4 --- log_Q Quality factor, Q, for logarithmic law coeff. 47 1X --- --- ')' 48-56 F9.3 --- sqr_x Square root law x coefficient 57-63 F7.3 --- sqr_y Square root law y coefficient 64-65 2X --- --- ' (' 66-71 F6.4 --- sqr_Q Quality factor, Q, for square root law coeff. 72 1X --- --- ')' -------------------------------------------------------------------------------- Notes for file: table2.dat, Passband-specific record -------------------------------------------------------------------------------- lin_Q: Quality factor, Q, as defined in section 3 of the printed paper. This number may help in choosing which limb-darkening law to use in any particular case. -------------------------------------------------------------------------------- Comments for files: model.001 to model.410 -------------------------------------------------------------------------------- This table is stored as 410 individual files, named MODEL.001, MODEL.002, ..., MODEL.410. Each file contains the monochromatic coefficients for each of the 1221 wavelength values of Kurucz's (1991) models (from 9.09 nm to 160 microns), together with intensities I(lambda,1). In particular, coefficients for large parts of the UV have never been published before and are now available. They may be of interest when analyzing satellite observations of stars and stellar systems. Each file is formatted as a repeating sequence of monochromatic limb-darkening coefficients. The first record lists the effective temperature and the logarithm of the surface gravity. A blank record follows, then a record giving the bolometric coefficients for this model (see Table 1), then another blank line. The remainder of the file contains the records with the coefficients of the linear law, logarithmic law and square root law, and the intensities I(lambda,1) for each of the specific wavelengths. Note that this format is not compatible with formatting in FITS ASCII tables format. -------------------------------------------------------------------------------- Byte-by-byte Description of files: model.001 to model.410, Header Records -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1-11 11X --- --- ' Teff =' 12-17 I6 K Teff Effective temperature 18-29 12X --- --- ' K, log g =' 30-33 F4.1 --- log_g Logarithm of the surface gravity 34-95 62X --- --- Additional info. constant from file to file -------------------------------------------------------------------------------- Byte-by-byte Description of files: model.001 to model.410, Bolometric coeff. -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1-11 11X --- --- ' bolometric' 12-20 F9.3 --- lin_x Linear limb-darkening coefficient, x 21-22 2X --- --- ' (' 23-28 F6.4 --- lin_Q Quality factor, Q, for the linear coefficient 29 1X --- --- ')' 30-38 F9.3 --- log_x Logarithmic law x coefficient 39-45 F7.3 --- log_y Logarithmic law y coefficient 46-47 2X --- --- ' (' 48-53 F6.4 --- log_Q Quality factor, Q, for logarithmic law coeff. 54 1X --- --- ')' 55-63 F9.3 --- sqr_x Square root law x coefficient 64-70 F7.3 --- sqr_y Square root law y coefficient 71-72 2X --- --- ' (' 73-78 F6.4 --- sqr_Q Quality factor, Q, for square root law coeff. 79 1X --- --- ')' -------------------------------------------------------------------------------- Byte-by-byte Description of files: model.001 to model.410, Monochromatic coeff. -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1-11 F11.2 nm Lambda Wavelength, lambda 12-20 F9.3 --- lin_x Linear limb-darkening coefficient, x 21-22 2X --- --- ' (' 23-28 F6.4 --- lin_Q Quality factor, Q, for the linear coefficient 29 1X --- --- ')' 30-38 F9.3 --- log_x Logarithmic law x coefficient 39-45 F7.3 --- log_y Logarithmic law y coefficient 46-47 2X --- --- ' (' 48-53 F6.4 --- log_Q Quality factor, Q, for logarithmic law coeff. 54 1X --- --- ')' 55-63 F9.3 --- sqr_x Square root law x coefficient 64-70 F7.3 --- sqr_y Square root law y coefficient 71-72 2X --- --- ' (' 73-78 F6.4 --- sqr_Q Quality factor, Q, for square root law coeff. 79 1X --- --- ')' 80-95 E16.3 --- Int Intensity [Units are: erg/s/cm^2/ster/nm] -------------------------------------------------------------------------------- ================================================================================ (End) Lee Brotzman [ADS] 20-Mar-1995