J/A+A/634/A93 Limb-darkening coefficients for compact stars (Claret+, 2020)
Gravity and limb-darkening coefficients for compact stars:
DA, DB and DBA eclipsing white dwarfs.
Claret A., Cukanovaite E., Burdge K., Tremblay P.-E., Parsons S., Marsh T.R.
<Astron. Astrophys. 634, A93 (2020)>
=2020A&A...634A..93C 2020A&A...634A..93C (SIMBAD/NED BibCode)
ADC_Keywords: Models, atmosphere ; Photometry, SDSS ; Photometry, UBVRI
Keywords: binaries: eclipsing - white dwarfs - stars: evolution -
planetary systems
Abstract:
The distribution of the specific intensity over the stellar disk is an
essential tool for modeling the light curves in eclipsing binaries,
planetary transits, and stellar diameters through interferometric
techniques, line profiles in rotating stars, gravitational
microlensing, etc. However, the available theoretical calculations are
mostly restricted to stars on the main sequence or the giant branch,
and very few calculations are available for compact stars.
The main objective of the present work is to extend these
investigations by
computing the gravity and limb-darkening coefficients for white dwarf
atmosphere models with hydrogen, helium, or mixed compositions (types
DA, DB, and DBA).
We computed gravity and limb-darkening coefficients for DA, DB, and
DBA white dwarfs atmosphere models, covering the transmission curves
of the Sloan, UBVRI, Kepler, TESS, and Gaia photometric systems.
Specific calculations for the HiPERCAM instrument were also carried
out. For all calculations of the limb-darkening coefficients we used
the least-squares method. Concerning the effects of tidal and
rotational distortions, we also computed for the first time the
gravity-darkening coefficients $y(λ)$ for white dwarfs using the
same models of stellar atmospheres as in the case of limb-darkening. A
more general differential equation was introduced to derive these
quantities, including the partial derivative
<∂lnIo(lambda)/∂lng)Teff.
Six laws were adopted to describe the specific intensity distribution:
linear, quadratic, square root, logarithmic, power-2, and a more
general one with four coefficients. The computations are presented for
the chemical compositions log[H/He]=-10.0 (DB), -2.0 (DBA) and He/H=0
(DA), with logg varying between 5.0 and 9.5 and effective temperatures
between 3750K-100000K. For effective temperatures higher than 40000K,
the models were also computed adopting nonlocal thermal equilibrium
(DA). The adopted mixing-length parameters are ML2/α= 0.8 (DA
case) and 1.25 (DB and DBA).
The results are presented in the form of 112 tables. Additional
calculations, such as for other photometric systems and/or different
values of log[H/He], logg, and Teff can be performed upon request.
Description:
For this study we computed three separate grids of 1D DA,
DB, and DBA models. Calculations for helium-dominated atmospheres are
motivated by the recent discovery of a DBA in a close binary system
(Burdge et al., 2019ApJ...886L..12B 2019ApJ...886L..12B).
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
tableu.dat 72 28686 u linear limb darkening coefficients,
Sloan (u'g'r'i'z'y'), UBVRI, HiPERCAM (ugriz)
and Kepler (Ke), TESS (Te), GAIA (Gbp, Gg, Grp)
tableab.dat 80 28686 *a,b quadratic limb darkening coefficients,
Sloan (u'g'r'i'z'y'), UBVRI, HiPERCAM (ugriz)
and Kepler (Ke), TESS (Te), GAIA (Gbp, Gg, Grp)
(SEE NOTE!!!)
tablecd.dat 80 28686 *c,d root-square limb darkening coefficients,
Sloan (u'g'r'i'z'y'), UBVRI, HiPERCAM (ugriz)
and Kepler (Ke), TESS (Te), GAIA (Gbp, Gg, Grp)
(SEE NOTE!!!)
tableef.dat 80 28686 *e,f logarithmic limb darkening coefficients,
Sloan (u'g'r'i'z'y'), UBVRI, HiPERCAM (ugriz)
and Kepler (Ke), TESS (Te), GAIA (Gbp, Gg, Grp)
(SEE NOTE!!!)
tablegh.dat 80 28686 *g,h power-2 limb darkening coefficients,
Sloan (u'g'r'i'z'y'), UBVRI, HiPERCAM (ugriz)
and Kepler (Ke), TESS (Te), GAIA (Gbp, Gg, Grp)
(SEE NOTE!!!)
tablea4.dat 96 28686 *a1,a2,a3,a4 limb darkening coefficients,
Sloan (u'g'r'i'z'y'), UBVRI, HiPERCAM (ugriz)
and Kepler (Ke), TESS (Te), GAIA (Gbp, Gg, Grp)
(SEE NOTE!!!)
tabley.dat 52 28686 *y GDCs,
Sloan (u'g'r'i'z'y'), UBVRI, HiPERCAM (ugriz)
and Kepler (Ke), TESS (Te), GAIA (Gbp, Gg, Grp)
(SEE NOTE!!!)
OriginalTab.tar 1097 182478 Original tables
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Note on tableab.dat tablecd.dat tableef.dat tablegh.dat tablea4.dat tabley.dat:
Please note that the Central Intensity listed in the tables must be multiplied
by 2 before utilizing it for observational analysis. Any other values listed
in the tables are not affected by this and can be used as listed.
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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/546/A14 : Limb-darkening for CoRoT, Kepler, Spitzer. I (Claret+, 2012)
J/A+A/552/A16 : Limb-darkening for CoRoT, Kepler, Spitzer. II (Claret+, 2013)
J/A+A/567/A3 : Limb-darkening coefficients for MOST (Claret+, 2014)
J/A+A/600/A30 : Limb-darkening for TESS satellite (Claret, 2017)
Byte-by-byte Description of file: tableu.dat
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Bytes Format Units Label Explanations
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1- 7 A7 --- Mod Model (G1)
9- 13 F5.2 [cm/s+2] logg Log10 Surface gravity
15- 22 F8.1 K Teff Effective temperature
24- 31 F8.4 [-] Z Log10 [H/He]
33- 39 F7.4 --- u Linear limb darkening coefficient u
41- 47 F7.4 --- sig chi2 of linear LDC
49- 60 E12.6 mW/m2/Hz/sr I Central intensity of linear LDC (G2)
62- 68 F7.4 --- Be Doppler beaming (BB) of linear LDC
70- 72 A3 --- Filter Filter
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Byte-by-byte Description of file: tableab.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 7 A7 --- Mod Model (G1)
9- 13 F5.2 [cm/s+2] logg Log10 Surface gravity
15- 22 F8.1 K Teff Effective temperature
24- 31 F8.4 [-] Z Log10 [H/He]
33- 39 F7.4 --- a Quadratic LDC coefficient a
41- 47 F7.4 --- b Quadratic LDC coefficient b
49- 55 F7.4 --- sig chi2 of quadratic LDC
57- 68 E12.6 mW/m2/Hz/sr I Central intensity of quadratic LDC (G2)
70- 76 F7.4 --- Be Doppler beaming (BB) of quadratic LDC
78- 80 A3 --- Filter Filter
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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- 7 A7 --- Mod Model (G1)
9- 13 F5.2 [cm/s+2] logg Log10 Surface gravity
15- 22 F8.1 K Teff Effective temperature
24- 31 F8.4 [-] Z Log10 [H/He]
33- 39 F7.4 --- c Root-square limb darkening coefficient c
41- 47 F7.4 --- d Root-square limb darkening coefficient d
49- 55 F7.4 --- sig chi2 for root-square LDC
57- 68 E12.6 mW/m2/Hz/sr I Central intensity for root-square LDC (G2)
70- 76 F7.4 --- Be Doppler beaming (BB) for root-square LDC
78- 80 A3 --- Filter Filter
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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- 7 A7 --- Mod Model (G1)
9- 13 F5.2 [cm/s+2] logg Log10 Surface gravity
15- 22 F8.1 K Teff Effective temperature
24- 31 F8.4 [-] Z Log10 [H/He]
33- 39 F7.4 --- e Logarithmic limb darkening coefficient e
41- 47 F7.4 --- f Logarithmic limb darkening coefficient f
49- 55 F7.4 --- sig chi2 for logarithmic LDC
57- 68 E12.6 mW/m2/Hz/sr I Central intensity for logarithmic LDC (G2)
70- 76 F7.4 --- Be Doppler beaming (BB) for logarithmic LDC
78- 80 A3 --- Filter Filter
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Byte-by-byte Description of file: tablegh.dat
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Bytes Format Units Label Explanations
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1- 7 A7 --- Mod Model (G1)
9- 13 F5.2 [cm/s+2] logg Log10 Surface gravity
15- 22 F8.1 K Teff Effective temperature
24- 31 F8.4 [-] Z Log10 [H/He]
33- 39 F7.4 --- g Power-2 limb darkening coefficient g
41- 47 F7.4 --- h Power-2 limb darkening coefficient h
49- 55 F7.4 --- sig chi2 of exponential LDC
57- 68 E12.6 mW/m2/Hz/sr I Central intensity of exponential LDC (G2)
70- 76 F7.4 --- Be Doppler beaming (BB) of exponential LDC
78- 80 A3 --- Filter Filter
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Byte-by-byte Description of file: tablea4.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 7 A7 --- Mod Model (G1)
9- 13 F5.2 [cm/s+2] logg Log10 Surface gravity
15- 22 F8.1 K Teff Effective temperature
24- 31 F8.4 [-] Z Log10 [H/He]
33- 39 F7.4 --- a1 4terms limb darkening coefficient a1
41- 47 F7.4 --- a2 4terms limb darkening coefficient a2
49- 55 F7.4 --- a3 4terms limb darkening coefficient a3
57- 63 F7.4 --- a4 4terms limb darkening coefficient a4
65- 71 F7.4 --- sig chi2 of 4terms LDC
73- 84 E12.6 mW/m2/Hz/sr I Central intensity of 4terms LDC (G2)
86- 92 F7.4 --- Be Doppler beaming (BB) of 4terms LDC
94- 96 A3 --- Filter Filter
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Byte-by-byte Description of file: tabley.dat
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Bytes Format Units Label Explanations
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1- 7 A7 --- Mod Model (G1)
10- 14 F5.2 [cm/s+2] logg Log10 Surface gravity
16- 23 F8.0 K Teff Effective temperature
25- 32 F8.4 [-] Z Log10 [H/He]
34- 40 F7.4 --- y1 GDC y1
42- 48 F7.4 --- y2 GDC y2
50- 52 A3 --- Filter Filter
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Global notes:
Note (G1): Models as follows:
DB = DB models
DBA = DBA models
DA = DA models
DA-NLTE = DA-NLTE models
Note (G2): units are ergs/cm2/s/Hz/ster.
For tables ab, cd, ef, gh, a4 and y, please note that the Central Intensity
listed in the tables must be multiplied by 2 before utilizing it for
observational analysis.
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Acknowledgements:
Antonio Claret, claret(at)iaa.es
History:
14-Feb-2020: on-line version with wrong CDS generated files
20-Mar-2020: corrected CDS generated files
(End) Patricia Vannier [CDS] 27-Jan-2020