J/A+A/641/A157 Limb-darkening coefficients for white dwarfs (Claret+, 2020)
Doppler beaming factors for white dwarfs, main sequence stars, and giant stars.
Limb-darkening coefficients for 3D (DA and DB) white dwarfs models.
Claret A., Cukanovaite E., Burdge K., Tremblay P.-E., Parsons S., Marsh T.R.
<Astron. Astrophys. 641, A157 (2020)>
=2020A&A...641A.157C 2020A&A...641A.157C (SIMBAD/NED BibCode)
ADC_Keywords: Models, atmosphere ; Photometry, SDSS ; Photometry, UBVRI
Keywords: white dwarfs - binaries: eclipsing - stars: atmospheres
Abstract:
Systematic theoretical calculations of Doppler beaming factors are
very scarce in the literature, mainly in the case of white dwarfs.
Additionally, there are no specific calculations for the
limb-darkening coefficients of 3D white dwarf models. The objective of
this research is to provide the astronomical community with Doppler
beaming calculations for a wide range of effective temperatures, local
gravities and hydrogen/metal content for white dwarfs as well as stars
on both the main sequence and the giant branch. In addition, for the
first time we also present the theoretical calculations of the
limb-darkening coefficients for 3D white dwarfs models. We computed
Doppler beaming factors for DA, DB and DBA white dwarf models, as well
as for main sequence and giant stars covering the transmission curves
of the Sloan, UBVRI, HiPERCAM, Kepler, TESS, and Gaia photometric
systems. The calculations of the limb-darkening coefficients for 3D
models were carried out using the least-squares method for the same
mentioned photometric systems. The input physics of the white dwarf
models for which we have computed the Doppler beaming factors are:
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
in the range 3750-100000K. The beaming factors were also calculated
assuming non-local thermodynamic equilibrium (NLTE) for the case of DA
white dwarfs with Teff>40000K. For the mixing-length parameters we
adopted ML2/α=0.8 (DA case) and 1.25 (DB and DBA). The Doppler
beaming factors for main sequence and giant stars were computed using
the ATLAS9 version, characterized by metallicities ranging from [-2.5,
0.2] solar abundances, with logg varying between 0 and 5.0 and
effective temperatures between 3500-50000K. The adopted microturbulent
velocity for these models was 2.0km/s. The limb-darkening coefficients
were computed for 3D DA and DB white dwarf models calculated with the
CO5BOLD radiation-hydrodynamics code. The parameter range covered by
3D DA models spans logg values between 7.0 and 9.0, Teff between 6000
and 15000K and He/H=0. The 3D DB models cover a similar parameter
range of logg between 7.5 and 9.0, Teff between 12000 and 34000K and
logH/He=-10.0. We adopted six laws for the computation of the
limb-darkening coefficients: linear, quadratic, square root,
logarithmic, power-2, and a general one with four coefficients. The
beaming factor calculations which use realistic models of stellar
atmospheres show that the black body approximation is not accurate,
mainly for the filters u, u', U, g, g' and B. The black body approach
is only valid for high effective temperatures and/or long effective
wavelengths. Therefore, for more accurate analyses of light curves, we
recommend the use of the beaming factors presented in this paper.
Concerning limb-darkening, the distribution of specific intensities
for 3D models indicates that in general these models are less bright
towards the limb than their 1D counterparts, which implies steeper
profiles. To describe these intensities better, we recommend the use
of the four-terms law (also for 1D models) given the level of
precision that is being achieved with Earth-based instruments, as well
as space missions such as Kepler, TESS or PLATO in the future.
Description:
Claret et al. (2020A&A...634A..93C 2020A&A...634A..93C, Cat. J/A+A/634/A93) derived LDCs
for a set of one-dimensional DA, DB, and DBA white dwarf models. Here
we compare these results to 3D model atmospheres for DA white dwarfs
(DA-3D; Tremblay et al. 2013A&A...559A.104T 2013A&A...559A.104T) in the ranges
logg=7.0-9.0 and Teff=6000-15000K, and for DB/DBA white dwarfs
(DBA-3D; Cukanovaite 2018MNRAS.481.1522C 2018MNRAS.481.1522C, 2019MNRAS.490.1010C 2019MNRAS.490.1010C in the
ranges logg=7.5-9.0 and Teff=12000-34000K.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
tablebe.dat 46 108654 Doppler beaming for WD-DA, WD-DB, WD-DBA,
WD-DA-NLTE and ATLAS model,
Sloan (u'g'r'i'z'y'), UBVRI, HiPERCAM (ugriz)
and Kepler (Ke), TESS (Te), GAIA (Gbp, Gg, Grp)
tableu.dat 69 2436 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 78 2436 a,b quadratic darkening coefficients,
Sloan (u'g'r'i'z'y'), UBVRI, HiPERCAM (ugriz)
and Kepler (Ke), TESS (Te), GAIA (Gbp, Gg, Grp)
tablecd.dat 78 2436 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)
tableef.dat 78 2436 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)
tablegh.dat 78 2436 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)
tablea4.dat 96 2436 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)
OriginalTab.tar 1128 18611 Original tables
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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)
J/A+A/634/A93 : Limb-darkening coefficients for compact stars (Claret+, 2020)
Byte-by-byte Description of file (#): tablebe.dat
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Bytes Format Units Label Explanations
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1- 10 A10 --- Model Model (G1)
12- 14 A3 --- Filt Filter (G2)
15- 19 F5.2 [cm/s2] logg Log10 Surface gravity
21- 28 F8.1 K Teff Effective temperature
30- 37 F8.4 --- Z Log10 [H/He]
39- 46 F8.4 --- Be Doppler beaming for Fitler band
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Byte-by-byte Description of file (#): tableu.dat
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Bytes Format Units Label Explanations
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1- 10 A10 --- Model [WD-DA-3D WD-DB-3D] Model (G1)
12- 14 A3 --- Filt Filter (G2)
16- 20 F5.2 [cm/s2] logg Log10 Surface gravity
22- 29 F8.1 K Teff Effective temperature
31- 38 F8.4 --- Z Log10 [H/He]
40- 47 F8.4 --- u Linear limb darkening coefficient u
49- 56 F8.4 --- sig chi2 of linear LDC
58- 69 E12.6 mW/m2/Hz/sr I Central intensity of linear LDC (G3)
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Byte-by-byte Description of file (#): tableab.dat
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Bytes Format Units Label Explanations
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1- 10 A10 --- Model [WD-DA-3D WD-DB-3D] Model (G1)
12- 14 A3 --- Filt Filter (G2)
16- 20 F5.2 [cm/s2] logg Log10 Surface gravity
22- 29 F8.1 K Teff Effective temperature
31- 38 F8.4 --- Z Log10 [H/He]
40- 47 F8.4 --- a quadratic LDC coefficient a
49- 56 F8.4 --- b quadratic LDC coefficient b
58- 65 F8.4 --- sig chi2 of quadratic LDC
67- 78 E12.6 mW/m2/Hz/sr I Central intensity of quadratic LDC (G3)
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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- 10 A10 --- Model [WD-DA-3D WD-DB-3D] Model (G1)
12- 14 A3 --- Filt Filter (G2)
16- 20 F5.2 [cm/s2] logg Log10 Surface gravity
22- 29 F8.1 K Teff Effective temperature
31- 38 F8.4 --- Z Log10 [H/He]
40- 47 F8.4 --- c Root-square limb darkening coefficient c
49- 56 F8.4 --- d Root-square limb darkening coefficient d
58- 65 F8.4 --- sig chi2 for root-square LDC
67- 78 E12.6 mW/m2/Hz/sr I Central intensity for root-square LDC (G3)
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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- 10 A10 --- Model [WD-DA-3D WD-DB-3D] Model (G1)
12- 14 A3 --- Filt Filter (G2)
16- 20 F5.2 [cm/s2] logg Log10 Surface gravity
22- 29 F8.1 K Teff Effective temperature
31- 38 F8.4 --- Z Log10 [H/He]
40- 47 F8.4 --- e Logarithmic limb darkening coefficient e
49- 56 F8.4 --- f Logarithmic limb darkening coefficient f
58- 65 F8.4 --- sig chi2 for logarithmic LDC
67- 78 E12.6 mW/m2/Hz/sr I Central intensity for logarithmic LDC (G3)
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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- 10 A10 --- Model [WD-DA-3D WD-DB-3D] Model (G1)
12- 14 A3 --- Filt Filter (G2)
16- 20 F5.2 [cm/s2] logg Log10 Surface gravity
22- 29 F8.1 K Teff Effective temperature
31- 38 F8.4 --- Z Log10 [H/He]
40- 47 F8.4 --- g Power-2 limb darkening coefficient g
49- 56 F8.4 --- h Power-2 limb darkening coefficient h
58- 65 F8.4 --- sig chi2 of exponential LDC
67- 78 E12.6 mW/m2/Hz/sr I Central intensity of exponential LDC (G3)
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Byte-by-byte Description of file (#): tablea4.dat
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Bytes Format Units Label Explanations
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1- 10 A10 --- Model [WD-DA-3D WD-DB-3D] Model (G1)
12- 14 A3 --- Filt Filter (G2)
16- 20 F5.2 [cm/s2] logg Log10 Surface gravity
22- 29 F8.1 K Teff Effective temperature
31- 38 F8.4 --- Z Log10 [H/He]
40- 47 F8.4 --- a1 4terms limb darkening coefficient a1
49- 56 F8.4 --- a2 4terms limb darkening coefficient a2
58- 65 F8.4 --- a3 4terms limb darkening coefficient a3
67- 74 F8.4 --- a4 4terms limb darkening coefficient a4
76- 83 F8.4 --- sig chi2 of 4terms LDC
85- 96 E12.6 mW/m2/Hz/sr I Central intensity of 4terms LDC (G3)
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Global notes:
Note (G1): Models as follows:
WD-DA-3D = WD DA 3D models
WD-DB-3D = WD DB 3D models
WD-DB = WD DB models
WD-DBA = WD DBA models
WD-DA = WD DA models
WD-DA-NLTE = WD DA-NLTE models
ATLAS = ATLAS model
Note (G2): Filters:
Ke = Kepler band
Tes = Tess band
Gb = Gaia Gbp band
G = Gaia G band
Gr = Gaia Grb band
u = HiPERCAM u band
g = HiPERCAM g band
r = HiPERCAM r band
i = HiPERCAM i band
z = HiPERCAM z band
u' = SDSS u' band
g' = SDSS g' band
r' = SDSS r' band
i' = SDSS i' band
z' = SDSS z' band
U = U band
B = B band
V = V band
R = R band
I = I band
Note (G3): units are ergs/cm2/s/Hz/ster.
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Acknowledgements:
Antonio Claret, claret(at)iaa.es
(End) Patricia Vannier [CDS] 29-Jul-2020