J/A+A/616/A39 Power-2 limb-darkening law from STAGGER-grid (Maxted, 2018)
Comparison of the power-2 limb-darkening law from the STAGGER-grid to Kepler
light curves of transiting exoplanets.
Maxted P.F.L.
<Astron. Astrophys. 616, A39 (2018)>
=2018A&A...616A..39M 2018A&A...616A..39M (SIMBAD/NED BibCode)
ADC_Keywords: Binaries, eclipsing ; Stars, normal ; Models, atmosphere
Keywords: techniques: photometric - binaries: eclipsing -
stars: fundamental parameters
Abstract:
Inaccurate limb-darkening models can be a significant source of error
in the analysis of the light curves for transiting exoplanet and
eclipsing binary star systems, particularly for high-precision light
curves at optical wavelengths. The power-2 limb-darkening law,
Iλ(µ)=1-c(1-µα), has recently been proposed as a
good compromise between complexity and precision in the treatment of
limb-darkening. My aim is to develop a practical implementation of the
power-2 limb-darkening law and to quantify the accuracy of this
implementation. I have used synthetic spectra based on the 3D stellar
atmosphere models from the Stagger-grid to compute the limb- darkening
for several passbands (UBVRI, CHEOPS, TESS, Kepler, etc.). The
parameters of the power-2 limb-darkening laws are optimized using a
least-squares fit to a simulated light curve computed directly from
the tabulated Iλ(µ) values. I use the transformed
parameters h1=1-c(1-2(-α)) and h2=c2(-α) to
directly compare these optimized limb-darkening parameters to the limb
darkening measured from Kepler light curves of 16 transiting exoplanet
systems. The posterior probability distributions (PPDs) of the
transformed parameters h1 and h2 resulting from the light curve
analysis are found to be much less strongly correlated than the PPDs
for c and α. The agreement between the computed and observed
values of (h1, h2) is generally very good but there are
significant differences between the observed and computed values for
Kepler-17, the only star in the sample that shows significant
variability between the eclipses due to magnetic activity (star
spots). The tabulation of h1 and h2 provided here can be used to
accurately model the light curves of transiting exoplanets. I also
provide estimates of the priors that should be applied to transformed
parameters h1 and h2 based on my analysis of the Kepler light
curves of 16 stars transiting exoplanets.
Description:
The power-2 limb-darkening law can be recommended for the analysis of
light curves for transiting exoplanet systems and binary stars for
stars with Teff, logg and [Fe/H] within the model grid range studied
here. Tabulations of the parameters of the power-2 limb-darkening law
have been provided and tested against very high-quality observations
of transiting exoplanet systems obtained with Kepler. These
observations have been used to quantify the uncertainties in the
parameters h1 and h2 for dwarf stars with [Fe/H]≥0 showing weak
magnetic activity. There may be a small bias in the computed values of
h1 and h2 compared to the best-fit values for magneticically
active stars, but this needs further investigation. Further work is
also needed to quantify the uncertainties in h1 and h2 for metal
poor stars and red giants.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table1.dat 89 2800 Specific intensity as function of mu
table2.dat 41 2800 Optimized power-2 limb-darkening law parameters
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See also:
J/A+A/573/A90 : STAGGER-grid of 3D stellar models. IV. (Magic+, 2015)
Byte-by-byte Description of file: table1.dat
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Bytes Format Units Label Explanations
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1- 2 A2 --- X Bandpass
4- 9 F6.1 K Teff Effective temperature
11- 13 F3.1 [cm/s2] logg Logarithm of surface gravity
15- 18 F4.1 --- [Fe/H] Metallicity [Fe/H]
20- 22 F3.1 --- I(0.00) Specific intensity Iλ(µ=0.00)
24- 29 F6.4 --- I(0.01) Specific intensity Iλ(µ=0.01)
31- 36 F6.4 --- I(0.05) Specific intensity Iλ(µ=0.05)
38- 43 F6.4 --- I(0.10) Specific intensity Iλ(µ=0.10)
45- 50 F6.4 --- I(0.20) Specific intensity Iλ(µ=0.20)
52- 57 F6.4 --- I(0.30) Specific intensity Iλ(µ=0.30)
59- 64 F6.4 --- I(0.50) Specific intensity Iλ(µ=0.50)
66- 71 F6.4 --- I(0.70) Specific intensity Iλ(µ=0.70)
73- 78 F6.4 --- I(0.80) Specific intensity Iλ(µ=0.80)
80- 85 F6.4 --- I(0.90) Specific intensity Iλ(µ=0.90)
87- 89 F3.1 --- I(1.00) Specific intensity Iλ(µ=1.00)
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Byte-by-byte Description of file: table2.dat
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Bytes Format Units Label Explanations
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1- 2 A2 --- X Bandpass
4- 9 F6.1 K Teff Effective temperature
11- 13 F3.1 [cm/s2] logg Logarithm of surface gravity
15- 18 F4.1 --- [Fe/H] Metallicity [Fe/H]
20- 24 F5.3 --- c c parameter
26- 30 F5.3 --- alpha α parameter
32- 36 F5.3 --- h1 h1 (=1-c(1-2(-α)) parameter
38- 41 F4.2 --- h2 h2 (=c2(-α) parameter
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Acknowledgements:
Pierre F.L. Maxted, p.maxted(at)keele.ac.uk
(End) Pierre F.L. Maxted [Univ. Keele], Patricia Vannier [CDS] 25-Apr-2018