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<ri:Resource created="2018-08-10T12:38:00Z" status="active" updated="2025-05-19T09:50:00Z" version="1.2" xmlns:ri="http://www.ivoa.net/xml/RegistryInterface/v1.0" xmlns:vr="http://www.ivoa.net/xml/VOResource/v1.0" xmlns:vs="http://www.ivoa.net/xml/VODataService/v1.1" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.ivoa.net/xml/VOResource/v1.0 http://vo.ari.uni-heidelberg.de/docs/schemata/VOResource.xsd http://www.ivoa.net/xml/VODataService/v1.1 http://vo.ari.uni-heidelberg.de/docs/schemata/VODataService.xsd" xsi:type="vs:CatalogService"><title>Power-2 limb-darkening law from STAGGER-grid</title><shortName>J/A+A/616/A39</shortName><identifier>ivo://CDS.VizieR/J/A+A/616/A39</identifier><altIdentifier>doi:10.26093/cds/vizier.36160039</altIdentifier><curation><publisher ivo-id="ivo://CDS">CDS</publisher><creator><name>Maxted P.F.L.</name></creator><date role="Updated">2018-09-26T07:09:29Z</date><date role="Created">2018-08-10T12:38:00Z</date><contact><name>CDS support team</name><address>CDS, Observatoire de Strasbourg, 11 rue de l'Universite, F-67000 Strasbourg, France</address><email>cds-question@unistra.fr</email></contact></curation><content><subject>eclipsing-binary-stars</subject><subject>astronomical-models</subject><subject>stellar-atmospheres</subject><description>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, I_{lambda}_({mu})=1-c(1-{mu}^{alpha}^), 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 I_{lambda}_({mu}) values. I use the transformed parameters h_1_=1-c(1-2^(-{alpha})^) and h_2_=c2^(-{alpha}^) 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 h_1_ and h_2_ resulting from the light curve analysis are found to be much less strongly correlated than the PPDs for c and {alpha}. The agreement between the computed and observed values of (h_1_, h_2_) 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 h_1_ and h_2_ 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 h_1_ and h_2_ based on my analysis of the Kepler light curves of 16 stars transiting exoplanets.</description><source format="bibcode">2018A&amp;A...616A..39M</source><referenceURL>https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/616/A39</referenceURL><type>Catalog</type><contentLevel>Research</contentLevel><relationship><relationshipType>IsServedBy</relationshipType><relatedResource ivo-id="ivo://CDS.VizieR/TAP">TAP VizieR generic service</relatedResource></relationship><relationship><relationshipType>related-to</relationshipType><relatedResource ivo-id="ivo://CDS.VizieR/J/A+A/573/A90">J/A+A/573/A90 : STAGGER-grid of 3D stellar models. IV. (Magic+, 2015)</relatedResource></relationship></content><rights>https://cds.unistra.fr/vizier-org/licences_vizier.html</rights><capability><interface xsi:type="vr:WebBrowser"><accessURL use="full">https://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/A+A/616/A39</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/A+A/616/A39</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/A+A/616/A39</mirrorURL></interface></capability><capability><interface xsi:type="vs:ParamHTTP"><accessURL use="base">https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/A+A/616/A39</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/votable?-source=J/A+A/616/A39</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/A+A/616/A39</mirrorURL><queryType>GET</queryType><resultType>text/xml+votable</resultType></interface></capability><capability standardID="ivo://ivoa.net/std/TAP#aux"><interface xsi:type="vs:ParamHTTP" role="std"><accessURL use="base">https://tapvizier.cds.unistra.fr/TAPVizieR/tap</accessURL></interface></capability><coverage><footprint ivo-id="ivo://ivoa.net/std/moc"/></coverage><tableset><schema><name>default</name><table><name>J/A+A/616/A39/table1</name><description>Specific intensity as function of mu</description><column><name>recno</name><description>Record number assigned by the VizieR team. Should Not be used for identification.</description><ucd>meta.record</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>X</name><description>Bandpass</description><ucd>meta.id;phot</ucd><dataType xsi:type="vs:VOTableType" arraysize="2*">char</dataType></column><column><name>Teff</name><description>Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>logg</name><description>Logarithm of surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>[Fe/H]</name><description>Metallicity [Fe/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>I(0.00)</name><description>Specific intensity I_{lambda}_({mu}=0.00)</description><ucd>spect.line.intensity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>I(0.01)</name><description>Specific intensity I_{lambda}_({mu}=0.01)</description><ucd>spect.line.intensity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>I(0.05)</name><description>Specific intensity I_{lambda}_({mu}=0.05)</description><ucd>spect.line.intensity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>I(0.10)</name><description>Specific intensity I_{lambda}_({mu}=0.10)</description><ucd>spect.line.intensity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>I(0.20)</name><description>Specific intensity I_{lambda}_({mu}=0.20)</description><ucd>spect.line.intensity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>I(0.30)</name><description>Specific intensity I_{lambda}_({mu}=0.30)</description><ucd>spect.line.intensity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>I(0.50)</name><description>Specific intensity I_{lambda}_({mu}=0.50)</description><ucd>spect.line.intensity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>I(0.70)</name><description>Specific intensity I_{lambda}_({mu}=0.70)</description><ucd>spect.line.intensity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>I(0.80)</name><description>Specific intensity I_{lambda}_({mu}=0.80)</description><ucd>spect.line.intensity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>I(0.90)</name><description>Specific intensity I_{lambda}_({mu}=0.90)</description><ucd>spect.line.intensity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>I(1.00)</name><description>Specific intensity I_{lambda}_({mu}=1.00)</description><ucd>spect.line.intensity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column></table><table><name>J/A+A/616/A39/table2</name><description>Optimized power-2 limb-darkening law parameters</description><column><name>recno</name><description>Record number assigned by the VizieR team. Should Not be used for identification.</description><ucd>meta.record</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>X</name><description>Bandpass</description><ucd>meta.id;phot</ucd><dataType xsi:type="vs:VOTableType" arraysize="2*">char</dataType></column><column><name>Teff</name><description>Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>logg</name><description>Logarithm of surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>[Fe/H]</name><description>Metallicity [Fe/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>c</name><description>c parameter</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>alpha</name><description>{alpha} parameter</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>h1</name><description>h_1_ (=1-c(1-2^(-{alpha})^) parameter</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>h2</name><description>h_2_ (=c2^(-{alpha}^) parameter</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column></table></schema></tableset></ri:Resource>