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<ri:Resource created="1999-02-27T12:39:55Z" 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>Limb-darkening coefficients in binaries</title><shortName>J/AJ/106/2096</shortName><identifier>ivo://CDS.VizieR/J/AJ/106/2096</identifier><altIdentifier>doi:10.26093/cds/vizier.51062096</altIdentifier><curation><publisher ivo-id="ivo://CDS">CDS</publisher><creator><name>VAN HAMME W.</name></creator><date role="Updated">2023-04-06T16:50:04Z</date><date role="Created">1999-02-27T12:39:55Z</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>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 {mu}m) and tables of passband-specific coefficients for commonly used photometric filters.</description><source format="bibcode">1993AJ....106.2096V</source><referenceURL>https://cdsarc.cds.unistra.fr/viz-bin/cat/J/AJ/106/2096</referenceURL><type>Catalog</type><contentLevel>Research</contentLevel><relationship><relationshipType>IsServedBy</relationshipType><relatedResource ivo-id="ivo://CDS.VizieR/TAP">TAP VizieR generic service</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/AJ/106/2096</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/AJ/106/2096</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/AJ/106/2096</mirrorURL></interface></capability><capability><interface xsi:type="vs:ParamHTTP"><accessURL use="base">https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/AJ/106/2096</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/votable?-source=J/AJ/106/2096</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/AJ/106/2096</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/AJ/106/2096/table1</name><description>Bolometric limb-darkening coefficients</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>Model</name><description>Model number</description><ucd>meta.id;stat.fit</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>Teff</name><description>Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>log(g)</name><description>Logarithm of the surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>xBol</name><description>Bolometric linear limb-darkening coefficient x</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>QBol</name><description>Quality factor (1)</description><ucd>meta.code.qual</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>xLog</name><description>Logarithmic law x coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>yLog</name><description>Logarithmic law y coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>QLog</name><description>Quality factor (1)</description><ucd>meta.code.qual</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>xSqu</name><description>Square root law x coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>ySqu</name><description>Square root law y coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>QSqu</name><description>Quality factor (1)</description><ucd>meta.code.qual</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column></table><table><name>J/AJ/106/2096/table2</name><description>Passband-specific limb-darkening coefficients</description><column><name>ySqu</name><description>Square root law y coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>QSqu</name><description>Quality factor (1)</description><ucd>meta.code.qual</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><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>Model</name><description>Model number</description><ucd>meta.id;stat.fit</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>Teff</name><description>Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>log(g)</name><description>Logarithm of the surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Pass</name><description>Passband (2)</description><ucd>meta.code</ucd><dataType xsi:type="vs:VOTableType" arraysize="4*">char</dataType></column><column><name>xLin</name><description>Linear limb-darkening coefficient</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>QLin</name><description>Quality factor (1)</description><ucd>meta.code.qual</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>xLog</name><description>Logarithmic law x coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>yLog</name><description>Logarithmic law y coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>QLog</name><description>Quality factor (1)</description><ucd>meta.code.qual</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>xSqu</name><description>Square root law x coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column></table><table><name>J/AJ/106/2096/table3a</name><description>Models parameters</description><column><name>Model</name><description>Model number</description><ucd>meta.id;stat.fit</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><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>Teff</name><description>Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>log(g)</name><description>Logarithm of the surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>A</name><description>Abundance (always solar abundance)</description><unit>Sun</unit><ucd>phys.abund</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Vturb</name><description>Microturbulent velocity</description><unit>km/s</unit><ucd>phys.veloc.microTurb</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>l/H</name><description>[]? Convective parameter</description><ucd>stat.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column></table><table><name>J/AJ/106/2096/table3b</name><description>Bolometric coefficients</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>Model</name><description>Model number</description><ucd>meta.id;stat.fit</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>lambda</name><description>[]? Wavelength</description><unit>nm</unit><ucd>em.wl</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>xBol</name><description>Linear limb-darkening coefficient</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>QBol</name><description>Quality factor (1)</description><ucd>meta.code.qual</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>xLog</name><description>Logarithmic law x coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>yLog</name><description>Logarithmic law y coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>QLog</name><description>Quality factor (1)</description><ucd>meta.code.qual</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>xSqu</name><description>Square root law x coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>ySqu</name><description>Square root law y coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>QSqu</name><description>Quality factor (1)</description><ucd>meta.code.qual</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>I</name><description>? Intensity, I(lambda, mu=1)</description><unit>mW.m**-2.sr**-1.nm**-1</unit><ucd>spect.line.intensity</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column></table><table><name>J/AJ/106/2096/table3c</name><description>Monochromatic coefficients</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>Model</name><description>Model number</description><ucd>meta.id;stat.fit</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>lambda</name><description>[]? Wavelength</description><unit>nm</unit><ucd>em.wl</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>xBol</name><description>Linear limb-darkening coefficient</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>QBol</name><description>Quality factor (1)</description><ucd>meta.code.qual</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>xLog</name><description>Logarithmic law x coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>yLog</name><description>Logarithmic law y coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>QLog</name><description>Quality factor (1)</description><ucd>meta.code.qual</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>xSqu</name><description>Square root law x coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>ySqu</name><description>Square root law y coefficient</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>QSqu</name><description>Quality factor (1)</description><ucd>meta.code.qual</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>I</name><description>? 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