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<ri:Resource created="2022-01-17T13:42:25Z" 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>CHEOPS limb and gravity-darkening coefficients</title><shortName>J/other/RNAAS/5.</shortName><identifier>ivo://CDS.VizieR/J/other/RNAAS/5.13</identifier><curation><publisher ivo-id="ivo://CDS">CDS</publisher><creator><name>Claret A.</name></creator><date role="Updated">2022-05-18T13:55:31Z</date><date role="Created">2022-01-17T13:42:25Z</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>astronomical-models</subject><subject>stellar-atmospheres</subject><subject>photometry</subject><description>The goal of this Research Note is to provide the theoretical calculations of the limb-darkening coefficients (LDC) and gravity-darkening coefficients (GDC) for the space mission CHEOPS. We use two stellar atmosphere models: ATLAS (plane-parallel) and PHOENIX with spherical symmetry covering a wide range of effective temperatures, local gravities, and hydrogen/metal. These grids cover 19 metallicities ranging from 10^-5^ up to 10^+1^ solar abundances, 0&lt;=logg&lt;=6.0 and 2300K&lt;=Te&lt;=50000K. The specific intensity distribution was fitted using six approaches: linear, quadratic, square root, logarithmic, power-2, and a series with four terms. The calculations of the gravity darkening coefficient were performed for both stellar atmosphere models adopting an improved formulation.</description><source format="bibcode">2021RNAAS...5...13C</source><referenceURL>https://cdsarc.cds.unistra.fr/viz-bin/cat/J/other/RNAAS/5.13</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/other/RNAAS/5.13</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/other/RNAAS/5.13</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/other/RNAAS/5.13</mirrorURL></interface></capability><capability><interface xsi:type="vs:ParamHTTP"><accessURL use="base">https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/other/RNAAS/5.13</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/votable?-source=J/other/RNAAS/5.13</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/other/RNAAS/5.13</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/other/RNAAS/5.13/table1</name><description>u linear limb darkening coefficients PHOENIX-COND models v.tu=2.0 km/s for CHEOPS (LSM)</description><column><name>logg</name><description>Surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</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>Teff</name><description>Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>ZR</name><description>log10 [metal/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>u</name><description>linear limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>mu-cri</name><description>{mu}_cri_ (CHEOPS)</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>chi2</name><description>chi2</description><ucd>stat.fit.chi2</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column></table><table><name>J/other/RNAAS/5.13/table2</name><description>a,b quadratic limb darkening coefficients PHOENIX-COND models, v.tu=2.0 km/s for CHEOPS (LSM)</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>logg</name><description>Surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</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>ZR</name><description>log10 [metal/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>a</name><description>quadrat limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>b</name><description>quadrat limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>mu-cri</name><description>{mu}_cri_ (CHEOPS)</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>chi2</name><description>chi2</description><ucd>stat.fit.chi2</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column></table><table><name>J/other/RNAAS/5.13/table3</name><description>c,d square-root limb darkening coefficients PHOENIX-COND models v.tu=2 km/s for CHEOPS (LSM)</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>logg</name><description>Surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</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>ZR</name><description>log10 [metal/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>c</name><description>sqrt limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>d</name><description>sqrt limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>mu-cri</name><description>{mu}_cri_ (CHEOPS)</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>chi2</name><description>chi2</description><ucd>stat.fit.chi2</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column></table><table><name>J/other/RNAAS/5.13/table4</name><description>e,f logarithmic limb darkening coefficients PHOENIX-COND models v.tu=2.0 km/s for CHEOPS (LSM)</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>logg</name><description>Surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</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>ZR</name><description>log10 [metal/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>e</name><description>loga limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>f</name><description>loga limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>mu-cri</name><description>{mu}_cri_ (CHEOPS)</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>chi2</name><description>chi2</description><ucd>stat.fit.chi2</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column></table><table><name>J/other/RNAAS/5.13/table5</name><description>g,h power-2 limb darkening coefficients PHOENIX-COND models v.tu=2.0 km/s for CHEOPS (LSM)</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>logg</name><description>Surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</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>ZR</name><description>log10 [metal/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>g</name><description>power-2 limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>h</name><description>power-2 limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>mu-cri</name><description>{mu}_cri_ (CHEOPS)</description><ucd>stat.fit.param</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>chi2</name><description>chi2</description><ucd>stat.fit.chi2</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column></table><table><name>J/other/RNAAS/5.13/table6</name><description>a_1,a_2,a_3,a_4 limb darkening coefficients PHOENIX-COND models v.tu=2.0 km/s for CHEOPS (LSM)</description><column><name>recno</name><description>Record number assigned by the VizieR team. 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Should Not be used for identification.</description><ucd>meta.record</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>logg</name><description>Surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</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>ZR</name><description>log [metal/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Vel</name><description>microturbulent velocity</description><unit>km/s</unit><ucd>phys.veloc</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>u</name><description>linear limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>chi2</name><description>chi2</description><ucd>stat.fit.chi2</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column></table><table><name>J/other/RNAAS/5.13/table8</name><description>a,b quadratic limb darkening coefficients ATLAS models, all metallicities, v.tu=2,0,1,4,8 km/s for CHEOPS (LSM)</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>logg</name><description>Surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</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>ZR</name><description>log [metal/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Vel</name><description>microturbulent velocity</description><unit>km/s</unit><ucd>phys.veloc</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>a</name><description>quadrat limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>b</name><description>quadrat limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>chi2</name><description>chi2</description><ucd>stat.fit.chi2</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column></table><table><name>J/other/RNAAS/5.13/table9</name><description>c,d square-root limb darkening coefficients ATLAS models, all metallicities, v.tu=2,0,1,4,8 km/s for CHEOPS (LSM)</description><column><name>recno</name><description>Record number assigned by the VizieR team. 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Should Not be used for identification.</description><ucd>meta.record</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>logg</name><description>Surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</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>ZR</name><description>log [metal/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Vel</name><description>microturbulent velocity</description><unit>km/s</unit><ucd>phys.veloc</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>e</name><description>loga limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>f</name><description>loga limb darkening coefficient LDC (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>chi2</name><description>chi2</description><ucd>stat.fit.chi2</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column></table><table><name>J/other/RNAAS/5.13/table11</name><description>g,h power-2 limb darkening coefficients ATLAS models, all metallicities, v.tu=2,0,1,4,8 km/s for CHEOPS (LSM)</description><column><name>Vel</name><description>microturbulent velocity</description><unit>km/s</unit><ucd>phys.veloc</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>g</name><description>power-2 limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>h</name><description>power-2 limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>chi2</name><description>chi2</description><ucd>stat.fit.chi2</ucd><dataType xsi:type="vs:VOTableType">double</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>logg</name><description>Surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</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>ZR</name><description>log [metal/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column></table><table><name>J/other/RNAAS/5.13/table12</name><description>a_1,a_2,a_3,a_4 limb darkening coefficients ATLAS models, all metallicities, v.tu=2,0,1,4,8 km/s for CHEOPS (LSM)</description><column><name>chi2</name><description>chi2</description><ucd>stat.fit.chi2</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>a4</name><description>4-terms limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</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>logg</name><description>Surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</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>ZR</name><description>log [metal/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Vel</name><description>microturbulent velocity</description><unit>km/s</unit><ucd>phys.veloc</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>a1</name><description>4-terms limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>a2</name><description>4-terms limb darkening coefficient(CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>a3</name><description>4-terms limb darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column></table><table><name>J/other/RNAAS/5.13/table13</name><description>y1,y2 gravity darkening coefficients PHOENIX-COND models, v.tu=2.0 km/s for CHEOPS</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>logg</name><description>Log10 Surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Teff</name><description>Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>ZR</name><description>log10 [metal/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>y1</name><description>gravity darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>y2</name><description>gravity darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column></table><table><name>J/other/RNAAS/5.13/table14</name><description>y1,y2 gravity darkening coefficients ATLAS models, all metallicities, v.tu=2,0,1,4,8 km/s for CHEOPS</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>ZR</name><description>log10 [metal/H]</description><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Vel</name><description>microturbulent velocity</description><unit>km/s</unit><ucd>phys.veloc</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>logg</name><description>log10 Surface gravity</description><unit>log(cm.s**-2)</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>logTeff</name><description>log10 Effective temperature</description><unit>log(K)</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>y1</name><description>gravity darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>y2</name><description>gravity darkening coefficient (CHEOPS)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column></table></schema></tableset></ri:Resource>