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<ri:Resource created="2011-04-05T08:27:14Z" 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</title><shortName>J/A+A/529/A75</shortName><identifier>ivo://CDS.VizieR/J/A+A/529/A75</identifier><altIdentifier>doi:10.26093/cds/vizier.35290075</altIdentifier><curation><publisher ivo-id="ivo://CDS">CDS</publisher><creator><name>Claret A.</name></creator><creator><name>Bloemen S.</name></creator><date role="Updated">2017-06-29T08:56:26Z</date><date role="Created">2011-04-05T08:27:14Z</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>infrared-photometry</subject><subject>visible-astronomy</subject><subject>sloan-photometry</subject><subject>medium-band-photometry</subject><subject>Wide-band photometry</subject><description>The degree of complexity of physics due to proximity effects in close binary stars is one of the most important challenges in theoretical stellar physics. The knowledge of how the specific intensity is distributed over the stellar disk is primordial to model the light curves of eclipsing binaries and planetary transits correctly. In order to provide theoretical input for light curve modelling codes, we present new calculations of gravity- and limb darkening coefficients for a wide range of effective temperatures, gravities, metallicities and microturbulent velocities. We have computed limb darkening coefficients for several atmosphere models, covering the transmission curves of the Kepler, CoRoT and Spitzer space missions as well as more widely used passbands (Stroemgren, Johnson-Cousins, Sloan). In addition to these computations, which were computed by adopting the Least-Square Method, we also performed calculations for the bi-parametric approximations by adopting the Flux Conservation Method to provide users with an additional tool to estimate the theoretical error bars. To facilitate the modelling of the effects of tidal and rotational distortions, we computed the GDCs y({lambda}) using the same models of stellar atmospheres as in the case of limb-darkening. Compared to previous work, a more general differential equation was used which now takes into account local gravity variations and the effects of convection. The limb darkening coefficients were computed with a larger numerical resolution (100um points instead of 15 or 17 as is often used in the ATLAS models) and five equations were used to describe the specific intensities (linear, quadratic, root-square, logarithmic and a 4-coefficient law (Equation 5)). Concerning the GDCs, the influence of the local gravity on y({lambda}) is shown as well as the effects of convection, which turn out to be very significant for cool stars. The results are tabulated for log(g)'s ranging from 0.0 to 5.0,-5.0&lt;=log[M/H]&lt;=+1, 2000K&lt;=Teff&lt;=50000K and for 5 values of the microturbulent velocity (0, 2, 4, 6, 8). ATLAS and PHOENIX plane-parallel atmosphere models were used for all the computations.</description><source format="bibcode">2011A&amp;A...529A..75C</source><referenceURL>https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/529/A75</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+AS/110/329">J/A+AS/110/329 : LTE model atmospheres coeff. (Diaz-cordoves+, 1995)</relatedResource><relatedResource ivo-id="ivo://CDS.VizieR/J/A+AS/114/247">J/A+AS/114/247 : Limb-darkening coeff. for RIJHK (Claret+, 1995)</relatedResource><relatedResource ivo-id="ivo://CDS.VizieR/J/A+A/335/647">J/A+A/335/647 : Limb-darkening coeff. for ubvyUBVRIJHK (Claret 1998)</relatedResource><relatedResource ivo-id="ivo://CDS.VizieR/J/A+A/405/1095">J/A+A/405/1095 : Limb-darkening coeff. from ATLAS9 models (Barban+, 2003)</relatedResource><relatedResource ivo-id="ivo://CDS.VizieR/J/A+A/510/A21">J/A+A/510/A21 : Stellar limb-darkening coeff. (Sing, 2010)</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/529/A75</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/A+A/529/A75</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/A+A/529/A75</mirrorURL></interface></capability><capability><interface xsi:type="vs:ParamHTTP"><accessURL use="base">https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/A+A/529/A75</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/votable?-source=J/A+A/529/A75</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/A+A/529/A75</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"/><waveband>Optical</waveband><waveband>Infrared</waveband></coverage><tableset><schema><name>default</name><table><name>J/A+A/529/A75/tableu</name><description>u linear 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>logg</name><description>[0/5] 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>[2000/50000] Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Z</name><description>[-5/1] Metallicity (log[M/H])</description><unit>log(Sun)</unit><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>xi</name><description>[0/8] 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 u (G2)</description><ucd>pos.distance</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Filt</name><description>Filter (G1)</description><ucd>meta.id;instr.filter</ucd><dataType xsi:type="vs:VOTableType" arraysize="2*">char</dataType></column><column><name>Met</name><description>[LF] Method (Least-Square or Flux Conservation)</description><ucd>meta.id;stat.fit</ucd><dataType xsi:type="vs:VOTableType" arraysize="1*">char</dataType></column><column><name>Mod</name><description>Model (ATLAS or PHOENIX)</description><ucd>instr.setup;meta.modelled</ucd><dataType xsi:type="vs:VOTableType" arraysize="1*">char</dataType></column></table><table><name>J/A+A/529/A75/table-af</name><description>2-parameter limb darkening coefficients: quadratic , root-square and logarithmic (equations 2, 3 and 4)</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>[0/5] 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>[2000/50000] Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Z</name><description>[-5/1] Metallicity (log[M/H])</description><unit>log(Sun)</unit><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>xi</name><description>[0/8] Microturbulent velocity</description><unit>km/s</unit><ucd>phys.veloc</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>a</name><description>Quadratic limb darkening coefficient a (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>b</name><description>Quadratic limb darkening coefficient b (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Filt</name><description>Filter (G1)</description><ucd>meta.id;instr.filter</ucd><dataType xsi:type="vs:VOTableType" arraysize="2*">char</dataType></column><column><name>Met</name><description>[LF] Method (Least-Square or Flux Conservation)</description><ucd>meta.id;stat.fit</ucd><dataType xsi:type="vs:VOTableType" arraysize="1*">char</dataType></column><column><name>Mod</name><description>Model (ATLAS or PHOENIX)</description><ucd>instr.setup;meta.modelled</ucd><dataType xsi:type="vs:VOTableType" arraysize="1*">char</dataType></column><column><name>c</name><description>Root-square limb darkening coefficient c (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>d</name><description>Root-square limb darkening coefficient d (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>e</name><description>Logarithmic limb darkening coefficient e (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>f</name><description>Logarithmic limb darkening coefficient f (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column></table><table><name>J/A+A/529/A75/tableeq5</name><description>a1, a2, a3, a4 limb darkening coefficients from equation 5</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>[0/5] 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>[2000/50000] Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Z</name><description>[-5/1] Metallicity (log[M/H])</description><unit>log(Sun)</unit><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>xi</name><description>[0/8] Microturbulent velocity</description><unit>km/s</unit><ucd>phys.veloc</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>a1</name><description>Equation 5 limb darkening coefficient a1 (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>a2</name><description>Equation 5 limb darkening coefficient a2 (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>a3</name><description>Equation 5 limb darkening coefficient a3 (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>a4</name><description>Equation 5 limb darkening coefficient a4 (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Filt</name><description>Filter (G1)</description><ucd>meta.id;instr.filter</ucd><dataType xsi:type="vs:VOTableType" arraysize="2*">char</dataType></column><column><name>Met</name><description>[LF] Method (Least-Square or Flux Conservation)</description><ucd>meta.id;stat.fit</ucd><dataType xsi:type="vs:VOTableType" arraysize="1*">char</dataType></column><column><name>Mod</name><description>Model (ATLAS or PHOENIX)</description><ucd>instr.setup;meta.modelled</ucd><dataType xsi:type="vs:VOTableType" arraysize="1*">char</dataType></column></table><table><name>J/A+A/529/A75/tabley</name><description>y gravity 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>logg</name><description>[0/5] 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>[3.3/4.7] Effective temperature</description><unit>log(K)</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Z</name><description>[-5/1] Metallicity (log[M/H])</description><unit>log(Sun)</unit><ucd>phys.abund.Z</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>xi</name><description>[2/8] Microturbulent velocity</description><unit>km/s</unit><ucd>phys.veloc</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>y</name><description>Gravity darkening coefficient y (1)</description><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Filt</name><description>Filter (G1)</description><ucd>meta.id;instr.filter</ucd><dataType xsi:type="vs:VOTableType" arraysize="2*">char</dataType></column><column><name>Mod</name><description>Model (ATLAS or PHOENIX)</description><ucd>instr.setup;meta.modelled</ucd><dataType xsi:type="vs:VOTableType" arraysize="1*">char</dataType></column></table></schema></tableset></ri:Resource>