<?xml-stylesheet href='/static/xsl/oai.xsl' type='text/xsl'?>
<ri:Resource created="2012-12-27T14:04:05Z" status="active" updated="2025-06-13T15:25:00Z" 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 for CoRoT, Kepler, Spitzer</title><shortName>J/A+A/546/A14</shortName><identifier>ivo://CDS.VizieR/J/A+A/546/A14</identifier><altIdentifier>doi:10.26093/cds/vizier.35460014</altIdentifier><curation><publisher ivo-id="ivo://CDS">CDS</publisher><creator><name>Claret A.</name></creator><creator><name>Hauschildt P.H.</name></creator><creator><name>Witte S.</name></creator><date role="Updated">2017-06-26T11:49:49Z</date><date role="Created">2012-12-27T14:04:05Z</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 knowledge of how the specific intensity is distributed over the stellar disk is crucial for interpreting the light curves of extrasolar transiting planets, double-lined eclipsing binaries, and other astrophysical phenomena. To provide theoretical inputs for light curve modelling codes, we present new calculations of limb-darkening coefficients for the spherically symmetric PHOENIX models. The limb-darkening coefficients were computed by covering the transmission curves of Kepler, CoRoT, and Spitzer space missions, as well as the passbands of the Stromgren, Johnson-Cousins, Sloan, and 2MASS. These computations adopted the least-square method. In addition, we also calculated the linear and bi-parametric approximations by adopting the flux conservation method as an additional tool for estimating the theoretical error bars in the limb-darkening coefficients. Six laws were used to describe the specific intensity distribution: linear, quadratic, square root, logarithmic, exponential, and a more general one with 4 terms. The computations are presented for the solar chemical composition, with logg varying between 2.5 and 5.5 and effective temperatures between 1500K-4800K. The adopted Microturbulent velocity and the mixing-length parameters are 2.0km/s and 2.0, respectively. Model are for solar metallicity.</description><source format="bibcode">2012A&amp;A...546A..14C</source><referenceURL>https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/546/A14</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/363/1081">J/A+A/363/1081 : Non-linear limb-darkening law for LTE models (Claret, 2000)</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><relatedResource ivo-id="ivo://CDS.VizieR/J/A+A/529/A75">J/A+A/529/A75 : Limb-darkening coefficients (Claret+, 2011)</relatedResource><relatedResource ivo-id="ivo://CDS.VizieR/J/A+A/552/A16">J/A+A/552/A16 : Limb-darkening for CoRoT, Kepler, Spitzer. II. (Claret+, 2013)</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/546/A14</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/A+A/546/A14</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/A+A/546/A14</mirrorURL></interface></capability><capability><interface xsi:type="vs:ParamHTTP"><accessURL use="base">https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/A+A/546/A14</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/votable?-source=J/A+A/546/A14</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/A+A/546/A14</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/546/A14/limb6</name><description>Limb-darkening coefficients for the non-linear law for spherical and quasi-spherical PHOENIX models</description><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>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>[2.5/5.5] 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>[1500/4800] Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Z</name><description>[0] 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] Microturbulent velocity {xi}</description><unit>km/s</unit><ucd>phys.veloc</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>a1</name><description>Equation 6 limb darkening coefficient a1 (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>a2</name><description>Equation 6 limb darkening coefficient a2 (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>a3</name><description>Equation 6 limb darkening coefficient a3 (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>a4</name><description>Equation 6 limb darkening coefficient a4 (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>Met</name><description>[L] Method (Least-Square)</description><ucd>meta.id;stat.fit</ucd><dataType xsi:type="vs:VOTableType" arraysize="1*">char</dataType></column><column><name>Mod</name><description>[qs s] quasi-spherical/spherical PHOENIX model</description><ucd>stat.param;meta.modelled</ucd><dataType xsi:type="vs:VOTableType" arraysize="2*">char</dataType></column></table><table><name>J/A+A/546/A14/meritqs</name><description>Merit functions of limb-darkening coefficients in quasi-spherical PHOENIX models</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>[2.5/5.5] Surface gravity</description><unit>cm.s**-2</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Teff</name><description>[1500/4800] Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Z</name><description>[0] 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] Microturbulent velocity {xi}</description><unit>km/s</unit><ucd>phys.veloc</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>m1</name><description>merit function for fit#1 (G2)</description><ucd>stat.fit.goodness</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>m2</name><description>merit function for fit#2 (G2)</description><ucd>stat.fit.goodness</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>m3</name><description>merit function for fit#3 (G2)</description><ucd>stat.fit.goodness</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>m4</name><description>merit function for fit#4 (G2)</description><ucd>stat.fit.goodness</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>m5</name><description>merit function for fit#5 (G2)</description><ucd>stat.fit.goodness</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>m6</name><description>merit function for fit#6 (G2)</description><ucd>stat.fit.goodness</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column></table><table><name>J/A+A/546/A14/merits</name><description>Merit functions of limb-darkening coefficients in spherical PHOENIX models</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>[2.5/5.5] Surface gravity</description><unit>cm.s**-2</unit><ucd>phys.gravity</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Teff</name><description>[1500/4800] Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Z</name><description>[0] 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] Microturbulent velocity {xi}</description><unit>km/s</unit><ucd>phys.veloc</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>m5</name><description>merit function for fit#5 (G2)</description><ucd>stat.fit.goodness</ucd><dataType xsi:type="vs:VOTableType">double</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>m6</name><description>merit function for fit#6 (G2)</description><ucd>stat.fit.goodness</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column></table><table><name>J/A+A/546/A14/limb5</name><description>Limb-darkening coefficients for the exponential coefficients for spherical and quasi-spherical PHOENIX models</description><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>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>[2.5/5.5] 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>[1500/4800] Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Z</name><description>[0] 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] Microturbulent velocity {xi}</description><unit>km/s</unit><ucd>phys.veloc</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>g</name><description>Exponential limb darkening coefficient g (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>h</name><description>Exponential limb darkening coefficient h (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>Met</name><description>[L] Method (Least-Square)</description><ucd>meta.id;stat.fit</ucd><dataType xsi:type="vs:VOTableType" arraysize="1*">char</dataType></column><column><name>Mod</name><description>[qs s] quasi-spherical/spherical PHOENIX model</description><ucd>stat.param;meta.modelled</ucd><dataType xsi:type="vs:VOTableType" arraysize="2*">char</dataType></column></table><table><name>J/A+A/546/A14/limb1-4</name><description>1- and 2-parameter limb-darkening coefficients for quasi-spherical PHOENIX models: 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>[2.5/5.5] 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>[1500/4800] Effective temperature</description><unit>K</unit><ucd>phys.temperature.effective</ucd><dataType xsi:type="vs:VOTableType">float</dataType></column><column><name>Z</name><description>[0] 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] Microturbulent velocity {xi}</description><unit>km/s</unit><ucd>phys.veloc</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>[qs] quasi-spherical PHOENIX model</description><ucd>stat.param;meta.modelled</ucd><dataType xsi:type="vs:VOTableType" arraysize="2*">char</dataType></column><column><name>u</name><description>Linear limb darkening coefficient u (G2)</description><ucd>pos.distance</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>Merit</name><description>Corresponding figure of merit</description><ucd>meta.ref.url</ucd><dataType xsi:type="vs:VOTableType" arraysize="*">char</dataType></column><column><name>a</name><description>Quadratic limb darkening coefficient a (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>b</name><description>Quadratic limb darkening coefficient b (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>c</name><description>Root-square limb darkening coefficient c (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>d</name><description>Root-square limb darkening coefficient d (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>e</name><description>Logarithmic limb darkening coefficient e (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column><column><name>f</name><description>Logarithmic limb darkening coefficient f (G2)</description><ucd>phot.limbDark</ucd><dataType xsi:type="vs:VOTableType">double</dataType></column></table></schema></tableset></ri:Resource>