J/A+A/674/A63ivo://CDS.VizieR/J/A+A/674/A63doi:10.26093/cds/vizier.36740063CDSClaret A.Southworth J.2024-11-28T20:03:56Z2023-06-01T13:50:32ZCDS support team

CDS, Observatoire de Strasbourg, 11 rue de l'Universite, F-67000 Strasbourg, France

cds-question@unistra.frastronomical-modelsstellar-atmospheresvisible-astronomysloan-photometryinfrared-photometrybroad-band-photometryThe phenomenon of limb-darkening is relevant to many topics in astrophysics, including the analysis of light curves of eclipsing binaries, optical interferometry, measurement of stellar diameters, line profiles of rotating stars, gravitational microlensing, and transits of extrasolar planets. Multiple parametric limb-darkening laws have been presented, and there are many available sources of theoretical limb-darkening coefficients (LDCs) calculated using stellar model atmospheres. The power-2 limb-darkening law allows a very good representation of theoretically predicted intensity profiles, but few LDCs are available for this law from spherically symmetric model atmospheres. We therefore present such coefficients in this work. We computed LDCs for the space missions Gaia, Kepler, TESS, and CHEOPS and for the passbands uvby, UBVRIJHK, and SDSS ugriz, using the PHOENIX-COND spherical models. We adopted two methods to characterise the truncation point, which sets the limb of the star: the first (M1) uses the point where the derivative dI(r)/dr is at its maximum --- where I(r) is the specific intensity as a function of the normalised radius r --- corresponding to {mu}_cri_, and the second (M2) uses the midpoint between the point {mu}_cri_ and the point located at {mu}_cri-1_. The LDCs were computed adopting the Levenberg-Marquardt least-squares minimisation method, with a resolution of 900 equally spaced {mu} points, and covering 823 model atmospheres for a solar metallicity, effective temperatures of 2300 to 12000K, logg values from 0.0 to 6.0, and microturbulent velocities of 2km/s. As our previous calculations of LDCs using spherical models included only 100{mu} points, we also updated the calculations for the four-parameter law for the passbands listed above, and compared them with those from the power-2 law. Comparisons between the quality of the fits provided by the power-2 and four-parameter laws show that the latter presents a lower merit function, chi^2^, than the former for both cases (M1 and M2). This is important when choosing the best approach for a particular science goal.2023A&A...674A..63Chttps://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/674/A63CatalogResearchIsServedByTAP VizieR generic servicerelated-toJ/A+AS/114/247 : Limb-darkening coefficients for R I J H K (Claret+, 1995)J/A+A/335/647 : Limb-darkening coefficients for ubvyUBVRIJHK (Claret 1998)J/A+A/401/657 : Non-linear limb-darkening law for LTE models. II.J/A+A/428/1001 : Non-linear limb-darkening law for LTE models. III.J/A+A/529/A75 : Limb-darkening coefficients (Claret+, 2011)J/A+A/546/A14 : Limb-darkening for CoRoT, Kepler, Spitzer (Claret+, 2012)J/A+A/552/A16 : Limb-darkening for CoRoT, Kepler, Spitzer. II. (Claret+, 2013)J/A+A/600/A30 : Limb-darkening for TESS satellite (Claret, 2017)J/A+A/618/A20 : Limb-darkening for TESS, Kepler, Corot, MOST (Claret, 2018)J/A+A/634/A93 : Limb-darkening coefficients for compact stars (Claret+, 2020)J/A+A/641/A157 : Limb-darkening coefficients for white dwarfs (Claret+, 2020)https://cds.unistra.fr/vizier-org/licences_vizier.htmlhttps://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/A+A/674/A63https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/A+A/674/A63http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/A+A/674/A63https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/A+A/674/A63https://vizier.iucaa.in/viz-bin/votable?-source=J/A+A/674/A63http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/A+A/674/A63GETtext/xml+votablehttps://tapvizier.cds.unistra.fr/TAPVizieR/tapOpticalInfrareddefaultJ/A+A/674/A63/table1Eq.2 PHOENIX, Gaia, Kepler,TESS,CHEOPS/M1CHI2Gpower-2 chi2 (G)stat.fit.chi2doublerecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintloggLog10 Surface gravitylog(cm.s**-2)phys.gravityfloatTeffEffective temperatureKphys.temperature.effectivefloatZ[0] log10 [M/H]phys.abund.ZfloatVel[2] Microturbulent velocitykm/sphys.velocfloatgGbppower-2 limb darkening coefficient g (Gbp)phot.limbDarkdoublegGpower-2 limb darkening coefficient g (G)phot.limbDarkdoublegGrppower-2 limb darkening coefficient g (Grp)phot.limbDarkdoublegKeppower-2 limb darkening coefficient g (KEP)phot.limbDarkdoublegTESSpower-2 limb darkening coefficient g (TESS)phot.limbDarkdoublegCHEOPSpower-2 limb darkening coefficient g (CHEOPS)phot.limbDarkdoublehGbppower-2 limb darkening coefficient h (Gbp)phot.limbDarkdoublehGpower-2 limb darkening coefficient h (G)phot.limbDarkdoublehGrppower-2 limb darkening coefficient h (Grp)phot.limbDarkdoublehKEPpower-2 limb darkening coefficient h (KEP)phot.limbDarkdoublehTESSpower-2 limb darkening coefficient h (TESS)phot.limbDarkdoublehCHEOPSpower-2 limb darkening coefficient h (CHEOPS)phot.limbDarkdoublemucriGbppower-2 {mu}_cri_ point (Gbp)stat.fit.paramdoublemucriGpower-2 {mu}_cri_ point (G)stat.fit.paramdoublemucriGrppower-2 {mu}_cri_ point (Grp)stat.fit.paramdoublemucriKEPpower-2 {mu}_cri_ point (KEP)stat.fit.paramdoublemucriTESSpower-2 {mu}_cri_ point (TESS)stat.fit.paramdoublemucriCHEOPSpower-2 {mu}_cri_ point (CHEOPS)stat.fit.paramdoubleCHI2Gbppower-2 chi2 (Gbp)stat.fit.chi2doubleCHI2Grppower-2 chi2 (Grp)stat.fit.chi2doubleCHI2KEPpower-2 chi2 (KEP)stat.fit.chi2doubleCHI2TESSpower-2 chi2 (TESS)stat.fit.chi2doubleCHI2CHEOPSpower-2 chi2 (CHEOPS)stat.fit.chi2doubleJ/A+A/674/A63/table2Eq.2 PHOENIX, Gaia, Kepler,TESS,CHEOPS/M2recnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintloggLog10 Surface gravitylog(cm.s**-2)phys.gravityfloatTeffEffective temperatureKphys.temperature.effectivefloatZ[0] log10 [M/H]phys.abund.ZfloatVel[2] Microturbulent velocitykm/sphys.velocfloatgGbppower-2 limb darkening coefficient g (Gbp)phot.limbDarkdoublegGpower-2 limb darkening coefficient g (G)phot.limbDarkdoublegGrppower-2 limb darkening coefficient g (Grp)phot.limbDarkdoublegKeppower-2 limb darkening coefficient g (KEP)phot.limbDarkdoublegTESSpower-2 limb darkening coefficient g (TESS)phot.limbDarkdoublegCHEOPSpower-2 limb darkening coefficient g (CHEOPS)phot.limbDarkdoublehGbppower-2 limb darkening coefficient h (Gbp)phot.limbDarkdoublehGpower-2 limb darkening coefficient h (G)phot.limbDarkdoublehGrppower-2 limb darkening coefficient h (Grp)phot.limbDarkdoublehKEPpower-2 limb darkening coefficient h (KEP)phot.limbDarkdoublehTESSpower-2 limb darkening coefficient h (TESS)phot.limbDarkdoublehCHEOPSpower-2 limb darkening coefficient h (CHEOPS)phot.limbDarkdoublemucriGbppower-2 {mu}_cri_ point (Gbp)stat.fit.paramdoublemucriGpower-2 {mu}_cri_ point (G)stat.fit.paramdoublemucriGrppower-2 {mu}_cri_ point (Grp)stat.fit.paramdoublemucriKEPpower-2 {mu}_cri_ point (KEP)stat.fit.paramdoublemucriTESSpower-2 {mu}_cri_ point (TESS)stat.fit.paramdoublemucriCHEOPSpower-2 {mu}_cri_ point (CHEOPS)stat.fit.paramdoubleCHI2Gbppower-2 chi2 (Gbp)stat.fit.chi2doubleCHI2Gpower-2 chi2 (G)stat.fit.chi2doubleCHI2Grppower-2 chi2 (Grp)stat.fit.chi2doubleCHI2KEPpower-2 chi2 (KEP)stat.fit.chi2doubleCHI2TESSpower-2 chi2 (TESS)stat.fit.chi2doubleCHI2CHEOPSpower-2 chi2 (CHEOPS)stat.fit.chi2doubleJ/A+A/674/A63/table3Eq.3 PHOENIX, Gaia, Kepler,TESS,CHEOPS/M1recnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintloggLog10 Surface gravitylog(cm.s**-2)phys.gravityfloatTeffEffective temperatureKphys.temperature.effectivefloatZ[0] log10 [M/H]phys.abund.ZfloatVel[2] Microturbulent velocitykm/sphys.velocfloata1Gbp4-terms limb darkening coefficient a1 (Gbp)phot.limbDarkdoublea1G4-terms limb darkening coefficient a1 (G)phot.limbDarkdoublea1Grp4-terms limb darkening coefficient a1 (Grp)phot.limbDarkdoublea1KEP4-terms limb darkening coefficient a1 (KEP)phot.limbDarkdoublea1TESS4-terms limb darkening coefficient a1 (TESS)phot.limbDarkdoublea1CHEOPS4-terms limb darkening coefficient a1 (CHEOPS)phot.limbDarkdoublea2Gbp4-terms limb darkening coefficient a2 (Gbp)phot.limbDarkdoublea2G4-terms limb darkening coefficient a2 (G)phot.limbDarkdoublea2Grp4-terms limb darkening coefficient a2 (Grp)phot.limbDarkdoublea2KEP4-terms limb darkening coefficient a2 (KEP)phot.limbDarkdoublea2TESS4-terms limb darkening coefficient a2 (TESS)phot.limbDarkdoublea2CHEOPS4-terms limb darkening coefficient a2 (CHEOPS)phot.limbDarkdoublea3Gbp4-terms limb darkening coefficient a3 (Gbp)phot.limbDarkdoublea3G4-terms limb darkening coefficient a3 (G)phot.limbDarkdoublea3Grp4-terms limb darkening coefficient a3 (Grp)phot.limbDarkdoublea3KEP4-terms limb darkening coefficient a3 (KEP)phot.limbDarkdoublea3TESS4-terms limb darkening coefficient a3 (TESS)phot.limbDarkdoublea3CHEOPS4-terms limb darkening coefficient a3 (CHEOPS)phot.limbDarkdoublea4Gbp4-terms limb darkening coefficient a4 (Gbp)phot.limbDarkdoublea4G4-terms limb darkening coefficient a4 (G)phot.limbDarkdoublea4Grp4-terms limb darkening coefficient a4 (Grp)phot.limbDarkdoublea4KEP4-terms limb darkening coefficient a4 (KEP)phot.limbDarkdoublea4TESS4-terms limb darkening coefficient a4 (TESS)phot.limbDarkdoublea4CHEOPS4-terms limb darkening coefficient a4 (CHEOPS)phot.limbDarkdoublemucriGbp4-terms {mu}_cri_ point (Gbp)stat.fit.paramdoublemucriG4-terms {mu}_cri_ point (G)stat.fit.paramdoublemucriGrp4-terms {mu}_cri_ point (Grp)stat.fit.paramdoublemucriKEP4-terms {mu}_cri_ point (KEP)stat.fit.paramdoublemucriTESS4-terms {mu}_cri_ point (TESS)stat.fit.paramdoublemucriCHEOPS4-terms {mu}_cri_ point (CHEOPS)stat.fit.paramdoubleCHI2Gbp4-terms {mu}_cri_ point (Gbp)stat.fit.chi2doubleCHI2G4-terms chi2 (G)stat.fit.chi2doubleCHI2Grp4-terms chi2 (Grp)stat.fit.chi2doubleCHI2KEP4-terms chi2 (KEP)stat.fit.chi2doubleCHI2TESS4-terms chi2 (TESS)stat.fit.chi2doubleCHI2CHEOPS4-terms chi2 (CHEOPS)stat.fit.chi2doubleJ/A+A/674/A63/table4Eq.3 PHOENIX, Gaia, Kepler,TESS,CHEOPS/M2CHI2G4-terms chi2 (G)stat.fit.chi2doublea1Gbp4-terms limb darkening coefficient a1 (Gbp)phot.limbDarkdoublerecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintloggLog10 Surface gravitylog(cm.s**-2)phys.gravityfloatTeffEffective temperatureKphys.temperature.effectivefloatZ[0] log10 [M/H]phys.abund.ZfloatVel[2] Microturbulent velocitykm/sphys.velocfloata1G4-terms limb darkening coefficient a1 (G)phot.limbDarkdoublea1Grp4-terms limb darkening coefficient a1 (Grp)phot.limbDarkdoublea1KEP4-terms limb darkening coefficient a1 (KEP)phot.limbDarkdoublea1TESS4-terms limb darkening coefficient a1 (TESS)phot.limbDarkdoublea1CHEOPS4-terms limb darkening coefficient a1 (CHEOPS)phot.limbDarkdoublea2Gbp4-terms limb darkening coefficient a2 (Gbp)phot.limbDarkdoublea2G4-terms limb darkening coefficient a2 (G)phot.limbDarkdoublea2Grp4-terms limb darkening coefficient a2 (Grp)phot.limbDarkdoublea2KEP4-terms limb darkening coefficient a2 (KEP)phot.limbDarkdoublea2TESS4-terms limb darkening coefficient a2 (TESS)phot.limbDarkdoublea2CHEOPS4-terms limb darkening coefficient a2 (CHEOPS)phot.limbDarkdoublea3Gbp4-terms limb darkening coefficient a3 (Gbp)phot.limbDarkdoublea3G4-terms limb darkening coefficient a3 (G)phot.limbDarkdoublea3Grp4-terms limb darkening coefficient a3 (Grp)phot.limbDarkdoublea3KEP4-terms limb darkening coefficient a3 (KEP)phot.limbDarkdoublea3TESS4-terms limb darkening coefficient a3 (TESS)phot.limbDarkdoublea3CHEOPS4-terms limb darkening coefficient a3 (CHEOPS)phot.limbDarkdoublea4Gbp4-terms limb darkening coefficient a4 (Gbp)phot.limbDarkdoublea4G4-terms limb darkening coefficient a4 (G)phot.limbDarkdoublea4Grp4-terms limb darkening coefficient a4 (Grp)phot.limbDarkdoublea4KEP4-terms limb darkening coefficient a4 (KEP)phot.limbDarkdoublea4TESS4-terms limb darkening coefficient a4 (TESS)phot.limbDarkdoublea4CHEOPS4-terms limb darkening coefficient a4 (CHEOPS)phot.limbDarkdoublemucriGbp4-terms {mu}_cri_ point (Gbp)stat.fit.paramdoublemucriG4-terms {mu}_cri_ point (G)stat.fit.paramdoublemucriGrp4-terms {mu}_cri_ point (Grp)stat.fit.paramdoublemucriKEP4-terms {mu}_cri_ point (KEP)stat.fit.paramdoublemucriTESS4-terms {mu}_cri_ point (TESS)stat.fit.paramdoublemucriCHEOPS4-terms {mu}_cri_ point (CHEOPS)stat.fit.paramdoubleCHI2Gbp4-terms {mu}_cri_ point (Gbp)stat.fit.chi2doubleCHI2Grp4-terms chi2 (Grp)stat.fit.chi2doubleCHI2KEP4-terms chi2 (KEP)stat.fit.chi2doubleCHI2TESS4-terms chi2 (TESS)stat.fit.chi2doubleCHI2CHEOPS4-terms chi2 (CHEOPS)stat.fit.chi2doubleJ/A+A/674/A63/table5Eq.2 PHOENIX, ugriz/M1CHI2upower-2 chi2 (u)stat.fit.chi2doublerecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintloggLog10 Surface gravitylog(cm.s**-2)phys.gravityfloatTeffEffective temperatureKphys.temperature.effectivefloatZ[0] log10 [M/H]phys.abund.ZfloatVel[2] Microturbulent velocitykm/sphys.velocfloatgupower-2 limb darkening coefficient g (u)phot.limbDarkdoubleggpower-2 limb darkening coefficient g (g)phot.limbDarkdoublegrpower-2 limb darkening coefficient g (r)phot.limbDarkdoublegipower-2 limb darkening coefficient g (i)phot.limbDarkdoublegzpower-2 limb darkening coefficient g (z)phot.limbDarkdoublehupower-2 limb darkening coefficient h (u)phot.limbDarkdoublehgpower-2 limb darkening coefficient h (g)phot.limbDarkdoublehrpower-2 limb darkening coefficient h (r)phot.limbDarkdoublehipower-2 limb darkening coefficient h (i)phot.limbDarkdoublehzpower-2 limb darkening coefficient h (z)phot.limbDarkdoublemucriupower-2 {mu}_cri_ point (u)stat.fit.paramdoublemucrigpower-2 {mu}_cri_ point (g)stat.fit.paramdoublemucrirpower-2 {mu}_cri_ point (r)stat.fit.paramdoublemucriipower-2 {mu}_cri_ point (i)stat.fit.paramdoublemucrizpower-2 {mu}_cri_ point (z)stat.fit.paramdoubleCHI2gpower-2 chi2 (g)stat.fit.chi2doubleCHI2rpower-2 chi2 (r)stat.fit.chi2doubleCHI2ipower-2 chi2 (i)stat.fit.chi2doubleCHI2zpower-2 chi2 (z)stat.fit.chi2doubleJ/A+A/674/A63/table6Eq.2 PHOENIX, ugriz/M2recnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintloggLog10 Surface gravitylog(cm.s**-2)phys.gravityfloatTeffEffective temperatureKphys.temperature.effectivefloatZ[0] log10 [M/H]phys.abund.ZfloatVel[2] Microturbulent velocitykm/sphys.velocfloatgupower-2 limb darkening coefficient g (u)phot.limbDarkdoubleggpower-2 limb darkening coefficient g (g)phot.limbDarkdoublegrpower-2 limb darkening coefficient g (r)phot.limbDarkdoublegipower-2 limb darkening coefficient g (i)phot.limbDarkdoublegzpower-2 limb darkening coefficient g (z)phot.limbDarkdoublehupower-2 limb darkening coefficient h (u)phot.limbDarkdoublehgpower-2 limb darkening coefficient h (g)phot.limbDarkdoublehrpower-2 limb darkening coefficient h (r)phot.limbDarkdoublehipower-2 limb darkening coefficient h (i)phot.limbDarkdoublehzpower-2 limb darkening coefficient h (z)phot.limbDarkdoublemucriupower-2 {mu}_cri_ point (u)stat.fit.paramdoublemucrigpower-2 {mu}_cri_ point (g)stat.fit.paramdoublemucrirpower-2 {mu}_cri_ point (r)stat.fit.paramdoublemucriipower-2 {mu}_cri_ point (i)stat.fit.paramdoublemucrizpower-2 {mu}_cri_ point (z)stat.fit.paramdoubleCHI2upower-2 chi2 (u)stat.fit.chi2doubleCHI2gpower-2 chi2 (g)stat.fit.chi2doubleCHI2rpower-2 chi2 (r)stat.fit.chi2doubleCHI2ipower-2 chi2 (i)stat.fit.chi2doubleCHI2zpower-2 chi2 (z)stat.fit.chi2doubleJ/A+A/674/A63/table7Eq.3 PHOENIX, ugriz/M1recnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintloggLog10 Surface gravitylog(cm.s**-2)phys.gravityfloatTeffEffective temperatureKphys.temperature.effectivefloatZ[0] log10 [M/H]phys.abund.ZfloatVel[2] Microturbulent velocitykm/sphys.velocfloata1u4-terms limb darkening coefficient a1 (u)phot.limbDarkdoublea1g4-terms limb darkening coefficient a1 (g)phot.limbDarkdoublea1r4-terms limb darkening coefficient a1 (r)phot.limbDarkdoublea1i4-terms limb darkening coefficient a1 (i)phot.limbDarkdoublea1z4-terms limb darkening coefficient a1 (z)phot.limbDarkdoublea2u4-terms limb darkening coefficient a2 (u)phot.limbDarkdoublea2g4-terms limb darkening coefficient a2 (g)phot.limbDarkdoublea2r4-terms limb darkening coefficient a2 (r)phot.limbDarkdoublea2i4-terms limb darkening coefficient a2 (i)phot.limbDarkdoublea2z4-terms limb darkening coefficient a2 (z)phot.limbDarkdoublea3u4-terms limb darkening coefficient a3 (u)phot.limbDarkdoublea3g4-terms limb darkening coefficient a3 (g)phot.limbDarkdoublea3r4-terms limb darkening coefficient a3 (r)phot.limbDarkdoublea3i4-terms limb darkening coefficient a3 (i)phot.limbDarkdoublea3z4-terms limb darkening coefficient a3 (z)phot.limbDarkdoublea4u4-terms limb darkening coefficient a4 (u)phot.limbDarkdoublea4g4-terms limb darkening coefficient a4 (g)phot.limbDarkdoublea4r4-terms limb darkening coefficient a4 (r)phot.limbDarkdoublea4i4-terms limb darkening coefficient a4 (i)phot.limbDarkdoublea4z4-terms limb darkening coefficient a4 (z)phot.limbDarkdoublemucriu4-terms {mu}_cri_ point (u)stat.fit.paramdoublemucrig4-terms {mu}_cri_ point (g)stat.fit.paramdoublemucrir4-terms {mu}_cri_ point (r)stat.fit.paramdoublemucrii4-terms {mu}_cri_ point (i)stat.fit.paramdoublemucriz4-terms {mu}_cri_ point (z)stat.fit.paramdoubleCHI2u4-terms chi2 (u)stat.fit.chi2doubleCHI2g4-terms chi2 (g)stat.fit.chi2doubleCHI2r4-terms chi2 (r)stat.fit.chi2doubleCHI2i4-terms chi2 (i)stat.fit.chi2doubleCHI2z4-terms chi2 (z)stat.fit.chi2doubleJ/A+A/674/A63/table8Eq.3 PHOENIX, ugriz/M2Z[0] log10 [M/H]phys.abund.ZfloatrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintloggLog10 Surface gravitylog(cm.s**-2)phys.gravityfloatTeffEffective temperatureKphys.temperature.effectivefloatVel[2] Microturbulent velocitykm/sphys.velocfloata1u4-terms limb darkening coefficient a1 (u)phot.limbDarkdoublea1g4-terms limb darkening coefficient a1 (g)phot.limbDarkdoublea1r4-terms limb darkening coefficient a1 (r)phot.limbDarkdoublea1i4-terms limb darkening coefficient a1 (i)phot.limbDarkdoublea1z4-terms limb darkening coefficient a1 (z)phot.limbDarkdoublea2u4-terms limb darkening coefficient a2 (u)phot.limbDarkdoublea2g4-terms limb darkening coefficient a2 (g)phot.limbDarkdoublea2r4-terms limb darkening coefficient a2 (r)phot.limbDarkdoublea2i4-terms limb darkening coefficient a2 (i)phot.limbDarkdoublea2z4-terms limb darkening coefficient a2 (z)phot.limbDarkdoublea3u4-terms limb darkening coefficient a3 (u)phot.limbDarkdoublea3g4-terms limb darkening coefficient a3 (g)phot.limbDarkdoublea3r4-terms limb darkening coefficient a3 (r)phot.limbDarkdoublea3i4-terms limb darkening coefficient a3 (i)phot.limbDarkdoublea3z4-terms limb darkening coefficient a3 (z)phot.limbDarkdoublea4u4-terms limb darkening coefficient a4 (u)phot.limbDarkdoublea4g4-terms limb darkening coefficient a4 (g)phot.limbDarkdoublea4r4-terms limb darkening coefficient a4 (r)phot.limbDarkdoublea4i4-terms limb darkening coefficient a4 (i)phot.limbDarkdoublea4z4-terms limb darkening coefficient a4 (z)phot.limbDarkdoublemucriu4-terms {mu}_cri_ point (u)stat.fit.paramdoublemucrig4-terms {mu}_cri_ point (g)stat.fit.paramdoublemucrir4-terms {mu}_cri_ point (r)stat.fit.paramdoublemucrii4-terms {mu}_cri_ point (i)stat.fit.paramdoublemucriz4-terms {mu}_cri_ point (z)stat.fit.paramdoubleCHI2u4-terms chi2 (u)stat.fit.chi2doubleCHI2g4-terms chi2 (g)stat.fit.chi2doubleCHI2r4-terms chi2 (r)stat.fit.chi2doubleCHI2i4-terms chi2 (i)stat.fit.chi2doubleCHI2z4-terms chi2 (z)stat.fit.chi2doubleJ/A+A/674/A63/table9Eq.2 PHOENIX, uvbyUBVRIJHK/M1CHI2Bpower-2 chi2 (B)stat.fit.chi2doubleCHI2Vpower-2 chi2 (V)stat.fit.chi2doubleCHI2Rpower-2 chi2 (R)stat.fit.chi2doubleCHI2Ipower-2 chi2 (I)stat.fit.chi2doubleCHI2Jpower-2 chi2 (J)stat.fit.chi2doubleCHI2Hpower-2 chi2 (H)stat.fit.chi2doubleCHI2Kpower-2 chi2 (K)stat.fit.chi2doubleTeffEffective temperatureKphys.temperature.effectivefloatCHI2Upower-2 chi2 (U)stat.fit.chi2doublerecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintloggLog10 Surface gravitylog(cm.s**-2)phys.gravityfloatZ[0] log10 [M/H]phys.abund.ZfloatVel[2] Microturbulent velocitykm/sphys.velocfloatgupower-2 limb darkening coefficient g (u)phot.limbDarkdoublegvpower-2 limb darkening coefficient g (v)phot.limbDarkdoublegbpower-2 limb darkening coefficient g (b)phot.limbDarkdoublegypower-2 limb darkening coefficient g (y)phot.limbDarkdoublegUpower-2 limb darkening coefficient g (U)phot.limbDarkdoublegBpower-2 limb darkening coefficient g (B)phot.limbDarkdoublegVpower-2 limb darkening coefficient g (V)phot.limbDarkdoublegRpower-2 limb darkening coefficient g (R)phot.limbDarkdoublegIpower-2 limb darkening coefficient g (I)phot.limbDarkdoublegJpower-2 limb darkening coefficient g (J)phot.limbDarkdoublegHpower-2 limb darkening coefficient g (H)phot.limbDarkdoublegKpower-2 limb darkening coefficient g (K)phot.limbDarkdoublehupower-2 limb darkening coefficient h (u)phot.limbDarkdoublehbpower-2 limb darkening coefficient h (v)phot.limbDarkdoublehvpower-2 limb darkening coefficient h (b)phot.limbDarkdoublehypower-2 limb darkening coefficient h (y)phot.limbDarkdoublehUpower-2 limb darkening coefficient h (U)phot.limbDarkdoublehBpower-2 limb darkening coefficient h (B)phot.limbDarkdoublehVpower-2 limb darkening coefficient h (V)phot.limbDarkdoublehRpower-2 limb darkening coefficient h (R)phot.limbDarkdoublehIpower-2 limb darkening coefficient h (I)phot.limbDarkdoublehJpower-2 limb darkening coefficient h (J)phot.limbDarkdoublehHpower-2 limb darkening coefficient h (H)phot.limbDarkdoublehKpower-2 limb darkening coefficient h (K)phot.limbDarkdoublemucriupower-2 {mu}_cri_ point (u)stat.fit.paramdoublemucrivpower-2 {mu}_cri_ point (v)stat.fit.paramdoublemucribpower-2 {mu}_cri_ point (b)stat.fit.paramdoublemucriypower-2 {mu}_cri_ point (y)stat.fit.paramdoublemucriUpower-2 {mu}_cri_ point (U)stat.fit.paramdoublemucriBpower-2 {mu}_cri_ point (B)stat.fit.paramdoublemucriVpower-2 {mu}_cri_ point (V)stat.fit.paramdoublemucriRpower-2 {mu}_cri_ point (R)stat.fit.paramdoublemucriIpower-2 {mu}_cri_ point (I)stat.fit.paramdoublemucriJpower-2 {mu}_cri_ point (J)stat.fit.paramdoublemucriHpower-2 {mu}_cri_ point (H)stat.fit.paramdoublemucriKpower-2 {mu}_cri_ point (K)stat.fit.paramdoubleCHI2upower-2 chi2 (u)stat.fit.chi2doubleCHI2vpower-2 chi2 (v)stat.fit.chi2doubleCHI2bpower-2 chi2 (b)stat.fit.chi2doubleCHI2ypower-2 chi2 (y)stat.fit.chi2doubleJ/A+A/674/A63/table10Eq.2 PHOENIX, uvbyUBVRIJHK/M2gupower-2 limb darkening coefficient g (u)phot.limbDarkdoublegvpower-2 limb darkening coefficient g (v)phot.limbDarkdoublegBpower-2 limb darkening coefficient g (B)phot.limbDarkdoublegVpower-2 limb darkening coefficient g (V)phot.limbDarkdoublegRpower-2 limb darkening coefficient g (R)phot.limbDarkdoublerecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintloggLog10 Surface gravitylog(cm.s**-2)phys.gravityfloatTeffEffective temperatureKphys.temperature.effectivefloatZ[0] log10 [M/H]phys.abund.ZfloatVel[2] Microturbulent velocitykm/sphys.velocfloatgbpower-2 limb darkening coefficient g (b)phot.limbDarkdoublegypower-2 limb darkening coefficient g (y)phot.limbDarkdoublegUpower-2 limb darkening coefficient g (U)phot.limbDarkdoublegIpower-2 limb darkening coefficient g (I)phot.limbDarkdoublegJpower-2 limb darkening coefficient g (J)phot.limbDarkdoublegHpower-2 limb darkening coefficient g (H)phot.limbDarkdoublegKpower-2 limb darkening coefficient g (K)phot.limbDarkdoublehupower-2 limb darkening coefficient h (u)phot.limbDarkdoublehbpower-2 limb darkening coefficient h (v)phot.limbDarkdoublehvpower-2 limb darkening coefficient h (b)phot.limbDarkdoublehypower-2 limb darkening coefficient h (y)phot.limbDarkdoublehUpower-2 limb darkening coefficient h (U)phot.limbDarkdoublehBpower-2 limb darkening coefficient h (B)phot.limbDarkdoublehVpower-2 limb darkening coefficient h (V)phot.limbDarkdoublehRpower-2 limb darkening coefficient h (R)phot.limbDarkdoublehIpower-2 limb darkening coefficient h (I)phot.limbDarkdoublehJpower-2 limb darkening coefficient h (J)phot.limbDarkdoublehHpower-2 limb darkening coefficient h (H)phot.limbDarkdoublehKpower-2 limb darkening coefficient h (K)phot.limbDarkdoublemucriupower-2 {mu}_cri_ point (u)stat.fit.paramdoublemucrivpower-2 {mu}_cri_ point (v)stat.fit.paramdoublemucribpower-2 {mu}_cri_ point (b)stat.fit.paramdoublemucriypower-2 {mu}_cri_ point (y)stat.fit.paramdoublemucriUpower-2 {mu}_cri_ point (U)stat.fit.paramdoublemucriBpower-2 {mu}_cri_ point (B)stat.fit.paramdoublemucriVpower-2 {mu}_cri_ point (V)stat.fit.paramdoublemucriRpower-2 {mu}_cri_ point (R)stat.fit.paramdoublemucriIpower-2 {mu}_cri_ point (I)stat.fit.paramdoublemucriJpower-2 {mu}_cri_ point (J)stat.fit.paramdoublemucriHpower-2 {mu}_cri_ point (H)stat.fit.paramdoublemucriKpower-2 {mu}_cri_ point (K)stat.fit.paramdoubleCHI2upower-2 chi2 (u)stat.fit.chi2doubleCHI2vpower-2 chi2 (v)stat.fit.chi2doubleCHI2bpower-2 chi2 (b)stat.fit.chi2doubleCHI2ypower-2 chi2 (y)stat.fit.chi2doubleCHI2Upower-2 chi2 (U)stat.fit.chi2doubleCHI2Bpower-2 chi2 (B)stat.fit.chi2doubleCHI2Vpower-2 chi2 (V)stat.fit.chi2doubleCHI2Rpower-2 chi2 (R)stat.fit.chi2doubleCHI2Ipower-2 chi2 (I)stat.fit.chi2doubleCHI2Jpower-2 chi2 (J)stat.fit.chi2doubleCHI2Hpower-2 chi2 (H)stat.fit.chi2doubleCHI2Kpower-2 chi2 (K)stat.fit.chi2doubleJ/A+A/674/A63/table11Eq.3 PHOENIX, uvbyUBVRIJHK/M1mucriy4-terms {mu}_cri_ point (y)stat.fit.paramdoublerecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintloggLog10 Surface gravitylog(cm.s**-2)phys.gravityfloatTeffEffective temperatureKphys.temperature.effectivefloatZ[0] log10 [M/H]phys.abund.ZfloatVel[2] Microturbulent velocitykm/sphys.velocfloata1u4-terms limb darkening coefficient a1 (u)phot.limbDarkdoublea1v4-terms limb darkening coefficient a1 (v)phot.limbDarkdoublea1b4-terms limb darkening coefficient a1 (b)phot.limbDarkdoublea1y4-terms limb darkening coefficient a1 (y)phot.limbDarkdoublea1U4-terms limb darkening coefficient a1 (U)phot.limbDarkdoublea1B4-terms limb darkening coefficient a1 (B)phot.limbDarkdoublea1V4-terms limb darkening coefficient a1 (V)phot.limbDarkdoublea1R4-terms limb darkening coefficient a1 (R)phot.limbDarkdoublea1I4-terms limb darkening coefficient a1 (I)phot.limbDarkdoublea1J4-terms limb darkening coefficient a1 (J)phot.limbDarkdoublea1H4-terms limb darkening coefficient a1 (H)phot.limbDarkdoublea1K4-terms limb darkening coefficient a1 (K)phot.limbDarkdoublea2u4-terms limb darkening coefficient a2 (u)phot.limbDarkdoublea2v4-terms limb darkening coefficient a2 (v)phot.limbDarkdoublea2b4-terms limb darkening coefficient a2 (b)phot.limbDarkdoublea2y4-terms limb darkening coefficient a2 (y)phot.limbDarkdoublea2U4-terms limb darkening coefficient a2 (U)phot.limbDarkdoublea2B4-terms limb darkening coefficient a2 (B)phot.limbDarkdoublea2V4-terms limb darkening coefficient a2 (V)phot.limbDarkdoublea2R4-terms limb darkening coefficient a2 (R)phot.limbDarkdoublea2I4-terms limb darkening coefficient a2 (I)phot.limbDarkdoublea2J4-terms limb darkening coefficient a2 (J)phot.limbDarkdoublea2H4-terms limb darkening coefficient a2 (H)phot.limbDarkdoublea2K4-terms limb darkening coefficient a2 (K)phot.limbDarkdoublea3u4-terms limb darkening coefficient a3 (u)phot.limbDarkdoublea3v4-terms limb darkening coefficient a3 (v)phot.limbDarkdoublea3b4-terms limb darkening coefficient a3 (b)phot.limbDarkdoublea3y4-terms limb darkening coefficient a3 (y)phot.limbDarkdoublea3U4-terms limb darkening coefficient a3 (U)phot.limbDarkdoublea3B4-terms limb darkening coefficient a3 (B)phot.limbDarkdoublea3V4-terms limb darkening coefficient a3 (V)phot.limbDarkdoublea3R4-terms limb darkening coefficient a3 (R)phot.limbDarkdoublea3I4-terms limb darkening coefficient a3 (I)phot.limbDarkdoublea3J4-terms limb darkening coefficient a3 (J)phot.limbDarkdoublea3H4-terms limb darkening coefficient a3 (H)phot.limbDarkdoublea3K4-terms limb darkening coefficient a3 (K)phot.limbDarkdoublea4u4-terms limb darkening coefficient a4 (u)phot.limbDarkdoublea4v4-terms limb darkening coefficient a4 (v)phot.limbDarkdoublea4b4-terms limb darkening coefficient a4 (b)phot.limbDarkdoublea4y4-terms limb darkening coefficient a4 (y)phot.limbDarkdoublea4U4-terms limb darkening coefficient a4 (U)phot.limbDarkdoublea4B4-terms limb darkening coefficient a4 (B)phot.limbDarkdoublea4V4-terms limb darkening coefficient a4 (V)phot.limbDarkdoublea4R4-terms limb darkening coefficient a4 (R)phot.limbDarkdoublea4I4-terms limb darkening coefficient a4 (I)phot.limbDarkdoublea4J4-terms limb darkening coefficient a4 (J)phot.limbDarkdoublea4H4-terms limb darkening coefficient a4 (H)phot.limbDarkdoublea4K4-terms limb darkening coefficient a4 (K)phot.limbDarkdoublemucriu4-terms {mu}_cri_ point (u)stat.fit.paramdoublemucriv4-terms {mu}_cri_ point (v)stat.fit.paramdoublemucrib4-terms {mu}_cri_ point (b)stat.fit.paramdoublemucriU4-terms {mu}_cri_ point (U)stat.fit.paramdoublemucriB4-terms {mu}_cri_ point (B)stat.fit.paramdoublemucriV4-terms {mu}_cri_ point (V)stat.fit.paramdoublemucriR4-terms {mu}_cri_ point (R)stat.fit.paramdoublemucriI4-terms {mu}_cri_ point (I)stat.fit.paramdoublemucriJ4-terms {mu}_cri_ point (J)stat.fit.paramdoublemucriH4-terms {mu}_cri_ point (H)stat.fit.paramdoublemucriK4-terms {mu}_cri_ point (K)stat.fit.paramdoubleCHI2u4-terms chi2 (u)stat.fit.chi2doubleCHI2v4-terms chi2 (v)stat.fit.chi2doubleCHI2b4-terms chi2 (b)stat.fit.chi2doubleCHI2y4-terms chi2 (y)stat.fit.chi2doubleCHI2U4-terms chi2 (U)stat.fit.chi2doubleCHI2B4-terms chi2 (B)stat.fit.chi2doubleCHI2V4-terms chi2 (V)stat.fit.chi2doubleCHI2R4-terms chi2 (R)stat.fit.chi2doubleCHI2I4-terms chi2 (I)stat.fit.chi2doubleCHI2J4-terms chi2 (J)stat.fit.chi2doubleCHI2H4-terms chi2 (H)stat.fit.chi2doubleCHI2K4-terms chi2 (K)stat.fit.chi2doubleJ/A+A/674/A63/table12Eq.3 PHOENIX, uvbyUBVRIJHK/M2mucriB4-terms {mu}_cri_ point (B)stat.fit.paramdoublemucriJ4-terms {mu}_cri_ point (J)stat.fit.paramdoubleCHI2y4-terms chi2 (y)stat.fit.chi2doubleCHI2B4-terms chi2 (B)stat.fit.chi2doubleCHI2V4-terms chi2 (V)stat.fit.chi2doubleCHI2R4-terms chi2 (R)stat.fit.chi2doubleCHI2I4-terms chi2 (I)stat.fit.chi2doubleCHI2J4-terms chi2 (J)stat.fit.chi2doubleCHI2K4-terms chi2 (K)stat.fit.chi2doubleZ[0] log10 [M/H]phys.abund.ZfloatrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintloggLog10 Surface gravitylog(cm.s**-2)phys.gravityfloatTeffEffective temperatureKphys.temperature.effectivefloatVel[2] Microturbulent velocitykm/sphys.velocfloata1u4-terms limb darkening coefficient a1 (u)phot.limbDarkdoublea1v4-terms limb darkening coefficient a1 (v)phot.limbDarkdoublea1b4-terms limb darkening coefficient a1 (b)phot.limbDarkdoublea1y4-terms limb darkening coefficient a1 (y)phot.limbDarkdoublea1U4-terms limb darkening coefficient a1 (U)phot.limbDarkdoublea1B4-terms limb darkening coefficient a1 (B)phot.limbDarkdoublea1V4-terms limb darkening coefficient a1 (V)phot.limbDarkdoublea1R4-terms limb darkening coefficient a1 (R)phot.limbDarkdoublea1I4-terms limb darkening coefficient a1 (I)phot.limbDarkdoublea1J4-terms limb darkening coefficient a1 (J)phot.limbDarkdoublea1H4-terms limb darkening coefficient a1 (H)phot.limbDarkdoublea1K4-terms limb darkening coefficient a1 (K)phot.limbDarkdoublea2u4-terms limb darkening coefficient a2 (u)phot.limbDarkdoublea2v4-terms limb darkening coefficient a2 (v)phot.limbDarkdoublea2b4-terms limb darkening coefficient a2 (b)phot.limbDarkdoublea2y4-terms limb darkening coefficient a2 (y)phot.limbDarkdoublea2U4-terms limb darkening coefficient a2 (U)phot.limbDarkdoublea2B4-terms limb darkening coefficient a2 (B)phot.limbDarkdoublea2V4-terms limb darkening coefficient a2 (V)phot.limbDarkdoublea2R4-terms limb darkening coefficient a2 (R)phot.limbDarkdoublea2I4-terms limb darkening coefficient a2 (I)phot.limbDarkdoublea2J4-terms limb darkening coefficient a2 (J)phot.limbDarkdoublea2H4-terms limb darkening coefficient a2 (H)phot.limbDarkdoublea2K4-terms limb darkening coefficient a2 (K)phot.limbDarkdoublea3u4-terms limb darkening coefficient a3 (u)phot.limbDarkdoublea3v4-terms limb darkening coefficient a3 (v)phot.limbDarkdoublea3b4-terms limb darkening coefficient a3 (b)phot.limbDarkdoublea3y4-terms limb darkening coefficient a3 (y)phot.limbDarkdoublea3U4-terms limb darkening coefficient a3 (U)phot.limbDarkdoublea3B4-terms limb darkening coefficient a3 (B)phot.limbDarkdoublea3V4-terms limb darkening coefficient a3 (V)phot.limbDarkdoublea3R4-terms limb darkening coefficient a3 (R)phot.limbDarkdoublea3I4-terms limb darkening coefficient a3 (I)phot.limbDarkdoublea3J4-terms limb darkening coefficient a3 (J)phot.limbDarkdoublea3H4-terms limb darkening coefficient a3 (H)phot.limbDarkdoublea3K4-terms limb darkening coefficient a3 (K)phot.limbDarkdoublea4u4-terms limb darkening coefficient a4 (u)phot.limbDarkdoublea4v4-terms limb darkening coefficient a4 (v)phot.limbDarkdoublea4b4-terms limb darkening coefficient a4 (b)phot.limbDarkdoublea4y4-terms limb darkening coefficient a4 (y)phot.limbDarkdoublea4U4-terms limb darkening coefficient a4 (U)phot.limbDarkdoublea4B4-terms limb darkening coefficient a4 (B)phot.limbDarkdoublea4V4-terms limb darkening coefficient a4 (V)phot.limbDarkdoublea4R4-terms limb darkening coefficient a4 (R)phot.limbDarkdoublea4I4-terms limb darkening coefficient a4 (I)phot.limbDarkdoublea4J4-terms limb darkening coefficient a4 (J)phot.limbDarkdoublea4H4-terms limb darkening coefficient a4 (H)phot.limbDarkdoublea4K4-terms limb darkening coefficient a4 (K)phot.limbDarkdoublemucriu4-terms {mu}_cri_ point (u)stat.fit.paramdoublemucriv4-terms {mu}_cri_ point (v)stat.fit.paramdoublemucrib4-terms {mu}_cri_ point (b)stat.fit.paramdoublemucriy4-terms {mu}_cri_ point (y)stat.fit.paramdoublemucriU4-terms {mu}_cri_ point (U)stat.fit.paramdoublemucriV4-terms {mu}_cri_ point (V)stat.fit.paramdoublemucriR4-terms {mu}_cri_ point (R)stat.fit.paramdoublemucriI4-terms {mu}_cri_ point (I)stat.fit.paramdoublemucriH4-terms {mu}_cri_ point (H)stat.fit.paramdoublemucriK4-terms {mu}_cri_ point (K)stat.fit.paramdoubleCHI2u4-terms chi2 (u)stat.fit.chi2doubleCHI2v4-terms chi2 (v)stat.fit.chi2doubleCHI2b4-terms chi2 (b)stat.fit.chi2doubleCHI2U4-terms chi2 (U)stat.fit.chi2doubleCHI2H4-terms chi2 (H)stat.fit.chi2double