J/AJ/163/91ivo://CDS.VizieR/J/AJ/163/91doi:10.26093/cds/vizier/be-53-2vCDSJudkovsky Y.Ofir A.Aharonson O.2026-07-02T11:44:12Z2025-10-06T15:32:30ZCDS support team

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

cds-question@unistra.frexoplanetsvisible-astronomyphotometryastronomical-modelsWe apply AnalyticLC, an analytic model described in an accompanying paper, to interpret Kepler data of systems that contain two or three transiting planets. We perform tests to verify that the obtained solutions agree with full N-body integrations, and that the number of model parameters is statistically justified. We probe non-co-planar interactions via impact parameter variations (TbVs), enabled by our analytic model. The subset of systems with a valid solution includes 54 systems composed of 140 planets, more than half of which are without previously reported mass constraints. Overall we provide: (I) estimates of physical and orbital properties for all systems analyzed; (II) 102 planets with mass detections significant to better than 3{sigma}, 43 of which have masses below 5M{Earth}; and (III) 35 TbVs significant to better than 3{sigma}. We focus on select systems showing strong TbVs, which can result from either interaction among the known transiting planets, or with a nontransiting object, and provide: (IV) a method to constrain the parameters of such unseen companions. These results are enabled by an accurate 3D photodynamical model, of a kind expected to become increasingly important for modeling multidecade photometric and composite (radial velocity, astrometry) data sets.2022AJ....163...91Jhttps://cdsarc.cds.unistra.fr/viz-bin/cat/J/AJ/163/91CatalogResearchIsServedByTAP VizieR generic serviceIsServedByConesearch servicerelated-toI/355 : Gaia DR3 Part 1. Main source (Gaia Collaboration, 2022)V/133 : Kepler Input Catalog (Kepler Mission Team, 2009)IV/39 : TESS Input Catalog version 8.2 (TIC v8.2) (Paegert+, 2021)J/A+A/363/1081 : Non-linear limb-darkening law for LTE models (Claret 2000)J/ApJ/634/625 : Radial velocities and photometry of GJ 876 (Rivera+, 2005)J/ApJS/197/8 : Keplers candidate multiple transiting planets (Lissauer+, 2011)J/ApJ/750/114 : Kepler TTVs. IV. 4 multiple-planet systems (Fabrycky+, 2012)J/MNRAS/421/2342 : 4 Kepler systems transit timing observation (Steffen+, 2012)J/A+A/555/A58 : New Kepler planetary candidates (Ofir+, 2013)J/ApJ/790/146 : Planets in Kepler's multi-transiting systems (Fabrycky+, 2014)J/ApJ/787/80 : 139 Kepler planets transit time variations (Hadden+, 2014)J/ApJS/210/20 : Small Kepler planets radial velocities (Marcy+, 2014)J/ApJS/210/25 : Transit timing variation for 15 planetary pairs II. (Xie, 2014)J/A+A/573/A124 : Kepler-117 (KOI-209) transit-timing variations (Bruno+, 2015)J/ApJS/225/9 : Kepler TTVs IX. The full long-cadence data set (Holczer+, 2016)J/AJ/154/109 : California-Kepler Survey. III. Planet radii (Fulton+, 2017)J/ApJS/229/30 : Revised stellar proper. of Q1-17 Kepler targets (Mathur+, 2017)J/AJ/154/5 : Transit timing variations of 145 Kepler planets (Hadden+, 2017)J/A+A/605/A72 : Planetary systems AMD-stability (Laskar+, 2017)J/MNRAS/465/2634 : Kepler and K2 best candidates for planets (Armstrong+2017)J/A+A/618/A41 : Photometry of Kepler-9b and c transits (Freudenthal+, 2018)J/AJ/156/264 : California-Kepler Survey VII. Planet radius gap (Fulton+, 2018)J/ApJS/234/9 : A spectral approach to transit timing variations (Ofir+, 2018)J/AJ/155/48 : California-Kepler Survey. V. Masses and radii (Weiss+, 2018)J/ApJS/235/38 : Kepler planetary cand. VIII. DR25 reliability (Thompson+2018)J/AJ/157/145 : HIRES RVs of three compact, multiplanet systems (Mills+, 2019)J/AJ/159/280 : Gaia-Kepler stellar properties cat.I. KIC stars (Berger+, 2020)J/ApJ/890/23 : NUV and FUV measurements of planet host stars (Loyd+, 2020)J/AJ/161/246 : Tansit time variations for 12 exoplanets (Jontof-Hutter+, 2021)http://exoplanetarchive.ipac.caltech.edu/index.html : NASA Exoplanets Archivehttps://cds.unistra.fr/vizier-org/licences_vizier.htmlhttps://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/AJ/163/91https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/AJ/163/91http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/AJ/163/91https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/AJ/163/91https://vizier.iucaa.in/viz-bin/votable?-source=J/AJ/163/91http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/AJ/163/91GETtext/xml+votablehttps://tapvizier.cds.unistra.fr/TAPVizieR/tapCone search capability for table J/AJ/163/91/planets (List of analyzed planets (Table added by CDS))https://vizier.cds.unistra.fr/viz-bin/conesearch/J/AJ/163/91/planets?https://vizier.iucaa.in/viz-bin/conesearch/J/AJ/163/91/planets?http://vizieridia.saao.ac.za/viz-bin/conesearch/J/AJ/163/91/planets?GETtext/xml+votable180.050000true285.573976738.40088250.005555555555555556https://cdsarc.cds.unistra.fr/viz-bin/moc/J/AJ/163/91?format=asciiOpticaldefaultJ/AJ/163/91/planetsList of analyzed planets (Table added by CDS)recnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintKeplerKepler star identifiermeta.id;meta.maincharprimarym_KeplerKepler identifier component for the planetmeta.code.multipcharKOI[41.01/2842.03] Kepler Object of Interest identifiermeta.idfloatKIC[3217264/12314973]? Kepler Input Catalog identifier (V/133, J/ApJS/229/30, IV/39)meta.idintnullableNorbNumber of solutions that pass all tests for this planet (link to Table A1)meta.numberintnullableNallNumber of solutions for this planet (link to Table A2)meta.numberintnullablefSolPlanet whose system has a valid dynamical solution (link to Table A3)meta.numberintnullablefIPvarPlanet with significant impact parameter variations (link to Table A4)meta.numberintnullablefNoSolPlanet whose system has no dynamical solution (link to Table A5)meta.numberintnullableSimbadSimbad column added by the CDSmeta.ref.urlchar_RARight Ascension (J2000) from SIMBAD (not part of the original data)degpos.eq.ra;meta.main_DEDeclination (J2000) from SIMBAD (not part of the original data)degpos.eq.dec;meta.mainJ/AJ/163/91/tablea1Physical and orbital elements of our solutions that pass all testsrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintAdopted[0/1] Adopted solution (1=yes)meta.codeintID[1/5] Solution identifiermeta.idintKeplerKepler star identifiermeta.id;meta.maincharprimarym_KeplerKepler identifier component for the planetmeta.code.multipcharKOI[41.01/2711.02] Kepler Object of Interest identifiermeta.idfloatPer[1.73/160.02] Mean orbital perioddtime.period;stat.meandoubleE_Mp[0.17/37] Upper uncertainty on Mp(5.97236x10+24kg)stat.error;stat.max;phys.massfloate_Mp[-45/-0.14] Lower uncertainty on Mp(5.97236x10+24kg)stat.error;stat.min;phys.massfloatrhop[0.08/49] Absolute planet density; derived from RhoRel and literature stellar densityg.cm**-3phys.densityfloatE_rhop[0.015/20] Upper uncertainty on rhopg.cm**-3stat.error;stat.max;phys.densityfloate_rhop[-45/-0.014] Lower uncertainty on rhopg.cm**-3stat.error;stat.min;phys.densityfloatMp/Ms[1.63/1429] Planet-to-star mass ratio(10-6)phys.mass;arith.ratiofloatE_Mp/Ms[0.21/58] Upper uncertainty on Mp/Ms(10-6)stat.error;stat.max;phys.massfloate_Mp/Ms[-67/-0.25] Lower uncertainty on Mp/Ms(10-6)stat.error;stat.min;phys.massfloatMp[0.39/597] Absolute planet mass; derived from Mp/Ms and literature stellar mass(5.97236x10+24kg)phys.massfloatRp[0.96/12.05] Absolute planet radius; derived from ror and literature stellar radius(6.3781x10+6m)phys.size.radiusfloatE_Rp[0.019/0.55] Upper uncertainty on Rp(6.3781x10+6m)stat.error;stat.max;phys.size.radiusfloate_Rp[-0.48/-0.021] Lower uncertainty on Rp(6.3781x10+6m)stat.error;stat.min;phys.size.radiusfloatdex[-0.18/0.24] Eccentricity difference to preceding planet; x is pointing at the observersrc.orbital.eccentricityfloatE_dex[2e-3/0.13] Upper uncertainty on dexstat.error;stat.max;src.orbital.eccentricityfloate_dex[-0.2/2.1e-3] Lower uncertainty on dexstat.error;stat.min;src.orbital.eccentricityfloatdey[-0.25/0.41] Eccentricity difference to preceding planet; y is the direction perpendicular to the line of sight pointing with the planets motion along transitsrc.orbital.eccentricityfloatE_dey[1.8e-3/0.15] Upper uncertainty on deystat.error;stat.max;src.orbital.eccentricityfloate_dey[-0.43/-2e-3] Lower uncertainty on deystat.error;stat.min;src.orbital.eccentricityfloatix[-29/35] ix=i*cos(Omega) is the inclination component corresponding to the inclination around to the line of sight ("roll angle")degsrc.orbital.inclinationfloatE_ix[0/22.6] Upper uncertainty on ixdegstat.error;stat.max;src.orbital.inclinationfloate_ix[-20.1/0] Lower uncertainty on ixdegstat.error;stat.min;src.orbital.inclinationfloatiy[-4.4/7.1] iy=i*sin(Omega) is the inclination component corresponding to the inclination relative to the line of sightdegsrc.orbital.inclinationfloatE_iy[5.8e-3/6.14] Upper uncertainty on iydegstat.error;stat.max;src.orbital.inclinationfloate_iy[-2.33/-5e-3] Lower uncertainty on iydegstat.error;stat.min;src.orbital.inclinationfloatJ/AJ/163/91/tablea2Light curve, transit, and mean motion resonance (MMR) proximity parameters of all analyzed planetsKeplerKepler star identifiermeta.id;meta.maincharprimaryTTVStd[2.4e-5/362.7] Best model Transit Time Variation (TTV) standard deviationminstat.stdev;src.var.amplitude;time.epochdoubleJ[0/5] J of the nearest first-order resonance J:J-1 with the planet from the inside. If the planet is innermost, the value is 0.src.orbitalintrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintAdopted[0/1] Adopted solution (1=yes)meta.codeintID[1/5] Solution identifiermeta.idintm_KeplerKepler identifier component for the planetmeta.code.multipcharKOI[41.01/2842.03] Kepler Object of Interest identifiermeta.idfloatPer[1.04/265.5] Mean orbital perioddtime.period;stat.meandoubleDelta[-1/0.5] Normalized distance from the J:J-1 resonance with the planet from the inside. If the planet is innermost, the value is 0.pos.distance;arith.ratiodoubleSPer[0/6612] Super-period of the J:J-1 resonance with the planet from the inside. If the planet is innermost, the value is 0.dtime.perioddoubleTdur0[0/12.8] Transit duration at first data time stamphtime.durationfloatE_Tdur0[0/2.3] Upper uncertainty on Tdur0hstat.error;stat.max;time.durationfloate_Tdur0[-3.1/-5.1e-3] Tdur0 uncertaintyhstat.error;stat.min;time.durationfloatTau0[0/153]? Ingress-egress time at first data time stampmintime.durationfloatnullableE_Tau0[0/156] Upper uncertainty on Tau0minstat.error;stat.max;time.durationdoublee_Tau0[-35/-0.011] Tau0 uncertaintyminstat.error;stat.min;time.durationfloatb0[-1.2/1.1] Impact parameter at BKJD=0 (Kepler Barycentric Julian Day)src.impactParamdoubleE_b0[5e-4/2.11] Upper uncertainty on b0stat.error;stat.max;src.impactParamdoublee_b0[-1.8/-5e-4] Lower uncertainty on b0stat.error;stat.min;src.impactParamdoubledb/dt[-0.82/0.82] Mean impact parameter variations rateyr**-1time;arith.ratiodoubleE_db/dt[8.6e-7/0.1] Upper uncertainty on db/dtyr**-1stat.error;stat.max;arith.ratedoublee_db/dt[-0.12/-1e-6] Lower uncertainty on db/dtyr**-1stat.error;stat.min;arith.ratedoubleJ/AJ/163/91/tablea3Stellar parameters of the systems for which valid dynamical solutions were foundKeplerKepler star identifiermeta.id;meta.maincharprimaryrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintKOI[41/2711] Kepler Object of Interest identifiermeta.idintKIC[3217264/12314973] Kepler Input Catalog identifier (V/133, J/ApJS/229/30, IV/39)meta.idintSourceSource for Ms and Rsmeta.bibcharu1[0.31/0.67] First limb-darkening coeff, taken from nexi (NASA Exoplanets Archive; NExScI)phot.limbDarkfloatu2[0.07/0.37] Second limb-darkening coeff, taken from nexi (NASA Exoplanets Archive; NExScI)phot.limbDarkfloatMs[0.5/1.41] Absolute stellar masssolMassphys.massfloatE_Ms[0.01/0.09] Upper uncertainty on MssolMassstat.error;stat.max;phys.massfloate_Ms[-0.09/-0.01] Lower uncertainty on MssolMassstat.error;stat.min;phys.massfloatRs[0.5/1.9] Absolute stellar radiussolRadphys.size.radiusfloatE_Rs[6e-3/0.2] Upper uncertainty on RssolRadstat.error;stat.max;phys.size.radiusfloate_Rs[-0.13/-9e-3] Lower uncertainty on RssolRadstat.error;stat.min;phys.size.radiusfloatB20Data for this system in Gaia-Kepler stellar properties catalog. I. KIC stars (Berger+, 2020) (link to J/ApJS/217/31)meta.numberintnullableJ/AJ/163/91/tablea4Planets with significant impact parameter variationsrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintAdopted[0/1] Adopted solution (1=yes)meta.codeintKeplerKepler planet identifiermeta.id;meta.maincharprimaryKOI[41.01/2672.02] Kepler Object of Interest identifiermeta.idfloatPer[1.5/130.2] Mean orbital perioddtime.period;stat.meandoubleNp[2/3] Model number of planetsmeta.numberintPos[1/3] Planet position within the system, from inside to outsideposintb0[-1/1] Impact parameter at BKJD=0 (Kepler Barycentric Julian Day)src.impactParamdoubleE_b0[5e-4/0.13] Upper uncertainty on b0stat.error;stat.max;src.impactParamdoublee_b0[-0.11/-5e-4] Lower uncertainty on b0stat.error;stat.min;src.impactParamdoubledb/dt[-0.76/0.06] Mean impact parameter variations rateyr**-1time;arith.ratiodoubleE_db/dt[3.9e-5/0.05] Upper uncertainty on db/dtyr**-1stat.error;stat.max;arith.ratedoublee_db/dt[-0.04/-3.8e-5] Lower uncertainty on db/dtyr**-1stat.error;stat.min;arith.ratedoublem_KeplerKepler identifier component for the planetmeta.code.multipcharJ/AJ/163/91/tablea5Systems with no dynamical solutionrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintKeplerKepler star identifiermeta.id;meta.maincharprimaryKOI[124/2842] Kepler Object of Interest identifiermeta.idintNp[2/3] Number of planets in the systemmeta.numberintReasonRejection reason (1)meta.notechar