J/AJ/155/205ivo://CDS.VizieR/J/AJ/155/205doi:10.26093/cds/vizier.51550205CDSHsu D.C.Ford E.B.Ragozzine D.Morehead R.C.2019-01-08T08:56:13Z2018-12-13T07:35:56ZCDS support team

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

cds-question@unistra.frexoplanetsf-starsastronomical-modelsWe present a new framework to characterize the occurrence rates of planet candidates identified by Kepler based on hierarchical Bayesian modeling, approximate Bayesian computing (ABC), and sequential importance sampling. For this study, we adopt a simple 2D grid in planet radius and orbital period as our model and apply our algorithm to estimate occurrence rates for Q1-Q16 planet candidates orbiting solar-type stars. We arrive at significantly increased planet occurrence rates for small planet candidates (R_p_<1.25 R_{Earth}_) at larger orbital periods (P>80 day) compared to the rates estimated by the more common inverse detection efficiency method (IDEM). Our improved methodology estimates that the occurrence rate density of small planet candidates in the habitable zone of solar-type stars is 1.6_-0.5_^+1.2^ per factor of 2 in planet radius and orbital period. Additionally, we observe a local minimum in the occurrence rate for strong planet candidates marginalized over orbital period between 1.5 and 2 R_{Earth}_ that is consistent with previous studies. For future improvements, the forward modeling approach of ABC is ideally suited to incorporating multiple populations, such as planets, astrophysical false positives, and pipeline false alarms, to provide accurate planet occurrence rates and uncertainties. Furthermore, ABC provides a practical statistical framework for answering complex questions (e.g., frequency of different planetary architectures) and providing sound uncertainties, even in the face of complex selection effects, observational biases, and follow-up strategies. In summary, ABC offers a powerful tool for accurately characterizing a wide variety of astrophysical populations.2018AJ....155..205Hhttps://cdsarc.cds.unistra.fr/viz-bin/cat/J/AJ/155/205CatalogResearchIsServedByTAP VizieR generic servicerelated-toJ/ApJ/784/45 : Kepler's multiple planet candidates. III. (Rowe+, 2014)J/ApJ/790/146 : Planets in Kepler's multi-transiting systems (Fabrycky+, 2014)J/ApJS/211/2 : Revised stellar properties of Q1-16 Kepler targetsJ/ApJ/809/8 : Terrestrial planet occurrence rates for KOI starsJ/ApJ/812/46 : Transit metric for Q1-Q17 Kepler candidates (Thompson+, 2015)J/ApJ/814/130 : Planet occurrence rates calculated for KOIs (Mulders+, 2015)J/ApJS/217/18 : Potential transit signals in Kepler Q1-Q17 (Seader+, 2015)J/ApJS/217/31 : Kepler planetary candidates. VI. 4yr Q1-Q16 (Mullally+, 2015)J/ApJ/828/99 : Kepler pipeline transit signal recovery. III.J/ApJS/224/12 : Kepler planetary candidates. VII. 48-month (Coughlin+, 2016)https://cds.unistra.fr/vizier-org/licences_vizier.htmlhttps://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/AJ/155/205https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/AJ/155/205http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/AJ/155/205https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/AJ/155/205https://vizier.iucaa.in/viz-bin/votable?-source=J/AJ/155/205http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/AJ/155/205GETtext/xml+votablehttps://tapvizier.cds.unistra.fr/TAPVizieR/tapdefaultJ/AJ/155/205/table1ABC, simplified Bayesian model, and IDEM estimated occurrence rates for Q1-Q16 KOI catalog planet candidates associated with FGK starsl_Bay[<] Limit flag on Baymeta.code.errorcharrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintb_Per[0.5/160] Lower value of period bindtime.period;stat.minfloatB_Per[1.25/320] Upper value of period bindtime.period;stat.maxfloatb_Rad[0.5/12] Lower value of radius bin(6.3781x10+6m)phys.size.radius;stat.minfloatB_Rad[0.75/16] Upper value of radius bin(6.3781x10+6m)phys.size.radius;stat.maxfloatl_ABC[<] Limit flag on ABCmeta.code.errorcharABC[3.6e-05/1.4] Full approximate Bayesian computing (ABC) model estimated planet occurrence ratestat.fit.paramdoublee_ABC[2.2e-05/0.13]? Lower limit uncertainty in ABCstat.error;stat.mindoublenullableE_ABC[3.2e-05/0.19]? Upper limit uncertainty in ABCstat.error;stat.maxdoublenullableBay[2.4e-05/0.8] Simplified Bayesian model estimated planet occurrence ratestat.fit.paramdoublee_Bay[3.1e-05/0.086]? Uncertainty in Baystat.errordoublenullableIDEM[2.7e-05/0.174]? Inverse detection efficiency method (IDEM) estimated planet occurrence ratestat.fit.paramdoublenullablee_IDEM[2.6e-05/0.066]? Uncertainty in IDEMstat.errordoublenullable