Kepler Object of Interest Network II. Photodynamical modelling of Kepler-9 over 8 years of transit observations

Abstract

The Kepler Object of Interest Network (KOINet) is a multi-site network of telescopes around the globe organised to follow up transiting planet candidate KOIs with large transit timing variations (TTVs). Its main goal is to complete their TTV curves, as the Kepler telescope no longer observes the original Kepler field. Combining Kepler and new ground-based transit data we improve the modelling of these systems. To this end, we have developed a photodynamical model, and we demonstrate its performance using the Kepler-9 system as an example. Our comprehensive analysis combines the numerical integration of the system's dynamics over the time span of the observations along with the transit light curve model. This model is coupled with a Markov chain Monte Carlo algorithm, allowing the exploration of the model parameter space. Applied to the Kepler-9 long cadence data, short cadence data and 13 new transit observations collected by KOINet between the years 2014 to 2017, our modelling provides well constrained predictions for the next transits and the system's parameters. We have determined the densities of the planets Kepler-9b and 9c to the very precise values of rho_b = 0.439 +/-0.023 g/cm3 and rho_c = 0.322 +/- 0.017 g/cm3. Our analysis reveals that Kepler-9c will stop transiting in about 30 years. This results from strong dynamical interactions between Kepler-9b and 9c, near 2:1 resonance, that leads to a periodic change in inclination. Over the next 30 years the inclination of Kepler-9c (-9b) will decrease (increase) slowly. This should be measurable by a substantial decrease (increase) in the transit duration, in as soon as a few years' time. Observations that contradict this prediction might indicate the presence of additional objects. If this prediction proves true, this behaviour opens up a unique chance to scan the different latitudes of a star.

arXiv comment24 pages, 22 figures

References in corpus (43)

• emcee: The MCMC Hammer
• Gaia Data Release 2. Summary of the contents and survey properties
• The Gaia mission
• Modules for Experiments in Stellar Astrophysics (MESA)
• The Transiting Exoplanet Survey Satellite
• Modules for Experiments in Stellar Astrophysics (MESA): Giant Planets, Oscillations, Rotation, and Massive Stars
• Modules for Experiments in Stellar Astrophysics (MESA): Binaries, Pulsations, and Explosions
• MESA Isochrones and Stellar Tracks (MIST). I: Solar-Scaled Models
• Analytic Lightcurves for Planetary Transit Searches
• MESA Isochrones and Stellar Tracks (MIST) 0: Methods for the construction of stellar isochrones
• The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms
• The PLATO 2.0 Mission
• Achieving better than 1 minute accuracy in the Heliocentric and Barycentric Julian Dates
• Ages for illustrative field stars using gyrochronology: viability, limitations and errors
• On detecting terrestrial planets with timing of giant planet transits
• DHP Framework: Digital Health Passports Using Blockchain -- Use case on international tourism during the COVID-19 pandemic
• Architecture and Dynamics of Kepler's Candidate Multiple Transiting Planet Systems
• Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian order. V. Spin Effects
• A Closely-Packed System of Low-Mass, Low-Density Planets Transiting Kepler-11
• Temperate Earth-sized planets transiting a nearby ultracool dwarf star
• Identifying Exoplanets with Deep Learning: A Five Planet Resonant Chain around Kepler-80 and an Eighth Planet around Kepler-90
• Parameter Estimation from Time-Series Data with Correlated Errors: A Wavelet-Based Method and its Application to Transit Light Curves
• The California-Kepler Survey. I. High Resolution Spectroscopy of 1305 Stars Hosting Kepler Transiting Planets
• Binning is sinning: morphological light-curve distortions due to finite integration time
• Planetary Candidates Observed by Kepler VI: Planet Sample from Q1-Q16 (47 Months)
• Modeling Kepler transit light curves as false positives: Rejection of blend scenarios for Kepler-9, and validation of Kepler-9d, a super-Earth-size planet in a multiple system
• CHEOPS: A Transit Photometry Mission for ESA's Small Mission Programme
• Kepler Planet Masses and Eccentricities from TTV Analysis
• High-precision photometry by telescope defocussing. I. The transiting planetary system WASP-5
• A First Comparison of Kepler Planet Candidates in Single and Multiple Systems
• Transit Timing Observations from Kepler. VIII Catalog of Transit Timing Measurements of the First Twelve Quarters
• TTVFast: An efficient and accurate code for transit timing inversion problems
• Secure TTV Mass Measurements: Ten Kepler Exoplanets between 3 and 8 Earth Masses with Diverse Densities and Incident Fluxes
• The Starspots of HAT-P-11: Evidence for a Solar-like Dynamo
• Measurement of planet masses with transit timing variations due to synodic "chopping" effects
• Migration of two massive planets into (and out of) first order mean motion resonances
• The Planetary Mass-Radius Relation and its Dependence on Orbital Period as Measured by Transit Timing Variations and Radial Velocities
• TRADES: A new software to derive orbital parameters from observed transit times and radial velocities. Revisiting Kepler-11 and Kepler-9
• Stellar Spin-Orbit Alignment for Kepler-9, a Multi-transiting Planetary system with Two Outer Planets Near 2:1 Resonance
• Qatar-1: indications for possible transit timing variations
• Kepler Object of Interest Network I. First results combining ground and space-based observations of Kepler systems with transit timing variations
• Can stellar activity make a planet seem misaligned?
• Transiting Exoplanet Monitoring Project (TEMP). III. On the Relocation of the Kepler-9~b Transit

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• Diffuser-Assisted Infrared Transit Photometry for Four Dynamically Interacting \textit{Kepler} Systems
• The Kepler Giant Planet Search. I: A Decade of Kepler Planet-host Radial Velocities from W. M. Keck Observatory
• HARPS-N radial velocities confirm the low densities of the Kepler-9 planets
• K2-146: Discovery of Planet c, Precise Masses from Transit Timing, and Observed Precession
• TOI-216: Resonant Constraints on Planet Migration
• First Light of Engineered Diffusers at the Nordic Optical Telescope Reveal Time Variability in the Optical Eclipse Depth of WASP-12b
• Following up the Kepler field: Masses of Targets for transit timing and atmospheric characterization
• Transit Timing Variations in the three-planet system: TOI-270
• TESS Observations of Kepler systems with Transit Timing Variations
• A differentiable N-body code for transit timing and dynamical modeling. I. Algorithm and derivatives
• Physical Properties and Impact Parameter Variations of Kepler Planets from Analytic Light Curve Modeling
• Systematic search for long-term transit duration changes in Kepler transiting planets
• Characterization of the HD 108236 system with CHEOPS and TESS. Confirmation of a fifth transiting planet
• Transit Duration Variations in Multi-Planet Systems
• An Accurate 3D Analytic Model for Exoplanetary Photometry, Radial Velocity, and Astrometry
• Transit least-squares survey -- III. A $1.9R_{\oplus }$ transit candidate in the habitable zone of Kepler-160 and a nontransiting planet characterized by transit-timing variations
• Exploiting periodic orbits as dynamical clues for Kepler and K2 systems
• Transit Depth Variations Reveal TOI-216 b to be a Super-Puff
• Light-Curve Evolution due to Secular Dynamics and the Vanishing Transits of KOI 120.01
• A differentiable N-body code for transit timing and dynamical modelling -- II. Photodynamics
• Evidence for a Non-Dichotomous Solution to the Kepler Dichotomy: Mutual Inclinations of Kepler Planetary Systems from Transit Duration Variations