Transit timing to first order in eccentricity

Abstract

Characterization of transiting planets with transit timing variations (TTVs) requires understanding how to translate the observed TTVs into masses and orbital elements of the planets. This can be challenging in multi-planet transiting systems, but fortunately these systems tend to be nearly plane-parallel and low eccentricity. Here we present a novel derivation of analytic formulae for TTVs that are accurate to first order in the planet-star mass ratios and in the orbital eccentricities. These formulae are accurate in proximity to first order resonances, as well as away from resonance, and compare well with more computationally expensive N-body integrations in the low eccentricity, low mass-ratio regime when applied to simulated and to actual multi-transiting Kepler planet systems. We make code available for implementing these formulae.

Revised to match published version; associated code may be found at https://github.com/ericagol/TTVFaster

References in corpus (10)

• DHP Framework: Digital Health Passports Using Blockchain -- Use case on international tourism during the COVID-19 pandemic
• Eccentricity from transit photometry: small planets in Kepler multi-planet systems have low eccentricities
• TTVFast: An efficient and accurate code for transit timing inversion problems
• The mass of the Mars-sized exoplanet Kepler-138 b from transit timing
• Using long-term transit timing to detect terrestrial planets
• Measurement of planet masses with transit timing variations due to synodic "chopping" effects
• Planet Hunters VII. Discovery of a New Low-Mass, Low-Density Planet (PH3 c) Orbiting Kepler-289 with Mass Measurements of Two Additional Planets (PH3 b and d)
• The Exoplanet Orbital Eccentricity - Multiplicity Relation and the Solar System
• Periastron Precession Measurements in Transiting Extrasolar Planetary Systems at the Level of General Relativity
• The Effect of Conjunctions on the Transit Timing Variations of Exoplanets

Cited by in corpus (48)

• Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1
• Kepler Planet Masses and Eccentricities from TTV Analysis
• The Featureless Transmission Spectra of Two Super-Puff Planets
• Characterization of the K2-18 multi-planetary system with HARPS: A habitable zone super-Earth and discovery of a second, warm super-Earth on a non-coplanar orbit
• The K2-138 System: A Near-Resonant Chain of Five Sub-Neptune Planets Discovered by Citizen Scientists
• The Compositional Diversity of Low-Mass Exoplanets
• Kepler-411: a four-planet system with an active host star
• Numerical and Analytical Modelling of Transit Time Variations
• Kepler-108: A Mutually Inclined Giant Planet System
• Sensitivity bias in the mass-radius distribution from Transit Timing Variations and Radial Velocity measurements
• Dynamics and Transit Variations of Resonant Exoplanets
• Transit timing variation and transmission spectroscopy analyses of the hot Neptune GJ3470b
• Exoplanet characterisation in the longest known resonant chain: the K2-138 system seen by HARPS
• The CARMENES search for exoplanets around M dwarfs -- LP 714-47b (TOI 442.01): Populating the Neptune desert
• Long-Period Giant Companions to Three Compact, Multiplanet Systems
• Two Small Transiting Planets and a Possible Third Body Orbiting HD 106315
• Mass and Eccentricity Constraints in the WASP-47 Planetary System from a Simultaneous Analysis of Radial Velocities & Transit Timing Variations
• A spectral approach to transit timing variations
• A pair of warm giant planets near the 2:1 mean motion resonance around the K-dwarf star TOI-2202
• Evidence for Morning-to-Evening Limb Asymmetry on the Cool Low-Density Exoplanet WASP-107b
• Unbiasing the density of TTV-characterised sub-Neptunes: Update of the mass-radius relationship of 34 Kepler planets
• Transiting Exoplanet Monitoring Project (TEMP). VI. The Homogeneous Refinement of System Parameters for 39 Transiting Hot Jupiters with 127 New Light Curves
• Alleviating the transit timing variation bias in transit surveys. I. RIVERS: Method and detection of a pair of resonant super-Earths around Kepler-1705
• Following up the Kepler field: Masses of Targets for transit timing and atmospheric characterization
• Visual Analysis and Demographics of Kepler Transit Timing Variations
• A Simplified Photodynamical Model for Planetary Mass Determination in Low-Eccentricity Multi-Transiting Systems
• celmech: A Python package for celestial mechanics
• TESS Observations of Kepler systems with Transit Timing Variations
• Modal Decomposition of TTV - Inferring Planet Masses and Eccentricities
• A differentiable N-body code for transit timing and dynamical modeling. I. Algorithm and derivatives
• The GAPS Programme at TNG XL: A puffy and warm Neptune-sized planet and an outer Neptune-mass candidate orbiting the solar-type star TOI-1422
• K2-138 g: Spitzer Spots a Sixth Planet for the Citizen Science System
• Alleviating the Transit Timing Variations bias in transit surveys. II. RIVERS: Twin resonant Earth-sized planets around Kepler-1972 recovered from Kepler's false positive
• Pre-discovery transits of the exoplanets WASP-18 b and WASP-33 b from Hipparcos
• The CARMENES search for exoplanets around M dwarfs. Revisiting the GJ 581 multi-planetary system with new Doppler measurements from CARMENES, HARPS, and HIRES
• An Accurate 3D Analytic Model for Exoplanetary Photometry, Radial Velocity, and Astrometry
• The Efficiency of Geometric Samplers for Exoplanet Transit Timing Variation Models
• Validation of a Temperate Fourth Planet in the K2-133 Multi-planet System
• The Exoplanet Edge: Planets Don't Induce Observable TTVs with a Dominant TTV Period Faster than Half their Orbital Period
• Explicit relations and criteria for eclipses, transits and occultations
• A differentiable N-body code for transit timing and dynamical modelling -- II. Photodynamics
• Nauyaca: a new tool to determine planetary masses and orbital elements through transit timing analysis
• Mass Upper Bounds for Over 50 Kepler Planets Using Low-S/N Transit Timing Variations
• Scaling K2. V. Statistical Validation of 60 New Exoplanets From K2 Campaigns 2-18
• The multi-planet system TOI-5624: Four transiting sub-Neptunes with an outer companion revealed by transit-timing variations
• Stability of exoplanetary systems retrieved from scalar time series
• Modeling the Solar System I: Characterization Limits from Analytic Timing Variations
• The Dynamical Environment of Kepler-223 Planetary System