Watch transit times shift as planets gravitationally perturb each other—detect non-transiting planets from TTV signals
Transit timing variations (TTV) occur when gravitational interactions between planets perturb their orbits, causing transits to occur slightly earlier or later than predicted by a simple Keplerian model. This technique has discovered and characterized hundreds of exoplanets, including non-transiting planets and planets too small to detect by other methods. TTVs are particularly sensitive to planets in or near mean-motion resonances, where periodic tugs accumulate over time.
The Observed minus Calculated (O-C) diagram plots the difference between observed transit times and times predicted from a constant-period ephemeris. In an unperturbed system, O-C = 0 for all transits. Gravitational perturbations from other planets cause periodic deviations, creating characteristic sinusoidal or quasi-sinusoidal patterns. The amplitude, period, and phase of these variations encode information about the perturbing planet's mass, orbital period, and orbital phase relative to the transiting planet.
TTVs are dramatically amplified near mean-motion resonances (MMR), where orbital periods have simple integer ratios like 2:1, 3:2, or 5:3. At exact resonance, planets return to the same relative configuration repeatedly, and perturbations add coherently rather than averaging out. The TRAPPIST-1 system displays strong TTVs due to a complex resonant chain, with adjacent pairs near 8:5, 5:3, 3:2, 3:2, and 4:3 resonances. These TTVs enabled precise mass measurements for all seven planets, revealing Earth-like densities.
The TTV amplitude scales roughly as (M_pert / M_star) × (P²/|P₁ - P₂|), where M_pert is the perturbing planet's mass, P is the orbital period, and |P₁ - P₂| is the period difference. Near resonance, where |P₁ - P₂| is small, amplitudes can reach tens of minutes—easily detectable with Kepler or TESS photometry (precision ~1 minute). Away from resonance, TTVs decay rapidly and become difficult to detect unless the perturbing planet is very massive or the observation baseline is very long.
Inverting TTV signals to recover planetary masses and orbits is a complex nonlinear problem. Analytic approximations exist for first-order resonant interactions, but full N-body integration is often required to fit observed TTVs. The TTV pattern depends on both planets' masses, eccentricities, and orbital phases at epoch. Degeneracies can arise, particularly between mass and eccentricity, but multi-planet systems with multiple pairs of interacting planets provide additional constraints that break these degeneracies.
The first TTV detections came from Kepler photometry of multi-planet systems like Kepler-9, where two Saturn-mass planets near 2:1 resonance showed 4-hour timing variations. Kepler-36 exhibits extreme TTVs (up to 30 minutes) from a rocky super-Earth and a gaseous sub-Neptune in tightly-packed orbits with density contrast exceeding 8:1. The TRAPPIST-1 system, discovered in 2017, showcases TTVs as a mass-measurement technique: photometry alone constrained all seven planetary masses to ~15% precision, enabling habitability assessments without radial velocity follow-up.
TTVs excel where radial velocity (RV) struggles: low-mass planets around faint stars, tightly-packed systems where RV signals overlap, and planets around active stars where stellar noise dominates RV measurements. TTVs also detect non-transiting planets through their gravitational influence on transiting companions. However, TTVs require multi-planet systems and long observation baselines. Combining TTV and RV measurements provides the most complete characterization, yielding masses, densities, and dynamical states for compact planetary systems.