Deep learning estimates a non-transiting companion in the Kepler-88 system

In the Kepler-88 system, a deep-learning method uses changes in a transiting planet’s timing and transit duration to estimate the properties of a companion that does not cross its star from our viewpoint. Tests based on one million simulated systems produced estimates of the companion’s orbit and mass, with accuracy depending on the signal strength.

Star system: Kepler-88 | Distance from the Sun: 1231 light years

A deep-learning method can use the timing and duration of a planet’s transits to estimate the properties of a companion planet that does not transit its star. The approach was tested using Kepler-88 as a starting point, with the known properties of its inner, transiting planet held fixed while the outer companion’s mass and orbit varied. This targets systems where only one planet crosses the star from our viewpoint, leaving the other planet’s properties harder to measure.

The model reads transit timing variations, or TTVs: shifts in when a planet passes in front of its star, caused in part by the gravity of other planets. It also uses transit duration variations, or TDVs, which are changes in how long each transit lasts. A Transformer-based neural network analyzes patterns across the sequence of timing data. The model learned from one million simulated cases, with the stellar and transiting planet properties assumed to be known.

For the Kepler-88-based tests, the estimated outer planet’s orbital size and eccentricity had overall fractional errors of about 10 percent or less. The estimated planet mass had errors of roughly 10 to 30 percent. On a separate test set, errors fell below a few percent for systems whose TTV signals ranged from about 0.3 seconds to about five minutes. These results apply to the tested cases; systems with much weaker or stronger signals, additional planets, or stellar companions were identified as future extensions.

Key findings
The method uses transit timing and duration changes to estimate a non-transiting companion.
It was tested on a Kepler-88-based two-planet setup using one million simulations.
Overall fractional errors were about 10 percent or less for orbital size and eccentricity, and roughly 10 to 30 percent for planet mass.
Test-set errors were below a few percent for TTV signals from about 0.3 seconds to about five minutes.

Scientific study

A Deep Learning Framework for TTV Characterization: A Case Study of the Kepler-88 System (external link)