An alternative stable solution for the Kepler-419 system, obtained with the use of a genetic algorithm

TL;DR

This paper presents a genetic algorithm-based method to determine the orbital parameters and masses of exoplanets in the Kepler-419 system from transit timing variations, achieving a stable solution consistent with observations.

Contribution

It introduces a novel application of genetic algorithms to accurately infer exoplanetary system parameters from transit data, including non-transiting planets.

Findings

Successfully computed all system parameters matching observed transits.

Identified a stable orbital configuration for Kepler-419.

Demonstrated the method's effectiveness in modeling transit timing variations.

Abstract

The mid-transit times of an exoplanet may be non-periodic. The variations in the timing of the transits with respect to a single period, that is, the transit timing variations (TTVs), can sometimes be attributed to perturbations by other exoplanets present in the system, which may or may not transit the star. Our aim is to compute the mass and the six orbital elements of an non-transiting exoplanet, given only the central times of transit of the transiting body. We also aim to recover the mass of the star and the mass and orbital elements of the transiting exoplanet, suitably modified in order to decrease the deviation between the observed and the computed transit times by as much as possible. We have applied our method, based on a genetic algorithm, to the Kepler-419 system. We were able to compute all fourteen free parameters of the system, which, when integrated in time, give transits within the observational errors. We also studied the dynamics and the long-term orbital evolution of the Kepler-419 planetary system as defined by the orbital elements computed by us, in order to determine its stability.