Nauyaca: a New Tool to Determine Planetary Masses and Orbital Elements through Transit Timing Analysis

Abstract

Abstract The transit timing variations method is currently the most successful method to determine dynamical masses and orbital elements for Earth-sized transiting planets. Precise mass determination is fundamental to restrict planetary densities and thus infer planetary compositions. In this work, we present Nauyaca, a Python package dedicated to finding planetary masses and orbital elements through the fitting of observed midtransit times from an N-body approach. The fitting strategy consists of performing a sequence of minimization algorithms (optimizers) that are used to identify high probability regions in the parameter space. These results from optimizers are used for initialization of a Markov chain Monte Carlo method, using an adaptive Parallel-Tempering algorithm. A set of runs are performed in order to obtain posterior distributions of planetary masses and orbital elements. In order to test the tool, we created a mock catalog of synthetic planetary systems with different numbers of planets where all of them transit. We calculate their midtransit times to give them as an input to Nauyaca, testing statistically its efficiency in recovering the planetary parameters from the catalog. For the recovered planets, we find typical dispersions around the real values of ∼1–14 M ⊕ for masses, between 10–110 s for periods, and between ∼0.01–0.03 for eccentricities. We also investigate the effects of the signal-to-noise ratio and number of transits on the correct determination of the planetary parameters. Finally, we suggest choices of the parameters that govern the tool for the usage with real planets, according to the complexity of the problem and computational facilities.