Nauyaca: a new tool to determine planetary masses and orbital elements through transit timing analysis

Abstract

Transit Timing Variations (TTVs) 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 find planetary masses and orbital elements through the fitting of observed mid-transit times from a N-body approach. The fitting strategy consists in 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 (MCMC) 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 number of planets where all of them transit. We calculate their mid-transit 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 $\sim$1-14 M$_{\oplus}$ for masses, between 10-110 seconds for periods and between $\sim$0.01-0.03 for eccentricities. We also investigate the effects of the signal-to-noise and number of transits in 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.