7.3.2 Orbital model

Two different methods are used to carry out orbital fits to the astrometric data: (1) a hybrid implementation of a differential evolution Markov Chain Monte Carlo (DE-MCMC) algorithm and a (2) Genetic Algorithm (GA). All solutions published in Gaia DR3 were determined with a single-companion model, though the codes are designed to efficiently search for higher multiplicity models too. Both algorithms achieve convergence by maximising the same figure of merit, the Log-likelihood ($\ln ℒ$). More details can be found in Holl et al. (2023b).

The parameters that are optimized are the twelve orbital parameters of Section 7.2.5, plus an additional (non-linear) jitter term astrometric_jitter, i.e., a total of 13 parameters of which 9 linear and 4 non-linear.