Analytical determination of orbital elements using Fourier analysis

The ESA global astrometry space mission Gaia has been monitoring the position of a billion stars since 2014. analysis such massive dataset is challenging in terms data processing involved. In particular, blind detection and characterization single or multiple companions to (planets, brown dwarfs, stars) using requires highly efficient algorithms. this article, we present set analytical methods detect characterize scanning astrometric time series as well via combination radial velocity series. We propose general linear periodogram framework derive formulas for false alarm probability (FAP) peaks. Once significant peak identified, provide estimates all orbital elements companion based on Fourier decomposition signal. periodogram, FAP, can be computed separately tandem. These are complementary with more accurate computationally intensive numerical algorithms (e.g., least-squares minimization, Markov chain Monte-Carlo, genetic algorithms). our approximations used an initial condition accelerate convergence Our formalism partially implemented exoplanet pipeline third release. Since not yet publicly available, illustrate basis H ipparcos data, together on-ground CORALIE velocities, three targets known host companion: HD 223636 (HIP 117622), 17289 12726), 3277 2790).