| Issue |
A&A
Volume 667, November 2022
|
|
|---|---|---|
| Article Number | A172 | |
| Number of page(s) | 18 | |
| Section | Planets and planetary systems | |
| DOI | https://doi.org/10.1051/0004-6361/202244018 | |
| Published online | 29 November 2022 | |
Analytical determination of orbital elements using Fourier analysis
II. Gaia astrometry and its combination with radial velocities★
Département d’astronomie, Université de Genève,
chemin Pegasi 51,
1290
Versoix, Switzerland
e-mail: jean-baptiste.delisle@unige.ch
Received:
13
May
2022
Accepted:
13
September
2022
The ESA global astrometry space mission Gaia has been monitoring the position of a billion stars since 2014. The analysis of such a massive dataset is challenging in terms of the data processing involved. In particular, the blind detection and characterization of single or multiple companions to stars (planets, brown dwarfs, or stars) using Gaia astrometry requires highly efficient algorithms. In this article, we present a set of analytical methods to detect and characterize companions in scanning space astrometric time series as well as via a combination of astrometric and radial velocity time series. We propose a general linear periodogram framework and we derive analytical formulas for the false alarm probability (FAP) of periodogram peaks. Once a significant peak has been identified, we provide analytical estimates of all the orbital elements of the companion based on the Fourier decomposition of the signal. The periodogram, FAP, and orbital elements estimates can be computed for the astrometric and radial velocity time series separately or in tandem. These methods are complementary with more accurate and more computationally intensive numerical algorithms (e.g., least-squares minimization, Markov chain Monte-Carlo, genetic algorithms). In particular, our analytical approximations can be used as an initial condition to accelerate the convergence of numerical algorithms. Our formalism has been partially implemented in the Gaia exoplanet pipeline for the third Gaia data release. Since the Gaia astrometric time series are not yet publicly available, we illustrate our methods on the basis of Hipparcos data, together with on-ground CORALIE radial velocities, for three targets known to host a companion: HD 223636 (HIP 117622), HD 17289 (HIP 12726), and HD 3277 (HIP 2790).
Key words: planets and satellites: general / methods: analytical / astrometry / techniques: radial velocities
We provide an open-source implementation of the methods presented in this article: the kepmodel python package, installable with pip or conda. The sources are available at https://gitlab.unige.ch/jean-baptiste.delisle/kepmodel.
© J.-B. Delisle and D. Ségransan 2022
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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