Astrometry and exoplanets in the Gaia era : A Bayesian approach to detection and parameter recovery
(2018) In Astronomy and Astrophysics 614. Abstract
The Gaia mission is expected to make a significant contribution to the knowledge of exoplanet systems, both in terms of their number and of their physical properties. We develop Bayesian methods and detection criteria for orbital fitting, and revise the detectability of exoplanets in light of the inflight properties of Gaia. Limiting ourselves to oneplanet systems as a first step of the development, we simulate Gaia data for exoplanet systems over a grid of S/N, orbital period, and eccentricity. The simulations are then fit using Markov chain Monte Carlo methods. We investigate the detection rate according to three information criteria and the Δχ^{2}. For the Δχ^{2}, the effective number of degrees of freedom depends... (More)
The Gaia mission is expected to make a significant contribution to the knowledge of exoplanet systems, both in terms of their number and of their physical properties. We develop Bayesian methods and detection criteria for orbital fitting, and revise the detectability of exoplanets in light of the inflight properties of Gaia. Limiting ourselves to oneplanet systems as a first step of the development, we simulate Gaia data for exoplanet systems over a grid of S/N, orbital period, and eccentricity. The simulations are then fit using Markov chain Monte Carlo methods. We investigate the detection rate according to three information criteria and the Δχ^{2}. For the Δχ^{2}, the effective number of degrees of freedom depends on the mission length. We find that the choice of the Markov chain starting point can affect the quality of the results; we therefore consider two limit possibilities: an ideal case, and a very simple method that finds the starting point assuming circular orbits. We use 6644 and 4402 simulations to assess the fraction of false positive detections in a 5 yr and in a 10 yr mission, respectively; and 4968 and 4706 simulations to assess the detection rate and how the parameters are recovered. Using Jeffreys' scale of evidence, the fraction of false positives passing a strong evidence criterion is ≤ 0.2% (0.6%) when considering a 5 yr (10 yr) mission and using the Akaike information criterion or the WatanabeAkaike information criterion, and <0.02% (<0.06%) when using the Bayesian information criterion. We find that there is a 50% chance of detecting a planet with a minimum S/N = 2.3 (1.7). This sets the maximum distance to which a planet is detectable to ∼70 pc and ∼3.5 pc for a Jupitermass and Neptunemass planets, respectively, assuming a 10 yr mission, a 4 au semimajor axis, and a 1 M_{⊙} star. We show the distribution of the accuracy and precision with which orbital parameters are recovered. The period is the orbital parameter that can be determined with the best accuracy, with a median relative difference between input and output periods of 4.2% (2.9%) assuming a 5 yr (10 yr) mission. The median accuracy of the semimajor axis of the orbit can be recovered with a median relative error of 7% (6%). The eccentricity can also be recovered with a median absolute accuracy of 0.07 (0.06).
(Less)
 author
 Ranalli, P. ^{LU} ; Hobbs, D. ^{LU} and Lindegren, L. ^{LU}
 organization
 publishing date
 20180601
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Astrometry, Celestial mechanics, Methods: numerical, Methods: statistical, Planetary systems, Techniques: miscellaneous
 in
 Astronomy and Astrophysics
 volume
 614
 publisher
 EDP Sciences
 external identifiers

 scopus:85048882050
 ISSN
 00046361
 DOI
 10.1051/00046361/201730921
 language
 English
 LU publication?
 yes
 id
 6d43511b26c74bc192dc0a23be35ffd1
 date added to LUP
 20180706 10:35:10
 date last changed
 20180712 13:45:50
@article{6d43511b26c74bc192dc0a23be35ffd1, abstract = {<p>The Gaia mission is expected to make a significant contribution to the knowledge of exoplanet systems, both in terms of their number and of their physical properties. We develop Bayesian methods and detection criteria for orbital fitting, and revise the detectability of exoplanets in light of the inflight properties of Gaia. Limiting ourselves to oneplanet systems as a first step of the development, we simulate Gaia data for exoplanet systems over a grid of S/N, orbital period, and eccentricity. The simulations are then fit using Markov chain Monte Carlo methods. We investigate the detection rate according to three information criteria and the Δχ<sup>2</sup>. For the Δχ<sup>2</sup>, the effective number of degrees of freedom depends on the mission length. We find that the choice of the Markov chain starting point can affect the quality of the results; we therefore consider two limit possibilities: an ideal case, and a very simple method that finds the starting point assuming circular orbits. We use 6644 and 4402 simulations to assess the fraction of false positive detections in a 5 yr and in a 10 yr mission, respectively; and 4968 and 4706 simulations to assess the detection rate and how the parameters are recovered. Using Jeffreys' scale of evidence, the fraction of false positives passing a strong evidence criterion is ≤ 0.2% (0.6%) when considering a 5 yr (10 yr) mission and using the Akaike information criterion or the WatanabeAkaike information criterion, and <0.02% (<0.06%) when using the Bayesian information criterion. We find that there is a 50% chance of detecting a planet with a minimum S/N = 2.3 (1.7). This sets the maximum distance to which a planet is detectable to ∼70 pc and ∼3.5 pc for a Jupitermass and Neptunemass planets, respectively, assuming a 10 yr mission, a 4 au semimajor axis, and a 1 M<sub>⊙</sub> star. We show the distribution of the accuracy and precision with which orbital parameters are recovered. The period is the orbital parameter that can be determined with the best accuracy, with a median relative difference between input and output periods of 4.2% (2.9%) assuming a 5 yr (10 yr) mission. The median accuracy of the semimajor axis of the orbit can be recovered with a median relative error of 7% (6%). The eccentricity can also be recovered with a median absolute accuracy of 0.07 (0.06).</p>}, articleno = {A30}, author = {Ranalli, P. and Hobbs, D. and Lindegren, L.}, issn = {00046361}, keyword = {Astrometry,Celestial mechanics,Methods: numerical,Methods: statistical,Planetary systems,Techniques: miscellaneous}, language = {eng}, month = {06}, publisher = {EDP Sciences}, series = {Astronomy and Astrophysics}, title = {Astrometry and exoplanets in the Gaia era : A Bayesian approach to detection and parameter recovery}, url = {http://dx.doi.org/10.1051/00046361/201730921}, volume = {614}, year = {2018}, }