Letter to the Editor

The mass of β Pictoris c from β Pictoris b orbital motion

¹ LESIA, Observatoire de Paris, PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Janssen, 92195 Meudon, France
e-mail: sylvestre.lacour@obspm.fr
² European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching, Germany
³ Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA
⁴ Center for Astrophysics and Planetary Science, Department of Astronomy, Cornell University, Ithaca, NY 14853, USA
⁵ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁶ Max Planck Institute for extraterrestrial Physics, Giessenbachstraße 1, 85748 Garching, Germany
⁷ Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
⁸ Universidade de Lisboa – Faculdade de Ciências, Campo Grande, 1749-016 Lisboa, Portugal
⁹ CENTRA – Centro de Astrofísica e Gravitação, IST, Universidade de Lisboa, 1049-001 Lisboa, Portugal
¹⁰ Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
¹¹ Leiden Observatory, Leiden University, PO Box 9513 2300 RA Leiden, The Netherlands
¹² Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France
¹³ School of Physics and Astronomy, Monash University, Clayton, VIC, 3800 Melbourne, Australia
¹⁴ JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA
¹⁵ Institute of Physics, University of Cologne, Zülpicher Straße 77, 50937 Cologne, Germany
¹⁶ Max Planck Institute for Radio Astronomy, Auf dem Hügel 69, 53121 Bonn, Germany
¹⁷ Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
¹⁸ Universidade do Porto, Faculdade de Engenharia, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
¹⁹ School of Physics, University College Dublin, Belfield, Dublin 4, Ireland
²⁰ Space Telescope Science Institute, Baltimore, MD 21218, USA
²¹ European Southern Observatory, Casilla, 19001 Santiago 19, Chile
²² University of Exeter, Physics Building, Stocker Road, Exeter EX4 4QL, UK
²³ STAR Institute, Université de Liège, Allée du Six Août 19c, 4000 Liège, Belgium
²⁴ Astronomy Department, University of Michigan, Ann Arbor, MI 48109, USA
²⁵ Academia Sinica Institute of Astronomy and Astrophysics, 11F Astronomy-Mathematics Building, NTU/AS campus, No. 1, Section 4, Roosevelt Rd., Taipei 10617, Taiwan
²⁶ European Space Agency (ESA), ESA Office, Space Telescope Science Institute, Baltimore, MD 21218, USA
²⁷ Department of Astronomy, Stockholm University, Stockholm, Sweden
²⁸ Five College Astronomy Department, Amherst College, Amherst, MA 01002, USA

Received: 28 July 2021
Accepted: 26 August 2021

Abstract

Aims. We aim to demonstrate that the presence and mass of an exoplanet can now be effectively derived from the astrometry of another exoplanet.

Methods. We combined previous astrometry of β Pictoris b with a new set of observations from the GRAVITY interferometer. The orbital motion of β Pictoris b is fit using Markov chain Monte Carlo simulations in Jacobi coordinates. The inner planet, β Pictoris c, was also reobserved at a separation of 96 mas, confirming the previous orbital estimations.

Results. From the astrometry of planet b only, we can (i) detect the presence of β Pictoris c and (ii) constrain its mass to 10.04_−3.10^+4.53 M_Jup. If one adds the astrometry of β Pictoris c, the mass is narrowed down to 9.15_−1.06^+1.08 M_Jup. The inclusion of radial velocity measurements does not affect the orbital parameters significantly, but it does slightly decrease the mass estimate to 8.89_−0.75^+0.75 M_Jup. With a semimajor axis of 2.68 ± 0.02 au, a period of 1221 ± 15 days, and an eccentricity of 0.32 ± 0.02, the orbital parameters of β Pictoris c are now constrained as precisely as those of β Pictoris b. The orbital configuration is compatible with a high-order mean-motion resonance (7:1). The impact of the resonance on the planets’ dynamics would then be negligible with respect to the secular perturbations, which might have played an important role in the eccentricity excitation of the outer planet.