Unveiling the β Pictoris system, coupling high contrast imaging, interferometric, and radial velocity data

¹ IPAG, Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
e-mail: anne-marie.lagrange@univ-grenoble-alpes.fr
² LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Jules Janssen, 92195 Meudon, France
³ IMCCE – Observatoire de Paris, 77 Avenue Denfert-Rochereau, 75014 Paris, France
⁴ Pixyl, 5 Avenue du Grand Sablon, 38700 La Tronche, France
⁵ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁶ CRAL, UMR 5574, CNRS, Université de Lyon, Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69364 Lyon Cedex 07, France
⁷ INAF – Osservatorio Astronomico di Padova, Vicolo dellâ Osservatorio 5, 35122, Padova, Italy
⁸ Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA
⁹ GEPI, Observatoire de Paris, PSL University, CNRS; 5 Place Jules Janssen 92190 Meudon, France
¹⁰ Aix-Marseille Univ, CNRS, CNES, LAM, Marseille, France
¹¹ Núcleo de Astronomía, Facultad de Ingeniería, Universidad Diego Portales, Av. Ejercito 441, Santiago, Chile
¹² STAR Institute/Université de Liège, Liège, Belgium
¹³ Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
¹⁴ European Southern Observatory, Casilla 19001, Santiago 19, Chile
¹⁵ Universidade de Lisboa – Faculdade de Ciências, Campo Grande, 1749-016 Lisboa, Portugal
¹⁶ CENTRA – Centro de Astrofísica e Gravitação, IST, Universidade de Lisboa, 1049-001 Lisboa, Portugal
¹⁷ Unidad Mixta Internacional Franco-Chilena de Astronomía, CNRS/INSU UMI 3386 and Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile
¹⁸ School of Physics and Astronomy, Monash University, Clayton, VIC 3800, Melbourne, Australia
¹⁹ Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
²⁰ Max Planck Institute for extraterrestrial Physics, Gießenbachstraße 1, 85748 Garching, Germany
²¹ Institute of Physics, University of Cologne, Zülpicher Straße 77, 50937 Cologne, Germany
²² Max Planck Institute for Radio Astronomy, Auf dem Hügel 69, 53121 Bonn, Germany
²³ Universidade do Porto, Faculdade de Engenharia, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
²⁴ School of Physics, University College Dublin, Belfield, Dublin 4, Ireland
²⁵ Space Telescope Science Institute, Baltimore, MD 21218, USA
²⁶ Geneva Observatory, University of Geneva, Chemin des Mailettes 51, 1290 Versoix, Switzerland
²⁷ Department of Astronomy, Stockholm University, AlbaNova University Center, 10691 Stockholm, Sweden
²⁸ European Southern Observatory, Karl-Schwarzschild-StraßBe 2, 85748 Garching, Germany
²⁹ Research School of Astronomy & Astrophysics, Australian National University, ACT 2611, Australia
³⁰ Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA 02138, USA
³¹ INAF – Osservatorio Astrofisico di Catania, Via S. Sofia 78, 95123 Catania, Italy
³² Astronomy Department, University of Michigan, Ann Arbor, MI 48109, USA
³³ Cornell Center for Astrophysics and Planetary Science, Department of Astronomy, Cornell University, Ithaca, NY 14853, USA
³⁴ Hamburger Sternwarte, Gojenbergsweg 112 21029 Hamburg, Germany
³⁵ Institute for Particle Physics and Astrophysics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland

Received: 2 July 2020
Accepted: 21 August 2020

Abstract

Context. The nearby and young β Pictoris system hosts a well resolved disk, a directly imaged massive giant planet orbiting at ≃9 au, as well as an inner planet orbiting at ≃2.7 au, which was recently detected through radial velocity (RV). As such, it offers several unique opportunities for detailed studies of planetary system formation and early evolution.

Aims. We aim to further constrain the orbital and physical properties of β Pictoris b and c using a combination of high contrast imaging, long base-line interferometry, and RV data. We also predict the closest approaches or the transit times of both planets, and we constrain the presence of additional planets in the system.

Methods. We obtained six additional epochs of SPHERE data, six additional epochs of GRAVITY data, and five additional epochs of RV data. We combined these various types of data in a single Markov-chain Monte Carlo analysis to constrain the orbital parameters and masses of the two planets simultaneously. The analysis takes into account the gravitational influence of both planets on the star and hence their relative astrometry. Secondly, we used the RV and high contrast imaging data to derive the probabilities of presence of additional planets throughout the disk, and we tested the impact of absolute astrometry.

Results. The orbital properties of both planets are constrained with a semi-major axis of 9.8 ± 0.4 au and 2.7 ± 0.02 au for b and c, respectively, and eccentricities of 0.09 ± 0.1 and 0.27 ± 0.07, assuming the HIPPARCOS distance. We note that despite these low fitting error bars, the eccentricity of β Pictoris c might still be over-estimated. If no prior is provided on the mass of β Pictoris b, we obtain a very low value that is inconsistent with what is derived from brightness-mass models. When we set an evolutionary model motivated prior to the mass of β Pictoris b, we find a solution in the 10–11 M_Jup range. Conversely, β Pictoris c’s mass is well constrained, at 7.8 ± 0.4 M_Jup, assuming both planets are on coplanar orbits. These values depend on the assumptions on the distance of the β Pictoris system. The absolute astrometry HIPPARCOS-Gaia data are consistent with the solutions presented here at the 2σ level, but these solutions are fully driven by the relative astrometry plus RV data. Finally, we derive unprecedented limits on the presence of additional planets in the disk. We can now exclude the presence of planets that are more massive than about 2.5 M_Jup closer than 3 au, and more massive than 3.5 M_Jup between 3 and 7.5 au. Beyond 7.5 au, we exclude the presence of planets that are more massive than 1–2 M_Jup.

Conclusions. Combining relative astrometry and RVs allows one to precisely constrain the orbital parameters of both planets and to give lower limits to potential additional planets throughout the disk. The mass of β Pictoris c is also well constrained, while additional RV data with appropriate observing strategies are required to properly constrain the mass of β Pictoris b.