The VLT/NaCo large program to probe the occurrence of exoplanets and brown dwarfs at wide orbits

IV. Gravitational instability rarely forms wide, giant planets^⋆

¹ Aix Marseille Univ, CNRS, LAM, Laboratoire d’Astrophysique de Marseille, 13013 Marseille, France
e-mail: arthur.vigan@lam.fr
² SUPA, Institute for Astronomy, The University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK
³ INAF - Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122, Padova, Italy
⁴ Max-Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
⁵ SUPA, School of Physics and Astronomy, University of St Andrews, North Haugh, St. Andrews KY16 9SS, UK
⁶ St. Andrews Centre for Exoplanet Science, UK
⁷ Université Grenoble Alpes, IPAG, 38000 Grenoble, France
⁸ CNRS, IPAG, 38000 Grenoble, France
⁹ NASA Exoplanet Science Institute, California Institute of Technology, 770 S. Wilson Ave., Pasadena, CA, USA
¹⁰ Department of Physics and Astronomy, College of Charleston, Charleston, SC 29424 , USA
¹¹ INAF Osservatorio Astronomico di Capodimonte via Moiarello 16, 80131 Napoli, Italy
¹² Department of Astronomy, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden
¹³ Institute for Astronomy, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland
¹⁴ Núcleo de Astronomía, Facultad de Ingeniería, Universidad Diego Portales, Av. Ejercito 441, Santiago, Chile
¹⁵ Millennium Nucleus “Protoplanetary Disk”, Departamento de Astronomía, Universidad de Chile, Casilla 36- D Santiago, Chile
¹⁶ LESIA, Observatoire de Paris, CNRS, Université Paris Diderot, Université Pierre et Marie Curie, 5 place Jules Janssen, 92190 Meudon, France
¹⁷ European Southern Observatory, 3107 Alonso de Cordova, Vitacura, Santiago, Chile
¹⁸ European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany
¹⁹ INAF – Catania Astrophysical Observatory, via S. Sofia 78, 95123 Catania, Italy
²⁰ Observatoire de Haute-Provence, CNRS, Université d’Aix-Marseille, 04870 Saint-Michel-l’ Observatoire, France
²¹ Physikalisches Institut, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
²² CNRS, CFHT, 65-1238 Mamalahoa Hwy, Kamuela HI, USA
²³ Observatoire Astronomique de l’Université de Genève, Chemin des Maillettes 51, 1290 Sauverny, Switzerland

Received: 25 November 2016
Accepted: 6 March 2017

Abstract

Understanding the formation and evolution of giant planets (≥1 M_Jup) at wide orbital separation (≥5 AU) is one of the goals of direct imaging. Over the past 15 yr, many surveys have placed strong constraints on the occurrence rate of wide-orbit giants, mostly based on non-detections, but very few have tried to make a direct link with planet formation theories. In the present work, we combine the results of our previously published VLT/NaCo large program with the results of 12 past imaging surveys to constitute a statistical sample of 199 FGK stars within 100 pc, including three stars with sub-stellar companions. Using Monte Carlo simulations and assuming linear flat distributions for the mass and semi-major axis of planets, we estimate the sub-stellar companion frequency to be within 0.75–5.70% at the 68% confidence level (CL) within 20–300 AU and 0.5–75 M_Jup, which is compatible with previously published results. We also compare our results with the predictions of state-of-the-art population synthesis models based on the gravitational instability (GI) formation scenario with and without scattering. We estimate that in both the scattered and non-scattered populations, we would be able to detect more than 30% of companions in the 1–75 M_Jup range (95% CL). With the threesub-stellar detections in our sample, we estimate the fraction of stars that host a planetary system formed by GI to be within 1.0–8.6% (95% CL). We also conclude that even though GI is not common, it predicts a mass distribution of wide-orbit massive companions that is much closer to what is observed than what the core accretion scenario predicts. Finally, we associate the present paper with the release of the Direct Imaging Virtual Archive (DIVA), a public database that aims at gathering the results of past, present, and future direct imaging surveys.