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

III. The frequency of brown dwarfs and giant planets as companions to solar-type stars

¹ Institute for Astronomy (IfA), ETH, Wolfgang-Pauli-Str. 27, 8093 Zurich, Switzerland
e-mail: mreggiani@ulg.ac.be
² Département d’Astrophysique, Géophysique et Océanographie, Université de Liège, 17 Allée du Six Août, 4000 Liège, Belgium
³ UJF-Grenoble1/CNRS-INSU, Institut de Planétologie et d’Astrophysique de Grenoble UMR 5274, 38041 Grenoble, France
⁴ Aix-Marseille Université, CNRS, Laboratoire d’Astrophysique de Marseille, UMR 7326, 13388 Marseille, France
⁵ Institute for Astronomy, University of Edinburgh, Blackford Hill, Edinburgh EH9 3HJ, UK
⁶ INAF–Osservatorio Astronomico di Padova, Vicolo dell Osservatorio 5, 35122 Padova, Italy
⁷ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
⁸ LESIA, Observatoire de Paris Meudon, 5 place J. Janssen, 92195 Meudon, France
⁹ Max-Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
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 European Southern Observatory, Casilla 19001, Santiago 19, Chile
¹³ European Southern Observatory, Karl Schwarzschild St, 2, 85748 Garching, Germany
¹⁴ INAF–Catania Astrophysical Observatory, via S. So a 78, 95123 Catania, Italy
¹⁵ Physikalisches Institut, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
¹⁶ NASA Ames Research Center, Moffett Field, CA 94035, USA
¹⁷ Geneva Observatory, University of Geneva, Chemin des Maillettes 51, 1290 Versoix, Switzerland
¹⁸ Núcleo de Astronomía, Facultad de Ingeniería, Universidad Diego Portales, Av. Ejercito 441, Santiago, Chile
¹⁹ Millennium Nucleus “Protoplanetary Disk”, Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile

Received: 20 February 2015
Accepted: 26 October 2015

Abstract

Context. In recent years there have been many attempts to characterize the occurrence and distribution of stellar, brown dwarf (BD), and planetary-mass companions to solar-type stars with the aim of constraining formation mechanisms. From radial velocity observations a dearth of companions with masses between 10–40 M_Jupiter has been noticed at close separations, suggesting the possibility of a distinct formation mechanism for objects above and below this range.

Aims. We present a model for the substellar companion mass function (CMF). This model consists of the superposition of the planet and BD companion mass distributions, assuming that we can extrapolate the radial velocity measured CMF for planets to larger separations and the stellar companion mass-ratio distribution over all separations into the BD mass regime. By using both the results of the VLT/NaCo large program (NaCo-LP) and the complementary archive datasets, which probe the occurrence of planets and BDs on wide orbits around solar-type stars, we place some constraints on the planet and BD distributions.

Methods. We developed a Monte Carlo simulation tool to predict the outcome of a given survey, depending on the shape of the orbital parameter distributions (mass, semimajor axis, eccentricity, and inclination). Comparing the predictions with the results of the observations, we calculate the likelihood of different models and which models can be ruled out.

Results. Current observations are consistent with the proposed model for the CMF, as long as a sufficiently small outer truncation radius (≲100 AU) is introduced for the planet separation distribution. Some regions of parameter space can be excluded by the observations.

Conclusions. We conclude that the results of the direct imaging surveys searching for substellar companions around Sun-like stars are consistent with a combined substellar mass spectrum of planets and BDs. This mass distribution has a minimum between 10 and 50 M_Jupiter, in agreement with radial velocity measurements. In this picture the dearth of objects in this mass range would naturally arise from the shape of the mass distribution, without the introduction of any distinct formation mechanism for BDs. This kind of model for the CMF allows us to determine the probability for a substellar companion as a function of mass to have formed in a disk or from protostellar core fragmentation, as such mechanisms overlap in this mass range.