Dynamical models to explain observations with SPHERE in planetary systems with double debris belts^★

¹ INAF–Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
² Dipartimento di Fisica a Astronomia “G. Galilei”, Universita’ di Padova, via Marzolo, 8, 35121 Padova, Italy
³ LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris Diderot, Sorbonne Paris Cité, 75205 Paris, France
⁴ CRAL, UMR 5574, CNRS, Université Lyon 1, 9 avenue Charles André, 69561 Saint Genis Laval Cedex, France
⁵ Aix Marseille Univ., CNRS, LAM, Laboratoire d’Astrophysique de Marseille, 13013 Marseille, France
⁶ University of Atacama, Copayapu 485, Copiapo, Chile
⁷ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁸ Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, Hungarian Academy of Sciences, PO Box 67, 1525 Budapest, Hungary
⁹ European Southern Observatory, Karl Schwarzschild St, 2, 85748 Garching, Germany
¹⁰ Max-Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
¹¹ Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Av. Gran Bretaña 1111, Playa Ancha, Valparaíso, Chile
¹² Université Grenoble Alpes, IPAG, 38000 Grenoble, France
¹³ INAF–Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, 50125 Firenze, Italy
¹⁴ Institute for Astronomy, ETH Zurich, Wolfgang-Pauli Strasse 27, 8093 Zurich, Switzerland
¹⁵ Universidad de Chile, Camino el Observatorio, 1515 Santiago, Chile
¹⁶ Department of Physics, University of Oxford, Parks Rd, Oxford OX1 3PU, UK
¹⁷ Institute for Astronomy, The University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK
¹⁸ INAF–Osservatorio Astronomico di Catania, via Santa Sofia, 78 Catania, Italy
¹⁹ INAF–Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, 80131 Napoli, Italy
²⁰ Observatoire Astronomique de l’Université de Genève, Chemin des Maillettes 51, 1290 Sauverny, Switzerland
²¹ Leiden Observatory, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
²² Department of Astronomy, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden
²³ INAF – Istituto di Astrofisica Spaziale e Fisica Cosmica di Milano, via E. Bassini 15, 20133 Milano, Italy
²⁴ School of Earth & Space Exploration, Arizona State University, Tempe AZ 85287, USA
²⁵ Ural Federal University, Yekaterinburg 620002, Russia
²⁶ Department of Astronomy, University of Michigan, 1085 S. University, Ann Arbor, MI 48109, USA
²⁷ European Southern Observatory (ESO), Alonso de Córdova 3107, Vitacura, 19001 Casilla, Santiago, Chile
²⁸ Núcleo de Astronomía, Facultad de Ingeniería, Universidad Diego Portales, Av. Ejercito 441, Santiago, Chile

Received: 23 June 2016
Accepted: 6 October 2017

Abstract

Context. A large number of systems harboring a debris disk show evidence for a double belt architecture. One hypothesis for explaining the gap between the debris belts in these disks is the presence of one or more planets dynamically carving it. For this reason these disks represent prime targets for searching planets using direct imaging instruments, like the Spectro-Polarimetric High-constrast Exoplanet Research (SPHERE) at the Very Large Telescope.

Aim. The goal of this work is to investigate this scenario in systems harboring debris disks divided into two components, placed, respectively, in the inner and outer parts of the system. All the targets in the sample were observed with the SPHERE instrument, which performs high-contrast direct imaging, during the SHINE guaranteed time observations. Positions of the inner and outer belts were estimated by spectral energy distribution fitting of the infrared excesses or, when available, from resolved images of the disk. Very few planets have been observed so far in debris disks gaps and we intended to test if such non-detections depend on the observational limits of the present instruments. This aim is achieved by deriving theoretical predictions of masses, eccentricities, and semi-major axes of planets able to open the observed gaps and comparing such parameters with detection limits obtained with SPHERE.

Methods. The relation between the gap and the planet is due to the chaotic zone neighboring the orbit of the planet. The radial extent of this zone depends on the mass ratio between the planet and the star, on the semi-major axis, and on the eccentricity of the planet, and it can be estimated analytically. We first tested the different analytical predictions using a numerical tool for the detection of chaotic behavior and then selected the best formula for estimating a planet’s physical and dynamical properties required to open the observed gap. We then apply the formalism to the case of one single planet on a circular or eccentric orbit. We then consider multi-planetary systems: two and three equal-mass planets on circular orbits and two equal-mass planets on eccentric orbits in a packed configuration. As a final step, we compare each couple of values (M_p, a_p), derived from the dynamical analysis of single and multiple planetary models, with the detection limits obtained with SPHERE.

Results. For one single planet on a circular orbit we obtain conclusive results that allow us to exclude such a hypothesis since in most cases this configuration requires massive planets which should have been detected by our observations. Unsatisfactory is also the case of one single planet on an eccentric orbit for which we obtained high masses and/or eccentricities which are still at odds with observations. Introducing multi planetary architectures is encouraging because for the case of three packed equal-mass planets on circular orbits we obtain quite low masses for the perturbing planets which would remain undetected by our SPHERE observations. The case of two equal-mass planets on eccentric orbits is also of interest since it suggests the possible presence of planets with masses lower than the detection limits and with moderate eccentricity. Our results show that the apparent lack of planets in gaps between double belts could be explained by the presence of a system of two or more planets possibly of low mass and on eccentric orbits whose sizes are below the present detection limits.