A&A 624, A120 (2019) Astronomy https://doi.org/10.1051/0004-6361/201834641 & © ESO 2019 Astrophysics Survivability of planetary systems in young and dense star clusters A. van Elteren1, S. Portegies Zwart1, I. Pelupessy2, M. X. Cai1, and S. L. W. McMillan3 1 Leiden Observatory, Leiden University, 2300RA Leiden, The Netherlands e-mail: [email protected] 2 The Netherlands eScience Center, The Netherlands 3 Department of Physics, Drexel University, Philadelphia, PA 19104, USA Received 14 November 2018 / Accepted 12 February 2019 ABSTRACT Aims. We perform a simulation using the Astrophysical Multipurpose Software Environment of the Orion Trapezium star cluster in which the evolution of the stars and the dynamics of planetary systems are taken into account. Methods. The initial conditions from earlier simulations were selected in which the size and mass distributions of the observed circumstellar disks in this cluster are satisfactorily reproduced. Four, five, or size planets per star were introduced in orbit around the 500 solar-like stars with a maximum orbital separation of 400 au. Results. Our study focuses on the production of free-floating planets. A total of 357 become unbound from a total of 2522 planets in the initial conditions of the simulation. Of these, 281 leave the cluster within the crossing timescale of the star cluster; the others remain bound to the cluster as free-floating intra-cluster planets. Five of these free-floating intra-cluster planets are captured at a later time by another star. Conclusions. The two main mechanisms by which planets are lost from their host star, ejection upon a strong encounter with another star or internal planetary scattering, drive the evaporation independent of planet mass of orbital separation at birth. The effect of small perturbations due to slow changes in the cluster potential are important for the evolution of planetary systems. In addition, the probability of a star to lose a planet is independent of the planet mass and independent of its initial orbital separation. As a consequence, the mass distribution of free-floating planets is indistinguishable from the mass distribution of planets bound to their host star. Key words. methods: numerical – planets and satellites: dynamical evolution and stability – planet-star interactions – gravitation 1. Introduction that the number of free-floating planets with masses exceeding that of Jupiter is about one-quarter of the number of main- In recent years several free-floating planets, i.e., planets not sequence stars in the Milky Way Galaxy, whereas Jupiter-mass orbiting a star, have been discovered by direct infrared imaging planets appear to be twice as common as main-sequence stars (Pacucci et al. 2013) and by catch in gravitational microlensing (Sumi et al. 2011). Interestingly, Earth-mass free floaters are esti- surveys (Sumi et al. 2011; Gaudi 2012; Gould & Yee 2013). Fol- mated to be only comparable in number to main-sequence stars lowing star formation theory planets could in principle form in (Cassan et al. 2012); there appears to be a peak in the number of isolation (Gahm et al. 2007; Liu et al. 2013; Haworth et al. 2015), free-floating planets around the mass of Jupiter. but it seems more likely that they form according to the canoni- If rogue planets are liberated upon a strong encounter with cal coagulation process in a disk orbiting a host star (Kant 1755). another star in a cluster, this process is likely to take place If planets are not formed in isolation, there are three major mech- during its early evolution after circumstellar disks have coagu- anisms by which planets can be liberated. A planet may become lated into planets and most of the primordial gas has been lost. unbound as a result of (i) dynamical interaction with another star By this time, the stellar density is still sufficiently high that (Hurley & Shara 2002; Vorobyov et al. 2017; Cai et al. 2017, strong encounters between stars are common (Portegies Zwart & 2018; Zheng et al. 2015), (ii) scattering interactions among the Jílková 2015). Young star clusters may, therefore, make an planets in a multi-planet system (Veras & Raymond 2012; Cai important contribution to the production of free-floating plan- et al. 2017, 2018), (iii) copious mass loss in a post-AGB phase ets. However, this is at odds with the low number of free-floating (Veras et al. 2015; Veras 2016) or supernova explosion of the host planets seen in star clusters. Only one rogue planet was found in star (Blaauw 1961), and (iv) the ejection of fragments when the the TW Hydra association (Schneider et al. 2016) and a dozen protoplanetary disk is perturbed (Vorobyov et al. 2017). The rel- candidates were found in the sigma Orionis cluster (Zapatero ative importance of each of these and other possible processes Osorio et al. 2013), but no planets were found in the Pleiades are hard to assess, but the four listed here are probably most cluster despite active searches (Zapatero Osorio et al. 2014). common. These estimates are in sharp contrast to the number of aster- A total of 20 free-floating planet candidates have been iden- oids and other sol¯ ¯ı lapides¯ 1 expected from the star formation tified (Udalski et al. 2008; Wright et al. 2010; Winn & Fabrycky processes (Portegies Zwart et al. 2018a). 2015; Mróz et al. 2019). Two of these orbit each other in the binary-planet 2MASS J11193254-1137466 (Best et al. 2017), but all others are single. Weak micro-lensing searches indicate 1 solus¯ lapis, means “lonely rock” in Latin. Article published by EDP Sciences A120, page 1 of 16 A&A 624, A120 (2019) The majority of free-floating planets appear as part of the were reproduced. We considered these conditions suitable for field population, but this may be a selection effect of the meth- our follow-up study assuming that some of the surviving disks ods used to find them (Winn & Fabrycky 2015). To some degree, would produce a planetary system. The cluster in the study of however, their relatively high abundance in the field does not Portegies Zwart(2016) was born in virial equilibrium with a come as a surprise. If every star that turns into a white dwarf fractal density distribution with dimension F = 1:6. The clus- liberates its planets (and other debris), the number of isolated ter initially contained 1500 stars with a virial radius of 0.5 pc. free floaters should exceed the number of white dwarfs at least At an age of 1 Myr the size distribution of the disks in this clus- by the average number of planets per star. Many of these stars ter is indistinguishable from the observed size distribution of 95 are then already part of the field population once they turn into ionized protoplanetary disks larger than 100 au in the Trapezium white dwarfs, giving a natural reduction of free-floating planets cluster (Vicente & Alves 2005). in clusters compared to the field population. However, this would We adopt the earlier reconstructed initial parameters for the mean that dynamical interactions and internal planetary instabil- Trapezium cluster and populate the stars that have a surviving ities have a minor contribution to the formation of free-floating disk with a planetary system. The 500 stars with a disk size of planets. at least 10 au at the end of their simulation received either four, In order to investigate the consequences of stellar evolution five, or six planets with a mean mass of 0:3 MJupiter. The planets and dynamical interactions on the production of free-floating are assumed to have circular orbits in a randomly∼ oriented plane. planets, we perform a series of calculations in which we take the The correlation between orbital separation and planet mass was relevant processes into account. The main question we address selected from the oligarchic growth model for planetary systems is to what degree the dynamics of a star cluster contribute to the by Hansen & Murray(2013) and Kokubo & Ida(2002). formation and variety of free-floating planets, and what is the After the initialization, we continue the evolution of the star relative importance of the various channels for producing these cluster including its planetary systems for 10 Myr to an age of planets. 11 Myr. At that time about half the cluster stars are unbound. Planetary systems in our simulation are born stable in the In the following Sect.2 we describe the setup of our numeri- sense that allowing the systems to evolve in isolation would not cal experiment, followed by a description of the initial conditions result in dynamical interactions among the planets. This enables in Sect.3. We report on the results in Sect.4, discuss the us to study specifically the relative contribution of dynamical results in Sect.5 and eventually, in Sect.6, we summarize our interactions on the production of free-floating planets. The stars findings. In AppendixA we validate the adopted Nemesis in our simulations that receive a planetary system are selected method for integrating planetary systems in stellar clusters. such that they remain on the main sequence for the entire dura- tion of the simulation. Stellar mass loss, therefore, does not 2. Methods specifically affect these planetary systems. As a result, in the absence of dynamical interactions these planetary systems are Integrating planetary systems in star clusters is complicated by not expected to be affected by either internal planetary dynamics the wide range in timescales, ranging from days to millions of nor by stellar mass loss. years, and the wide range of masses, ranging from Earth-mass We include, in our simulations, the gravitational interactions up to about 100 M . The first complication directly indicates that between the stars, the interactions inside the planetary systems, many planetary systems have to be integrated over many orbits, and the mass loss due to stellar evolution.