Planetary systems in star clusters
aa r X i v : . [ a s t r o - ph . E P ] S e p Mem. S.A.It. Vol. 153, 498 c (cid:13) SAIt 2016
Memorie della
Planetary systems in star clusters
M.B.N. Kouwenhoven , , Qi Shu , , Maxwell Xu Cai , , , and Rainer Spurzem , , Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, 111 Ren’aiRoad, Dushu Lake Higher Education Town, Suzhou Industrial Park, Suzhou, 215123, P.R.China e-mail: [email protected] Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Lu 5,Haidian Qu, Beijing 100871, P.R. China Department of Astronomy, School of Physics, Peking University, Yiheyuan Lu 5, HaidianQu, Beijing 100871, P.R. China Leiden Observatory, Leiden University, PO Box 9513, 2300 RA, Leiden, The Netherlands National Astronomical Observatories of China and Key Lab for ComputationalAstrophysics, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District,Beijing 100012, P.R. China Astronomisches Rechen-Institut, Zentrum f¨ur Astronomie, University of Heidelberg,M¨onchhofstrasse 12-14, 69120 Heidelberg, Germany
Abstract.
Thousands of confirmed and candidate exoplanets have been identified in re-cent years. Consequently, theoretical research on the formation and dynamical evolutionof planetary systems has seen a boost, and the processes of planet-planet scattering, secu-lar evolution, and interaction between planets and gas / debris disks have been well-studied.Almost all of this work has focused on the formation and evolution of isolated planetarysystems, and neglect the e ff ect of external influences, such as the gravitational interactionwith neighbouring stars. Most stars, however, form in clustered environments that eitherquickly disperse, or evolve into open clusters. Under these conditions, young planetary sys-tems experience frequent close encounters with other stars, at least during the first 10 − years, which a ff ects planets orbiting at any period range, as well as their debris structures. Key words.
Exoplanets: dynamical evolution, formation – galaxies: globular clusters, openclusters – solar system: asteroids, comets – techniques: N -body simulations
1. Introduction
Observations have shown that young stars arealmost exclusively found in groups, suggest-ing that stars form in clustered environments.Following the star formation process and gasexpulsion phase, these stellar groupings mayeither virialise within several crossing times(e.g., Allison et al. 2009) and evolve in to starclusters that may survive for hundreds of mil-lions of years, or disperse within several tens of millions of years (e.g., de Grijs & Parmentier2007). These observations, together with iso-topic ratios in meteorites that indicate that asupernova explosion occurred within ∼ ouwenhoven, Shu, Cai & Spurzem: Planetary systems in star clusters 499 encounters were frequent, and their dynamicalarchitectures may have been a ff ected by suchencounters. The major uncertainty, of course,is how important the e ff ect of those encoun-ters was, and for how long these stars remainedpart of this environment. As exoplanets appearto be substantially more common in the Solarneighbourhood than in star clusters, this indeedsuggests that close stellar encounters have a de-structive e ff ect on planetary systems, unless theplanet formation process is less e ffi cient in en-vironments that result in long-lived star clus-ters. In this article we provide a brief reviewon our strategy to answer these issues.
2. Single-planet systems in clusters
Observations, as well as the core-accretion sce-nario and the disk-fragmentation scenario forthe formation of planetary-mass objects pre-dict the formation of multiple planets, ratherthan single-planet systems, in circumstellardisks (e.g., Zhou et al. 2007; Stamatellos et al.2011; Xie et al. 2014). This multiplicity intro-duces planet-planet interactions and contributeto the fragility of these systems. Nevertheless,it is valuable to study single-planet systems,as these provide upper limits for the stabilityof such systems. Single-planet systems in starclusters are substantially easier to model thanmulti-planet systems (see § N -body simulations and Monte Carlo simula-tions, was carried out by Spurzem et al. (2009).In their study of single-planet systems in large( N =
300 000) clusters, they find that, as ex-pected, close (nearly parabolic, adiabatic) en-counters are responsible for many of the dis-ruptions. They also stress, however, that thecumulative e ff ect of numerous weak (hyper-bolic adiabatic) encounters can lead to substan-tial changes in the orbital elements of plan-ets, which may result orbit crossing and sub-sequent decay of multi-planet systems. Parker& Quanz (2012) and Zheng et al. (2015) mod-elled single-planet systems in star clusters,with the aim of obtaining relations for survivalrates in di ff erent environments and for di ff er-ent orbital periods. Zheng et al. (2015) obtain function fits for the survival and decay ratesof single-planet systems in di ff erent cluster en-vironments. As multiplicity decreases survivalrates of planetary systems, these provide upperlimits for planetary survival rates.
3. Free-floating planets in clusters
Following the escape from their host stars,free-floating planets (FFPs) become part ofthe star clusters dynamics. FFPs with veloc-ities above the local escape velocity may es-cape immediately, while the others remainpart of the star clusters, where they have asmall chance of being re-captured by anotherstar (e.g., Kouwenhoven et al. 2010; Perets& Kouwenhoven 2012), but the majority ulti-mately escapes from the star cluster throughejection or evaporation (e.g., Liu et al. 2013).Wang et al. (2015a) carried out an extensivestudy on the behaviour of free-floating plan-ets in star clusters, and find that FFPs (withejection velocities below the local escape ve-locity) typically remain part of the cluster forlong times, and experience several (sometimesup to hundreds of) close ( < ff by the Galactic tidal field. Atany time, a FFP has statistically a 40% largerchance of being ejected than a typical star.FFPs are thus mostly ejected at early times,although several remain bound to the clusteruntil its dissolution. The linearly decreasingtrend of the FFP-to-star ratio among clustermembers found by Wang et al. (2015a) indi-cates that surveys for free-floating planets instar clusters are will likely be most successfulin young environments.
4. Multi-planet systems in clusters
Modelling multi-planet systems in star clus-ters is complex due to the enormous rangesin masses, positions, and velocities. Round-o ff errors in the calculation of the dynamicalproperties of stars are generally disastrous formodelling the evolution of planetary systems(except for certain special cases which can be
00 Kouwenhoven, Shu, Cai & Spurzem: Planetary systems in star clusters modelled as perturbed two-body or three-bodysystems; e.g., Shara et al. 2016). The study ofmulti-planet systems in star clusters has beenhampered by these computational di ffi cultiesfor long. Malmberg et al. (2011) and Hao etal. (2013) approximated the situation by mod-elling the close encounters with stars that occurin a star cluster, and carrying out separate sim-ulations using MERCURY6 (Chambers 1999), in-stead of carrying out full star cluster simula-tions with multi-planet systems. Malmberg etal. (2011) noted that a close encounter can re-sult in the ejection of planets long (up to tens ofmillions of years) after the encounter occurred.Hao et al. (2013) found that even close-in plan-ets, which are themselves not directly a ff ectedby close encounters, may experience a colli-sion or ejection due to planet-planet scatter-ing. Hao et al. (2013) also stressed the impor-tance of the planetary mass spectrum. Whenperturbing the outermost planets of our ownSolar system, for example, Jupiter’s large in-ertia almost guarantees dynamical protectionof the inner Solar system. With the newly im-plemented HDF5 storage scheme in NBODY6++ (Cai et al. 2015) and the development of theAMUSE framework (e.g., Portegies Zwart etal. 2013; Pelupessy et al. 2013), it recently be-came possible to combine the planetary dy-namics code
MERCURY6 with the star clustercode
NBODY6++ (Spurzem 1999) in
AMUSE (Caiet al. 2016). In an upcoming publication (Caiet al., in prep.) we will outline the diversedynamical outcomes of perturbed multi-planetsystems in star clusters, confirming the impor-tance of the interplay between the e ff ect of en-counters on outer planets and the subsequentplanet-planet scattering and secular interac-tions, and also confirming Hao et al. (2013)’sfindings that even the closest-in planets are (in-directly) a ff ected by stellar encounters.
5. Debris structures in star clusters
Our Solar system contains billions of comets,Kuiper Belt objects (KBOs) and asteroids.There is no reason to expect that other starslack similar debris systems. In crowded stel-lar environments the analogs of the Kuiper Beltand Oort Cloud may be substantially alteredby close encounters (e.g., Brasser & Schwamb 2015). As comets a ff ect the prospects for lifeat planets in the habitable zone, both destruc-tively (impacts) and constructively (water de-livery), modelling the evolution of circumstel-lar debris in star cluster environments is par-ticularly interesting. These processes are par-ticularly important when the stellar density ishigh, such as in open or globular clusters. Overrecent years, N -body simulation software formodelling star clusters has been significantlyimproved, allowing us to model globular clus-ters containing more than a million stars overa Hubble time using the NBODY6++GPU code(Wang et al. 2015b, 2016). This code is highlyoptimised for star cluster simulations and veryfast. This is exactly the reason why it is notpossible to use
NBODY6++GPU for star clus-ters with massless particles such as comets,as many of these optimisations, such as KS-regularisation, the neighbour scheme, and in-dividual time steps, are not suitable for largenumbers of bodies with mass ratios approach-ing zero. For this reason, a new release of thecode,
NBODY6++GPU-MASSLESS , is now underdevelopment (Shu et al, in prep). This codewill be able to run simulations of star clus-ters containing hundreds of thousands of starsand massless particles, allowing us to study theevolution of Oort Clouds, Kuiper Belts, aster-oid belts, and planetesimal disks in crowdedstellar environments, as well as free-floatingcomets, asteroids, and planetesimals.
6. Summary
Most planetary systems spend the first 10 − years of their existence in crowded stel-lar environments, while a small fraction re-side in open cluster or globular clusters forup to billions of years. Gravitational interac-tions with neighbouring stars shape these plan-etary systems, leading to orbital reconfigura-tions, planet-planet scattering events, ejections,and physical collisions. Debris structures, con-sisting of comets, asteroids, KBOs, and plan-etesimals, are also shaped by these stellar en-counters. We have carried out N -body simu-lations of planetary systems and free-floatingplanets in star clusters, and present our firstresults above. Despite the enormous advancesthat were made using N -body codes, many ouwenhoven, Shu, Cai & Spurzem: Planetary systems in star clusters 501 physical processes are still di ffi cult to model,such as the e ff ect of gas dynamics and stel-lar feedback that is often seen in star-formingregions (e.g., Bik et al. 2010), the inclusionof the processes of core-accretion and disk-fragmentation that are responsible for planetformation (e.g., Li et al. 2015, 2016), com-bined with very large fractions of primordialstellar binaries (e.g., Kouwenhoven et al. 2005,2007, 2009). With the development of newsoftware and hardware, realistic simulations ofplanetary systems, from birth to old age, willbecome possible in the near future. Acknowledgements.
M.B.N.K. was supported bythe Peter and Patricia Gruber Foundation, by thePeking University One Hundred Talent Fund (985),and by the National Natural Science Foundation ofChina (grants 11010237, 11050110414, 11173004,11573004). This publication was made possi-ble through the support of a grant from theJohn Templeton Foundation and the NationalAstronomical Observatories of Chinese Academyof Sciences. We acknowledge support by ChineseAcademy of Sciences through the Silk RoadProject at NAOC, through the Chinese Academyof Sciences Visiting Professorship for SeniorInternational Scientists, Grant Number 2009S1-5 (R.S.), and through the Qianren special for-eign experts program of China. The specialGPU accelerated supercomputer laohu at theCenter of Information and Computing at NationalAstronomical Observatories, Chinese Academy ofSciences, funded by Ministry of Finance of PeoplesRepublic of China under the grant ZDY Z2008-2,has been used for some simulations.
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