List of Publications

On the survival of resonant and non-resonant planetary systems in star clusters

Stock, Katja; Cai, Maxwell X.; Spurzem, Rainer; Kouwenhoven, M. B. N.; Portegies Zwart, Simon

Despite the discovery of thousands of exoplanets in recent years, the number of known exoplanets in star clusters remains tiny. This may be a consequence of close stellar encounters perturbing the dynamical evolution of planetary systems in these clusters. Here, we present the results from direct N-body simulations of multiplanetary systems embedded in star clusters containing N = 8k, 16k, 32k, and 64k stars. The planetary systems, which consist of the four Solar system giant planets Jupiter, Saturn, Uranus, and Neptune, are initialized in different orbital configurations, to study the effect of the system architecture on the dynamical evolution of the entire planetary system, and on the escape rate of the individual planets. We find that the current orbital parameters of the Solar system giants (with initially circular orbits, as well as with present-day eccentricities) and a slightly more compact configuration, have a high resilience against stellar perturbations. A configuration with initial mean-motion resonances of 3:2, 3:2, and 5:4 between the planets, which is inspired by the Nice model, and for which the two outermost planets are usually ejected within the first 105 yr, is in many cases stabilized due to the removal of the resonances by external stellar perturbation and by the rapid ejection of at least one planet. Assigning all planets the same mass of 1 MJup almost equalizes the survival fractions. Our simulations reproduce the broad diversity amongst observed exoplanet systems. We find not only many very wide and/or eccentric orbits, but also a significant number of (stable) retrograde orbits.

Linking the formation and fate of exo-Kuiper belts within Solar system analogues

Veras, Dimitri; Reichert, Katja; Flammini Dotti, Francesco; Cai, Maxwell X.; Mustill, Alexander J.; Shannon, Andrew; McDonald, Catriona H.; Portegies Zwart, Simon; Kouwenhoven, M. B. N.; Spurzem, Rainer

Escalating observations of exo-minor planets and their destroyed remnants both passing through the Solar system and within white dwarf planetary systems motivate an understanding of the orbital history and fate of exo-Kuiper belts and planetesimal discs. Here, we explore how the structure of a 40-1000 au annulus of planetesimals orbiting inside of a Solar system analogue that is itself initially embedded within a stellar cluster environment varies as the star evolves through all of its stellar phases. We attempt this computationally challenging link in four parts: (1) by performing stellar cluster simulations lasting 100 Myr, (2) by making assumptions about the subsequent quiescent 11 Gyr main-sequence evolution, (3) by performing simulations throughout the giant branch phases of evolution, and (4) by making assumptions about the belt's evolution during the white dwarf phase. Throughout these stages, we estimate the planetesimals' gravitational responses to analogues of the four Solar system giant planets, as well as to collisional grinding, Galactic tides, stellar flybys, and stellar radiation. We find that the imprint of stellar cluster dynamics on the architecture of ≳100 km-sized exo-Kuiper belt planetesimals is retained throughout all phases of stellar evolution unless violent gravitational instabilities are triggered either (1) amongst the giant planets, or (2) due to a close (≪103 au) stellar flyby. In the absence of these instabilities, these minor planets simply double their semimajor axis while retaining their primordial post-cluster eccentricity and inclination distributions, with implications for the free-floating planetesimal population and metal-polluted white dwarfs.

On the survivability of planets in young massive clusters and its implication of planet orbital architectures in globular clusters

Cai, Maxwell X.; Portegies Zwart, S.; Kouwenhoven, M. B. N.; Spurzem, Rainer

As of 2019 August, among the more than 4000 confirmed exoplanets, only one has been detected in a globular cluster (GC) M4. The scarce of exoplanet detections motivates us to employ direct N-body simulations to investigate the dynamical stability of planets in young massive clusters (YMC), which are potentially the progenitors of GCs. In an N = 128 k cluster of virial radius 1.7 pc (comparable to Westerlund-1), our simulations show that most wide-orbit planets (a ≥ 20 au) will be ejected within a time-scale of 10 Myr. Interestingly, more than 70 per cent of planets with a < 5 au survive in the 100 Myr simulations. Ignoring planet-planet scattering and tidal damping, the survivability at t Myr as a function of initial semimajor axis a0 in au in such a YMC can be described as fsurv(a0, t) = -0.33log10(a0)(1 - e-0.0482t) + 1. Upon ejection, about 28.8 per cent of free-floating planets (FFPs) have sufficient speeds to escape from the host cluster at a crossing time-scale. The other FFPs will remain bound to the cluster potential, but the subsequent dynamical evolution of the stellar system can result in the delayed ejection of FFPs from the host cluster. Although a full investigation of planet population in GCs requires extending the simulations to multiGyr, our results suggest that wide-orbit planets and free-floating planets are unlikely to be found in GCs.

Planetary systems in a star cluster I: the Solar system scenario

lammini Dotti, Francesco; Kouwenhoven, M. B. N.; Cai, Maxwell Xu; Spurzem, Rainer

Young stars are mostly found in dense stellar environments, and even our own Solar system may have formed in a star cluster. Here, we numerically explore the evolution of planetary systems similar to our own Solar system in star clusters. We investigate the evolution of planetary systems in star clusters. Most stellar encounters are tidal, hyperbolic, and adiabatic. A small fraction of the planetary systems escape from the star cluster within 50 Myr; those with low escape speeds often remain intact during and after the escape process. While most planetary systems inside the star cluster remain intact, a subset is strongly perturbed during the first 50 Myr. Over the course of time, 0.3% - 5.3% of the planets escape, sometimes up to tens of millions of years after a stellar encounter occurred. Survival rates are highest for Jupiter, while Uranus and Neptune have the highest escape rates. Unless directly affected by a stellar encounter itself, Jupiter frequently serves as a barrier that protects the terrestrial planets from perturbations in the outer planetary system. In low-density environments, Jupiter provides protection from perturbations in the outer planetary system, while in high-density environments, direct perturbations of Jupiter by neighbouring stars is disruptive to habitable-zone planets. The diversity amongst planetary systems that is present in the star clusters at 50 Myr, and amongst the escaping planetary systems, is high, which contributes to explaining the high diversity of observed exoplanet systems in star clusters and in the Galactic field.

Galactic tide and local stellar perturbations on the Oort cloud: creation of interstellar comets

Torres, S.; Cai, M. X.; Brown, A. G. A.; Portegies Zwart, S.

Comets in the Oort cloud evolve under the influence of internal and external perturbations, such as giant planets, stellar passages, and the Galactic gravitational tidal field. We aim to study the dynamical evolution of the comets in the Oort cloud, accounting for the perturbation of the Galactic tidal field and passing stars. We base our study on three main approaches; analytic, observational, and numerical. We first construct an analytical model of stellar encounters. We find that individual perturbations do not modify the dynamics of the comets in the cloud unless very close (<0.5 pc) encounters occur. Using proper motions, parallaxes, and radial velocities from Gaia DR2 and combining them with the radial velocities from other surveys, we then construct an astrometric catalogue of the 14 659 stars that are within 50 pc of the Sun. For all these stars we calculate the time and distance of closest approach to the Sun. We find that the cumulative effect of relatively distant (≤1 pc) passing stars can perturb the comets in the Oort cloud. Finally, we study the dynamical evolution of the comets in the Oort cloud under the influence of multiple stellar encounters from stars that pass within 2.5 pc of the Sun and the Galactic tidal field over ±10 Myr. We use the Astrophysical Multipurpose Software Environment (AMUSE), and the GPU-accelerated direct N-body code ABIE. We considered two models for the Oort cloud, compact (a ≤ 0.25 pc) and extended (a ≤ 0.5 pc). We find that the cumulative effect of stellar encounters is the major perturber of the Oort cloud for a compact configuration while for the extended configuration the Galactic tidal field is the major perturber. In both cases the cumulative effect of distant stellar encounters together with the Galactic tidal field raises the semi-major axis of 1.1% of the comets at the edge of the Oort cloud up to interstellar regions (a > 0.5 pc) over the 20 Myr period considered. This leads to the creation of transitional interstellar comets (TICs), which might become interstellar objects due to external perturbations. This raises the question of the formation, evolution, and current status of the Oort cloud as well as the existence of a "cloud" of objects in the interstellar space that might overlap with our Oort cloud, when considering that other planetary systems should undergo similar processes leading to the ejection of comets.

Survivability of planetary systems in young and dense star clusters

van Elteren, A.; Portegies Zwart, S.; Pelupessy, I.; Cai, M. X.; McMillan, S. L. W.

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.

The Orbital Eccentricity of Small Planet Systems

Van Eylen, Vincent; Albrecht, Simon; Huang, Xu; MacDonald, Mariah G.; Dawson, Rebekah I.; Cai, Maxwell X.; Foreman-Mackey, Daniel; Lundkvist, Mia S.; Silva Aguirre, Victor; Snellen, Ignas; Winn, Joshua N.

We determine the orbital eccentricities of individual small Kepler planets, through a combination of asteroseismology and transit light-curve analysis. We are able to constrain the eccentricities of 51 systems with a single transiting planet, which supplement our previous measurements of 66 planets in multi-planet systems. Through a Bayesian hierarchical analysis, we find evidence that systems with only one detected transiting planet have a different eccentricity distribution than systems with multiple detected transiting planets. The eccentricity distribution of the single-transiting systems is well described by the positive half of a zero-mean Gaussian distribution with a dispersion σe = 0.32 ± 0.06, while the multiple-transit systems are consistent with {σ }e={0.083}-0.020+0.015. A mixture model suggests a fraction of {0.76}-0.12+0.21 of single-transiting systems have a moderate eccentricity, represented by a Rayleigh distribution that peaks at {0.26}-0.06+0.04. This finding may reflect differences in the formation pathways of systems with different numbers of transiting planets. We investigate the possibility that eccentricities are self-excited in closely packed planetary systems, as well as the influence of long-period giant companion planets. We find that both mechanisms can qualitatively explain the observations. We do not find any evidence for a correlation between eccentricity and stellar metallicity, as has been seen for giant planets. Neither do we find any evidence that orbital eccentricity is linked to the detection of a companion star. Along with this paper, we make available all of the parameters and uncertainties in the eccentricity distributions, as well as the properties of individual systems, for use in future studies.

Stability of exomoons around the Kepler transiting circumbinary planets

Hamers, Adrian S.; Cai, Maxwell X.; Roa, Javier; Leigh, Nathan

The Kepler mission has detected a number of transiting circumbinary planets (CBPs). Although currently not detected, exomoons could be orbiting some of these CBPs, and they might be suitable for harbouring life. A necessary condition for the existence of such exomoons is their long-term dynamical stability. Here, we investigate the stability of exomoons around the Kepler CBPs using numerical N-body integrations. We determine regions of stability and obtain stability maps in the (am, ipm) plane, where am is the initial exolunar semimajor axis with respect to the CBP, and ipm is the initial inclination of the orbit of the exomoon around the planet with respect to the orbit of the planet around the stellar binary. Ignoring any dependence on ipm, for most Kepler CBPs, the stability regions are well described by the location of the 1:1 mean motion commensurability of the binary orbit with the orbit of the moon around the CBP. This is related to a destabilizing effect of the binary compared to the case if the binary were replaced by a single body, and which is borne out by corresponding three-body integrations. For high inclinations, the evolution is dominated by Lidov-Kozai oscillations, which can bring moons in dynamically stable orbits to close proximity within the CBP, triggering strong interactions such as tidal evolution, tidal disruption, or direct collisions. This suggests that there is a dearth of highly inclined exomoons around the Kepler CBPs, whereas coplanar exomoons are dynamically allowed.

A MODEST review

Varri, Anna Lisa; Cai, Maxwell Xu; Concha-Ramírez, Francisca; Dinnbier, František; Lützgendorf, Nora; Pavlík, Václav; Rastello, Sara; Sollima, Antonio; Wang, Long; Zocchi, Alice

We present an account of the state of the art in the fields explored by the research community invested in "Modeling and Observing DEnse STellar systems". For this purpose, we take as a basis the activities of the MODEST-17 conference, which was held at Charles University, Prague, in September 2017. Reviewed topics include recent advances in fundamental stellar dynamics, numerical methods for the solution of the gravitational N-body problem, formation and evolution of young and old star clusters and galactic nuclei, their elusive stellar populations, planetary systems, and exotic compact objects, with timely attention to black holes of different classes of mass and their role as sources of gravitational waves.

Such a breadth of topics reflects the growing role played by collisional stellar dynamics in numerous areas of modern astrophysics. Indeed, in the next decade many revolutionary instruments will enable the derivation of positions and velocities of individual stars in the Milky Way and its satellites, and will detect signals from a range of astrophysical sources in different portions of the electromagnetic and gravitational spectrum, with an unprecedented sensitivity. On the one hand, this wealth of data will allow us to address a number of long-standing open questions in star cluster studies; on the other hand, many unexpected properties of these systems will come to light, stimulating further progress of our understanding of their formation and evolution.

Planetary Systems in Star Clusters: the dynamical evolution and survival

Flammini Dotti, F.; Cai, Maxwell Xu; Spurzem, Rainer; Kouwenhoven, M. B. N.

Most stars form in crowded stellar environments. Such star forming regions typically dissolve within ten million years, while others remain bound as stellar groupings for hundreds of millions to billions of years, and then become the open clusters or globular clusters that are present in our Milky Way galaxy today. A large fraction of stars in the Galaxy hosts planetary companions. To understand the origin and dynamical evolution of such exoplanet systems, it is necessary to carefully study the effect of their environments. Here, we combine theoretical estimates with state-of-the-art numerical simulations of evolving planetary systems similar to our own solar system in different star cluster environments. We combine the planetary system evolution code, and the star cluster evolution code, integrated in the multi-physics environment. With our study we can constrain the effect of external perturbations of different environments on the planets and debris structures of a wide variety of planetary systems, which may play a key role for the habitability of exoplanets in the Universe.