# Publications

## List of Publications

#### 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.

#### The origin of interstellar asteroidal objects like 1I/2017 U1 Oumuamua

Portegies Zwart, Simon; Torres, Santiago; Pelupessy, Inti; Bédorf, Jeroen; Cai, Maxwell X.

We study the origin of the interstellar object 1I/2017 U1 Oumuamua by juxtaposing estimates based on the observations with simulations. We speculate that objects like Oumuamua are formed in the debris disc as left over from the star and planet formation process, and subsequently liberated. The liberation process is mediated either by interaction with other stars in the parental star cluster, by resonant interactions within the planetesimal disc or by the relatively sudden mass loss when the host star becomes a compact object. Integrating Oumuamua backward in time in the Galactic potential together with stars from the Gaia-TGAS catalogue we find that about 1.3 Myr ago Oumuamua passed the nearby star HIP 17288 within a mean distance of 1.3 pc. By comparing nearby observed L-dwarfs with simulations of the Galaxy, we conclude that the kinematics of Oumuamua is consistent with relatively young objects of 1.1-1.7 Gyr. We just met Oumuamua by chance, and with a derived mean Galactic density of ∼3 × 105 similarly sized objects within 100 au from the Sun or ∼1014 per cubic parsec we expect about 2-12 such visitors per year within 1 au from the Sun.

#### The signatures of the parental cluster on field planetary systems

Cai, Maxwell Xu; Portegies Zwart, Simon; van Elteren, Arjen

Due to the high stellar densities in young clusters, planetary systems formed in these environments are likely to have experienced perturbations from encounters with other stars. We carry out direct N-body simulations of multiplanet systems in star clusters to study the combined effects of stellar encounters and internal planetary dynamics. These planetary systems eventually become part of the Galactic field population as the parental cluster dissolves, which is where most presently known exoplanets are observed. We show that perturbations induced by stellar encounters lead to distinct signatures in the field planetary systems, most prominently, the excited orbital inclinations and eccentricities. Planetary systems that form within the cluster's half-mass radius are more prone to such perturbations. The orbital elements are most strongly excited in the outermost orbit, but the effect propagates to the entire planetary system through secular evolution. Planet ejections may occur long after a stellar encounter. The surviving planets in these reduced systems tend to have, on average, higher inclinations and larger eccentricities compared to systems that were perturbed less strongly. As soon as the parental star cluster dissolves, external perturbations stop affecting the escaped planetary systems, and further evolution proceeds on a relaxation time-scale. The outer regions of these ejected planetary systems tend to relax so slowly that their state carries the memory of their last strong encounter in the star cluster. Regardless of the stellar density, we observe a robust anticorrelation between multiplicity and mean inclination/eccentricity. We speculate that the Kepler dichotomy' observed in field planetary systems is a natural consequence of their early evolution in the parental cluster.

#### Planetary systems in star clusters

Kouwenhoven, M. B. N.; Shu, Qi; Cai, Maxwell Xu; Spurzem, Rainer

Thousands of confirmed and candidate exoplanets have been identified in recent years. Consequently, theoretical research on the formation and dynamical evolution of planetary systems has seen a boost, and the processes of planet-planet scattering, secular 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 planetary systems, and neglect the effect of external influences, such as the gravitational interaction with neighbouring stars. Most stars, however, form in clustered environments that either quickly disperse, or evolve into open clusters. Under these conditions, young planetary systems experience frequent close encounters with other stars, at least during the first $10^6$ - $10^7$ years, which affects planets orbiting at any period range, as well as their debris structures.