# Publications

## List of Publications

#### 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.

#### SiMon: Simulation Monitor for Computational Astrophysics

Qian, Penny Xuran; Cai, Maxwell Xu; Portegies Zwart, Simon; Zhu, Ming

Scientific discovery via numerical simulations is important in modern astrophysics. This relatively new branch of astrophysics has become possible due to the development of reliable numerical algorithms and the high performance of modern computing technologies. These enable the analysis of large collections of observational data and the acquisition of new data via simulations at unprecedented accuracy and resolution. Ideally, simulations run until they reach some pre-determined termination condition, but often other factors cause extensive numerical approaches to break down at an earlier stage. In those cases, processes tend to be interrupted due to unexpected events in the software or the hardware. In those cases, the scientist handles the interrupt manually, which is time-consuming and prone to errors. We present the Simulation Monitor (SiMon) to automatize the farming of large and extensive simulation processes. Our method is light-weight, it fully automates the entire workflow management, operates concurrently across multiple platforms and can be installed in user space. Inspired by the process of crop farming, we perceive each simulation as a crop in the field and running simulation becomes analogous to growing crops. With the development of SiMon we relax the technical aspects of simulation management. The initial package was developed for extensive parameter searchers in numerical simulations, but it turns out to work equally well for automating the computational processing and reduction of observational data reduction.

#### Block Time Step Storage Scheme for Astrophysical N-body Simulations

Cai, Maxwell Xu; Meiron, Yohai; Kouwenhoven, M. B. N.; Assmann, Paulina; Spurzem, Rainer

Astrophysical research in recent decades has made significant progress thanks to the availability of various N-body simulation techniques. With the rapid development of high-performance computing technologies, modern simulations have been able to use the computing power of massively parallel clusters with more than $10^5$GPU cores. While unprecedented accuracy and dynamical scales have been achieved, the enormous amount of data being generated continuously poses great challenges for the subsequent procedures of data analysis and archiving. In this paper, we propose an adaptive storage scheme for simulation data, inspired by the block time step (BTS) integration scheme found in a number of direct $N$-body integrators available nowadays, as an urgent response to these challenges. The proposed scheme, namely, the BTS storage scheme, works by minimizing the data redundancy by assigning individual output frequencies to the data as required by the researcher. As demonstrated by benchmarks, the proposed scheme is applicable to a wide variety of simulations. Despite the main focus of developing a solution for direct $N$-body simulation data, the methodology is transferable for grid-based or tree-based simulations where hierarchical time stepping is used.

#### Evolution of star clusters on eccentric orbits

Cai, Maxwell Xu; Gieles, Mark; Heggie, Douglas C.; Varri, Anna Lisa

We study the evolution of star clusters on circular and eccentric orbits using direct N-body simulations. We model clusters with initially $N = 8 {\rm k}$ and $N = 16 {\rm k}$ single stars of the same mass, orbiting around a point-mass galaxy. For each orbital eccentricity that we consider, we find the apogalactic radius at which the cluster has the same lifetime as the cluster with the same N on a circular orbit. We show that then, the evolution of bound particle number and half-mass radius is approximately independent of eccentricity. Secondly, when we scale our results to orbits with the same semimajor axis, we find that the lifetimes are, to first order, independent of eccentricity. When the results of Baumgardt and Makino for a singular isothermal halo are scaled in the same way, the lifetime is again independent of eccentricity to first order, suggesting that this result is independent of the galactic mass profile. From both sets of simulations, we empirically derive the higher order dependence of the lifetime on eccentricity. Our results serve as benchmark for theoretical studies of the escape rate from clusters on eccentric orbits. Finally, our results can be useful for generative models for cold streams and cluster evolution models that are confined to spherical symmetry and/or time-independent tides, such as Fokker-Planck models, Monte Carlo models, and (fast) semi-analytic models.