arXiv subjects

Maxwell Xu Cai

Publications and source records attributed to Maxwell Xu Cai.

12 recordsLinked to original sources

arXiv2024

Hot Jupiter Formation in Dense Star Clusters

Hot Jupiters (HJ) are defined as Jupiter-mass exoplanets orbiting around their host star with an orbital period < 10 days. It is assumed that HJ do not form in-situ but ex-situ. Recent discoveries show that star clusters contribute to the formation of HJ. We present direct $N$-body simulations of planetary systems in star clusters and analyze the formation of HJ in them. We combine two direct $N$-body codes: NBODY6++GPU for the dynamics of dense star clusters with 32 000 and 64 000 stellar members and LonelyPlanets used to follow 200 identical planetary systems around solar mass stars in those star clusters. We use different sets with 3, 4, or 5 planets and with the innermost planet at a semi-major axis of 5 au or 1 au and follow them for 100 Myr in our simulations. The results indicate that HJs are generated with high efficiency in dense star clusters if the innermost planet is already close to the host star at a semi-major axis of 1 au. If the innermost planet is initially beyond a semi-major axis of 5 au, the probability of a potential HJ ranges between $1.5-4.5$ percent. Very dense stellar neighborhoods tend to eject planets rather than forming HJs. A correlation between HJ formation and angular momentum deficit (AMD) is not witnessed. Young Hot Jupiters ($t_{\rm age} < 100$ Myrs) have only been found, in our simulations, in planetary systems with the innermost planet at a semi-major axis of 1 au.

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arXiv2019

Planets In Young Massive Clusters: On the survivability of planets in young massive clusters and its implication of planet orbital architectures in globular clusters

As of August 2019, 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 (YMCs), which are potentially the progenitors of GCs. In an $N=128{\rm k}$ cluster of virial radius 1.7 pc (comparable to Westerlund-1), our simulations show that most wide-orbit planets ($a\geq 20$~au) will be ejected within a timescale of 10 Myr. Interestingly, more than $70\%$ 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 semi-major axis $a_0$ in au in such a YMC can be described as $f_{\rm surv}(a_0, t)=-0.33 \log_{10}(a_0) \left(1 - e^{-0.0482t} \right) + 1$. Upon ejection, about $28.8\%$ of free-floating planets (FFPs) have sufficient speeds to escape from the host cluster at a crossing timescale. 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 multi-Gyr, our results suggest that wide-orbit planets and free-floating planets are unlikely to be found in GCs.

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arXiv2019

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

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

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arXiv2018

Planetary Systems in Star Clusters: the dynamical evolution and survival

Most stars, perhaps even all 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 REBOUND planetary system evolution code, and the NBODY6++GPU star cluster evolution code, integrated in the AMUSE 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.

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arXiv2018

A MODEST review

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.

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arXiv2017

The signatures of the parental cluster on field planetary systems

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 multi-planet 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 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.

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arXiv2017

SiMon: Simulation Monitor for Computational Astrophysics

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.

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arXiv2017

Stability of Multiplanetary Systems in Star Clusters

Most stars form in star clusters and stellar associated. To understand the roles of star cluster environments in shaping the dynamical evolution of planetary systems, we carry out direct $N$-body simulations of four planetary systems models in three different star cluster environments with respectively N=2k, 8k and 32k stars. In each cluster, an ensemble of initially identical planetary systems are assigned to solar-type stars with $\sim 1 M_{\odot}$ and evolved for 50~Myr. We found that following the depletion of protoplanetary disks, external perturbations and planet-planet interactions are two driving mechanisms responsible for the destabilization of planetary systems. The planet survival rate varies from $\sim 95\%$ in the N=2k cluster to $\sim 60\%$ in the N=32k cluster, which suggests that most planetary systems can indeed survive in low-mass clusters, except in the central regions. We also find that planet ejections through stellar encounters are cumulative processes, as only $\sim 3\%$ of encounters are strong enough to excite the eccentricity by $Δe \geq 0.5$. Short-period planets can be perturbed through orbit crossings with long-period planets. When taking into account planet-planet interactions, the planet ejection rate nearly doubles, and therefore multiplicity contributes to the vulnerability of planetary systems. In each ensemble, $\sim 0.2\%$ of planetary orbits become retrograde due to random directions of stellar encounters. Our results predict that young low-mass star clusters are promising sites for next-generation planet surveys, yet low planet detection rates are expected in dense globular clusters such as 47 Tuc. Nevertheless, planets in denser stellar environments are likely to have shorter orbital periods, which enhances their detectability.

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arXiv2016

Planetary systems in star clusters

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 1-10 Myr, which affects planets orbiting at any period range, as well as their debris structures.

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arXiv2015

Evolution of star clusters on eccentric orbits

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 semi-major 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.

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arXiv2015

Block Time Step Storage Scheme for Astrophysical N-body Simulations

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 take 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. As an urgent response to these challenges, in this paper we propose an adaptive storage scheme for simulation data, inspired by the block time step integration scheme found in a number of direct $N$-body integrators available nowadays. The proposed scheme, namely the block time step storage scheme, works by minimizing the data redundancy with assignments of data with individual output frequencies 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.

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arXiv2015

Planetary Systems in Star Clusters

In the solar neighborhood, where the typical relaxation timescale is larger than the cosmic age, at least 10\% to 15\% of Sun-like stars have planetary systems with Jupiter-mass planets. In contrast, dense star clusters, charactered by frequent close encounters, have been found to host very few planets. We carry out numerical simulations with different initial conditions to investigate the dynamical stability of planetary systems in star cluster environments.

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