Survivability of planetary systems in young and dense star clusters

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.

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Planetary systems in star clusters

Proceedings of the International Astronomical Union ◽

10.1017/s1743921315007875 ◽

2014 ◽

Vol 10 (S312) ◽

pp. 235-236 ◽

Cited By ~ 1

Author(s):

Maxwell Xu Cai ◽

Rainer Spurzem ◽

M. B. N. Kouwenhoven

Keyword(s):

Numerical Simulations ◽

Initial Conditions ◽

Star Clusters ◽

Planetary Systems ◽

Star Cluster ◽

Dynamical Stability ◽

Solar Neighborhood ◽

Close Encounters

AbstractIn 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, characterized 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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Planetary systems in a star cluster II: intermediate-mass black holes and planetary systems

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa2188 ◽

2020 ◽

Vol 497 (3) ◽

pp. 3623-3637

Author(s):

Francesco Flammini Dotti ◽

M B N Kouwenhoven ◽

Qi Shu ◽

Wei Hao ◽

Rainer Spurzem

Keyword(s):

Black Holes ◽

Star Clusters ◽

Planetary Systems ◽

Dynamical Evolution ◽

Star Cluster ◽

High Mass ◽

Intermediate Mass ◽

Massive Black Holes ◽

Mass Segregation ◽

Intermediate Mass Black Holes

ABSTRACT Most stars form in dense stellar environments. It is speculated that some dense star clusters may host intermediate-mass black holes (IMBHs), which may have formed from runaway collisions between high-mass stars, or from the mergers of less massive black holes. Here, we numerically explore the evolution of populations of planets in star clusters with an IMBH. We study the dynamical evolution of single-planet systems and free-floating planets, over a period of 100 Myr, in star clusters without an IMBH, and in clusters with a central IMBH of mass $100\, \mathrm{M}_\odot$ or $200\, \mathrm{M}_\odot$. In the central region ($r\lesssim 0.2$ pc), the IMBH’s tidal influence on planetary systems is typically 10 times stronger than the average neighbour star. For a star cluster with a $200\, \mathrm{M}_\odot$ IMBH, the region in which the IMBH’s influence is stronger within the virial radius (∼1 pc). The IMBH quenches mass segregation, and the stars in the core tend to move towards intermediate regions. The ejection rate of both stars and planets is higher when an IMBH is present. The rate at which planets are expelled from their host star rate is higher for clusters with higher IMBH masses, for t < 0.5trh, while remains mostly constant while the star cluster fills its Roche lobe, similar to a star cluster without an IMBH. The disruption rate of planetary systems is higher in initially denser clusters, and for wider planetary orbits, but this rate is substantially enhanced by the presence of a central IMBH.

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

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz2346 ◽

2019 ◽

Vol 489 (2) ◽

pp. 2280-2297 ◽

Cited By ~ 10

Author(s):

Francesco Flammini Dotti ◽

M B N Kouwenhoven ◽

Maxwell Xu Cai ◽

Rainer Spurzem

Keyword(s):

Solar System ◽

Planetary System ◽

Survival Rates ◽

Star Clusters ◽

Planetary Systems ◽

Star Cluster ◽

Habitable Zone ◽

Escape Process ◽

Exoplanet Systems ◽

High Diversity

ABSTRACTYoung 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, $0.3\!-\!5.3{{\ \rm per\ cent}}$ 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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Overview of dynamical mechanisms of secular evolution

Proceedings of the International Astronomical Union ◽

10.1017/s1743921314005821 ◽

2012 ◽

Vol 10 (H16) ◽

pp. 318-318

Author(s):

Daniel Pfenniger

Keyword(s):

Steady State ◽

Initial Conditions ◽

Star Clusters ◽

Planetary Systems ◽

Stable Steady State ◽

Newtonian Physics ◽

Secular Evolution ◽

The Galaxy ◽

Galactic Astronomy ◽

Isolated Systems

AbstractGravity-bound isolated systems, from stars, planetary systems, star clusters to galaxies, share common properties where evolution is the rule. Typically if they start forming at a well defined epoch they tend to change significantly over a timescale comparable to their present age. So evolution is never truly stopped, it just proceeds slower and slower: after a rapid, violent phase a slower, secular phase follows. In galactic astronomy for many decades the paradigm was rather that after a short violent time galaxies would settle in a stable steady state just consuming gas into stars. Actually today it appears that the progressive appearance of galaxy systematic morphologies and the slowing pace of mergers indicate that common intrinsic dynamical factors continue to shape galaxies towards similar properties irrespective of their largely different formation histories and initial conditions. Newtonian physics supplemented by a weakly dissipative component provides an amazing amount of explanations for the galaxy properties, like exponential stellar disks, spirals, bars, and peanut-shaped bulges. The purpose of this talk is to review these mechanisms of dynamical secular evolution.

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Dynamical Evolution of Star Clusters with Intermediate Mass Black Holes and Primordial Binaries

Proceedings of the International Astronomical Union ◽

10.1017/s1743921308015706 ◽

2007 ◽

Vol 3 (S246) ◽

pp. 256-260

Author(s):

Michele Trenti

Keyword(s):

Black Hole ◽

Binary Stars ◽

Initial Conditions ◽

Relaxation Times ◽

Star Clusters ◽

Dynamical Evolution ◽

Star Cluster ◽

Core Collapse ◽

Large Set ◽

Intermediate Mass

AbstractThe evolution of a star cluster is strongly influenced by the presence of primordial binaries and of a central black hole, as dynamical interactions within the core prevents a deep core collapse under these conditions. We present the results from a large set of direct N-body simulations of star clusters that include an intermediate mass black hole, single and binary stars. We highlight the structural and dynamical differences for the various cases showing in particular that on a timescale of a few relaxation times the density profile of the star cluster does no longer depend on the details of the initial conditions but only on the efficiency of the energy generation due to gravitational encounters at the center of the system.

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The Cumulative Effect of Stellar Encounters on Multi-Planet Systems in Star Clusters

Proceedings of the International Astronomical Union ◽

10.1017/s1743921313012763 ◽

2012 ◽

Vol 8 (S293) ◽

pp. 171-173

Author(s):

Wei Hao ◽

M. B. N. Kouwenhoven

Keyword(s):

Planetary System ◽

Star Clusters ◽

Planetary Systems ◽

Dynamical Evolution ◽

Cumulative Effect ◽

Star Cluster ◽

Secular Evolution ◽

Perturbed System ◽

Orbital Periods

AbstractDistant stellar encouters can substantially affect the dynamical evolution of existing stellar and planetary systems (e.g., Malmberg et al. 2007; Spurzem et al. 2009). Although planets with small orbital periods are not directly affected by encountering stars, the secular evolution of a perturbed system may result in the ejection of the innermost planets, or physical collisions between the innermost planets and the host star, hundreds of thousands of years after a weak encounter with a neighboring star occurs. Here we present the results of our study on the cumulative effect of distant stellar encounters on multi-planet systems in star clusters, and how these results depend on the properties of the star cluster in which a planetary system is born (for details we refer to Hao & Kouwenhoven, in prep.). With our simulations we explain the scarcity of exoplanets in star clusters, not only for those in wide orbits (affected by stellar encounters), but also in close orbits (affected by the secular evolution of the system following an encounter).

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QELSS diffusion data for moderately broad molar mass distribution polymer samples compared with data from classical gradient techniques

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19891821 ◽

1989 ◽

Vol 54 (7) ◽

pp. 1821-1829

Author(s):

Bedřich Porsch ◽

Simon King ◽

Lars-Olof Sundelöf

Keyword(s):

Diffusion Coefficient ◽

Mass Distribution ◽

Molar Mass ◽

Molar Mass Distribution ◽

Diffusion Data ◽

Mass Distributions ◽

Classical Diffusion ◽

Polydisperse Polymer

The differences between the QELSS and classical diffusion coefficient of a polydisperse polymer resulting from distinct definitions of experimentally accessible average values are calculated for two assumed specific forms of molar mass distributions. Predicted deviations are compared with the experiment using NBS 706 standard polystyrene. QELSS Dz of this sample relates within 2-4% to the classical diffusion coefficient, if the Schulz-Zimm molar mass distribution is assumed to be valid. In general, differences between the height-area and QELSS diffusion coefficient of about 20% may be found for Mw/Mn ~ 2, and this value may increase above 35%, if strongly tailing molar mass distribution pertains to the sample.

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Formation of supermassive black hole seeds in nuclear star clusters via gas accretion and runaway collisions

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab402 ◽

2021 ◽

Author(s):

Arpan Das ◽

Dominik R G Schleicher ◽

Nathan W C Leigh ◽

Tjarda C N Boekholt

Keyword(s):

Black Holes ◽

Initial Conditions ◽

High Redshift ◽

Star Clusters ◽

Gas Reservoir ◽

Highly Sensitive ◽

Stellar Collisions ◽

Key Variables ◽

Chaotic Nature ◽

Gas Accretion

Abstract More than two hundred supermassive black holes (SMBHs) of masses ≳ 109 M⊙ have been discovered at z ≳ 6. One promising pathway for the formation of SMBHs is through the collapse of supermassive stars (SMSs) with masses ∼103 − 5 M⊙ into seed black holes which could grow upto few times 109 M⊙ SMBHs observed at z ∼ 7. In this paper, we explore how SMSs with masses ∼103 − 5 M⊙ could be formed via gas accretion and runaway stellar collisions in high-redshift, metal-poor nuclear star clusters (NSCs) using idealised N-body simulations. We explore physically motivated accretion scenarios, e.g. Bondi-Hoyle-Lyttleton accretion and Eddington accretion, as well as simplified scenarios such as constant accretions. While gas is present, the accretion timescale remains considerably shorter than the timescale for collisions with the most massive object (MMO). However, overall the timescale for collisions between any two stars in the cluster can become comparable or shorter than the accretion timescale, hence collisions still play a crucial role in determining the final mass of the SMSs. We find that the problem is highly sensitive to the initial conditions and our assumed recipe for the accretion, due to the highly chaotic nature of the problem. The key variables that determine the mass growth mechanism are the mass of the MMO and the gas reservoir that is available for the accretion. Depending on different conditions, SMSs of masses ∼103 − 5 M⊙ can form for all three accretion scenarios considered in this work.

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Do ultracompact dwarf galaxies form monolithically or as merged star cluster complexes?

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab330 ◽

2021 ◽

Vol 502 (4) ◽

pp. 5185-5199

Author(s):

Hamidreza Mahani ◽

Akram Hasani Zonoozi ◽

Hosein Haghi ◽

Tereza Jeřábková ◽

Pavel Kroupa ◽

...

Keyword(s):

Dwarf Galaxies ◽

Initial Conditions ◽

Mass Function ◽

Star Cluster ◽

Initial Mass Function ◽

Central Mass ◽

Cluster Complexes ◽

V Band ◽

Stellar Masses ◽

The Imf

ABSTRACT Some ultracompact dwarf galaxies (UCDs) have elevated observed dynamical V-band mass-to-light (M/LV) ratios with respect to what is expected from their stellar populations assuming a canonical initial mass function (IMF). Observations have also revealed the presence of a compact dark object in the centres of several UCDs, having a mass of a few to 15 per cent of the present-day stellar mass of the UCD. This central mass concentration has typically been interpreted as a supermassive black hole, but can in principle also be a subcluster of stellar remnants. We explore the following two formation scenarios of UCDs: (i) monolithic collapse and (ii) mergers of star clusters in cluster complexes as are observed in massively starbursting regions. We explore the physical properties of the UCDs at different evolutionary stages assuming different initial stellar masses of the UCDs and the IMF being either universal or changing systematically with metallicity and density according to the integrated Galactic IMF theory. While the observed elevated M/LV ratios of the UCDs cannot be reproduced if the IMF is invariant and universal, the empirically derived IMF that varies systematically with density and metallicity shows agreement with the observations. Incorporating the UCD-mass-dependent retention fraction of dark remnants improves this agreement. In addition, we apply the results of N-body simulations to young UCDs and show that the same initial conditions describing the observed M/LV ratios reproduce the observed relation between the half-mass radii and the present-day masses of the UCDs. The findings thus suggest that the majority of UCDs that have elevated M/LV ratios could have formed monolithically with significant remnant-mass components that are centrally concentrated, while those with small M/LV values may be merged star cluster complexes.

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Shock-induced star cluster formation in colliding galaxies

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311000846 ◽

2010 ◽

Vol 6 (S270) ◽

pp. 483-486 ◽

Cited By ~ 1

Author(s):

Takayuki R. Saitoh ◽

Hiroshi Daisaka ◽

Eiichiro Kokubo ◽

Junichiro Makino ◽

Takashi Okamoto ◽

...

Keyword(s):

High Resolution ◽

Shock Compression ◽

Smoothed Particle Hydrodynamics ◽

Formation Process ◽

Cluster Formation ◽

Star Clusters ◽

Star Cluster ◽

Particle Hydrodynamics ◽

Smoothed Particle ◽

Number Of Particles

AbstractWe studied the formation process of star clusters using high-resolutionN-body/smoothed particle hydrodynamics simulations of colliding galaxies. The total number of particles is 1.2×108for our high resolution run. The gravitational softening is 5 pc and we allow gas to cool down to ~10 K. During the first encounter of the collision, a giant filament consists of cold and dense gas found between the progenitors by shock compression. A vigorous starburst took place in the filament, resulting in the formation of star clusters. The mass of these star clusters ranges from 105−8M⊙. These star clusters formed hierarchically: at first small star clusters formed, and then they merged via gravity, resulting in larger star clusters.

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