arXiv subjects

Simon F. Portegies Zwart

Publications and source records attributed to Simon F. Portegies Zwart.

At least 37 records · Page 2Linked to original sources

arXiv2016

Secular dynamics of hierarchical multiple systems composed of nested binaries, with an arbitrary number of bodies and arbitrary hierarchical structure. First applications to multiplanet and multistar systems

We present a method for studying the secular gravitational dynamics of hierarchical multiple systems consisting of nested binaries, which is valid for an arbitrary number of bodies and arbitrary hierarchical structure. We derive the Hamiltonian of the system and expand it in terms of the -- assumed to be -- small ratios $x_i$ of binary separations. At the lowest nontrivial expansion order (quadrupole order, second order in $x_i$), the Hamiltonian consists of terms which, individually, depend on binary pairs. At higher orders, in addition to terms depending on binary pairs, we also find terms which, individually, depend on more than two binaries. In general, at order $n$ in $x_i$, individual terms depend on at most $n-1$ binaries. We explicitly derive the Hamiltonian including all terms up and including third order in $x_i$ (octupole order), and including the binary pairwise terms up and including fifth order in $x_i$. These terms are orbit averaged, and we present a new algorithm for efficiently solving the equations of motion. This algorithm is highly suitable for studying the secular evolution of hierarchical systems with complex hierarchies, making long-term integrations of such systems feasible. We show that accurate results are obtained for multiplanet systems with semimajor axis ratios as large as $\approx 0.4$, provided that high-order terms are included. In addition to multiplanet systems with a single star, we apply our results to multistar systems with multiple planets.

astro-ph.SR↗

arXiv2014

Probing the formation of planetesimals in the Galactic Centre using Sgr A* flares

Flares in X-ray and near infrared are observed above the quiescent emission of the supermassive black hole (SBH) in the Galactic Centre (GC) at a rate of approximately once per day. One proposed energy source for these flares is the tidal disruption of planetesimals with radius $\gtrsim 10$ km passing within $\sim$ 1 AU of the SBH. Very little is known about the formation and evolution of planetesimals in galactic nuclei such as the GC, making predictions for flaring event rates uncertain. We explore two scenarios for the formation of planetesimals in the GC: (1) in a large-scale cloud bound to the SBH, and (2) in debris discs around stars. We model their orbital evolution around the SBH using the Fokker-Planck equation and investigate the effect of gravitational interactions with various relevant perturbers. Our predicted flaring rate, $\approx 0.6 \, \mathrm{day^{-1}}$, is nearly independent of the distribution of perturbers. Moreover, it is insensitive to scenarios (1) or (2). The assumed number of planetesimals per star is consistent with debris discs around stars in the Solar neighbourhood. In scenario (1) this implies that the number of planetesimals formed in the large-scale cloud is strongly correlated with the number of stars, and this requires finetuning for our results to be consistent with the observed flaring rate. We favour the alternative explanation that planetesimals in the GC are formed in debris discs around stars, similar to the Solar neighbourhood.

astro-ph.GA↗

arXiv2014

A connected component-based method for efficiently integrating multiscale $N$-body systems

We present a novel method for efficient direct integration of gravitational N-body systems with a large variation in characteristic time scales. The method is based on a recursive and adaptive partitioning of the system based on the connected components of the graph generated by the particle distribution combined with an interaction-specific time step criterion. It uses an explicit and approximately time-symmetric time step criterion, and conserves linear and angular momentum to machine precision. In numerical tests on astrophysically relevant setups, the method compares favourably to both alternative Hamiltonian-splitting integrators as well as recently developed block time step-based GPU-accelerated Hermite codes. Our reference implementation is incorporated in the HUAYNO code, which is freely available as a part of the AMUSE framework.

astro-ph.IM↗

arXiv2014

Relativistic dynamics of stars near a supermassive black hole

General relativistic precession limits the ability of gravitational encounters to increase the eccentricity $e$ of orbits near a supermassive black hole (SBH). This "Schwarzschild barrier" (SB) has been shown to play an important role in the orbital evolution of stars like the galactic center S-stars. However, the evolution of orbits below the SB, $e>e_\mathrm{SB}$, is not well understood; the main current limitation is the computational complexity of detailed simulations. Here we present an $N$-body algorithm that allows us to efficiently integrate orbits of test stars around a SBH including general relativistic corrections to the equations of motion and interactions with a large ($\gtrsim 10^3$) number of field stars. We apply our algorithm to the S-stars and extract diffusion coefficients describing the evolution in angular momentum $L$. We identify three angular momentum regimes, in which the diffusion coefficients depend in functionally different ways on $L$. Regimes of lowest and highest $L$ are well-described in terms of non-resonant relaxation (NRR) and resonant relaxation (RR), respectively. In addition, we find a new regime of "anomalous relaxation" (AR). We present analytic expressions, in terms of physical parameters, that describe the diffusion coefficients in all three regimes, and propose a new, empirical criterion for the location of the SB in terms of the $L$-dependence of the diffusion coefficients. Subsequently we apply our results to obtain the steady-state distribution of angular momentum for orbits near a SBH.

astro-ph.GA↗

arXiv2012

N-body Integrators with Individual Time Steps from Hierarchical Splitting

We review the implementation of individual particle time-stepping for N-body dynamics. We present a class of integrators derived from second order Hamiltonian splitting. In contrast to the usual implementation of individual time-stepping, these integrators are momentum conserving and show excellent energy conservation in conjunction with a symmetrized time step criterion. We use an explicit but approximate formula for the time symmetrization that is compatible with the use of individual time steps. No iterative scheme is necessary. We implement these ideas in the HUAYNO (available online at www.amusecode.org) code and present tests of the integrators and show that the presented integration schemes shows good energy conservation, with little or no systematic drift, while conserving momentum and angular momentum to machine precision for long term integrations.

astro-ph.IM↗

arXiv2012

The formation of young dense star clusters through mergers

Young star clusters like R136 in the Large Magellanic Cloud and NGC 3603, Westerlund 1, and 2 in the Milky Way are dynamically more evolved than expected based on their current relaxation times. In particular, the combination of a high degree of mass segregation, a relatively low central density, and the large number of massive runaway stars in their vicinity are hard to explain with the monolithic formation of these clusters. Young star clusters can achieve such a mature dynamical state if they formed through the mergers of a number of less massive clusters. The shorter relaxation times of less massive clusters cause them to dynamically evolve further by the time they merge, and the merger product preserves the memory of the dynamical evolution of its constituent clusters. With a series of $N$-body simulations, we study the dynamical evolution of single massive clusters and those that are assembled through merging smaller clusters together. We find that the formation of massive star clusters through the mergers of smaller clusters can reproduce the currently observed spatial distribution of massive stars, the density, and the characteristics (number and mass distribution) of the stars ejected as runaways from young dense clusters. We therefore conclude that these clusters and possibly other young massive star clusters formed through the mergers of smaller clusters.

astro-ph.GA↗

arXiv2011

Formation versus destruction: the evolution of the star cluster population in galaxy mergers

(Abridged) Interacting galaxies are well-known for their high star formation rates and rich star cluster populations, but the rapidly changing tidal field can also efficiently destroy clusters. We use numerical simulations of merging disc galaxies to investigate which mechanism dominates. The simulations include a model for the formation and dynamical disruption of the entire star cluster population. We find that the dynamical heating of clusters by tidal shocks is about an order of magnitude higher in interacting galaxies than in isolated galaxies. This is driven by the increased gas density, and is sufficient to destroy star clusters at a higher rate than new clusters are formed: the total number of clusters in the merger remnant is 2-50% of the amount in the progenitor discs, with low-mass clusters being disrupted preferentially. By adopting observationally motivated selection criteria, we find that the observed surplus of star clusters in nearby merging galaxies is caused by the bias to detect young, massive clusters. We provide a general expression for the survival fraction of clusters, which increases with the gas depletion time-scale. Due to the preferential disruption of low-mass clusters, the mass distribution of the surviving star clusters in a merger remnant develops a peak at a mass of about 10^3 Msun, which evolves to higher masses at a rate of 0.3-0.4 dex per Gyr. The peak mass initially depends weakly on the galactocentric radius, but this correlation disappears as the system ages. We discuss the similarities between the cluster populations of the simulated merger remnants and (young) globular cluster systems. Our results suggest that the combination of cluster formation and destruction should be widespread in the dense star-forming environments at high redshifts, which could provide a natural origin to present-day globular cluster systems.

astro-ph.CO↗

arXiv2011

Modeling the formation and evolution of star cluster populations in galaxy simulations

(Abridged) The formation and evolution of star cluster populations are related to the galactic environment. Cluster formation is governed by processes acting on galactic scales, and star cluster disruption is driven by the tidal field. In this paper, we present a self-consistent model for the formation and evolution of star cluster populations, for which we combine an N-body/SPH galaxy evolution code with semi-analytic models for star cluster evolution. The model includes star formation, feedback, stellar evolution, and star cluster disruption by two-body relaxation and tidal shocks. We apply the model by simulating a suite of 9 isolated disc galaxies and 24 galaxy mergers. The evolutionary histories of individual clusters in these simulations are discussed to illustrate how the environment of clusters changes in time and space. The resulting variability of the disruption rate with time and space affects the properties of star cluster populations. The combined effect of clusters escaping their dense formation sites (`cluster migration') and the preferential disruption of clusters residing in dense environments (`natural selection') implies that the mean disruption rate of the population decreases with cluster age. This affects the slope of the cluster age distribution, which becomes a function of the star formation rate density. The evolutionary histories of clusters in a galaxy merger vary widely and determine which clusters survive the merger. This impacts the age distributions and the locations of the surviving clusters at all times during a merger. We conclude that accounting for the interplay between the formation, disruption, and orbital histories of clusters enables a more sophisticated interpretation of observed properties of cluster populations, thereby extending the role of cluster populations as tracers of galaxy evolution.

astro-ph.CO↗

arXiv2010

The early dynamical evolution of cool, clumpy star clusters

Observations and theory both suggest that star clusters form sub-virial (cool) with highly sub-structured distributions. We perform a large ensemble of N-body simulations of moderate-sized (N=1000) cool, fractal clusters to investigate their early dynamical evolution. We find that cool, clumpy clusters dynamically mass segregate on a short timescale, that Trapezium-like massive higher-order multiples are commonly formed, and that massive stars are often ejected from clusters with velocities > 10 km/s (c.f. the average escape velocity of 2.5 km/s). The properties of clusters also change rapidly on very short timescales. Young clusters may also undergo core collapse events, in which a dense core containing massive stars is hardened due to energy losses to a halo of lower-mass stars. Such events can blow young clusters apart with no need for gas expulsion. The warmer and less substructured a cluster is initially, the less extreme its evolution.

astro-ph.GA↗

arXiv2010

The Quest for the Sun's Siblings: an Exploratory Search in the Hipparcos Catalogue

We describe the results of a search for the remnants of the Sun's birth cluster among stars in the Hipparcos Catalogue. This search is based on the predicted phase space distribution of the Sun's siblings from simple simulations of the orbits of the cluster stars in a smooth Galactic potential. For stars within 100 pc the simulations show that it is interesting to examine those that have small space motions relative to the Sun. From amongst the candidate siblings thus selected there are six stars with ages consistent with that of the Sun. Considering their radial velocities and abundances only one potential candidate, HIP 21158, remains but essentially the result of the search is negative. This is consistent with predictions by Portegies Zwart (2009) on the number of siblings near the Sun. We discuss the steps that should be taken in anticipation of the data from the Gaia mission in order to conduct fruitful searches for the Sun's siblings in the future.

astro-ph.GA↗

arXiv2009

The Relation Between the Globular Cluster Mass and Luminosity Functions

The relation between the globular cluster luminosity function (GCLF, dN/dlogL) and globular cluster mass function (GCMF, dN/dlogM) is considered. Due to low-mass star depletion, dissolving GCs have mass-to-light (M/L) ratios that are lower than expected from their metallicities. This has been shown to lead to an M/L ratio that increases with GC mass and luminosity. We model the GCLF and GCMF and show that the power law slopes inherently differ (1.0 versus 0.7, respectively) when accounting for the variability of M/L. The observed GCLF is found to be consistent with a Schechter-type initial cluster mass function and a mass-dependent mass-loss rate.

astro-ph.GA↗

arXiv2009

On the Interpretation of the Globular Cluster Luminosity Function

The conversion of the globular cluster luminosity function (GCLF, dN/dlogL) to the globular cluster mass function (GCMF, dN/dlogM) is addressed. Dissolving globular clusters (GCs) become preferentially depleted in low-mass stars, which have a high mass-to-light ratio. This has been shown to result in a mass-to-light ratio (M/L) that increases with GC luminosity or mass, because more massive GCs have lost a smaller fraction of their stars than low-mass GCs. Using GC models, we study the influence of the luminosity dependency of M/L on the inferred GCMF. The observed GCLF is consistent with a powerlaw or Schechter type GC initial mass function in combination with a cluster mass-dependent mass loss rate. Below the peak, the logarithmic slope of the GCMF is shallower than that of the GCLF (0.7 versus 1.0), whereas the peak mass is 0.1-0.3 dex lower when accounting for the variability of M/L than in the case where a constant M/L is adopted.

astro-ph.GA↗

arXiv2009

Using the minimum spanning tree to trace mass segregation

We present a new method to detect and quantify mass segregation in star clusters. It compares the minimum spanning tree (MST) of massive stars with that of random stars. If mass segregation is present, the MST length of the most massive stars will be shorter than that of random stars. This difference can be quantified (with an associated significance) to measure the degree of mass segregation. We test the method on simulated clusters in both 2D and 3D and show that the method works as expected. We apply the method to the Orion Nebula Cluster (ONC) and show that the method is able to detect the mass segregation in the Trapezium with a `mass segregation ratio' Λ_{MSR}=8.0 \pm 3.5 (where Λ_{MSR}=1 is no mass segregation) down to 16 \Msun, and also that the ONC is mass segregated at a lower level (~2.0 \pm 0.5) down to 5 \Msun. Below 5 \Msun we find no evidence for any further mass segregation in the ONC.

astro-ph.GA↗

arXiv2006

Reconstructing the Initial Relaxation Time of Young Star Clusters in the Large Magellanic Cloud

We reconstruct the initial two-body relaxation time at the half mass radius for a sample of young $\aplt 300$ Myr star clusters in the large Magellanic cloud. We achieve this by simulating star clusters with 12288 to 131072 stars using direct $N$-body integration. The equations of motion of all stars are calculated with high precision direct $N$-body simulations which include the effects of the evolution of single stars and binaries. We find that the initial relaxation times of the sample of observed clusters in the large Magellanic cloud ranges from about 200 Myr to about 2 Gyr. The reconstructed initial half-mass relaxation times for these clusters has a much narrower distribution than the currently observed distribution, which ranges over more than two orders of magnitude.

astro-ph↗

arXiv2006

A dynamical origin for early mass segregation in young star clusters

Some young star clusters show a degree of mass segregation that is inconsistent with the effects of standard two-body relaxation from an initially unsegregated system without substructure, in virial equilibrium, and it is unclear whether current cluster formation models can account for this degree of initial segregation in clusters of significant mass. In this Letter we demonstrate that mergers of small clumps that are either initially mass segregated, or in which mass segregation can be produced by two-body relaxation before they merge, generically lead to larger systems which inherit the progenitor clumps' segregation. We conclude that clusters formed in this way are naturally mass segregated, accounting for the anomalous observations and suggesting that this process of prompt mass segregation due to initial clumping should be taken fully into account in constructing cluster dynamical models.

astro-ph↗

arXiv2004

Disruption time scales of star clusters in different galaxies

The observed average lifetime of the population of star clusters in the Solar Neighbourhood, the Small Magellanic Cloud and in selected regions of M51 and M33 is compared with simple theoretical predictions and with the results of N-body simulations. The empirically derived lifetimes (or disruption times) of star clusters depend on their initial mass as t_dis ~ Mcl^0.60 in all four galaxies. N-body simulations have shown that the predicted disruption time of clusters in a tidal field scales as t_dis^pred ~ t_rh^0.75 t_cr^0.25, where t_rh is the initial half-mass relaxation time and t_cr is the crossing time for a cluster in equilibrium. We show that this can be approximated accurately by t_dis^pred ~ M_cl^0.62 for clusters in the mass range of about 10^3 to 10^6 M_sun, in excellent agreement with the observations. Observations of clusters in different extragalactic environments show that t_dis also depends on the ambient density in the galaxies where the clusters reside. Linear analysis predicts that the disruption time will depend on the ambient density of the cluster environment as t_dis ~ rho_amb^-0.5. This relation is consistent with N-body simulations.

astro-ph↗

arXiv2004

Ultraluminous X-ray Sources as Intermediate Mass Black Holes Fed by Tidally Captured Stars

The nature of ultraluminous X-ray sources (ULXs) is presently unknown. A possible explanation is that they are accreting intermediate mass black holes (IBHs) that are fed by Roche lobe overflow from a tidally captured stellar companion. We show that a star can circularize around an IBH without being destroyed by tidal heating (in contrast to the case of M_bh> 10^6 M_sun massive black holes in galactic centers, where survival is unlikely). We find that the capture and circularization rate is of the order of 5 \times 10^-8 yr^-1, almost independently of the cluster's relaxation time. We follow the luminosity evolution of the binary system during the main sequence Roche lobe overflow phase and show it can maintain ULX-like luminosities for >10 Myr. In particular, we show that the ULX in the young cluster MGG-11 in star-burst galaxy M82, which possibly harbors an IBH, is well explained by this mechanism, and we predict that \gtrsim 10% of similar clusters with IBHs have a tidally captured circularized star. The cluster can evaporate on a time-scale shorter than the lifetime of the binary. This raises the possibility of a ULX that outlives its host cluster, or even lights up only after the cluster has evaporated, in agreement with observations of host-less ULXs.

astro-ph↗

arXiv2003

The efficiency of the spiral-in of a black hole to the Galactic centre

We study the efficiency at which a black hole or dense star cluster spirals-in to the Galactic centre. This process takes place on a dynamical friction time scale, which depends on the value of the Coulomb logarithm ln(L). We determine the accurate value of this parameter using the direct N-body method, a tree algorithm and a particle-mesh technique with up to 2 million plus one particles. The three different techniques are in excellent agreement. Our result for the Coulomb logarithm appears to be independent of the number of particles. We conclude that ln(L) = 6.6 +/- 0.6 for a massive point particle in the inner few parsec of the Galactic bulge. For an extended object, like a dense star cluster, ln(L) is smaller, with a value of the logarithm argument L inversely proportional to the object size.

astro-ph↗