arXiv subjects

Rainer Spurzem

Publications and source records attributed to Rainer Spurzem.

At least 19 recordsLinked to original sources

arXiv2026

Primordial Binary Stars, Mass segregation and Fractality Effects on the Early Evolution of Young Open Clusters

We want to understand how the combined effect of initial substructure, primordial mass segregation, and primordial binaries affects the dynamical evolution of the cluster, and which one of these features is the most important to agree with observations. Methods. We use Nbody6++GPU to simulate the dynamics of star clusters with initial substructure, primordial mass segregation, and primordial binaries, and we also study the relative importance of the processes. Initial models were generated by a modified version of McLuster, and we compared our results with observational data from Pang et al. 2022 database of open clusters. Our results show that primordial mass segregation and binaries do not change the result already obtained in previous works, as the time scale on which initial substructure disappears is of the order of few Myrs. However, we also find that in the presence of initial substructure, primordial mass segregation does not lead to an early expansion of the cluster. The processes in the core, discussed in previous works, lead to a loss of low mass stars and early expansion, are postponed in the presence of initial substructure. Finally, we find from comparison with observed clusters that primordial mass segregation is not a fundamental process to reproduce observational data.

astro-ph.GA↗

arXiv2026

Direct N-body simulations of rotating and extremely massive Population III star clusters

Aims. We present eight direct N-body simulations with NBODY6++GPU of extremely massive, initially rotating Population III star clusters with 1.01 x 10^5 stars. Methods. Our models include primordial binaries, a continuous initial mass function, differential rotation, tidal mass loss, updated fitting formulae for extremely massive metal-poor Population III stars, and general-relativistic merger recoil kicks. We assess their impact on cluster dynamics. Results. All runs form black holes below, within, and above the pair-instability gap, with multi-generation growth. Faster-rotating clusters core-collapse earlier; post-collapse clusters host a rotating, axisymmetric subsystem of intermediate-mass black holes (IMBHs) at the centre and an expanding halo of lower-mass objects. Pair-instability supernovae and compact-object formation at ~2-3 Myr sharply reduce total mass and a large fraction of the cluster's angular momentum. All Population III clusters in our simulations have the gravothermal-gravogyro catastrophe phase. Conclusions. We confirm two of the hypothesized formation channels of galactic nucleus seed black holes: gravitational runaway mergers of black holes and of Population III stars, which core-collapse into IMBHs thereafter. A higher initial star cluster bulk rotation correlates with earlier core collapse and, in the event counts reported here, with more coalescences and collisions, as well as lower retained (compact) binary abundances. Initial bulk rotation is a primary control parameter of cluster evolution: faster rotation accelerates early angular-momentum transport, gravothermal collapse, mass segregation, and amplifies post-collapse expansion, which also favours the formation of a compact central IMBH subsystem.

astro-ph.GA↗

arXiv2026

Formation and disruption of wide binaries in star clusters revealed by N-body simulations

Wide (soft) binaries are expected to be rapidly disrupted in dense stellar environments, yet they are observed in both the Galactic field and open clusters (OCs). In this paper, we investigate the formation and disruption of wide binaries in star clusters using direct N-body simulations. We perform simulations containing 10,000 objects with varying binary fractions and initial bulk rotation to give an in-depth look into the dynamical evolution of wide binaries in star clusters. We find that wide binaries dominate early disruption and formation processes during the initial high-density phase of cluster evolution. We propose two semi-analytical models to reproduce the evolution of the wide-binary population in simulations. The exponential model consists of an early, rapid-disruption phase with a time less than 10 Myr, driven by frequent encounters at high density, and a longer, relaxation-driven phase between 200 and 300 Myr. The broken power-law model provides break timescales when the decrease of wide binaries slows down during the early and long-term disruption. All timescales from both models agree with each other and decrease with increasing stellar density induced by high primordial binary fraction and cluster rotation. Wide binary disruption is mostly responsible for the early decline in the total binary fraction of the cluster. Such disruption leads to the decrease of radial binary fraction toward the cluster center until 500 Myr. Our results suggest low-density OCs or stellar groups younger than 10 Myr as the optimal environments for detecting wide binaries and provide a physical framework for understanding their contribution to the Galactic field population.

astro-ph.GA↗

arXiv2026

Modeling Tidal Disruption Events and Compact Object Plunges in Nuclear Star Clusters

We study tidal disruption events (TDEs) and compact object inspirals in nuclear star clusters (NSCs) hosting a central supermassive black hole (SMBH), focusing on their role in SMBH growth. Using the STARDISK version of the direct N-body code NBODY6++GPU, we perform pilot simulations with two improved models: one for mass fallback from TDEs and another for compact object plunges based on orbital decay timescales. Our results show that mass accretion via TDEs peaks within the first 2 Myr and decreases more rapidly for higher initial SMBH masses, with roughly half the disrupted stellar debris being accreted. Compact object accretion is confined mostly to orbits with pericenters between 4 and 27 Schwarzschild radii and is suppressed by an order of magnitude when inspiral criteria are applied.

astro-ph.GA↗

arXiv2026

Pulsars and Millisecond Pulsars I: Advancements, Open Questions and finding Gaps via statistical insights

We present a statistical study of pulsars and millisecond pulsars (MSPs) based on multiwavelength observations in the Galactic Field and Globular Clusters. We examine their emission properties, timing behavior, and spatial distributions, and discuss how theoretical models are required to interpret these observational trends. We focus on the magnetic field spin relation, including spin up through accretion in binaries and spin down driven by magnetic dipole radiation. Using numerical tools such as NBODY6++GPU, CMC, and COMPASS, we explore how dynamical interactions and binary evolution shape the properties of compact objects. Despite major progress, several open questions remain regarding binary interactions, magnetic field evolution, and the incorporation of pulsar physics into large scale simulations. Our analysis highlights the need for improved modeling frameworks to better understand the formation pathways and long term evolution of pulsars and MSPs.

astro-ph.HE↗

arXiv2026

Pulsars and Millisecond Pulsars II: Deep diving into the Evolutionary Mechanisms

This second paper in our series investigates the evolutionary mechanisms that shape pulsars and millisecond pulsars (MSPs) across different astrophysical environments. We focus on the physical processes that govern spin evolution, magnetic field decay, binary interactions, and recycling pathways. Using observational constraints together with theoretical models, we examine how accretion, magnetic braking, and dynamical encounters contribute to the long-term evolution of compact objects. We also explore how these mechanisms differ between the Galactic Field and Globular Clusters, where stellar densities and interaction rates vary significantly. By integrating insights from population studies and numerical tools such as NBODY6++GPU, CMC, and COMPASS, we aim to clarify the dominant channels that lead to the formation and transformation of pulsars and MSPs. Our results highlight key uncertainties in current models and outline the physical ingredients required for more accurate simulations of compact object evolution.

astro-ph.HE↗

arXiv2026

The long-term evolution of Ultra Faint Dwarf Galaxies and observational implications

Context. In the Local Group, dwarf spheroidal galaxies (dSphs) and ultra-faint dwarf galaxies (UFDs) exhibit large velocity dispersions. These values are generally attributed to the presence of substantial amounts of dark matter (DM), in line with the predictions of the standard model of galaxy formation. However, alternative, more conservative explanations exist, such as non-virialized dynamical states induced by tidal interactions, the presence of stellar streams, and artificial inflation of the velocity dispersion caused by binary-star orbital motion. Aims. We study the dynamical evolution of UFDs using purely stellar ("dry") dynamics, without invoking DM. We dynamically evolve our systems up to a Hubble time and compare our results with observational studies and previous theoretical work. Methods. We employ direct high precision NBODY simulations performed with the NBODY6++GPU code. We explore the role of binaries in inflating the velocity dispersion of low-mass host galaxies. We also present both the stellar and dynamical evolution of the stellar population, which is necessary to properly interpret our results. Results. We find that, in all our models, the UFD remains globally quasi-stationary for approximately 3000 Myr. Subsequently, the system undergoes mass segregation and experiences a phase resembling core collapse. Red giants and white dwarfs (WD) are found to play significant, but distinct, roles. Red giants provide the dominant contribution to the luminosity, whereas WDs constitute the largest fraction of the non-luminous component, accounting for approximately 13% of the total stellar population. Finally, if not taken into account properly, velocity dispersion measurements can be strongly biased by the presence of a significant binary population, which can lead to substantial overestimates of velocity dispersion in UFDs

astro-ph.GA↗

arXiv2026

The effects of star-gas interactions on binary evolution in open clusters

Star-gas interactions can provide gravitational feedback that influences the dynamical evolution of stellar clusters, through processes such as dynamical friction (DF) and its non-dissipative counterpart, negative dynamical friction (NDF). Using the \texttt{PeTar} code, we perform direct $N$-body simulations of an open cluster initially containing $10^4$ stars, evolving within a gaseous medium spanning a range of ambient densities. Our results demonstrate that NDF associated with stellar outflows interacting with the surrounding gas can enhance the rate of cluster expansion, preferentially transporting stars toward the cluster outskirts. This behavior is accompanied by a more rapid decline in the number of binaries composed of a neutron star and a main-sequence star. A statistical analysis of binary orbital parameters further indicates that, compared to DF-dominated evolution, NDF tends to retain systems with larger semi-major axes and lower eccentricities. Outflow-ambient gas interactions can modify the dynamical processing of binaries in star clusters, leading to changes in the survival fraction and composition of the remaining binary population.

astro-ph.GA↗

arXiv2025

From Nbody1 to Nbody7: the Growth of Sverres Industry

From NBODY1 to NBODY6 : The Growth of an Industry is the title of a 1999 invited review by Sverre Aarseth, for Publications of the Astronomical Society of the Pacific (PASP). I took this as an inspiration for the title of this paper; it describes how Sverres NBODY Industry has further grown since 90s of the previous century, and how it is further flourishing and hopefully developing, in his spirit, even after the sad news of his passing away reached us. My contact and friendship with Sverre started a few decades ago being sent to Cambridge to learn NBODY5, counting input parameters, and learning about the fact that even a sophisticated code (which had already at that time quite a history) requires permanent maintenance and bug fixes. Managed by Sverre, who relentlessly ran his code and responded to the widely spread crowd of customer colleagues. There has been a phase of massive and fast development and improvements due to vectorization, parallelization, GRAPE and GPU acceleration, and Sverre has been always on top of it if not ahead, but also fully adopting ideas of collaborators, once they tested well. NBODY6++GPU and NBODY7 entered the scene, and also recent new competitors, such as PETAR or BIFROST . We all have learnt a lot from Sverre, and strive to continue in his open-minded spirit, for open source and exchange. A striking evidence for the further growth of the industry is the number of papers here (and two of them follow in this session, but also in other sessions) using and further developing the aforementioned codes, as well as the occurrence of new and competing codes, which keep the field alive.

astro-ph.IM↗

arXiv2025

Dynamical evolution of massless particles in star clusters with NBODY6++GPU-MASSLESS: II. The long-term evolution of free-floating comets

Context. Comets, asteroids, planetesimals, free-floating planets and brown dwarfs, are continuously injected into the intra-cluster environment after expulsion from their host planetary systems or binary system. The dynamics of large populations of such free-floating comets (ffcs) in a star cluster environment is not yet fully understood. Aims. We investigate the dynamical evolution of comet populations in star clusters, and characterize the kinematics and ejection rates of ffc in a star cluster. Moreover, we determine whether a different initial energy distribution affects the mass segregation of the less massive population. Methods. We carry out simulations using the N-body code NBODY6++GPU-MASSLESS (Flammini Dotti et al. 2025), which allows fast integration of star clusters that contain large numbers of massless particles, to characterize the dynamics of populations of low-mass particles with sub-virial and super-virial distributions. Results. Comets do not participate in the mass segregation process, similarly to planet-size objects, regardless of their initial energy distribution. The latter is slightly changing the whole dynamical evolution at the start of the simulation. We only observe an initial relaxation or collapse of the objects for super-virial and sub-virial ratios, respectively. The external regions of the ffcs population tend to be pulled back in the cluster core at the end of the simulation, suggesting the gravitational pull of the stars is pulling them back in the core. This phenomenon occurs at later times if the system in virial equilibrium. Compared to less massive bodies, brown dwarfs experiences more mass segregation the inner regions tend to be more mixed with the stellar population

astro-ph.EP↗

arXiv2025

Intermediate Mass Black Hole Binary Evolution in Nuclear Star Clusters: the effect of the stellar mass black hole population

In this study, we investigate the dynamics of Intermediate-Mass Black Hole (IMBH) binaries within Nuclear Star Clusters (NSCs) that contain a population of stellar-mass black holes (BHs). We examine how these stellar and BH populations influence the dynamics of the IMBH binary and, in turn, how the evolving IMBH binary affects the surrounding stellar and BH populations. We conduct high-resolution $N$-body simulations of NSCs constructed based on observational parameters from two local dwarf galaxies: NGC205 and NGC404. For the first time, we achieve a star particle mass resolution of $1\rm\;M_{\odot}$ and a BH mass resolution of $10\rm\;M_{\odot}$. This level of resolution is crucial for accurately modeling the collisional dynamics of these dense systems. Including stellar-mass BHs within the stellar population significantly influences the IMBH binary dynamics, nearly doubling the sinking rate and halving the merger time. During the initial phase of the inspiral, the IMBH binary disrupts both the stellar and BH cusps. However, the BH cusp quickly regains its steep slope due to its shorter relaxation time and continues to dominate the evolution of the IMBH binary, despite being much less massive compared to the stellar component. We uncover an interesting mechanism in which BHs first efficiently extract energy from the IMBH binary and then transfer this energy to the surrounding stars, allowing the BHs to spiral back toward the center of the system and restart the process. Our results imply that, although stellar mass BHs are a minor component of a stellar population, they can significantly facilitate IMBH growth within NSCs via mergers. We also notice that these dense systems can potentially boost Intermediate Mass Ratio Inspirals (IMRIs) predominantly on radial orbits.

astro-ph.GA↗

arXiv2025

Modelling Millisecond Pulsar Populations in Globular Clusters with NBODY6++GPU

Millisecond pulsars (MSPs) are neutron stars with spin periods as short as a few milliseconds, formed through mass accretion from companion stars. In the dense environments of globular clusters (GCs), MSPs are likely to originate through dynamically assembled interacting binaries. Over 300 MSPs have been detected in GCs to date, more than half of the known Galactic MSP population. In this work, we model MSP populations in intermediate-mass GCs using the direct $N$-body code \textsc{NBODY6++GPU}. We update the code by implementing pulsar spin-down due to magnetic braking and spin-up through accretion, and use this framework to model the pulsar population in the globular cluster M71 to investigate the pulsar population within and the associated gravitational wave transients.

astro-ph.HE↗

arXiv2025

NbodyCP:A direct N-body simulation code for composite stellar populations of single and binary star clusters

It is well-known that some star clusters contain composite stellar populations (CSPs), in which the metallicities or (and) ages of stars are different. The formation and evolution of such clusters and their stellar populations remain unclear. Both single and binary cluster channels may lead to such CSPs. In order to simulate the formation and evolution of such CSPs in star clusters, this work develops a code of direct N-body simulation of CSPs, NbodyCP. It is applied to different clusters, in particular, to binary clusters. It shows that CSPs and different kinds of cluster pairs can be formed via dynamical processes. This will help to partially explain the formation of CSPs and various clusters. Some special cluster structures, e.g., two cores or bar-like shape, are shown to be the results of evolution of some binary clusters. The simulation also shows that the separation between the members of a binary cluster affects the time of two member clusters to combine or move away significantly.

astro-ph.GA↗

arXiv2025

DRAGON-III simulation: modelling million-body globular and nuclear star clusters

As a continuation of DRAGON-II, we present the DRAGON-III project, which focuses on the simulations of million-body globular clusters and nuclear clusters over 10 Gyr. We report on its preliminary results on globular clusters. The first 100 Myr of the simulations have produced 41 pulsars, 191 X-ray binaries, 17 gravitational wave sources, and one black hole-black hole merger due to the loss of orbital energy in the form of gravitational wave emission. The inclusion of initial soft binaries brings surprisingly interesting results, including one IMBH in a binary black hole, and compact object binaries resembling the Gaia-BH1 and the wide black hole-giant binary reported in Wang et al. (2024, Nat. Astro.).

astro-ph.GA↗

arXiv2025

Evolution of star clusters with initial bulk rotation via N-body simulations

Young star clusters can inherit bulk rotation from the molecular clouds from which they have formed. This rotation can affect the long-term evolution of a star cluster and its constituent stellar populations. In this study, we aim to characterize the effects of different degrees of initial rotation on star clusters with primordial binaries. The simulations are performed using NBODY6++GPU. We find that initial rotation strongly affects the early evolution of star clusters. Rapidly rotating clusters show angular momentum transport from the inner parts to the outskirts, resulting in a core collapse. Angular momentum transport is accompanied by a highly elongated bar-like structure morphology. The effects of bulk rotation are reduced on the timescale of two-body relaxation. Rotating and non-rotating clusters experience changes in the direction of angular momentum near the dissolution and early evolution due to the tidal field, respectively. We present synthetic observations of simulated clusters for comparison with future observations in filters of Gaia, CSST, and HST. This work shows the effects of bulk rotation on systems with primordial binaries and could be used for the identification of rotation signatures in observed open clusters.

astro-ph.GA↗

arXiv2025

Rapid formation of a very massive star >50000 $M_\odot$ and subsequently an IMBH from runaway collisions. Direct N-body and Monte Carlo simulations of dense star clusters

Context. We present simulations of a massive young star cluster using \textsc{Nbody6++GPU} and \textsc{MOCCA}. The cluster is initially more compact than previously published models, with one million stars, a total mass of $5.86 \times 10^5~\mathrm{M}_{\odot}$, and a half-mass radius of $0.1~\mathrm{pc}$. Aims. We analyse the formation and growth of a very massive star (VMS) through successive stellar collisions and investigate the subsequent formation of an intermediate-mass black hole (IMBH) in the core of a dense star cluster. Methods. We use both direct \textit{N}-body and Monte Carlo simulations, incorporating updated stellar evolution prescriptions (SSE/BSE) tailored to massive stars and VMSs. These include revised treatments of stellar radii, rejuvenation, and mass loss during collisions. While the prescriptions represent reasonable extrapolations into the VMS regime, the internal structure and thermal state of VMSs formed through stellar collisions remain uncertain, and future work may require further refinement. Results. We find that runaway stellar collisions in the cluster core produce a VMS exceeding $5 \times 10^4~\mathrm{M}_{\odot}$ within 5 Myr, which subsequently collapses into an IMBH. Conclusions. Our model suggests that dense stellar environments may enable the formation of very massive stars and massive black hole seeds through runaway stellar collisions. These results provide a potential pathway for early black hole growth in star clusters and offer theoretical context for interpreting recent JWST observations of young, compact clusters at high redshift.

astro-ph.GA↗

arXiv2025

Formation and Evolution of Compact Binaries Containing Intermediate Mass Black Holes in Dense Star Clusters`

We investigate the evolution of star clusters containing intermediate-mass black hole (IMBH) of $300$ to $5000\ \mathrm{M}_\odot$, focusing on the formation and evolution of IMBH-stellar mass black holes (SBHs; $M_{\rm BH} \lesssim 10^2\ \mathrm{M}_\odot$) binaries. Dense stellar systems like globular clusters (GCs) or nuclear star clusters offer unique laboratories for studying the existence and impact of IMBHs. IMBHs residing in GCs have been under speculation for decades, with their broad astrophysical implications for the cluster's dynamical evolution, stellar population, GW signatures, among others. While existing GW observatories such as the Advanced Laser Interferometer Gravitational-wave Observatory (aLIGO) target binaries with relatively modest mass ratios, $q \lesssim 10$, future observatories such as the Einstein Telescope (ET) and the Laser Interferometer Space Antenna (LISA) will detect intermediate-mass ratio inspirals (IMRIs) with $q > 10$. This work explores the potential for detecting IMRIs adopting these upcoming telescopes. For our experiments, we perform multiple direct $N$-body simulations with IMBHs utilizing Nbody6++GPU, after implementing the GW merger schemes for IMBHs. We then study the statistical properties of the resulting IMRIs, such as the event rates and orbital properties. Assuming that IMRIs with a signal-to-noise ratio $S/N > 8$ are detectable, we derive the following detection rates for each observatory: $\lesssim 0.02\mathrm{yr}^{-1}$ for aLIGO, $\sim 101 - 355 \mathrm{yr}^{-1}$ for ET, $\sim 186 - 200 \mathrm{yr}^{-1}$ for LISA, $\sim 0.24 - 0.34 \mathrm{yr}^{-1}$ for aSOGRO, and $\sim 3880 - 4890 \mathrm{yr}^{-1}$ for DECIGO. Our result confirms the capability of detecting IMRIs with future GW telescopes.

astro-ph.GA↗

arXiv2024

Dynamical evolution of massless particles in star clusters with NBODY6++GPU-MASSLESS: I. Free-floating MLPs

Context. Low-mass bodies, such as comets, asteroids, planetesimals, and free-floating planets, are continuously injected into the intra-cluster environment after expulsion from their host planetary systems. These can be modeled as massless particles (MLPs, hereafter). The dynamics of large populations of MLPs, however, has yet received little attention in literature. Aims. We investigate the dynamical evolution of MLP populations in star clusters, and characterize their kinematics and ejection rates. Methods. We present NBODY6++GPU-MASSLESS, a modified version of the N-body simulation code NBODY6++GPU, that allows fast integration of star clusters that contain large numbers of massless particles (MLPs). NBODY6++GPU-MASSLESS contains routines specifically directed at the dynamical evolution of low-mass bodies, such as planets. Results. Unlike stars, MLPs do not participate in the mass segregation process. Instead, MLPs mostly follow the gravitational potential of the star cluster, which gradually decreases over time due to stellar ejections and stellar evolution. The dynamical evolution of MLPs is primarily affected by the evolution of the core of the star cluster. This is most apparent in the outer regions for clusters with higher initial densities. High escape rates of MLPs are observed before the core-collapse, after which escape rates remain stable. Denser star clusters undergo a more intense core collapse, but this does not impact the dynamical evolution of MLPs. The speeds of escaping stars are similar to those of escaping MLPs, when disregarding the high-velocity ejections of neutron stars during the first 50 Myr.

astro-ph.SR↗