Thursday, June 19
Monte Carlo N-body Methods for Star Cluster Dynamics
Monte Carlo methods for star cluster dynamics have been used for nearly 50 years as a rapid technique for modeling the collisional N-body problem. In this talk, I will review the state-of-the-art in these methods, and describe what they can tell us about star clusters, their evolution, and the unique binaries and transients they produce. I will also describe new advances in Monte Carlo methods which will allow us to model star clusters in full 3D, while preserving the inherent speed of these methods over direct N-body
Formation and evolution of star clusters in the early universe using self-consistent hybrid hydro/direct N-body simulations
Star clusters are dense stellar systems requiring precise collisional gravity calculations, traditionally studied using direct N-body simulations to explore dynamics, stellar evolution, X-ray binaries, and intermediate-mass black hole (IMBH) formation. To extend these simulations to galactic and cosmological scales, I developed Enzo-Abyss, a novel hybrid integrating cosmological magneto-hydrodynamics (Enzo) and direct N-body dynamics (Abyss). By treating galactic dynamics as quasi-stationary relative to star clusters, NewEnzo uniquely bridges vastly different dynamical timescales. I enhanced Enzo-Abyss by implementing co-moving coordinates for cosmic expansion to simulate early-universe star cluster formation. Furthermore, for a self-consistent study of first star clusters, I am integrating star-by-star stellar physics (AEOS), sophisticated black hole formation and evolution processes, and targeted cosmological simulations to explore runaway stellar mergers, providing critical insights into early star cluster evolution and IMBH formation.
Fast dynamical modelling of globular clusters; constraints on initial conditions and black hole physics.
Populations of stellar-mass black holes (BHs) in globular clusters (GCs) strongly influence their dynamical evolution and lifetimes. Recently, we used multimass equilibrium models of Milky Way GCs to explore the present-day BH populations of a large sample of clusters, based on several observables, including velocity dispersions, density profiles and stellar mass functions. We have now combined these equilibrium models with the new rapid cluster evolution model “clusterBH”, which simulates the bulk properties of tidally-limited GCs and their BH subsystems over time. These coupled models allow us to hierarchically place constraints on the initial conditions of real GCs, based only on their observable present-day conditions. These models also provide a framework for probing the highly uncertain physics surrounding the formation of BHs, such as their natal kicks, by experimenting with flexible prescriptions and common assumptions and analyzing the impacts on the formation, evolution and present-day structure of Milky Way GCs. In this presentation, will describe these new coupled models, and present the results of their application to both mock observations of N-body models and a large sample of real Milky Way GCs.
BPASS Predictions of Compact Remnant Binaries in the Milky Way
We present a study using the Binary Population and Spectral Synthesis code (BPASS) that predicts the Galactic population of binaries that contain a black hole or neutron star. By incorporating the stellar evolution models from the BPASS suite with a Milky Way analogue galaxy from the Feedback in Realistic Environment (FIRE) simulation suite, we can generate a theoretical population of quiescent compact remnant binaries as well as x-ray binaries within our Galaxy. We split the population into quiescent systems before and after their binary interactions, to investigate how such systems evolve and to further understand their role as supernovae remnants. Furthermore, we explore the code’s output of x-ray binaries with a focus on how they can be studied as transients for systems that appear to be quiescent. We predict the distribution of masses and orbital periods for these systems and compare these to the current observed distributions within our Galaxy, including the recently discovered Gaia Black Hole systems. The remnant masses produced by the code for the pre-interaction systems serve to give us the most accurate measurement of the masses for compact remnants that form from supernovae. We find that the agreement in general is reasonable but there are strong indications that we need to include new physical processes within BPASS to be able to more accurately reproduce the observed compact remnant distributions. These being ablation from pulsars and a revised supernova kick prescription.
Stellar binaries orbiting supermassive black holes should often shrink to near-contact separations
Binary stars orbiting supermassive black holes are involved in a range of (often observable) astronomical processes. Here, we focus on a unique interplay of dynamical effects that sculpts this population’s demographics over time. The eccentricities of these binaries may be raised to nearly unity through secular von-Ziepel-Lidov-Kozai oscillations. If these oscillations drive a binary’s pericenter separation down to a few stellar radii, the orbit may lose energy through stellar tidal interactions, rapidly reducing its semimajor axis until the two stars are nearly in contact. Through a novel set of secular-evolution simulations, we find that the fraction of systems that shrink in this way is ~5x larger than previously thought. There are two causes for this boost: (1) we consider the impact of diffusive dynamical stellar tides (rather than assuming a model based on equilibrium tides), and (2) we consider vector resonant relaxation and gravitational perturbations from passing stars (rather than treating the stellar binary + supermassive black hole system as effectively isolated). Applying this work to the Galactic Center, we find that roughly half of the stellar binaries within a parsec of Sgr A* should shrink to near-contact separations before their stars leave the main sequence.
From direct N-body to deep-learning: modelling the internal dynamics of globular clusters
The increasing number of highly detailed observations of globular clusters (GCs) is transforming our understanding of their compact object populations and shedding new light on their formation in the high-redshift universe. This calls for the development of new realistic models that can simultaneously capture both the kinematic and stellar population properties of GCs over their 13-billion-year evolution. In this talk, I will present my current efforts in modeling realistic GCs, with a particular focus on a forward-modeling approach to interpret current and future observations. I will first introduce a new suite of >20 realistic N-body simulations, run with NBODY6+++GPU, incorporating stellar evolution, diverse external tidal fields, internal rotation, and a realistic number of stars (N = 250k–1.5M). These simulations are designed to reproduce the internal kinematic features of Milky Way GCs, with a particular emphasis on their angular momentum content. Their realistic number of stars also enables us to carry out direct comparisons with Galactic GCs and helps establish a link between present-day and primordial cluster properties. I will then demonstrate how deep-learning techniques —specifically convolutional neural networks trained on synthetic images— can maximize the scientific return of these computationally expensive simulations for a direct comparison with observations. In particular, I will highlight recent developments in the pi-DOC deep-learning algorithm, designed to measure the dynamical and morphological properties of GCs in both the Milky Way and Andromeda. These promising results suggest that detailed dynamical studies of GCs could soon be extended beyond the Local Group, providing new valuable insights into the formation and evolution of these ancient stellar systems.
Exploring hierarchical star cluster and massive black hole seed formation using a hierarchical 4th order forward integrator
The observations by the James Webb Space Telescope (JWST) and hydrodynamical solar mass resolution star cluster formation simulations suggest that early star formation was dense, clumpy and clustered, and that massive star cluster formation is an inherently hierarchical process. I explore the consequences of such hierarchical cluster assembly for the formation of supermassive black hole (SMBH) seeds through runaway stellar collisions in dense, massive star clusters. I present my recent improvements of the direct N-body code BIFROST based on the hierarchical 4th order forward symplectic integrator, Nvidia/AMD hardware acceleration, post-Newtonian algorithmic regularization methods as well as single and binary stellar evolution prescriptions. Using BIFROST, I model the formation of 12 hierarchically assembled million solar mass star clusters including initial populations of single, binary and triple stars. Intermediate mass black holes (IMBH) up to 10000 solar masses form in the simulations through stellar collisions, tidal disruption events and gravitational wave (GW) driven black hole mergers, and frequently >2 SMBH seeds end up in the assembled cluster. These IMBHs interact leading to rapid GW mergers within 10 Myr. I will discuss the characteristic GW fingerprint of the hierarchical cluster assembly: an equal-mass GW merger in the IMBH mass range, observable using the next-generation GW observatories including the Laser Interferometer Space Antenna and the Einstein Telescope.
Evolution of Rotating Clusters and Formation of Binary Black Holes
We perform N-body simulations to examine the properties of dynamically formed binary black holes (BBHs) in a cluster taking into account cluster rotation. We assume a rotating King model and apply initial conditions varying rotational parameters. Our results show that the evolution of a rotating cluster is generally faster than that of a non-rotating one, as expected. In particular, rotating clusters tend to eject more particles during the early phase of their evolution. This results in (i) an acceleration of cluster evaporation as the rotation speed increases, and (ii) a reduction in the formation of binary black holes. We find that the evolution of a rotating cluster shows a degeneracy between rotation and tidal condition of a cluster within its host galaxy. For example, we find that the evolution of a fast-rotating, underfilling cluster is similar to that of a non-rotating, filling cluster. In addition to studying evolution, we examine the properties of BBHs ejected from rotating clusters. BBHs formed and ejected from fast-rotating clusters are more likely to be wider (lower hardness values) and to move slower (lower velocities). Improved sensitivities in future gravitational-wave observations will allow us to determine the origins of BBHs.
Unveiling the dance of off-center black hole duets: Insights from Jacobi capture in dwarf galaxies
It is well established that massive black holes reside in the central regions of virtually all types of known galaxies. Recent observational and numerical studies however challenge this picture, suggesting that intermediate-mass black holes in dwarf galaxies may be found on orbits far from the center. In this talk, I will present my recent work on the dynamics of off-center black holes in dwarf galaxies. I introduce a new scenario to describe off-center mergers of massive black holes, starting with a Jacobi capture. I find that these captures are a complex and chaotic phenomenon and I quantify how the likelihood of capture depends on the simulation parameters. I show that Jacobi captures in cored dwarf galaxies facilitate the formation of off-center black hole binaries. While my setup only allows for temporary captures, it has been shown that dissipative forces from stellar populations can stabilize the captures, motivating further investigation into their role in forming stable binary systems within stripped nuclei or globular clusters. My work shows that off-center mergers can have a major impact on the mass growth of black holes, and therefore they can play a fundamental role for the understanding of gravitational wave signals in the context of future observatories, such as LISA.
Stellar collisions – Blue straggler stars and electromagnetic transients
In dense stellar environments, stars can physically collide. Stellar collisions play a key role in shaping the stellar population at the centers of stellar clusters and galactic nuclei. Depending on the collision’s kinetic energy, different outcomes arise. When the collision kinetic energy is smaller than the binding energy of the colliding stars, the two stars merge into a more massive star, which can manifest as a group of stars appearing younger and bluer than their surroundings — known as blue straggler stars. Conversely, if the collision kinetic energy is larger, as in nuclear stellar clusters around a supermassive black hole, the colliding stars may be partially or completely destroyed, producing expanding ejecta. This process can generate bright flares, making these events promising nuclear transients. In this talk, I will discuss the properties of collision products in these two regimes. In the first part, I will explore magnetic field amplification in low-velocity collisions as a potential solution to the “angular momentum” problem for blue straggler stars. In the second part, I will discuss the observables of high-velocity collisions involving both giants and main-sequence stars and those of subsequent accretion of the ejecta onto the supermassive black hole.
X-ray emission from helium star+black hole binaries as probes of tidally induced spin-up of second-born black holes
Tidally induced spin-up of stripped helium stars in short-period (< 1 d) binaries with black holes (BHs) has been proposed as one of the possible mechanisms to reproduce the high-spin tail of the BH spin distribution derived from gravitational wave (GW) merger observations. At such short periods, a fraction of the intense stellar wind from the stripped helium stars may be accreted by the BHs, and its gravitational potential energy may be released as X-rays. We estimate lower limits on the X-ray luminosity and its observability from the population of stripped helium star+BH binaries that evolve into GW mergers. We find that 10-50 % of stripped-helium stars in the above population transfer enough wind matter onto the BH to produce X-ray luminosities above 10**35 erg/s, up to 10**39 erg/s. Such binaries should be observable as X-ray bright systems at 0.1, 0.5 and 1 Zsun, representing Sextans A, the Large Magellanic Cloud (LMC) and the Solar neighbourhood, respectively. We show that most of these X-ray-bright systems also have the shortest orbital periods where tides spin up the stripped helium star component. The formation efficiency of these systems increases with decreasing metallicity. Wolf-Rayet stars in our Milky Way identified as non-coronal X-ray emitters in the eRosita survey are ideal targets to derive empirical constraints on the predicted evolutionary pathway of tidally spun-up second-born BHs. Such binaries are essential to constrain the binary physics assumptions of gravitational wave palaeontology, where the degeneracies may not be resolved simply by an exponential rise in GW merger events in O4/O5.
Modeling Normal Pulsars in Globular Clusters via NBODY6++GPU
Recent discoveries by JWST have shed new light on the population of massive black holes (MBHs), challenging existing theoretical models of MBH formation, growth, and feedback. In this context, I investigate hierarchical black hole (BH) mergers within active galactic nuclei (AGNs), which stand out with respect to other dynamical environments for three main reasons: enhanced binary formation due to migration traps, accelerated binary inspiral due to gas hardening and high merger remnant retention due to the deep gravitational potential of the SMBH. I will present the main results of my new semi-analytical model, which allows me to effectively explore the parameter space while capturing all the main physical processes involved. I will show that the mass of the SMBH has a relevant impact on the properties of binary BH mergers, potentially leading to the formation of MBHs (up to 10.000 solar masses). We model the SMBH mass function across cosmic time by combining observational data from the local universe with simulated data from the semi-analytical code CAT. We explore two scenarios for growth of SMBHs: either the SMBH growth happens via Bondi-Hoyle-Lyttleton spherical accretion with a maximum allowed limit at the Eddington rate, or occasional super-Eddington accretion can be triggered by gas-rich galaxy mergers. We construct samples of mock GW observations for the Einstein Telescope, which can be useful to constrain the SMBH mass distribution at high redshift and constrain their seeding mechanism.
Dynamics of Binary Stars and Multiple Stellar Populations in Globular Clusters
The complex interplay between binary stars and the different dynamical properties of multiple stellar populations in globular clusters shapes a unique dynamical evolution of both systems. Using a series of numerical simulations, this study investigates how binary star properties evolve within the diverse environments created by multiple stellar populations. We examine how global properties like binary fraction and spatial mixing of different populations evolve over time, as well as how binaries show distinct radial trends compared to single stars. In addition, we analyze the unique dynamics of binaries including stellar remnants and examine the characteristics of mixed binaries (binaries composed of stars belonging to different populations). By understanding these dynamical processes, we aim to provide insights into the long-term evolution of both binary stars and globular clusters and explore the dynamical implications of the different initial structural properties of multiple stellar populations imprinted at the time of their formation.
Dynamical formation of compact binary systems detected by Gaia astrometry
The Gaia mission and its follow-up observations have discovered compact binaries not involved in mass transfer, so-called Gaia Black Holes (BHs) and Gaia Neutron Stars (NSs). These compact binaries, which have orbital periods of more than 100 days, are completely new populations. These discoveries challenge the conventional binary evolution model. We have shown that open clusters can be promising formation sites of Gaia BHs by means of N-body simulation (Tanikawa et al. 2024, MNRAS, 527, 4031; Tanikawa et al. 2024, OJAp, 7, 39). Moreover, we have found that a few percent of Gaia BHs may indeed harbor binary BHs, and may be identified by spectroscopy with an accuracy of 1 m/s (Tanikawa et al. 2024, arXiv:2407.03662). One binary BH will be present in Gaia BHs detected from Gaia DR4 or Final DR.
Kitchen Sink N-body Models (bug hunting with Sverre)
This presentation will review the process of working with Sverre Aarseth to add stellar and binary evolution to the NBODY codes – contributing to the Growth of the Industry – and will look at some of the realistic star cluster models that have been produced as a result.
From NBODY1 to NBODY7: the growth of Sverre’s 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 will describe how Sverre’s 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 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 learnt a lot from Sverre, and strive to continue in his openminded 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. A quick brainstorming will be done to illuminate what probably needs to be done in the future to keep this amazing, ingenious, but also sometimes confusing and irritating software package alive – it has benefitted from the hard work done by generations of astrophysicists and code developers. Does it have a chance to continue its development by new generations of students and scientists in the coming age of AI assisted programming, of AI partly replacing supercomputing, of APP-style software interfaces?
DRAGON-III simulation: modelling million-body globular and nuclear star clusters over cosmic time
Star clusters are self-gravitating stellar systems found throughout galaxies and the Universe. Globular clusters, abundant in galactic disks and spheroids, serve as ideal laboratories for studying stellar evolution alongside Newtonian and relativistic dynamics, revealing complex structural properties through high-resolution observations. Nuclear clusters, which often host supermassive black holes in massive elliptical galaxies, can influence the evolution of their host galaxies, generating tidal disruption events as stars or compact objects interact with the central black hole. The previous study of Dragon-II (Arca Sedda et al. 2023) successfully revealed astrophysical details of these dynamical systems, including gravitational wave signals from compact object mergers that would be measured by LIGO/Virgo/KAGRA. As a continuation of DRAGON-II, we present the DRAGON-III project and report on its preliminary results, which focuses on the simulations of million-body globular clusters and million-body nuclear clusters over 10 Gyr.
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 msun, focusing on the formation and evolution of IMBH-stellar mass black holes SBHs; M_BH < 10^2 msun 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 < 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: < 0.02 yr^-1 for aLIGO, ~ 101 - 355 yr^-1 for ET, ~ 186 - 200 yr^-1 for LISA, ~ 0.24 - 0.34 yr^-1 for aSOGRO, and ~ 3880 - 4890 yr^-1 for DECIGO. Our result confirms the capability of detecting IMRIs with future GW telescopes.