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We simulate mergers between star clusters embedded within their natal giant molecular cloud. We extract initial conditions from cloud-scale simulations of cluster formation and introduce different prescriptions for primordial binaries. We find that simulations that do not include primordial binaries result in a larger fraction of unbound stars than simulations which include a prescription for binaries based on observations. We also find a preferred direction of motion for stars that become unbound during the merger. Sub-cluster mergers within realistic gas environments promote binary disruption while mergers between idealized, gas-rich spherical clusters do not produce the same disruption. Binary systems with smaller semi-major axes are disrupted in simulations of sub-cluster mergers within their natal environment compared to simulations that do not include the realistic gas environment. We conclude that binary disruption and the production of an anisotropic distribution of unbound stars are the natural consequences of sub-cluster mergers during star cluster assembly., Comment: 13 pages, 8 figures. Re-submitted to ApJ following favourable referee report

We use the stellar evolution code BPASS and the gravitational wave simulation code LEGWORK to simulate populations of compact binaries that may be detected by the in-development space-based gravitational wave (GW) detector LISA. Specifically, we simulate the Magellanic Clouds and binary populations mimicking several globular clusters, neglecting dynamical effects. We find that the Magellanic Clouds would have a handful of detectable sources each, but for globular clusters the amount of detectable sources would be less than one. We compare our results to earlier research and find that our predicted numbers are several tens of times lower than calculations using the stellar evolution code BSE that take dynamical effects into account, but also calculations using the stellar evolution code SeBa for the Magellanic Clouds. This correlates with earlier research which compared BPASS models for GW sources in the Galactic disk with BSE models and found a similarly sized discrepancy. We analyse and explain this discrepancy as being caused by differences between the stellar evolution codes, particularly in the treatment of mass transfer and common-envelope events in binaries, where in BPASS mass transfer is more likely to be stable and tends to lead to less orbital shrinkage in the common-envelope phase than in other codes. This difference results in fewer compact binaries with periods short enough to be detected by LISA existing in the BPASS population. For globular clusters, we conclude that the impact of dynamical effects is uncertain from the literature, but the differences in stellar evolution have an effect of a factor of a few tens., Comment: 11 pages, 2 figures, 4 tables. Submitted to A&A

Unlike the Solar System planets, thousands of smaller bodies beyond Neptune orbit the Sun on eccentric ($e >$ 0.1) and ($i>$ 3$^\circ$) orbits. While migration of the giant planets during the early stages of Solar System evolution can induce substantial scattering of trans-Neptunian objects (TNO), this process cannot account for the small number of distant TNOs ($r_p >$ 60 au) outside the planets' reach. The alternative scenario of the close flyby of another star can instead produce all these TNO features simultaneously, but the possible parameter space for such an encounter is vast. Here, we compare observed TNO properties with thousands of flyby simulations to determine the specific properties of a flyby that reproduces all the different dynamical TNO populations, their location and their relative abundance and find that a 0.8$^{+0.1}_{-0.1}$ $M_{\odot}$ star passing at a distance of $ r_p =$ 110 $\mathbf{\pm}$ 10 au, inclined by $i$ = 70$^\circ$ $^{+5}_{-10}$ gives a near-perfect match. This flyby also replicates the retrograde TNO population, which has proved difficult to explain. Such a flyby is reasonably frequent; at least 140 million solar-type stars in the Milky Way are likely to have experienced a similar one. In light of these results, we predict that the upcoming Vera Rubin telescope will reveal that distant and retrograde TNOs are relatively common., Comment: 15 pages, 3 figures Open access version of original Nature Astronomy available under 10.1038/s41550-024-02349-x

We investigate the ability of Diffusion Variational Autoencoder ($\Delta$VAE) with unit sphere $\mathcal{S}^2$ as latent space to capture topological and geometrical structure and disentangle latent factors in datasets. For this, we introduce a new diagnostic of disentanglement: namely the topological degree of the encoder, which is a map from the data manifold to the latent space. By using tools from homology theory, we derive and implement an algorithm that computes this degree. We use the algorithm to compute the degree of the encoder of models that result from the training procedure. Our experimental results show that the $\Delta$VAE achieves relatively small LSBD scores, and that regardless of the degree after initialization, the degree of the encoder after training becomes $-1$ or $+1$, which implies that the resulting encoder is at least homotopic to a homeomorphism.

Mass segregation is seen in many star clusters, but whether massive stars form in the center of a cluster or migrate there dynamically is still debated. N-body simulations have shown that early dynamical mass segregation is possible when sub-clusters merge to form a dense core with a small crossing time. However, the effect of gas dynamics on both the formation and dynamics of the stars could inhibit the formation of the dense core. We aim to study the dynamical mass segregation of star cluster models that include gas dynamics and self-consistently form stars from the dense substructure in the gas. Our models use the Torch framework, which is based on AMUSE and includes stellar and magnetized gas dynamics, as well as stellar evolution and feedback from radiation, stellar winds, and supernovae. Our models consist of three star clusters forming from initial turbulent spherical clouds of mass $10^{4,5,6}\rm~M_\odot$ and radius $11.7\rm~pc$ that have final stellar masses of $3.6\times10^3\rm~M_\odot$, $6.5\times10^4\rm~M_\odot$, and $8.9\times10^5\rm~M_\odot$, respectively. There is no primordial mass segregation in the model by construction. All three clusters become dynamically mass segregated at early times via collapse confirming that this mechanism occurs within sub-clusters forming directly out of the dense substructure in the gas. The dynamics of the embedded gas and stellar feedback do not inhibit the collapse of the cluster. We find that each model cluster becomes mass segregated within $2~$Myr of the onset of star formation, reaching the levels observed in young clusters in the Milky Way. However, we note that the exact values are highly time-variable during these early phases of evolution. Massive stars that segregate to the center during core collapse are likely to be dynamically ejected, a process that can decrease the overall level of mass segregation again., Comment: Submitted to A&A. 8 pages, 4 figures

We present {\sc Venice}, an operator splitting algorithm to integrate a numerical model on a hierarchy of timescales. {\sc Venice} allows a wide variety of different physical processes operating a different scales to be coupled on individual and adaptive time-steps. It therewith mediates the development of complex multi-scale and multi-physics simulation environments with a wide variety of independent components. The coupling between various physical models and scales is dynamic, and realized through (Strang) operators splitting using adaptive time steps. We demonstrate the functionality and performance of this algorithm using astrophysical models of a stellar cluster, first coupling gravitational dynamics and stellar evolution, then coupling internal gravitational dynamics with dynamics within a galactic background potential, and finally combining these models while also introducing dwarf galaxy-like perturbers. These tests show numerical convergence for decreasing coupling timescales, demonstrate how {\sc Venice} can improve the performance of a simulation by shortening coupling timescales when appropriate, and provide a case study of how {\sc Venice} can be used to gradually build up and tune a complex multi-physics model. Although the examples couple complete numerical models, {\sc Venice} can also be used to efficiently solve systems of stiff differential equations., Comment: Accepted for publication by A&A

Context: Current exoplanet formation studies tend to overlook the birth environment of stars in clustered environments. The effect of this environment on the planet-formation process, however, is important, especially in the earliest stage. Aims: We investigate the differences in planet populations forming in star-cluster environments through pebble accretion and compare these results with the planet formation around isolated stars. We try to provide potential signatures on the young planetary systems to guide future observation. Methods: We design and present a new planet population synthesis code for clustered environments. The planet formation model is based on pebble accretion and includes migration in the circumstellar disk. The disk's gas and dust are evolved in 1D simulations considering the effects of photo-evaporation of the nearby stars. Results: Planetary systems in a clustered environment are different than those born in isolation; the environmental effects are important for a wide range of observable parameters and the eventual architecture of the planetary systems. Planetary systems born in a clustered environment lack cold Jupiters compared to isolated planetary systems. This effect is more pronounced for low-mass stars ($\lesssim$0.2 $M_\odot$). On the other hand, planetary systems born in clusters show an excess of cold Neptune around these low-mass stars. Conclusions: In future observations, finding an excess of cold Neptunes and a lack of cold Jupiters could be used to constrain the birth environments of these planetary systems. Exploring the dependence of cold Jupiter's intrinsic occurrence rate on stellar mass provides insights into the birth environment of their proto-embryos., Comment: 13 pages 10 figures. Accepted for publication in A&A

We introduce a class of trainable nonlinear operators based on semirings that are suitable for use in neural networks. These operators generalize the traditional alternation of linear operators with activation functions in neural networks. Semirings are algebraic structures that describe a generalised notation of linearity, greatly expanding the range of trainable operators that can be included in neural networks. In fact, max- or min-pooling operations are convolutions in the tropical semiring with a fixed kernel. We perform experiments where we replace the activation functions for trainable semiring-based operators to show that these are viable operations to include in fully connected as well as convolutional neural networks (ConvNeXt). We discuss some of the challenges of replacing traditional activation functions with trainable semiring activations and the trade-offs of doing so.

Dynamical interactions in star clusters are an efficient mechanism to produce the coalescing binary black holes (BBHs) that have been detected with gravitational waves (GWs). We want to understand how BBH coalescence can occur during - or after - binary-single interactions with different mass ratios. We perform gravitational scattering experiments of binary-single interactions using different mass ratios of the binary components ($q_2\equiv m_2/m_1\le1$) and the incoming single ($q_3\equiv m_3/m_1$). We extract cross sections and rates for (i) GW capture during resonant interactions; (ii) GW inspiral in between resonant interactions and apply the results to different globular cluster conditions. We find that GW capture during resonant interactions is most efficient if $q_2\simeq q_3$ and that the mass-ratio distribution of BBH coalescence due to inspirals is $\propto m_1^{-1}q^{2.9+\alpha}$, where $\alpha$ is the exponent of the BH mass function. The total rate of GW captures and inspirals depends mostly on $m_1$ and is relatively insensitive to $q_2$ and $q_3$. We show that eccentricity increase by non-resonant encounters approximately doubles the rate of BBH inspiral in between resonant encounters. For a given GC mass and radius, the BBH merger rate in metal-rich GCs is approximately double that of metal-poor GCs, because of their (on average) lower BH masses ($m_1$) and steeper BH mass function, yielding binaries with lower $q$. Our results enable the translating from the mass-ratio distribution of dynamically formed BBH mergers to the underlying BH mass function. The additional mechanism that leads to a doubling of the inspirals provides an explanation for the reported high fraction of in-cluster inspirals in $N$-body models of clusters., Comment: 14 pages, 7 figures

Two main mechanisms have classically been proposed for the formation of runaway stars. In the binary supernova scenario (BSS), a massive star in a binary explodes as a supernova, ejecting its companion. In the dynamical ejection scenario, a star is ejected during a strong dynamical encounter between multiple stars. We propose a third mechanism for the formation of runaway stars: the subcluster ejection scenario (SCES), where a subset of stars from an infalling subcluster is ejected out of the cluster via a tidal interaction with the contracting gravitational potential of the assembling cluster. We demonstrate the SCES in a star-by-star simulation of the formation of a young massive cluster from a $10^6\rm~M_\odot$ gas cloud using the Torch framework. This star cluster forms hierarchically through a sequence of subcluster mergers determined by the initial turbulent, spherical conditions of the gas. We find that these mergers drive the formation of runaway stars in our model. Late-forming subclusters fall into the central potential, where they are tidally disrupted, forming tidal tails of runaway stars that are distributed highly anisotropically. Runaways formed in the same SCES have similar ages, velocities, and ejection directions. Surveying observations, we identify several SCES candidate groups with anisotropic ejection directions. The SCES is capable of producing runaway binaries: two wide dynamical binaries in infalling subclusters were tightened through ejection. This allows for another velocity kick via subsequent via a subsequent BSS ejection. An SCES-BSS ejection is a possible avenue for the creation of hypervelocity stars unbound to the Galaxy. We expect nonspherical initial gas distributions to increase the number of calculated runaway stars. The observation of groups of runaway stars formed via the SCES can thus reveal the assembly history of their natal clusters., Comment: 11 pages, 10 figures. Accepted for publication in A&A. Abstract abridged for arXiv

The three-body problem (3BP) poses a longstanding challenge in physics and celestial mechanics. Despite the impossibility of obtaining general analytical solutions, statistical theories have been developed based on the ergodic principle. This assumption is justified by chaos, which is expected to fully mix the accessible phase space of the 3BP. This study probes the presence of regular (i.e. non chaotic) trajectories within the 3BP and assesses their impact on statistical escape theories. Using numerical simulations, we establish criteria for identifying regular trajectories and analyse their impact on statistical outcomes. Our analysis reveals that regular trajectories occupy up to 32% of the phase space, and their outcomes defy the predictions of statistical escape theories. The coexistence of regular and chaotic regions at all scales is characterized by a multi-fractal behaviour. Integration errors manifest as numerical chaos, artificially enhancing the mixing of the phase space and affecting the reliability of individual simulations, yet preserving the statistical correctness of an ensemble of realizations. Our findings underscore the challenges in applying statistical escape theories to astrophysical problems, as they may bias results by excluding the outcome of regular trajectories. This is particularly important in the context of formation scenarios of gravitational wave mergers, where biased estimates of binary eccentricity can significantly impact estimates of coalescence efficiency and detectable eccentricity., Comment: 15 pages, 13 figures, accepted for publication in Astronomy & Astrophysics

Within the magnetospheric radius, the geometry of accretion flow in X-ray pulsars is shaped by a strong magnetic field of a neutron star. Starting at the magnetospheric radius, accretion flow follows field lines and reaches the stellar surface in small regions located close to the magnetic poles of a star. At low mass accretion rates, the dynamic of the flow is determined by gravitational attraction and rotation of the magnetosphere due to the centrifugal force. At the luminosity range close to the Eddington limit and above it, the flow is additionally affected by the radiative force. We construct a model simulating accretion flow dynamics over the magnetosphere, assuming that the flow strictly follows field lines and is affected by gravity, radiative and centrifugal forces only. The magnetic field of a NS is taken to be dominated by the dipole component of arbitrary inclination with respect to the accretion disc plane. We show that accretion flow becomes unstable at high mass accretion rates and tends to fluctuate quasi-periodically with a typical period comparable to the free-fall time from the inner disc radius. The inclination of a magnetic dipole with respect to the disc plane and strong anisotropy of X-ray radiation stabilise the mass accretion rate at the poles of a star, but the surface density of material covering the magnetosphere fluctuates even in this case., Comment: 14 pages, 13 figures, submitted to MNRAS

Located at the core of the Galactic Centre, the S-star cluster serves as a remarkable illustration of chaos in dynamical systems. The long-term chaotic behaviour of this system can be studied with gravitational $N$-body simulations. By applying a small perturbation to the initial position of star S5, we can compare the evolution of this system to its unperturbed evolution. This results in the two solutions diverging exponentially, defined by the separation in position space $\delta_{r}$, with an average Lyapunov timescale of $\sim$420 yr, corresponding to the largest positive Lyapunov exponent. Even though the general trend of the chaotic evolution is governed in part by the supermassive black hole Sagittarius $\rm A^{*}$ (Sgr $\rm A^{*}$), individual differences between the stars can be noted in the behaviour of their phase-space curves. We present an analysis of the individual behaviour of the stars in this Newtonian chaotic dynamical system. The individuality of their behaviour is evident from offsets in the position space separation curves of the S-stars and the black hole. We propose that the offsets originate from the initial orbital elements of the S-stars, where Sgr $\rm A^{*}$ is considered in one of the focal points of the Keplerian orbits. Methods were considered to find a relationship between these elements and the separation in position space. Symbolic regression turns out to provide the clearest diagnostics for finding an interpretable expression for the problem. Our symbolic regression model indicates that $\left\langle\delta_r\right\rangle \propto e^{2.3}$, implying that the time-averaged individual separation in position space increases rapidly with the initial eccentricity of the S-stars., Comment: Accepted for publication in A&A

The mode of star formation that results in the formation of globular clusters and young massive clusters is difficult to constrain through observations. We present models of massive star cluster formation using the Torch framework, which uses AMUSE to couple distinct multi-physics codes that handle star formation, stellar evolution and dynamics, radiative transfer, and magnetohydrodynamics. We upgrade Torch by implementing the N-body code PeTar, thereby enabling Torch to handle massive clusters forming from $10^6\rm\, M_\odot$ clouds with $\ge10^5$ individual stars. We present results from Torch simulations of star clusters forming from $10^4, 10^5$, and $10^6\rm M_\odot$ turbulent, spherical gas clouds (named M4, M5, M6) of radius $R=11.7$ pc. We find that star formation is highly efficient and becomes more so at higher cloud mass and surface density. For M4, M5, and M6 with initial surface densities $2.325\times 10^{1,2,3}\rm\, M_\odot\, pc^{-2}$, after a free-fall time of $t_{ff}=6.7,2.1,0.67$ Myr, we find that $\sim30\%$, 40%, and 60% of the cloud mass has formed into stars, respectively. The final integrated star formation efficiency is $32\%,\, 65\%$, and 85\% for M4, M5, and M6. Observations of nearby clusters similar to M4 have similar integrated star formation efficiencies of $\leq30\%$. The M5 and M6 models represent a different regime of cluster formation that is more appropriate for the conditions in starburst galaxies and gas-rich galaxies at high redshift, and that leads to a significantly higher efficiency of star formation. We argue that young massive clusters build up through short efficient bursts of star formation in regions that are sufficiently dense ($\ge 10^2 \rm\,M_\odot\,pc^{-2}$) and massive ($\ge10^5\rm\, M_\odot$). In such environments, the dynamical time of the cloud becomes short enough that stellar feedback cannot act quickly enough to slow star formation., Comment: Submitted to A&A

Aims: Investigate properties of a cluster of intermediate-mass black holes surrounding a supermassive black hole. Methods: We simulate clusters of equal-mass intermediate-mass black holes ($m_{\rm{IMBH}} = 10^{3}$ ${\rm{M_\odot}}$) initialised in a shell between $0.15\leq r$ [pc] $\leq 0.25$ centered about a supermassive black hole. We explore the influence of the cluster population and supermassive black hole mass on the merger rate, the ejection rate and the escape velocity. For $M_{\text{SMBH}} = 4\times10^{6}$ ${\rm {M}_\odot}$, we use both a Newtonian and post-Newtonian formalism, going up to the 2.5th order and including cross-terms. For the other two SMBH masses ($M_{\rm{SMBH}} = 4\times10^{5}$ ${\rm{M_\odot}}$ and $M_{\rm{SMBH}} = 4\times10^{7}$ $\rm{M_\odot}$), we model the system only taking into account relativistic effects. The simulations end once a black hole escapes the cluster, a merger occurs, or the system has evolved till $100$ Myr. Results: The post-Newtonian formalism accelerates the loss rate of intermediate-mass black holes. Ejections occur more often for lower supermassive black hole masses while more massive ones increase the rate of mergers. Although relativistic effects allow for circularisation, all merging binaries have $e \gtrsim 0.97$. Strong gravitational wave signals are suppressed during our Newtonian calculations. Weaker and more frequent signals are expected from gravitational wave radiation emitted in a fly-by. In our post-Newtonian calculations, $30/406$ of the gravitational wave events capable of being observed with LISA and $\mu$Ares are detected as gravitational wave capture binaries with the remaining being in-cluster mergers. Throughout our investigation, no IMBH-IMBH binaries were detected., Comment: 18 pages, 18 figures

The recently observed population of 540 free-floating Jupiter-mass objects, including 40 dynamically soft pairs in the Trapezium cluster have raised interesting questions on their formation and evolution. We test various scenarios for the origin and survivability of these free floating Jupiter-mass objects and Jupiter-mass Binary Objects (JuMBOs) in the Trapezium cluster. The numerical calculations are performed by direct N-body integration of the stars and planets in the Trapezium cluster starting with a wide variety of planets in various configurations. We discuss four models: SPP, in which selected stars have two outer orbiting Jupiter-mass planets; SPM, where selected stars are orbited by Jupiter-mass planet-moon pairs; ISF in which JuMBOs form in situ with the stars, and FFC, where we introduce a population of free-floating single Jupiter-mass objects, but no initialized binaries. Models FFC and SPP fail to produce enough JuMBOs. Models SPM can produce sufficient JuMBOs, but requires unusually wide orbits for the planet-moon system around the star. The observed JuMBOs and free-floating Jupiter-mass objects in the Trapezium cluster are best reproduced if they formed in pairs and as free-floaters together with the other stars in a smooth (Plummer) density profile with a virial radius of 0.5pc. A fractal stellar distribution also works, but requires relatively recent formations (>0.2Myr after the other stars formed) or a high (50%) initial binary fraction. This would make the primordial binary fraction of JuMBOs even higher than the already large observation fraction of 8%. The fraction of JuMBOs will continue to drop with time, and the lack of JuMBOs in Upper Scorpius could then result in its higher age, causing more JuMBOs to be ionized. We then also predict that the interstellar density of Jupiter-mass objects (mostly singles with 2% lucky surviving binaries) is 0.05/pc$^{3}$., Comment: Accepted for publiation in golden open-access journal SciPost Astronomy, see https://scipost.org/submission/scipost_202312_00003v1/ Software available at: https://github.com/spzwart/JuMBOs.git Simulation data available at: https://zenodo.org/records/10149241

Recently we estimated that about 5 percent of supermassive black hole triple systems are fundamentally unpredictable. These gargantuan chaotic systems are able to exponentially magnify Planck length perturbations to astronomical scales within their interaction timescale. These results were obtained in the zero angular momentum limit, which we naively expected to be the most chaotic. Here, we generalise to triple systems with arbitrary angular momenta by systematically varying the initial virial ratio. We find the surprising result that increasing the angular momentum enhances the chaotic properties of triples. This is not only explained by the longer life times, allowing for a prolonged exponential growth, but also the maximum Lyapunov exponent itself increases. For the ensemble of initially virialised triple systems, we conclude that the percentage of unpredictable supermassive black hole triples increases to about 30 percent. A further increase up to about 50 percent is reached when considering triples on smaller astrophysical scales. Fundamental unpredictability is thus a generic feature of chaotic, self-gravitating triple populations., Comment: 13 pages, 11 figures, 2 tables. Submitted to MNRAS

Simulating the evolution of the gravitational N-body problem becomes extremely computationally expensive as N increases since the problem complexity scales quadratically with the number of bodies. We study the use of Artificial Neural Networks (ANNs) to replace expensive parts of the integration of planetary systems. Neural networks that include physical knowledge have grown in popularity in the last few years, although few attempts have been made to use them to speed up the simulation of the motion of celestial bodies. We study the advantages and limitations of using Hamiltonian Neural Networks to replace computationally expensive parts of the numerical simulation. We compare the results of the numerical integration of a planetary system with asteroids with those obtained by a Hamiltonian Neural Network and a conventional Deep Neural Network, with special attention to understanding the challenges of this problem. Due to the non-linear nature of the gravitational equations of motion, errors in the integration propagate. To increase the robustness of a method that uses neural networks, we propose a hybrid integrator that evaluates the prediction of the network and replaces it with the numerical solution if considered inaccurate. Hamiltonian Neural Networks can make predictions that resemble the behavior of symplectic integrators but are challenging to train and in our case fail when the inputs differ ~7 orders of magnitude. In contrast, Deep Neural Networks are easy to train but fail to conserve energy, leading to fast divergence from the reference solution. The hybrid integrator designed to include the neural networks increases the reliability of the method and prevents large energy errors without increasing the computing cost significantly. For this problem, the use of neural networks results in faster simulations when the number of asteroids is >70., Comment: Accepted for publication in the Journal of Computational Physics

We investigate the chaotic behavior of the S-star cluster in the Galactic center using precise $N$-body calculations, free from round-off or discretization errors. Our findings reveal that chaos among the Galactic center S-stars arises from close encounters, particularly among pairs and near the massive central body. These encounters induce perturbations, causing sudden changes in the orbital energies of the interacting stars. Consequently, neighboring solutions experience roughly exponential growth in separation. We propose a theory of "punctuated chaos" that describes the S-star cluster's chaotic behavior. This phenomenon results from nearly linear growth in the separation between neighboring orbits after repeated finite perturbations. Each participating star's orbit experiences discrete, abrupt changes in energy due to the perturbations. The cumulative effect of these events is further amplified by the steady drift in orbital phase. In the Galactic center, perturbations originate from coincidental encounters occurring within a distance of $\aplt 100$\,au between at least two stars (in some cases, three stars). Our model satisfactorily explains the observed exponential growth in the 27 S-star cluster. We determine that the S-star system has a Lyapunov time scale of approximately 462 +/-74 years. For the coming millennium, chaos in the S-star cluster will be driven mainly by a few of the closest orbiting stars: S2, S5, S6, S8, S9, S14, S18, S31, S21, S24, S27, S29, and S38., Comment: Accepted for publication in MNRAS

Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these exponents are critical for understanding the stability and predictability of observed systems. This essay presents a new model for chaos in systems with eccentric and crossing orbits. Here, exponential divergence is not a continuous process but rather the cumulative effect of an ever-increasing linear response driven by discrete events at regular intervals, i.e., punctuated chaos. We show that long-lived systems with punctuated chaos can magnify Planck length perturbations to astronomical scales within their lifetime, rendering them fundamentally indeterministic., Comment: Essay written for the Gravity Research Foundation 2023 Awards for Essays on Gravitation (Honorable Mention). Accepted by International Journal of Modern Physics D

Terzan 5 is a heavily obscured stellar system located in the inner Galaxy. It has been postulated to be a stellar relic, a Bulge Fossil Fragment witnessing the complex history of the assembly of the Milky Way bulge. In this paper, we follow the chemical enrichment of a set of putative progenitors of Terzan 5 to assess whether the chemical properties of this cluster fit within a formation scenario in which it is the remnant of a primordial building block of the bulge. We can explain the metallicity distribution function and the runs of different element-to-iron abundance ratios as functions of [Fe/H] derived from optical-infrared spectroscopy of giant stars in Terzan 5, by assuming that the cluster experienced two major star formation bursts separated by a long quiescent phase. We further predict that the most metal-rich stars in Terzan 5 are moderately He-enhanced and a large spread of He abundances in the cluster, Y = 0.26-0.335. We conclude that current observations fit within a formation scenario in which Terzan 5 originated from a pristine, or slightly metal-enriched, gas clump about one order of magnitude more massive than its present-day mass. Losses of gas and stars played a major role in shaping Terzan 5 the way we see it now. The iron content of the youngest stellar population is better explained if the white dwarfs that give rise to type Ia supernovae (the main Fe factories) sink towards the cluster center, rather than being stripped by the strong tidal forces exerted by the Milky Way in the outer regions., Comment: 14 pages, 2 tables, 8 figures, accepted for publication in ApJ

We perform simulations of star cluster formation to investigate the morphological evolution of embedded star clusters in the earliest stages of their evolution. We conduct our simulations with Torch, which uses the AMUSE framework to couple state-of-the-art stellar dynamics to star formation, radiation, stellar winds, and hydrodynamics in FLASH. We simulate a suite of $10^4$ M$_{\odot}$ clouds at 0.0683 pc resolution for $\sim$ 2 Myr after the onset of star formation, with virial parameters $\alpha$ = 0.8, 2.0, 4.0 and different random samplings of the stellar initial mass function and prescriptions for primordial binaries. Our simulations result in a population of embedded clusters with realistic morphologies (sizes, densities, and ellipticities) that reproduce the known trend of clouds with higher initial $\alpha$ having lower star formation efficiencies. Our key results are as follows: (1) Cluster mass growth is not monotonic, and clusters can lose up to half of their mass while they are embedded. (2) Cluster morphology is not correlated with cluster mass and changes over $\sim$ 0.01 Myr timescales. (3) The morphology of an embedded cluster is not indicative of its long-term evolution but only of its recent history: radius and ellipticity increase sharply when a cluster accretes stars. (4) The dynamical evolution of very young embedded clusters with masses $\lesssim$ 1000 M$_{\odot}$ is dominated by the overall gravitational potential of the star-forming region rather than by internal dynamical processes such as two- or few-body relaxation., Comment: 15 pages, 10 figures, to be published in MNRAS

Protoplanetary discs spend their lives in the dense environment of a star forming region. While there, they can be affected by nearby stars through external photoevaporation and dynamic truncations. We present simulations that use the AMUSE framework to couple the Torch model for star cluster formation from a molecular cloud with a model for the evolution of protoplanetary discs under these two environmental processes. We compare simulations with and without extinction of photoevaporation-driving radiation. We find that the majority of discs in our simulations are considerably shielded from photoevaporation-driving radiation for at least 0.5 Myr after the formation of the first massive stars. Radiation shielding increases disc lifetimes by an order of magnitude and can let a disc retain more solid material for planet formation. The reduction in external photoevaporation leaves discs larger and more easily dynamically truncated, although external photoevaporation remains the dominant mass loss process. Finally, we find that the correlation between disc mass and projected distance to the most massive nearby star (often interpreted as a sign of external photoevaporation) can be erased by the presence of less massive stars that dominate their local radiation field. Overall, we find that the presence and dynamics of gas in embedded clusters with massive stars is important for the evolution of protoplanetary discs., Comment: 23 pages, 22 figures, 1 table, accepted for publication in MNRAS

The earliest evolution of star clusters involves a phase of co-existence of both newly-formed stars, and the gas from which they are forming. Observations of the gas in such regions provide a wealth of data that can inform the simulations which are needed to follow the evolution of such objects forward in time. We present a method for transforming the observed gas properties into initial conditions for simulations that include gas, stars, and ongoing star formation. We demonstrate our technique using the Orion Nebula Cluster. Since the observations cannot provide all the necessary information for our simulations, we make choices for the missing data and assess the impact of those choices. We find that the results are insensitive to the adopted choices of the gas velocity in the plane of the sky. The properties of the surrounding gas cloud (e.g. overall density and size), however, have an effect on the star formation rate and pace of assembly of the resultant star cluster. We also analyze the stellar properties of the cluster and find that the stars become more tightly clustered and in a stronger radial distribution even as new stars form in the filament., Comment: 11 pages, 12 figures, accepted for publication in MNRAS

Feedback from massive stars plays an important role in the formation of star clusters. Whether a very massive star is born early or late in the cluster formation timeline has profound implications for the star cluster formation and assembly processes. We carry out a controlled experiment to characterize the effects of early-forming massive stars on star cluster formation. We use the star formation software suite \texttt{Torch}, combining self-gravitating magnetohydrodynamics, ray-tracing radiative transfer, $N$-body dynamics, and stellar feedback to model four initially identical $10^4$ M$_\odot$ giant molecular clouds with a Gaussian density profile peaking at $521.5 \mbox{ cm}^{-3}$. Using the \texttt{Torch} software suite through the \texttt{AMUSE} framework we modify three of the models to ensure that the first star that forms is very massive (50, 70, 100 M$_\odot$). Early-forming massive stars disrupt the natal gas structure, resulting in fast evacuation of the gas from the star forming region. The star formation rate is suppressed, reducing the total mass of stars formed. Our fiducial control model without an early massive star has a larger star formation rate and total efficiency by up to a factor of three and a higher average star formation efficiency per free-fall time by up to a factor of seven. Early-forming massive stars promote the buildup of spatially separate and gravitationally unbound subclusters, while the control model forms a single massive cluster., Comment: 17 pages, 7 figures. Published in ApJ

In order to help students learn how to write mathematical proofs, we adapt the Coq proof assistant into an educational tool we call Waterproof. Like with other interactive theorem provers, students write out their proofs inside the software using a specific syntax, and the software provides feedback on the logical validity of each step. Waterproof consists of two components: a custom proof language that allows formal, machine-verified proofs to be written in a style that closely resembles handwritten proofs, and a custom editor that allows these proofs to be combined with formatted text to improve readability. The editor can be used for Coq documents in general, but also offers special features designed for use in education. Student input, for example, can be limited to specific parts of the document to prevent exercises from being accidentally deleted. Waterproof has been used to supplement teaching the Analysis 1 course at Eindhoven University of Technology (TU/e) for the last four years. Students started using the specific formulations of proof steps from the custom proof language in their handwritten proofs; the explicit phrasing of these sentences helped to clarify the logical structure of their arguments., Comment: In Proceedings ThEdu'23, arXiv:2404.03709. The previous version (v1) of this paper contains more code snippets from the coq-waterproof library that showcase the Ltac2 tactic language

Neural Stochastic Differential Equations (NSDE) have been trained as both Variational Autoencoders, and as GANs. However, the resulting Stochastic Differential Equations can be hard to interpret or analyse due to the generic nature of the drift and diffusion fields. By restricting our NSDE to be of the form of Langevin dynamics, and training it as a VAE, we obtain NSDEs that lend themselves to more elaborate analysis and to a wider range of visualisation techniques than a generic NSDE. More specifically, we obtain an energy landscape, the minima of which are in one-to-one correspondence with latent states underlying the used data. This not only allows us to detect states underlying the data dynamics in an unsupervised manner, but also to infer the distribution of time spent in each state according to the learned SDE. More in general, restricting an NSDE to Langevin dynamics enables the use of a large set of tools from computational molecular dynamics for the analysis of the obtained results., Comment: 12 pages, 5 figures

Extreme accretion in X-ray pulsars (XRPs) results in radiation-driven outflows launched from the inner parts of the accretion disc. The outflows affect the apparent luminosity of the XRPs and their pulsations through the geometrical beaming. We model processes of geometrical beaming and pulse formation using Monte Carlo simulations. We confirm our earlier statement that strong amplification of luminosity due to the collimation of X-ray photons is inconsistent with a large pulsed fraction. Accounting for relativistic aberration due to possibly high outflow velocity ($\sim 0.2c$) does not affect this conclusion. We demonstrate that the beaming causes phase lags of pulsations. Within the opening angle of the accretion cavity formed by the outflows, phase lags tend to be sensitive to observers viewing angles. Variations in outflow geometry and corresponding changes of the phase lags might influence the detectability of pulsation in bright X-ray pulsars and ULXs. We speculate that the strong geometrical beaming is associated with large radiation pressure on the walls of accretion cavity due to multiple photons reflections. We expect that the mass loss rate limits geometrical beaming: strong beaming becomes possible only under sufficiently large fractional mass loss rate from the disc., Comment: accepted for publication MNRAS, 8 pages, 6 figures

We give an asymptotic expansion of the relative entropy between the heat kernel $q_Z(t,z,w)$ of a compact Riemannian manifold $Z$ and the normalized Riemannian volume for small values of $t$ and for a fixed element $z\in Z$. We prove that coefficients in the expansion can be expressed as universal polynomials in the components of the curvature tensor and its covariant derivatives at $z$, when they are expressed in terms of normal coordinates. We describe a method to compute the coefficients, and we use the method to compute the first three coefficients. The asymptotic expansion is necessary for an unsupervised machine-learning algorithm called the Diffusion Variational Autoencoder.

Advanced feedforward control methods enable mechatronic systems to perform varying motion tasks with extreme accuracy and throughput. The aim of this paper is to develop a data-driven feedforward controller that addresses input nonlinearities, which are common in typical applications such as semiconductor back-end equipment. The developed method consists of parametric inverse-model feedforward that is optimized for tracking error reduction by exploiting ideas from iterative learning control. Results on a simulated set-up indicate improved performance over existing identification methods for systems with nonlinearities at the input., Comment: 6 pages, 8 figures, to be presented at Modeling Estimation and Control Conference 2022 in Jersey City, NJ, to be published in IFAC-PapersOnLine

The fundamental laws of physics are time-symmetric, but our macroscopic experience contradicts this. The time reversibility paradox is partly a consequence of the unpredictability of Newton's equations of motion. We measure the dependence of the fraction of irreversible, gravitational N-body systems on numerical precision and find that it scales as a power law. The stochastic wave packet reduction postulate then introduces fundamental uncertainties in the Cartesian phase space coordinates that propagate through classical three-body dynamics to macroscopic scales within the triple's lifetime. The spontaneous collapse of the wave function then drives the global chaotic behavior of the Universe through the superposition of triple systems (and probably multi-body systems). The paradox of infinitesimal granularity then arises from the superposition principle, which states that any multi-body system is composed of an ensemble of three-body problems., Comment: Accepted for publication in IC M2 Physical Sciences AIP Conference Proceedings

We introduce a new prescription for the evolution of globular clusters (GCs) during the initial embedded gas phase into a Monte Carlo method. With a simplified version of the Monte Carlo MOCCA code embedded in the AMUSE framework, we study the survival of GCs after the removal of primordial gas. We first test our code and show that our results for the evolution of mass and Lagrangian radii are in good agreement with those obtained with N-body simulations. The Monte Carlo code enables a more rapid exploration of the evolution of systems with a larger number of stars than N-body simulations. We have carried out a new survey of simulations to explore the evolution of globular clusters with up to $N = 500000$ stars for a range of different star formation efficiencies and half-mass radii. Our study shows the range of initial conditions leading to the clusters' dissolution and those for which the clusters can survive this early evolutionary phase., Comment: 13 pages, 6 figures

We present a novel way of modeling common envelope evolution in binary and few-body systems. We consider the common envelope inspiral as driven by a drag force with a power-law dependence in relative distance and velocity. The orbital motion is resolved either by direct N-body integration or by solving the set of differential equations for the orbital elements as derived using perturbation theory. Our formalism can model the eccentricity during the common envelope inspiral, and it gives results consistent with smoothed particles hydrodynamical simulations. We apply our formalism to common envelope events from binary population synthesis models and find that the final eccentricity distribution resembles the observed distribution of post-common-envelope binaries. Our model can be used for time-resolved common-envelope evolution in population synthesis calculations or as part of binary interactions in direct N-body simulations of star clusters., Comment: 14 Pages, 8 Figures, accepted for publication in PRD

Some HII regions that surround young stellar clusters are bordered by molecular shells that appear to expand at a rate inconsistent with our current model simulations. In this study we focus on the dynamics of Sharpless 171 (including NGC 7822), which surrounds the cluster Berkeley 59. We aim to compare the velocity pattern over the molecular shell with the mean radial velocity of the cluster for estimates of the expansion velocities of different shell structures, and to match the observed properties with model simulations. Optical spectra of 27 stars located in Berkeley 59 were collected at the Nordic Optical Telescope, and a number of molecular structures scattered over the entire region were mapped in $^{13}$CO(1-0) at Onsala Space Observatory. We obtained radial velocities and MK classes for the cluster's stars. At least four of the O stars are found to be spectroscopic binaries, in addition to one triplet system. From these data we obtain the mean radial velocity of the cluster. From the $^{13}$CO spectra we identify three shell structures, expanding relative to the cluster at moderate velocity (4 km/s), high velocity (12 km/s), and in between. The high-velocity cloudlets extend over a larger radius and are less massive than the low-velocity cloudlets. We performed a model simulation to understand the evolution of this complex. Our simulation of the Sharpless 171 complex and Berkeley 59 cluster demonstrates that the individual components can be explained as a shell driven by stellar winds from the massive cluster members. However, our relatively simple model produces a single component. Modelling of the propagation of shell fragments through a uniform interstellar medium demonstrates that dense cloudlets detached from the shell are decelerated less efficiently than the shell itself. They can reach greater distances and retain higher velocities than the shell., Comment: 27 pages, 14 figures, 8 tables, 3 appendices. Accepted for publication in Astronomy & Astrophysics

Compton scattering is a key process shaping spectra formation and accretion flow dynamics in accreting strongly magnetized neutron stars. A strong magnetic field affects the scattering cross section and makes it dependent on photon energy, momentum, and polarization state. Using Monte Carlo simulations, we investigate statistical features of Compton scattering of polarized X-ray radiation in a strong magnetic field. Our analysis is focused on photon gas behaviour well inside the scattering region. We take into account the resonant scattering at the fundamental cyclotron frequency, thermal distribution of electrons at the ground Landau level, and bulk velocity of the electron gas. We show that (i) the photons scattered around the cyclotron energy by the electron gas at rest tend to acquire the final energy close to the cyclotron one with a very small dispersion measure; (ii) the redistribution of photons within the Doppler core of cyclotron resonance differs significantly from the complete redistribution; (iii) the efficiency of momentum transfer from photons to the electron gas is affected by the temperature of electron gas both for photons at cyclotron energy and below it; (iv) the momentum transfer from photons to the electron gas of non-zero bulk velocity is more efficient in the case of magnetic scattering., Comment: 18 pages, 13 figures, accepted for publication in Phys.Rev.D

The concept of the capacity of a compact set in $\mathbb R^n$ generalizes readily to noncompact Riemannian manifolds and, with more substantial work, to metric spaces (where multiple natural definitions of capacity are possible). Motivated by analytic and geometric considerations, and in particular Jauregui's definition of capacity-volume mass and Jauregui and Lee's results on the lower semicontinuity of the ADM mass and Huisken's isoperimetric mass, we investigate how the capacity functional behaves when the background spaces vary. Specifically, we allow the background spaces to consist of a sequence of local integral current spaces converging in the pointed Sormani--Wenger intrinsic flat sense. For the case of volume-preserving ($\mathcal{VF}$) convergence, we prove two theorems that demonstrate an upper semicontinuity phenomenon for the capacity: one version is for balls of a fixed radius centered about converging points; the other is for Lipschitz sublevel sets. Our approach is motivated by Portegies' investigation of the semicontinuity of eigenvalues under $\mathcal{VF}$ convergence. We include examples to show the semicontinuity may be strict, and that the volume-preserving hypothesis is necessary. Finally, there is a discussion on how capacity and our results may be used towards understanding the general relativistic total mass in non-smooth settings.

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational wave observations by LISA to probe the universe.

In pursuit of enhanced multi-agent collaboration, we analyze several on-policy deep reinforcement learning algorithms in the recently published Hanabi benchmark. Our research suggests a perhaps counter-intuitive finding, where Proximal Policy Optimization (PPO) is outperformed by Vanilla Policy Gradient over multiple random seeds in a simplified environment of the multi-agent cooperative card game. In our analysis of this behavior we look into Hanabi-specific metrics and hypothesize a reason for PPO's plateau. In addition, we provide proofs for the maximum length of a perfect game (71 turns) and any game (89 turns). Our code can be found at: https://github.com/bramgrooten/DeepRL-for-Hanabi, Comment: Accepted at ALA 2022 (Adaptive and Learning Agents Workshop at AAMAS 2022)

The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA's first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultracompact stellar-mass binaries, massive black hole binaries, and extreme or intermediate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe.

Previous investigations have revealed that eccentric super-Earths represent a class of planets which are particularly effective at transporting minor bodies towards white dwarfs and subsequently polluting their atmospheres with observable chemical signatures. However, the lack of discoveries of these planets beyond a few astronomical units from their host stars prompts a better understanding of their orbital architectures from their nascent birth cluster. Here, we perform stellar cluster simulations of 3-planet and 7-planet systems containing super-Earths on initially circular, coplanar orbits. We adopt the typical stellar masses of main-sequence progenitors of white dwarfs ($1.5\,\mathrm{M}_{\odot}$-$2.5\,\mathrm{M}_{\odot}$) as host stars and include 8,000 main-sequence stars following a Kroupa initial mass function in our clusters. Our results reveal that about 30 per cent of the simulated planets generate eccentricities of at least 0.1 by the time of cluster dissolution, which would aid white dwarf pollution. We provide our output parameters to the community for potential use as initial conditions for subsequent evolution simulations., Comment: 16 pages, 18 figures, accepted for publication in MNRAS

(Abridged) Surveys of protoplanetary disks in nearby star-forming regions (SFRs) have provided important information on their demographics, but due to their sample sizes, they cannot be used to study how disk properties vary with the environment. We conduct a survey of the unresolved millimeter continuum emission of 873 protoplanetary disks identified by Spitzer in the L1641 and L1647 regions of the Orion A cloud. This is the largest such survey yet, allowing us to identify even weak trends in the median disk mass as a function of position in the cloud and cluster membership. The sample detection rates and median masses are also compared to those of nearby (<300 pc) SFRs. The sample was observed with ALMA at 225 GHz, with a median rms of 0.08 mJy/beam (1.5 M$_{\oplus}$). The data were reduced and imaged using an innovative parallel data processing approach. We detect 58% (502/873) of the observed disks. This includes 20 disks with dust masses >100 M$_{\oplus}$, and two objects associated with extended dust emission. We infer a median disk dust mass in the full sample of $2.2^{+0.2}_{-0.2}$ M$_{\oplus}$. In L1641 and L1647 median dust masses are $2.1^{+0.2}_{-0.2}$ M$_{\oplus}$ and $2.6^{+0.4}_{-0.5}$ M$_{\oplus}$, respectively. The disk mass distribution of the full sample is similar to that of nearby low-mass SFRs at similar ages of 1-3 Myr. We find only weak trends in disk (dust) masses with galactic longitude and between the YSO clusters identified in the sample, with median masses varying by $\lesssim$ 50%. Age differences may explain these median disk mass variations. Apart from this, disk masses are essentially constant at scales of ~100 pc. This also suggests that the majority of disks, even in different SFRs, are formed with similar initial masses and evolve at similar rates, assuming no external irradiation, with disk mass loss rates of $\sim 10^{-8}$ M$_{\odot}$/yr., Comment: Accepted in A&A. 19 pages, 13 figures, 5 tables in the main text; 5 pages, 1 table and 5 additional figures in appendices

Mechatronic systems have increasingly high performance requirements for motion control. The low-frequency contribution of the flexible dynamics, i.e. the compliance, should be compensated for by means of snap feedforward to achieve high accuracy. Position-dependent compliance, which often occurs in motion systems, requires the snap feedforward parameter to be modeled as a function of position. Position-dependent compliance is compensated for by using a Gaussian process to model the snap feedforward parameter as a continuous function of position. A simulation of a flexible beam shows that a significant performance increase is achieved when using the Gaussian process snap feedforward parameter to compensate for position-dependent compliance., Comment: To appear in: 2022 IEEE American Control Conference. arXiv admin note: text overlap with arXiv:2201.07511

Mechatronic systems have increasingly stringent performance requirements for motion control, leading to a situation where many factors, such as position-dependency, cannot be neglected in feedforward control. The aim of this paper is to compensate for position-dependent effects by modeling feedforward parameters as a function of position. A framework to model and identify feedforward parameters as a continuous function of position is developed by combining Gaussian processes and feedforward parameter learning techniques. The framework results in a fully data-driven approach, which can be readily implemented for industrial control applications. The framework is experimentally validated and shows a significant performance increase on a commercial wire bonder., Comment: in IEEE 17th International Conference on Advanced Motion Control, Padova, Italy, 2022

Feedforward control is essential to achieving good tracking performance in positioning systems. The aim of this paper is to develop an identification strategy for inverse models of systems with nonlinear dynamics of unknown structure using input-output data, which directly delivers feedforward signals for a-priori unknown tasks. To this end, inverse systems are regarded as noncausal nonlinear finite impulse response (NFIR) systems and modeled as a Gaussian Process with a stationary kernel function that imposes properties such as smoothness and periodicity. The approach is validated experimentally on a consumer printer with friction and shown to lead to improved tracking performance with respect to linear feedforward., Comment: 7 pages, 9 figures

The velocity-space distribution of the solar neighbourhood stars shows complex substructures. Most of the previous studies use static potentials to investigate their origins. Instead we use a self-consistent $N$-body model of the Milky Way, whose potential is asymmetric and evolves with time. In this paper, we quantitatively evaluate the similarities of the velocity-space distributions in the $N$-body model and that of the solar neighbourhood, using Kullback-Leibler divergence (KLD). The KLD analysis shows the time evolution and spatial variation of the velocity-space distribution. The KLD fluctuates with time, which indicates the velocity-space distribution at a fixed position is not always similar to that of the solar neighbourhood. Some positions show velocity-space distributions with small KLDs (high similarities) more frequently than others. One of them locates at $(R,\phi)=(8.2\;\mathrm{kpc}, 30^{\circ})$, where $R$ and $\phi$ are the distance from the galactic centre and the angle with respect to the bar's major axis, respectively. The detection frequency is higher in the inter-arm regions than in the arm regions. In the velocity maps with small KLDs, we identify the velocity-space substructures, which consist of particles trapped in bar resonances. The bar resonances have significant impact on the stellar velocity-space distribution even though the galactic potential is not static., Comment: 9 pages, 11 figures. Accepted by MNRAS

The gravitational $N$-body problem, which is fundamentally important in astrophysics to predict the motion of $N$ celestial bodies under the mutual gravity of each other, is usually solved numerically because there is no known general analytical solution for $N>2$. Can an $N$-body problem be solved accurately by a neural network (NN)? Can a NN observe long-term conservation of energy and orbital angular momentum? Inspired by Wistom & Holman (1991)'s symplectic map, we present a neural $N$-body integrator for splitting the Hamiltonian into a two-body part, solvable analytically, and an interaction part that we approximate with a NN. Our neural symplectic $N$-body code integrates a general three-body system for $10^{5}$ steps without diverting from the ground truth dynamics obtained from a traditional $N$-body integrator. Moreover, it exhibits good inductive bias by successfully predicting the evolution of $N$-body systems that are no part of the training set., Comment: 7 pages, 2 figures, accepted for publication at the NeurIPS 2021 workshop "Machine Learning and the Physical Sciences"

In self-gravitating $N$-body systems, small perturbations introduced at the start, or infinitesimal errors that are produced by the numerical integrator or are due to limited precision in the computer, grow exponentially with time. For Newton's gravity, we confirm earlier results that for relatively homogeneous systems, this rate of growth per crossing time increases with $N$ up to $N \sim 30$, but that for larger systems, the growth rate has a weaker scaling with $N$. For concentrated systems, however, the rate of exponential growth continues to scale with $N$. In relativistic self-gravitating systems, the rate of growth is almost independent of $N$. This effect, however, is only noticeable when the system's mean velocity approaches the speed of light to within three orders of magnitude. The chaotic behavior of systems with more than a dozen bodies for the usually adopted approximation of only solving the pairwise interactions in the Einstein-Infeld-Hoffmann equation of motion is qualitatively different than when the interaction terms (or cross terms) are taken into account. This result provides a strong motivation for follow-up studies on the microscopic effect of general relativity on orbital chaos, and on the influence of higher-order cross-terms in the Taylor-series expansion of the Einstein-Infeld-Hoffmann equations of motion., Comment: A&A in press

We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the Brutus N-body code to include Post-Newtonian pairwise terms up to 2.5 order, and the first order Taylor expansion to the Einstein-Infeld-Hoffmann equations of motion. The degree to which our system is relativistic depends on the scaling of the total mass (the unit size was 1 parsec). Using the Brutus method of convergence, we test for time-reversibility in the conservative regime, and demonstrate that we are able to obtain definitive solutions to the relativistic three-body problem. It is also confirmed that the minimal required numerical accuracy for a successful time-reversibility test correlates with the amplification factor of an initial perturbation. When we take into account dissipative effects through gravitational wave emission, we find that the duration of the resonance, and the amount of exponential growth of small perturbations depend on the mass scaling. For a unit mass <= 10 MSun, the system behavior is indistinguishable from the Newtonian case, and the resonance always ends in a binary and one escaping body. For a mass scaling up to 1e7 MSun, relativity gradually becomes more prominent, but the majority of the systems still dissolve. The first mergers start to appear for a mass of ~1e5 MSun, and between 1e7 MSun and 1e9 MSun all systems end prematurely in a merger. These mergers are preceded by a gravitational wave driven in-spiral. For a mass scaling >= 1e9 MSun, all systems result in a gravitational wave merger upon the first close encounter. Relativistic three-body encounters thus provide an efficient pathway for resolving the final parsec problem. The onset of mergers at the characteristic mass scale of 1e7 MSun potentially leaves an imprint in the mass function of supermassive black holes., Comment: Accepted by Phys Rev D. 10 pages, 6 figures

Recently, several accreting M dwarf stars have been discovered with ages far exceeding the typical protoplanetary disc lifetime. These `Peter Pan discs' can be explained as primordial discs that evolve in a low-radiation environment. The persistently low masses of the host stars raise the question whether primordial discs can survive up to these ages around stars of higher mass. In this work we explore the way in which different mass loss processes in protoplanetary discs limit their maximum lifetimes, and how this depends on host star mass. We find that stars with masses $\lesssim$ 0.6 M$_\odot$ can retain primordial discs for $\sim$50 Myr. At stellar masses $\gtrsim$ 0.8 M$_\odot$, the maximum disc lifetime decreases strongly to below 50 Myr due to relatively more efficient accretion and photoevaporation by the host star. Lifetimes up to 15 Myr are still possible for all host star masses up to $\sim$2 M$_\odot$. For host star masses between 0.6 and 0.8 M$_\odot$, accretion ceases and an inner gap forms before 50 Myr in our models. Observations suggest that such a configuration is rapidly dispersed. We conclude that Peter Pan discs can only occur around M dwarf stars., Comment: Accepted by MNRAS, 8 pages, 5 figures

Hierarchical triple stars are ideal laboratories for studying the interplay between orbital dynamics and stellar evolution. Both stellar wind mass loss and three-body dynamics cooperate to destabilise triples, which can lead to a variety of astrophysical exotica. So far our understanding of their evolution was mainly built upon results from extensive binary-single scattering experiments. Starting from generic initial conditions, we evolve an extensive set of hierarchical triples using a combination of the triple evolution code TRES and an N-body code. We find that the majority of triples preserve their hierarchy throughout their evolution, which is in contradiction with the commonly adopted picture that unstable triples always experience a chaotic, democratic resonant interaction. The duration of the unstable phase is much longer than expected, so that stellar evolution cannot be neglected. Typically an unstable triple dissolve into a single star and a binary; sometimes democratically (the initial hierarchy is lost and the lightest body usually escapes), but also in a hierarchical way (the tertiary is ejected in a slingshot, independent of its mass). Collisions are common, and mostly involve the two original inner binary components still on the main-sequence. This contradicts the idea that collisions with a giant during democratic encounters dominate. Together with collisions in stable triples, we find that triple evolution is the dominant mechanism for stellar collisions in the Milky Way. Furthermore, our simulations produce runaway and walk-away stars with speeds up to several tens km/s, with a maximum of a few 100km/s. We suggest that destabilised triples can alleviate the tension behind the origin of the observed run-away stars. Lastly, we present a promising indicator to make general predictions for the fate of a specific triple, based on the initial inclination of the system., Comment: 25 pages, 15 figures, 3 tables, accepted by A&A. Reproduction package at DOI: 10.5281/zenodo.6319686