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We study the evolution of populations of binary stars within massive cluster-forming regions. We simulate the formation of young massive star clusters within giant molecular clouds with masses ranging from 2 x 10$^{4}$ to 3.2 x 10$^{5}$ M$_{\odot}$. We use Torch, which couples stellar dynamics, magnetohydrodynamics, star and binary formation, stellar evolution, and stellar feedback through the AMUSE framework. We find that the binary fraction decreases during cluster formation at all molecular cloud masses. The binaries' orbital properties also change, with stronger and quicker changes in denser, more massive clouds. Most of the changes we see can be attributed to the disruption of binaries wider than 100 au, although the close binary fraction also decreases in the densest cluster-forming region. The binary fraction for O stars remains above 90%, but exchanges and dynamical hardening are ubiquitous, indicating that O stars undergo frequent few-body interactions early during the cluster formation process. Changes to the populations of binaries are a by-product of hierarchical cluster assembly: most changes to the binary population take place when the star formation rate is high and there are frequent mergers between sub-clusters in the cluster-forming region. A universal primordial binary distribution based on observed inner companions in the Galactic field is consistent with the binary populations of young clusters with resolved stellar populations, and the scatter between clusters of similar masses could be explained by differences in their formation history., Comment: 15 pages, 8 figures, 3 tables. Submitted to ApJ

Massive stars are predominantly born in stellar associations or clusters. Their radiation fields, stellar winds, and supernovae strongly impact their local environment. In the first few million years of a cluster's life, massive stars are dynamically ejected running away from the cluster at high speed. However, the production rate of dynamically ejected runaways is poorly constrained. Here we report on a sample of 55 massive runaway stars ejected from the young cluster R136 in the Large Magellanic Cloud. Astrometric analysis with Gaia reveals two channels of dynamically ejected runaways. The first channel ejects massive stars in all directions and is consistent with dynamical interactions during and after the birth of R136. The second channel launches stars in a preferred direction and may be related to a cluster interaction. We find that 23-33% of the most luminous stars initially born in R136 are runaways. Model predictions have significantly underestimated the dynamical escape fraction of massive stars. Consequently, their role in shaping and heating the interstellar and galactic medium, along with their role in driving galactic outflows, is far more important than previously thought., Comment: Published in Nature on 2024 October 09. 39 pages, 17 figures

The Milky way Galaxy is brimming with free-floating objects, including stars, planets and planetesimals. For the purpose of this chapter, we define a free-floating object as a solid body that is not orbited by a considerably more massive body. A planet then is considered free floating if it is not orbiting a star but it may be orbiting another planet. A binary planet, or planet-moon pair that is not orbiting a star, is then considered free floating. Most free-floating objects are not born as such because most objects form in some sort of coordinated environmental effort, such as a star forming region or a circum-stellar disk. Free-floating stars then originate from dissolved clusters. Free floating planets are ejected from their parent star in an internal dynamical encounter with another planet or stripped from the star by other means such as a supernova or a nearby passing star. Free floating (interstellar) planetesimals probably form in a similar fashion as free-floating planets. The number of free-floating objects in the Galaxy can be large. With billions of stars and planets, and trillions of interstellar planetesimals. Although free-floating planets appear to be quite common (a few hundred have been observed), only two interstellar planetesimals have been discovered so far. The expectation, however, is that they outnumber the stars in the Galaxy by a considerable margin. We expect them to be found more frequently once large new instruments come online, such as the Vera Cooper Rubin Observatory., Comment: Preprint of a chapter for the 'Encyclopedia of Astrophysics' (Editor-in-Chief Ilya Mandel, Section Editor Dimitri Veras) to be published by Elsevier as a Reference Module

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

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

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

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

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

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

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

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 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

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

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

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

Interstellar objects (ISOs), the parent population of 1I/Oumuamua and 2I/Borisov, are abundant in the interstellar medium of the Milky Way. This means that the interstellar medium, including molecular cloud regions, has three components: gas, dust, and ISOs. From the observational constraints for the field density of ISOs drifting in the solar neighbourhood, we infer a typical molecular cloud of 10 pc diameter contains some 10$^{18}$ ISOs. At typical sizes ranging from hundreds of metres to tens of km, ISOs are entirely decoupled from the gas dynamics in these molecular clouds. Here we address the question of whether ISOs can follow the collapse of molecular clouds. We perform low-resolution simulations of the collapse of molecular clouds containing initially static ISO populations toward the point where stars form. In this proof-of-principle study, we find that the interstellar objects definitely follow the collapse of the gas -- and many become bound to the new-forming numerical approximations to future stars (sinks). At minimum, 40\% of all sinks have one or more ISO test particles gravitationally bound to them for the initial ISO distributions tested here. This value corresponds to at least $10^{10}$ actual interstellar objects being bound after three initial free-fall times. Thus, ISOs are a relevant component of star formation. We find that more massive sinks bind disproportionately large fractions of the initial ISO population, implying competitive capture of ISOs. Sinks can also be solitary, as their ISOs can become unbound again -- particularly if sinks are ejected from the system. Emerging planetary systems will thus develop in remarkably varied environments, ranging from solitary to richly populated with bound ISOs., Comment: 15 pages, 7 figures, accepted for ApJ

We present a chronology of the formation and early evolution of the Oort cloud by simulations. These simulations start with the Solar System being born with planets and asteroids in a stellar cluster orbiting the Galactic center. Upon ejection from its birth environment, we continue to follow the evolution of the Solar System while it navigates the Galaxy as an isolated planetary system. We conclude that the range in semi-major axis between 100au and several 10$^3$\,au still bears the signatures of the Sun being born in a 1000MSun/pc$^3$ star cluster, and that most of the outer Oort cloud formed after the Solar System was ejected. The ejection of the Solar System, we argue, happened between 20Myr and 50Myr after its birth. Trailing and leading trails of asteroids and comets along the Sun's orbit in the Galactic potential are the by-product of the formation of the Oort cloud. These arms are composed of material that became unbound from the Solar System when the Oort cloud formed. Today, the bulk of the material in the Oort cloud ($\sim 70$\%) originates from the region in the circumstellar disk that was located between $\sim 15$\,au and $\sim 35$\,au, near the current location of the ice giants and the Centaur family of asteroids. According to our simulations, this population is eradicated if the ice-giant planets are born in orbital resonance. Planet migration or chaotic orbital reorganization occurring while the Solar System is still a cluster member is, according to our model, inconsistent with the presence of the Oort cloud. About half the inner Oort cloud, between 100 and $10^4$\,au, and a quarter of the material in the outer Oort cloud, $\apgt 10^4$\,au, could be non-native to the Solar System but was captured from free-floating debris in the cluster or from the circumstellar disk of other stars in the birth cluster., Comment: Corrected proofs for publication in A&A

The evolution of circumstellar discs is influenced by their surroundings. The relevant processes include external photoevaporation due to nearby stars, and dynamical truncations. The impact of these processes on disc populations depends on the star-formation history and on the dynamical evolution of the region. Since star formation history and the phase-space characteristics of the stars are important for the evolution of the discs, we start simulating the evolution of the star cluster with the results of molecular cloud collapse simulations. In the simulation we form stars with circumstellar discs, which can be affected by different processes. Our models account for the viscous evolution of the discs, internal and external photoevaporation of gas, external photoevaporation of dust, and dynamical truncations. All these processes are resolved together with the dynamical evolution of the cluster, and the evolution of the stars. An extended period of star formation, lasting for at least 2 Myr, results in some discs being formed late. These late formed discs have a better chance of survival because the cluster gradually expands with time, and a lower local stellar density reduces the effects of photoevaporation and dynamical truncation. Late formed discs can then be present in regions of high UV radiation, solving the proplyd lifetime problem. We also find a considerable fraction of discs that lose their gas content, but remain sufficiently rich in solids to be able to form a rocky planetary system., Comment: Accepted for publication in MNRAS. 15 pages, 12 figures

The recent discovery of pulsating ultra-luminous X-ray sources (ULXs) shows that the apparent luminosity of accreting neutron stars (NSs) can exceed the Eddington luminosity by a factor of hundreds. The relation between the actual and apparent luminosity is a key ingredient in theoretical models of ULXs but it is still under debate. A typical feature of the discovered pulsating ULXs is a large pulsed fraction (PF). Using Monte Carlo simulations, we consider a simple geometry of accretion flow and test the possibility of simultaneous presence of a large luminosity amplification due the geometrical beaming and a high PF. We argue that these factors largely exclude each other and only a negligible fraction of strongly beamed ULX pulsars can show PF above 10 per cent. Discrepancy between this conclusion and current observations indicate that pulsating ULXs are not strongly beamed and their apparent luminosity is close to the actual one., Comment: 6 pages, 5 figures; accepted for publication in MNRAS

We simulate the formation and evolution of Oort clouds around the 200 nearest stars (within 16pc according to the Gaia DR2) database. This study is performed by numerically integrating the planets and minor bodies in orbit around the parent star and in the Galactic potential. The calculations start 1\,Gyr ago and continue for 100Myr into the future. In this time frame, we simulate how asteroids (and planets) are ejected from the star's vicinity and settle in an Oort cloud and how they escape the local stellar gravity to form tidal steams. A fraction of 0.0098 to 0.026 of the asteroids remain bound to their parent star. The orbits of these asteroids isotropizes and circularizes due to the influence of the Galactic tidal field to eventually form an Oort cloud between 10^4 and 2 10^5au. We estimate that 6% of the nearby stars may have a planet in its Oort cloud. The majority of asteroids (and some of the planets) become unbound from the parent star to become free floating in the Galactic potential. These soli lapides remain in a similar orbit around the Galactic center as their host star, forming dense streams of rogue interstellar asteroids and planets. The Solar system occasionally passes through such tidal streams, potentially giving rise to occasional close encounters with object in this stream. The two recently discovered objects, 1I/(2017 Q3) 'Oumuamua and 2I/(2019 Q4) Borisov, may be such objects. Although the direction from which an individual solus lapis originated cannot easily be traced back to the original host, multiple such objects coming from the same source might help to identify their origin. At the moment the Solar system is in the bow or wake of the tidal stream of 10 of the nearby stars which might contribute considerably to the interaction rate. (abridged), Comment: accepted for publication in A&A, see animation https://youtu.be/0fYeAW3e9bQ

The fraction of stars in binary systems within star clusters is important for their evolution, but what proportion of binaries form by dynamical processes after initial stellar accretion remains unknown. In previous work, we showed that dynamical interactions alone produced too few low-mass binaries compared to observations. We therefore implement an initial population of binaries in the coupled MHD and direct N-body star cluster formation code Torch. We compare simulations with, and without, initial binary populations and follow the dynamical evolution of the binary population in both sets of simulations, finding that both dynamical formation and destruction of binaries take place. Even in the first few million years of star formation, we find that an initial population of binaries is needed at all masses to reproduce observed binary fractions for binaries with mass ratios above the $q \geq 0.1$ detection limit. Our simulations also indicate that dynamical interactions in the presence of gas during cluster formation modify the initial distributions towards binaries with smaller primary masses, larger mass ratios, smaller semi-major axes and larger eccentricities. Systems formed dynamically do not have the same properties as the initial systems, and systems formed dynamically in the presence of an initial population of binaries differ from those formed in simulations with single stars only. Dynamical interactions during the earliest stages of star cluster formation are important for determining the properties of binary star systems., Comment: 15 pages, 14 figures, submitted to MNRAS and edited to address positive referee's report

Context. The star formation rates and stellar densities found in young massive clusters suggest that these stellar systems originate from gas at densities n(H$_2$) $>10^7$ cm$^{-3}$. Until today, however, the physical characterization of this ultra high density material remains largely unconstrained in observations. Aims. We investigated the density properties of the star-forming gas in the OMC-1 region located in the vicinity of the Orion Nebula Cluster (ONC). Methods. We mapped the molecular emission at 652 GHz in OMC-1 as part of the APEX-SEPIA660 Early Science. Results. We detect bright and extended N$_2$H$^+$ (J=7-6) line emission along the entire OMC-1 region. Comparisons with previous ALMA data of the (J=1-0) transition and radiative transfer models indicate that the line intensities observed in this N$_2$H$^+$ (7-6) line are produced by large mass reservoirs of gas at densities n(H$_2$) $>10^7$ cm$^{-3}$. Conclusions. The first detection of this N$_2$H$^+$ (7-6) line at parsec-scales demonstrates the extreme density conditions of the star-forming gas in young massive clusters such as the ONC. Our results highlight the unique combination of sensitivity and mapping capabilities of the new SEPIA660 receiver for the study of the ISM properties at high frequencies., Comment: 8 pages, 5 Figures. Accepted for publication by A&A

Despite the discovery of thousands of exoplanets in recent years, the number of known exoplanets in star clusters remains tiny. This may be a consequence of close stellar encounters perturbing the dynamical evolution of planetary systems in these clusters. Here, we present the results from direct $N$-body simulations of multiplanetary systems embedded in star clusters containing $N = 8k, 16k, 32k$, and $64k$ stars. The planetary systems, which consist of the four Solar system giant planets Jupiter, Saturn, Uranus, and Neptune, are initialized in different orbital configurations, to study the effect of the system architecture on the dynamical evolution of the entire planetary system, and on the escape rate of the individual planets. We find that the current orbital parameters of the Solar system giants (with initially circular orbits, as well as with present-day eccentricities) and a slightly more compact configuration, have a high resilience against stellar perturbations. A configuration with initial mean-motion resonances of 3:2, 3:2, and 5:4 between the planets, which is inspired by the Nice model, and for which the two outermost planets are usually ejected within the first $10^5$ yr, is in many cases stabilized due to the removal of the resonances by external stellar perturbation and by the rapid ejection of at least one planet. Assigning all planets the same mass of 1 Jovian mass almost equalizes the survival fractions. Our simulations reproduce the broad diversity amongst observed exoplanet systems. We find not only many very wide and/or eccentric orbits, but also a significant number of (stable) retrograde orbits., Comment: 21 pages, 21 figures, accepted by MNRAS

Circumstellar discs are the precursors of planetary systems and develop shortly after their host star has formed. In their early stages these discs are immersed in an environment rich in gas and neighbouring stars, which can be hostile for their survival. There are several environmental processes that affect the evolution of circumstellar discs, and external photoevaporation is arguably one of the most important ones. Theoretical and observational evidence point to circumstellar discs losing mass quickly when in the vicinity of massive, bright stars. In this work we simulate circumstellar discs in clustered environments in a range of stellar densities, where the photoevaporation mass-loss process is resolved simultaneously with the stellar dynamics, stellar evolution, and the viscous evolution of the discs. Our results indicate that external photoevaporation is efficient in depleting disc masses and that the degree of its effect is related to stellar density. We find that a local stellar density lower than 100 stars pc$^{-2}$ is necessary for discs massive enough to form planets to survive for \SI{2.0}{Myr}. There is an order of magnitude difference in the disc masses in regions of projected density 100 stars pc$^{-2}$ versus $10^4$ stars pc$^{-2}$. We compare our results to observations of the Lupus clouds, the Orion Nebula Cluster, the Orion Molecular Cloud-2, Taurus, and NGC 2024, and find that the trends observed between region density and disc masses are similar to those in our simulations., Comment: Accepted for publication in MNRAS. 9 pages, 4 figures

Gaia Data Release 2 revealed detailed structures of nearby stars in phase space. These include the Hercules stream, whose origin is still debated. Most of the previous numerical studies conjectured that the observed structures originate from orbits in resonance with the bar, based on static potential models for the Milky Way. We, in contrast, approach the problem via a self-consistent, dynamic, and morphologically well-resolved model, namely a full $N$-body simulation of the Milky Way. Our simulation comprises about 5.1 billion particles in the galactic stellar bulge, bar, disk, and dark-matter halo and is evolved to 10 Gyr. Our model's disk component is composed of 200 million particles, and its simulation snapshots are stored every 10 Myr, enabling us to resolve and classify resonant orbits of representative samples of stars. After choosing the Sun's position in the simulation, we compare the distribution of stars in its neighborhood with Gaia's astrometric data, thereby establishing the role of identified resonantly trapped stars in the formation of Hercules-like structures. From our orbital spectral-analysis we identify multiple, especially higher order resonances. Our results suggest that the Hercules stream is dominated by the 4:1 and 5:1 outer Lindblad and corotation resonances. In total, this yields a trimodal structure of the Hercules stream. From the relation between resonances and ridges in phase space, our model favored a slow pattern speed of the Milky-Way bar (40--45 $\mathrm{km \; s^{-1} \; kpc^{-1}}$)., Comment: 11 pages, 9 figures, MNRAS accepted

Understanding the formation of stellar clusters requires following the interplay between gas and newly formed stars accurately. We therefore couple the magnetohydrodynamics code FLASH to the N-body code ph4 and the stellar evolution code SeBa using the Astrophysical Multipurpose Software Environment (AMUSE) to model stellar dynamics, evolution, and collisional N-body dynamics and the formation of binary and higher-order multiple systems, while implementing stellar feedback in the form of radiation, stellar winds and supernovae in FLASH. We here describe the algorithms used for each of these processes. We denote this integrated package Torch. We then use this novel numerical method to simulate the formation and early evolution of several examples of open clusters of ~1000 stars formed from clouds with a mass range of 10^3-10^5 M_sun. Analyzing the effects of stellar feedback on the gas and stars of the natal clusters, we find that in these examples, the stellar clusters are resilient to disruption, even in the presence of intense feedback. This can even slightly increase the amount of dense, Jeans unstable gas by sweeping up shells; thus, a stellar wind strong enough to trap its own H II region shows modest triggering of star formation. Our clusters are born moderately mass segregated, an effect enhanced by feedback, and retained after the ejection of their natal gas, in agreement with observations., Comment: Accepted to ApJ. 29 pages, 18 figures. Source code at https://bitbucket.org/torch-sf/torch/ and documentation at https://torch-sf.bitbucket.io/

Escalating observations of exo-minor planets and their destroyed remnants both passing through the solar system and within white dwarf planetary systems motivate an understanding of the orbital history and fate of exo-Kuiper belts and planetesimal discs. Here we explore how the structure of a 40-1000 au annulus of planetesimals orbiting inside of a solar system analogue that is itself initially embedded within a stellar cluster environment varies as the star evolves through all of its stellar phases. We attempt this computationally challenging link in four parts: (1) by performing stellar cluster simulations lasting 100 Myr, (2) by making assumptions about the subsequent quiescent 11 Gyr main-sequence evolution, (3) by performing simulations throughout the giant branch phases of evolution, and (4) by making assumptions about the belt's evolution during the white dwarf phase. Throughout these stages, we estimate the planetesimals' gravitational responses to analogues of the four solar system giant planets, as well as to collisional grinding, Galactic tides, stellar flybys, and stellar radiation. We find that the imprint of stellar cluster dynamics on the architecture of $\gtrsim 100$ km-sized exo-Kuiper belt planetesimals is retained throughout all phases of stellar evolution unless violent gravitational instabilities are triggered either (1) amongst the giant planets, or (2) due to a close ($\ll 10^3$ au) stellar flyby. In the absence of these instabilities, these minor planets simply double their semimajor axis while retaining their primordial post-cluster eccentricity and inclination distributions, with implications for the free-floating planetesimal population and metal-polluted white dwarfs., Comment: Accepted for publication in MNRAS

Chaos is present in most stellar dynamical systems and manifests itself through the exponential growth of small perturbations. Exponential divergence drives time irreversibility and increases the entropy in the system. A numerical consequence is that integrations of the N-body problem unavoidably magnify truncation and rounding errors to macroscopic scales. Hitherto, a quantitative relation between chaos in stellar dynamical systems and the level of irreversibility remained undetermined. In this work we study chaotic three-body systems in free fall initially using the accurate and precise N-body code Brutus, which goes beyond standard double-precision arithmetic. We demonstrate that the fraction of irreversible solutions decreases as a power law with numerical accuracy. This can be derived from the distribution of amplification factors of small initial perturbations. Applying this result to systems consisting of three massive black holes with zero total angular momentum, we conclude that up to five percent of such triples would require an accuracy of smaller than the Planck length in order to produce a time-reversible solution, thus rendering them fundamentally unpredictable., Comment: Accepted for publication in MNRAS. 7 pages, 4 figures

Since its formulation by Sir Isaac Newton, the problem of solving the equations of motion for three bodies under their own gravitational force has remained practically unsolved. Currently, the solution for a given initialization can only be found by performing laborious iterative calculations that have unpredictable and potentially infinite computational cost, due to the system's chaotic nature. We show that an ensemble of solutions obtained using an arbitrarily precise numerical integrator can be used to train a deep artificial neural network (ANN) that, over a bounded time interval, provides accurate solutions at fixed computational cost and up to 100 million times faster than a state-of-the-art solver. Our results provide evidence that, for computationally challenging regions of phase-space, a trained ANN can replace existing numerical solvers, enabling fast and scalable simulations of many-body systems to shed light on outstanding phenomena such as the formation of black-hole binary systems or the origin of the core collapse in dense star clusters., Comment: 6 pages, 6 figures

We make use of APOGEE and $Gaia$ data to identify stars that are consistent with being born in the same association or star cluster as the Sun. We limit our analysis to stars that match solar abundances within their uncertainties, as they could have formed from the same Giant Molecular Cloud (GMC) as the Sun. We constrain the range of orbital actions that solar siblings can have with a suite of simulations of solar birth clusters evolved in static and time-dependent tidal fields. The static components of each galaxy model are the bulge, disk, and halo, while the various time-dependent components include a bar, spiral arms, and GMCs. In galaxy models without GMCs, simulated solar siblings all have $J_R < 122$ km $\rm s^{-1}$ kpc, $990 < L_z < 1986$ km $\rm s^{-1}$ kpc, and $0.15 < J_z < 0.58$ km $\rm s^{-1}$ kpc. Given the actions of stars in APOGEE and $Gaia$, we find 104 stars that fall within this range. One candidate in particular, Solar Sibling 1, has both chemistry and actions similar enough to the solar values that strong interactions with the bar or spiral arms are not required for it to be dynamically associated with the Sun. Adding GMCs to the potential can eject solar siblings out of the plane of the disk and increase their $J_z$, resulting in a final candidate list of 296 stars. The entire suite of simulations indicate that solar siblings should have $J_R < 122$ km $\rm s^{-1}$ kpc, $353 < L_z < 2110$ km $\rm s^{-1}$ kpc, and $J_z < 0.8$ km $\rm s^{-1}$ kpc. Given these criteria, it is most likely that the association or cluster that the Sun was born in has reached dissolution and is not the commonly cited open cluster M67., Comment: 12 pages, 9 figures, 3 tables, Accepted for publication in MNRAS

Planet-forming circumstellar disks are a fundamental part of the star formation process. Since stars form in a hierarchical fashion in groups of up to hundreds or thousands, the UV radiation environment that these disks are exposed to can vary in strength by at least six orders of magnitude. This radiation can limit the masses and sizes of the disks. Diversity in star forming environments can have long lasting effects in disk evolution and in the resulting planetary populations. We perform simulations to explore the evolution of circumstellar disks in young star clusters. We include viscous evolution, as well as the impact of dynamical encounters and external photoevaporation. We find that photoevaporation is an important process in destroying circumstellar disks: in regions of stellar density $\rho \sim 100 \mathrm{\ M}_\odot \mathrm{\ pc}^{-3}\mathrm{\ }$ around 80% of disks are destroyed before 2 Myr of cluster evolution. Our findings are in agreement with observed disk fractions in young star forming regions and support previous estimations that planet formation must start in timescales < 0.1 - 1 Myr., Comment: 13 pages, 14 figures. Accepted for publication in MNRAS

We present stellar_wind.py, a module that provides multiple methods of simulating stellar winds using smoothed particle hydrodynamics codes (SPH) within the astrophysical multipurpose software environment (AMUSE) framework. With the simple wind mode, we create SPH wind particles in a spherically symmetric shell. We inject the wind particles with a velocity equal to their terminal velocity. The accelerating wind mode is similar, but with this method particles can be injected with a lower initial velocity than the terminal velocity and they are accelerated away from the star according to an acceleration function. With the heating wind mode, SPH particles are created with zero initial velocity with respect to the star, but instead wind particles are given an internal energy based on the integrated mechanical luminosity of the star. This mode is designed to be used on longer timescales and larger spatial scales compared to the other two modes and assumes that the star is embedded in a gas cloud. For fast winds, we find that both the simple and accelerating mode can reproduce the desired velocity, density and temperature profiles. For slow winds, the simple wind mode is insufficient due to dominant hydrodynamical effects that change the wind velocities. The accelerating mode, with additional options to account for these hydrodynamical effects, can still reproduce the desired wind profiles. We test the heating mode by simulating both a normal wind and a supernova explosion of a single star in a uniform density medium. The stellar wind simulation results matches the analytical solution for an expanding wind bubble. The supernova simulation gives qualitatively correct results, but the simulated bubble expands faster than the analytical solution predicts. We conclude with an example of a triple star system which includes the colliding winds of all three stars., Comment: Accepted for publication in A&A

We describe a star cluster formation model that includes individual star formation from self-gravitating, magnetized gas, coupled to collisional stellar dynamics. The model uses the Astrophysical Multi-purpose Software Environment (AMUSE) to integrate an adaptive-mesh magnetohydrodynamics code (FLASH) with a fourth order Hermite N-body code (ph4), a stellar evolution code (SeBa), and a method for resolving binary evolution (multiples). This combination yields unique star formation simulations that allow us to study binaries formed dynamically from interactions with both other stars and dense, magnetized gas subject to stellar feedback during the birth and early evolution of stellar clusters. We find that for massive stars, our simulations are consistent with the observed dynamical binary fractions and mass ratios. However, our binary fraction drops well below observed values for lower mass stars, presumably due to unincluded binary formation during initial star formation. Further, we observe a build up of binaries near the hard-soft boundary that may be an important mechanism driving early cluster contraction., Comment: 14 pages, 12 figures. Submitted to ApJ

The galactic halo likely grew over time in part by assembling smaller galaxies, the so-called building blocks. We investigate if the properties of these building blocks are reflected in the halo white dwarf (WD) population in the Solar neighborhood. Furthermore, we compute the halo WD luminosity functions (WDLFs) for four major building blocks of five cosmologically motivated stellar haloes. We couple the SeBa binary population synthesis model to the Munich-Groningen semi-analytic galaxy formation model, applied to the high-resolution Aquarius dark matter simulations. Although the semi-analytic model assumes an instantaneous recycling approximation, we model the evolution of zero-age main sequence stars to WDs, taking age and metallicity variations of the population into account. Although the majority of halo stars is old and metal-poor and therefore the WDs in the different building blocks have similar properties (including present-day luminosity), we find in our models that the WDs originating from building blocks that have young and/or metal-rich stars can be distinguished from WDs that were born in other building blocks. In practice however, it will be hard to prove that these WDs really originate from different building blocks, as the variations in the halo WD population due to binary WD mergers result in similar effects. The five joined stellar halo WD populations that we modelled result in WDLFs that are very similar to each other. We find that simple models with a Kroupa or Salpeter initial mass function (IMF) fit the observed luminosity function slightly better, since the Chabrier IMF is more top-heavy, although this result is dependent on our choice of the stellar halo mass density in the Solar neighborhood., Comment: 16 pages, 16 figures, published in Astronomy & Astrophysics

We analyze the position of the two populations of blue stragglers in the globular cluster M30 in the Hertzsprung-Russell diagram. Both populations of blue stragglers are brighter than the cluster's turn-off, but one population (the blue blue-stragglers) align along the zero-age main-sequence whereas the (red) population is elevated in brightness (or colour) by $\sim 0.75$ mag. Based on stellar evolution and merger simulations we argue that the red population, which composes about 40\% of the blue stragglers in M 30, is formed at a constant rate of $\sim 2.8$ blue stragglers per Gyr over the last $\sim 10$ Gyr. The blue population is formed in a burst that started $\sim 3.2$ Gyr ago at a peak rate of $30$ blue stragglers per Gyr$^{-1}$ with an e-folding time scale of $0.93$ Gyr. We speculate that the burst resulted from the core collapse of the cluster at an age of about 9.8 Gyr, whereas the constantly formed population is the result of mass transfer and mergers through binary evolution. In that case about half the binaries in the cluster effectively result in a blue straggler., Comment: Accepted for publication as Letter in A&A

Stars with circumstellar disks may form in environments with high stellar and gas densities which affects the disks through processes like truncation from dynamical encounters, ram pressure stripping, and external photoevaporation. Circumstellar disks also undergo viscous evolution which leads to disk expansion. Previous work indicates that dynamical truncation and viscous evolution play a major role in determining circumstellar disk size and mass distributions. However, it remains unclear under what circumstances each of these two processes dominates. Here we present results of simulations of young stellar clusters taking viscous evolution and dynamical truncations into account. We model the embedded phase of the clusters by adding leftover gas as a background potential which can be present through the whole evolution of the cluster, or expelled after 1 Myr. We compare our simulation results to actual observations of disk sizes, disk masses, and accretion rates in star forming regions. We argue that the relative importance of dynamical truncations and the viscous evolution of the disks changes with time and cluster density. Viscous evolution causes the importance of dynamical encounters to increase in time, but the encounters cease soon after the expulsion of the leftover gas. For the clusters simulated in this work, viscous growth dominates the evolution of the disks., Comment: Added link to code developed for the paper, plus a couple new references. 11 pages, 6 figures. Accepted for publication in MNRAS

We construct a model for the Milky Way Galaxy composed of a stellar disc and bulge embedded in a dark-matter halo. All components are modelled as $N$-body systems with up to 8 billion equal-mass particles and integrated up to an age of 10\,Gyr. We find that net angular-momentum of the dark-matter halo with a spin parameter of $\lambda=0.06$ is required to form a relatively short bar ($\sim 4$\,kpc) with a high pattern speed (40--50\,km\,s$^{-1}$). By comparing our model with observations of the Milky Way Galaxy, we conclude that a disc mass of $\sim 3.7\times10^{10}M_{\odot}$ and an initial bulge scale length and velocity of $\sim 1$\,kpc and $\sim 300$\,km\,s$^{-1}$, respectively, fit best to the observations. The disc-to-total mass fraction ($f_{\rm d}$) appears to be an important parameter for the evolution of the Galaxy and models with $f_{\rm d}\sim 0.45$ are most similar to the Milky Way Galaxy. In addition, we compare the velocity distribution in the solar neighbourhood in our simulations with observations in the Milky Way Galaxy. In our simulations the observed gap in the velocity distribution, which is expected to be caused by the outer Lindblad resonance (the so-called Hercules stream), appears to be a time-dependent structure. The velocity distribution changes on a time scale of 20--30\,Myr and therefore it is difficult to estimate the pattern speed of the bar from the shape of the local velocity distribution alone., Comment: Accepted by MNRAS, 32 pages, 31 figures

Recent developments in computer hardware and software enable researchers to simulate the self-gravitating evolution of galaxies at a resolution comparable to the actual number of stars. Here we present the results of a series of such simulations. We performed $N$-body simulations of disk galaxies with between 100 and 500 million particles over a wide range of initial conditions. Our calculations include a live bulge, disk, and dark matter halo, each of which is represented by self-gravitating particles in the $N$-body code. The simulations are performed using the gravitational $N$-body tree-code Bonsai running on the Piz Daint supercomputer. We find that the time scale over which the bar forms increases exponentially with decreasing disk-mass fraction and that the bar formation epoch exceeds a Hubble time when the disk-mass fraction is $\sim0.35$. These results can be explained with the swing-amplification theory. The condition for the formation of $m=2$ spirals is consistent with that for the formation of the bar, which is also an $m=2$ phenomenon. We further argue that the non-barred grand-design spiral galaxies are transitional, and that they evolve to barred galaxies on a dynamical timescale. We also confirm that the disk-mass fraction and shear rate are important parameters for the morphology of disk galaxies. The former affects the number of spiral arms and the bar formation epoch, and the latter determines the pitch angle of the spiral arms., Comment: 23 pages; 29 figures. Accepted by MNRAS