arXiv subjects

Stephen L. W. McMillan

Publications and source records attributed to Stephen L. W. McMillan.

At least 19 recordsLinked to original sources

arXiv2025

Transferring Data from a Voronoi Mesh to an Adaptive Cartesian Grid in Pursuit of Self-consistent Top-down Star Formation

Unstructured Voronoi mesh simulations offer many advantages for simulating self-gravitating gas dynamics on galactic scales. Adaptive mesh refinement (AMR) can be a powerful tool for simulating the details of star cluster formation and gas dispersal by stellar feedback. Zooming in from galactic to local scales using the star cluster formation simulation package Torch requires transferring simulation data from one scale to the other. Therefore, we introduce VorAMR, a novel computational tool that interpolates data from an unstructured Voronoi mesh to an AMR Cartesian grid. VorAMR is integrated into the Torch package, which integrates the FLASH AMR magnetohydrodynamics code into the Astrophysical Multipurpose Software Environment. VorAMR interpolates data from an AREPO simulation to a FLASH AMR grid using a nearest-neighbor particle scheme, which can then be evolved within the Torch package, representing the first ever transfer of data from a Voronoi mesh to an AMR Cartesian grid. Interpolation from one numerical representation to another results in an error of a few percent in global mass and energy conservation, which could be reduced with higher-order interpolation of the Voronoi cells. We show that the postinterpolation Torch simulation evolves without numerical abnormalities. A preliminary Torch simulation is evolved for 3.22 Myr and compared to the original AREPO simulation over the same time period. We observe similarly distributed star cluster formation between the two simulations. More compact clusters are produced in the Torch simulation as well as 2.3 times as much stellar material as in AREPO, likely due to the differences in resolution.

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arXiv2025

Protostellar Jets in Star Cluster Formation and Evolution: I. Implementation and Initial Results

Stars form in clusters from the gravitational collapse of giant molecular clouds, which is opposed by a variety of physical processes, including stellar feedback. The interplay between these processes determines the star formation rate of the clouds. To study how feedback controls star formation, we use a numerical framework that is optimized to simulate star cluster formation and evolution. This framework, called Torch, combines the magnetohydrodynamical code FLASH with N-body and stellar evolution codes in the Astrophysical Multipurpose Software Environment (AMUSE). Torch includes stellar feedback from ionizing and non-ionizing radiation, stellar winds, and supernovae, but, until now, did not include protostellar jets. We present our implementation of protostellar jet feedback within the Torch framework and describe its free parameters. We then demonstrate our new module by comparing cluster formation simulations with and without jets. We find that the inclusion of protostellar jets slows star formation, even in clouds of up to M $= 2 \times 10^4$ M$_{\odot}$. We also find that the star formation rate of our lower mass clouds (M $= 5 \times 10^3$ M$_{\odot}$) is strongly affected by both the inclusion of protostellar jets and the chosen jet parameters, including the jet lifetime and injection velocity. We follow the energy budget for each simulation and find that the inclusion of jets systematically increases the kinetic energy of the gas at early times. The implementation of protostellar jet feedback in Torch opens new areas of investigation regarding the role of feedback in star cluster formation and evolution.

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arXiv2025

Massive star cluster formation III. Early mass segregation during cluster assembly

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.

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arXiv2025

Massive star cluster formation II. Runaway stars as fossils of sub-cluster mergers

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.

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arXiv2025

Massive star cluster formation I. High star formation efficiency while resolving feedback of individual stars

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 $\sim$30%, 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 $\leq$30%. The M5 and M6 models represent a different regime of cluster formation that is more appropriate for the conditions in starburst galaxies and gas-rich galaxies at high redshift, and that leads to a significantly higher efficiency of star formation. We argue that young massive clusters build up through short efficient bursts of star formation in regions that are sufficiently dense ($\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.

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arXiv2023

Early-Forming Massive Stars Suppress Star Formation and Hierarchical Cluster Assembly

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.

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arXiv2023

Early Evolution and 3D Structure of Embedded Star Clusters

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 $α$ = 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 $α$ 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.

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arXiv2021

Compositional Convection in the Deep Interior of Uranus

Uranus and Neptune share properties that are distinct from the other giant planets in the solar system, but they are also distinct from one another, particularly in their relative internal heat flux. Not only does Neptune emit about ten times the amount of heat that emitted by Uranus, the relative amount of emitted heat to the energy they absorb from the sun also differs greatly, being comparable at Uranus and the largest of all giant planets at Neptune. As a result, it is questionable whether thermal convection occurs within the interior of Uranus. However, the presence of an intrinsic magnetic field implies that interior fluid motions must exist. Here, we consider compositional convection driven by the release of hydrogen associated with the formation of large organic networks or diamond precipitation in the deep interior. We test this hypotheses using a set of numerical rotating convection models where the convective driving is varied between thermal and compositional sources and is sufficiently vigorous to not be strongly constrained by rotation. In most cases, we find ice-giant-like zonal flows develop, with three bands characterized by a retrograde equatorial jet and prograde jets at higher latitudes. Large-scale circulation cells also develop and lead to heat and mass fluxes that tend to exhibit local maxima along the equatorial plane. This similarity between convective flows driven by thermal and compositional buoyancy therefore predict Uranus and Neptune to have similar interior dynamics despite Uranus' minimal internal heat flow and may thus explain why both ice giants have comparable magnetic fields.

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arXiv2020

Implementing Primordial Binaries in Simulations of Star Cluster Formation with a Hybrid MHD and Direct N-Body Method

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.

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arXiv2020

Modelling of the Effects of Stellar Feedback during Star Cluster Formation Using a Hybrid Gas and N-Body Method

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.

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arXiv2020

TYCHO -- Realistically Simulating Exoplanets within Stellar Clusters I: Improving the Monte Carlo Approach

To fully understand the diverse population of exoplanets, we must study their early lives within open clusters, the birthplace of most stars with masses $>0.5M_\odot$ (including those currently in the field). Indeed, when we observe planets within clustered environments, we notice highly eccentric and odd systems that suggest the importance of dynamical pathways created by interactions with additional bodies (as in the case of HD 285507b). However, it has proven difficult to investigate these effects, as many current numerical solvers for the multi-scale $N$-body problem are simplified and limited in scope. To remedy this, we aim to create a physically complete computational solution to explore the role of stellar close encounters and interplanetary interactions in producing the observed exoplanet populations for both open cluster stars and field stars. We present a new code, TYCHO, which employs a variety of different computational techniques, including multiple $N$-body integration methods, close encounter handling, modified Monte Carlo scattering experiments, and a variety of empirically informed initial conditions. We discuss the methodology in detail, and its implementation within the AMUSE software framework. Approximately 1$\%$ of our systems are promptly disrupted by star-star encounters contributing to the rogue planets occurrence rate. Additionally, we find that close encounters which perturb long-period planets lead to 38.3$\%$ of solar-system-like planetary systems becoming long-term unstable.

astro-ph.EP↗

arXiv2019

Collisional N-Body Dynamics Coupled to Self-Gravitating Magnetohydrodynamics Reveals Dynamical Binary Formation

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.

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arXiv2016

Evolution of Binary Stars in Multiple-Population Globular Clusters - II. Compact Binaries

We present the results of a survey of N-body simulations aimed at exploring the evolution of compact binaries in multiple-population globular clusters.We show that as a consequence of the initial differences in the structural properties of the first-generation (FG) and the second-generation (SG) populations and the effects of dynamical processes on binary stars, the SG binary fraction decreases more rapidly than that of the FG population. The difference between the FG and SG binary fraction is qualitatively similar to but quantitatively smaller than that found for wider binaries in our previous investigations.The evolution of the radial variation of the binary fraction is driven by the interplay between binary segregation, ionization and ejection. Ionization and ejection counteract in part the effects of mass segregation but for compact binaries the effects of segregation dominate and the inner binary fraction increases during the cluster evolution. We explore the variation of the difference between the FG and the SG binary fraction with the distance from the cluster centre and its dependence on the binary binding energy and cluster structural parameters. The difference between the binary fraction in the FG and the SG populations found in our simulations is consistent with the results of observational studies finding a smaller binary fraction in the SG population.

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arXiv2015

Evolution of Binary Stars in Multiple-Population Globular Clusters

The discovery of multiple stellar populations in globular clusters has implications for all the aspects of the study of these stellar systems. In this paper, by means of N-body simulations, we study the evolution of binary stars in multiple-population clusters and explore the implications of the initial differences in the spatial distribution of different stellar populations for the evolution and survival of their binary stars. Our simulations show that initial differences between the spatial distribution of first-generation (FG) and second-generation (SG) stars can leave a fingerprint in the current properties of the binary population. SG binaries are disrupted more efficiently than those of the FG population resulting in a global SG binary fraction smaller than that of the FG. As for surviving binaries, dynamical evolution produces a difference between the SG and the FG binary binding energy distribution with the SG population characterized by a larger fraction of high binding energy (more bound) binaries. We have also studied the dependence of the binary properties on the distance from the cluster centre. Although the global binary fraction decreases more rapidly for the SG population, the local binary fraction measured in the cluster inner regions may still be dominated by SG binaries. The extent of the differences between the surviving FG and SG binary binding energy distribution also varies radially within the cluster and is larger in the cluster inner regions.

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arXiv2014

Dynamical Processes in Globular Clusters

Globular clusters are among the most congested stellar systems in the Universe. Internal dynamical evolution drives them toward states of high central density, while simultaneously concentrating the most massive stars and binary systems in their cores. As a result, these clusters are expected to be sites of frequent close encounters and physical collisions between stars and binaries, making them efficient factories for the production of interesting and observable astrophysical exotica. I describe some elements of the competition among stellar dynamics, stellar evolution, and other processes that control globular cluster dynamics, with particular emphasis on pathways that may lead to the formation of blue stragglers.

astro-ph.SR↗

arXiv2014

Kinematical fingerprints of star cluster early dynamical evolution

We study the effects of the external tidal field on the violent relaxation phase of star clusters dynamical evolution, with particular attention to the kinematical properties of the equilibrium configurations emerging at the end of this phase.We show that star clusters undergoing the process of violent relaxation in the tidal field of their host galaxy can acquire significant internal differential rotation and are characterized by a distinctive radial variation of the velocity anisotropy. These kinematical properties are the result of the symmetry breaking introduced by the external tidal field in the collapse phase and of the action of the Coriolis force on the orbit of the stars. The resulting equilibrium configurations are characterized by differential rotation, with a peak located between one and two half-mass radii. As for the anisotropy, similar to clusters evolving in isolation, the systems explored in this Letter are characterized by an inner isotropic core, followed by a region of increasing radial anisotropy. However for systems evolving in an external tidal field the degree of radial anisotropy reaches a maximum in the cluster intermediate regions and then progressively decreases, with the cluster outermost regions being characterized by isotropy or a mild tangential anisotropy. Young or old but less-relaxed dynamically young star clusters may keep memory of these kinematical fingerprints of their early dynamical evolution.

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arXiv2013

Simulating Star Clusters with the AMUSE Software Framework: I. Dependence of Cluster Lifetimes on Model Assumptions and Cluster Dissolution Modes

We perform a series of simulations of evolving star clusters using AMUSE (the Astrophysical Multipurpose Software Environment), a new community-based multi-physics simulation package, and compare our results to existing work. These simulations model a star cluster beginning with a King model distribution and a selection of power-law initial mass functions, and contain a tidal cut-off. They are evolved using collisional stellar dynamics and include mass loss due to stellar evolution. After determining that the differences between AMUSE results and prior publications are understood, we explored the variation in cluster lifetimes due to the random realization noise introduced by transforming a King model to specific initial conditions. This random realization noise can affect the lifetime of a simulated star cluster by up to 30%. Two modes of star cluster dissolution were identified: a mass evolution curve that contains a run-away cluster dissolution with a sudden loss of mass, and a dissolution mode that does not contain this feature. We refer to these dissolution modes as "dynamical" and "relaxation" dominated respectively. For Salpeter-like initial mass functions, we determined the boundary between these two modes in terms of the dynamical and relaxation time scales.

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arXiv2013

Evolution of star clusters in a cosmological tidal field

We present a method to couple N-body star cluster simulations to a cosmological tidal field, using the Astrophysical Multipurpose Software Environment. We apply this method to star clusters embedded in the CosmoGrid dark matter-only LambdaCDM simulation. Our star clusters are born at z = 10 (corresponding to an age of the Universe of about 500 Myr) by selecting a dark matter particle and initializing a star cluster with 32,000 stars on its location. We then follow the dynamical evolution of the star cluster within the cosmological environment. We compare the evolution of star clusters in two Milky-Way size haloes with a different accretion history. The mass loss of the star clusters is continuous irrespective of the tidal history of the host halo, but major merger events tend to increase the rate of mass loss. From the selected two dark matter haloes, the halo that experienced the larger number of mergers tends to drive a smaller mass loss rate from the embedded star clusters, even though the final masses of both haloes are similar. We identify two families of star clusters: native clusters, which become part of the main halo before its final major merger event, and the immigrant clusters, which are accreted upon or after this event; native clusters tend to evaporate more quickly than immigrant clusters. Accounting for the evolution of the dark matter halo causes immigrant star clusters to retain more mass than when the z=0 tidal field is taken as a static potential. The reason for this is the weaker tidal field experienced by immigrant star clusters before merging with the larger dark matter halo.

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