Simulations Of Star Cluster Formation Research Articles

Wide-binary eccentricity distribution in young star clusters: dependence on the binary separation and mass

Abstract We study the wide-binary eccentricity (e) distribution in young star clusters and the role of turbulence in setting the form of the e distribution using magnetohydrodynamical (MHD) simulations of star cluster formation. The simulations incorporate gravity, turbulence, magnetic fields, protostellar heating, and jets/outflows. We find that (1) simulations that employ purely compressive turbulence driving produce binaries with a superthermal e distribution (α > 1 in p(e)∝eα), while simulations with purely solenoidal driving or natural mixture of driving modes produce subthermal/thermal distributions (α ≤ 1), (2) the e distribution over the full range of binary separations in our simulations is set at the early stages of the star cluster formation process, (3) while binaries (separation of rpair ≤ 1000 AU) have subthermal to thermal e distributions (α ∼ 0.8), wide binaries (rpair > 1000 AU) have a superthermal distribution (α ∼ 1.8), and (4) low-mass binary systems (system masses of Msys ≤ 0.8 M⊙) have a highly superthermal distribution (α ∼ 2.4), whereas high-mass systems (Msys > 0.8 M⊙) exhibit a subthermal/thermal distribution (α ∼ 0.8). The binary eccentricity distribution is often modelled as a thermal distribution. However, our results suggest that the e distribution depends on the range of separation of the sampled binaries, which agrees with the findings from recent Gaia observations. We conclude that the dependence of the e distribution on the binary separation and mass is linked to the binary formation mechanism governed by the turbulent properties of the parent cloud.

The Interplay between the Initial Mass Function and Star Formation Efficiency through Radiative Feedback at High Stellar Surface Densities

The observed rest-UV luminosity function at cosmic dawn (z ∼ 8–14) measured by JWST revealed an excess of UV-luminous galaxies relative to many prelaunch theoretical predictions. A high star formation efficiency (SFE) and a top-heavy initial mass function (IMF) are among the mechanisms proposed for explaining this excess. Although a top-heavy IMF has been proposed for its ability to increase the light-to-mass ratio (ΨUV), the resulting enhanced radiative pressure from young stars could decrease the SFE, potentially driving galaxy luminosities back down. In this Letter, we use idealized radiation hydrodynamic simulations of star cluster formation to explore the effects of a top-heavy IMF on the SFE of clouds typical of the high-pressure conditions found at these redshifts. We find that the SFE in star clusters with solar-neighborhood-like dust abundance decreases with increasingly top-heavy IMFs—by ∼20% for an increase of a factor of 4 in ΨUV and by 50% for a factor of ∼10 in ΨUV. However, we find that an expected decrease in the dust-to-gas ratio (∼0.01 × solar) at these redshifts can completely compensate for the enhanced light output. This leads to a (cloud-scale; ∼10 pc) SFE that is ≳70% even for a factor of 10 increase in ΨUV, implying that highly efficient star formation is unavoidable for high surface density and low-metallicity conditions. Our results suggest that a top-heavy IMF, if present, likely coexists with efficient star formation in these galaxies.

On the frequencies of circumbinary discs in protostellar systems

ABSTRACT We report the analysis of circumbinary (CB) discs formed in a radiation hydrodynamical simulation of star cluster formation. We consider both pure binary stars and pairs within triple and quadruple systems. The protostellar systems are all young (ages < 105 yrs). We find that the systems that host a CB disc have a median separation of ≈11 au, and the median characteristic radius of the discs is ≈64 au. We find that 89 per cent of pure binaries with semimajor axes a < 1 au have a CB disc, and the occurrence rate of CB discs is bimodal with log-separation in pure binaries with a second peak at a ≈ 50 au. Systems with a > 100 au almost never have a CB disc. The median size of a CB disc is between ≈5 and 6 a depending on the order of the system, with higher order systems having larger discs relative to binary separation. We find the underlying distributions of mutual inclination between CB discs and binary orbits from the simulation are in good agreement with those of observed CB discs.

Early evolution and three-dimensional structure of embedded star clusters

ABSTRACT 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 104 M⊙ clouds at 0.0683 pc resolution for ∼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 ∼0.01 Myr time-scales. (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 ≲1000 M⊙ 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.

The statistical properties of stars at redshift, z = 5, compared with the present epoch

ABSTRACT We report the statistical properties of stars and brown dwarfs obtained from three radiation hydrodynamical simulations of star cluster formation with metallicities of 1, 1/10, and 1/100 of the solar value. The star-forming clouds are subjected to cosmic microwave background radiation that is appropriate for star formation at a redshift z = 5. The results from the three calculations are compared to each other, and to similar previously published calculations that had levels of background radiation appropriate for present-day (z = 0) star formation. Each of the calculations treats dust and gas temperatures separately and includes a thermochemical model of the diffuse interstellar medium. We find that whereas the stellar mass distribution is insensitive to the metallicity for present-day star formation, at z = 5 the characteristic stellar mass increases with increasing metallicity and the mass distribution has a deficit of brown dwarfs and low-mass stars at solar metallicity compared to the Galactic initial mass function. We also find that the multiplicity of M-dwarfs decreases with increasing metallicity at z = 5. These effects are a result of metal-rich gas being unable to cool to as low temperatures at z = 5 compared to at z = 0 due to the hotter cosmic microwave background radiation, which inhibits fragmentation at high densities.

The role of the turbulence driving mode for the initial mass function

ABSTRACT Turbulence is a critical ingredient for star formation, yet its role for the initial mass function (IMF) is not fully understood. Here we perform magnetohydrodynamical (MHD) simulations of star cluster formation including gravity, turbulence, magnetic fields, stellar heating, and outflow feedback to study the influence of the mode of turbulence driving on IMF. We find that simulations that employ purely compressive turbulence driving (COMP) produce a higher fraction of low-mass stars as compared to simulations that use purely solenoidal driving (SOL). The characteristic (median) mass of the sink particle (protostellar) distribution for COMP is shifted to lower masses by a factor of ∼1.5 compared to SOL. Our simulation IMFs capture the important features of the observed IMF form. We find that turbulence-regulated theories of the IMF match our simulation IMFs reasonably well in the high-mass and low-mass range, but underestimate the number of very low-mass stars, which form towards the later stages of our simulations and stop accreting due to dynamical interactions. Our simulations show that for both COMP and SOL, the multiplicity fraction is an increasing function of the primary mass, although the multiplicity fraction in COMP is higher than that of SOL for any primary mass range. We find that binary mass ratio distribution is independent of the turbulence driving mode. The average specific angular momentum of the sink particles in SOL is a factor of 2 higher than that for COMP. Overall, we conclude that the turbulence driving mode plays a significant role in shaping the IMF.

Infrared radiation feedback does not regulate star cluster formation

ABSTRACT We present 3D radiation-hydrodynamical (RHD) simulations of star cluster formation and evolution in massive, self-gravitating clouds, whose dust columns are optically thick to infrared (IR) photons. We use VETTAM – a recently developed, novel RHD algorithm, which uses the Variable Eddington Tensor closure – to model the IR radiation transport through the cloud. We also use realistic temperature (T) dependent IR opacities (κ) in our simulations, improving upon earlier works in this area, which used either constant IR opacities or simplified power laws (κ ∝ T2). We investigate the impact of the radiation pressure of these IR photons on the star formation efficiency of the cloud, and its potential to drive dusty winds. We find that IR radiation pressure is unable to regulate star formation or prevent accretion on to the star clusters, even for very high gas surface densities ($\Sigma \gt 10^5 \, \mathrm{M}_{\odot } \, \mathrm{pc}^{-2}$), contrary to recent semi-analytic predictions and simulation results using simplified treatments of the dust opacity. We find that the commonly adopted simplifications of κ ∝ T2 or constant κ for the IR dust opacities leads to this discrepancy, as those approximations overestimate the radiation force. By contrast, with realistic opacities that take into account the microphysics of the dust, we find that the impact of IR radiation pressure on star formation is very mild, even at significantly high dust-to-gas ratios (∼3 times solar), suggesting that it is unlikely to be an important feedback mechanism in controlling star formation in the ISM.

SIRIUS Project – IV. The formation history of the Orion Nebula Cluster driven by clump mergers

ABSTRACT The Orion Nebula Cluster (ONC) is an excellent example for understanding the formation of star clusters. Recent studies have shown that ONC has three distinct age populations and anisotropy in velocity dispersions, which are key characteristics for understanding the formation history of the ONC. In this study, we perform a smoothed-particle hydrodynamics/N-body simulation of star cluster formation from a turbulent molecular cloud. In this simulation, stellar orbits are integrated using a high-order integrator without gravitational softening; therefore, we can follow the collisional evolution of star clusters. We find that hierarchical formation causes episodic star formation that is observed in the ONC. In our simulation, star clusters evolve due to mergers of subclumps. The mergers bring cold gas with the clumps into the forming cluster. This enhances the star formation in the cluster centre. The dense cold gas in the cluster centre continues to form stars until the latest time. This explains the compact distribution of the youngest stars observed in the ONC. Subclump mergers also contribute to the anisotropy in the velocity dispersions and the formation of runaway stars. However, the anisotropy disappears within 0.5 Myr. The virial ratio of the cluster also increases after a merger due to the runaways. These results suggest that the ONC recently experienced a clump merger. We predict that most runaways originated from the ONC have already been found, but walkaways have not.

The velocity statistics of turbulent clouds in the presence of gravity, magnetic fields, radiation, and outflow feedback

ABSTRACTThe interaction of turbulence, magnetic fields, self-gravity, and stellar feedback within molecular clouds is crucial for understanding star formation. We study the effects of self-gravity and outflow feedback on the properties of the turbulent velocity via the SF over length-scales from ∼0.01 to 2 pc. We analyse a series of three-dimensional, magnetohydrodynamical (MHD) simulations of star cluster formation. We find outflow feedback can change the scaling of velocity fluctuations but still roughly being in between Kolmogorov and Burgers turbulence. We observe that self-gravity and protostellar outflows increase the velocity fluctuations over all length-scales. Outflows can amplify the velocity fluctuations by up to a factor of ∼7 on scales ∼0.01–0.2 pc and drive turbulence up to a scale of ∼1 pc. The amplified velocity fluctuations provide more support against gravity and enhance fragmentation on small scales. The self-gravity’s effect is more significant on smaller dense clumps and it increases the fraction of the compressive velocity component up to a scale of ∼0.2 pc. However, outflow feedback drives both solenoidal and compressive modes, but it induces a higher fraction of solenoidal modes relative to compressive modes. Thus, with outflows, the dense core ends up with a slightly higher fraction of solenoidal modes. We find that the compressible fraction is fairly constant with about 1/3 on scales ∼0.1–0.2 pc. The combined effect of enhanced velocity dispersion and reduced compressive fraction contributes to a reduction in the star formation rate.

The statistical properties of protostellar discs and their dependence on metallicity

ABSTRACT We present the analysis of the properties of large samples of protostellar discs formed in four radiation hydrodynamical simulations of star cluster formation. The four calculations have metallicities of 0.01, 0.1, 1, and 3 times solar metallicity. The calculations treat dust and gas temperatures separately and include a thermochemical model of the diffuse interstellar medium. We find that the radii of discs of bound protostellar systems tend to decrease with decreasing metallicity, with the median characteristic radius of discs in the 0.01 and 3 times solar metallicity calculations being ≈20 and ≈65 au, respectively. Disc masses and radii of isolated protostars also tend to decrease with decreasing metallicity. We find that the circumstellar discs and orbits of bound protostellar pairs, and the two spins of the two protostars are all less well aligned with each other with lower metallicity than with higher metallicity. These variations with metallicity are due to increased small-scale fragmentation due to lower opacities and greater cooling rates with lower metallicity, which increase the stellar multiplicity and increase dynamical interactions. We compare the disc masses and radii of protostellar systems from the solar metallicity calculation with recent surveys of discs around Class 0 and I objects in the Orion and Perseus star-forming regions. The masses and radii of the simulated discs have similar distributions to the observed Class 0 and I discs.

The IMF and multiplicity of stars from gravity, turbulence, magnetic fields, radiation, and outflow feedback

ABSTRACT We perform a series of three-dimensional, magnetohydrodynamical simulations of star cluster formation including gravity, turbulence, magnetic fields, stellar radiative heating, and outflow feedback. We observe that the inclusion of protostellar outflows (1) reduces the star formation rate by a factor of ∼2, (2) increases fragmentation, and (3) shifts the initial mass function (IMF) to lower masses by a factor of 2.0 ± 0.2, without significantly affecting the overall shape of the IMF. The form of the sink particle (protostellar objects) mass distribution obtained from our simulations matches the observational IMFs reasonably well. We also show that turbulence-based theoretical models of the IMF agree well with our simulation IMF in the high-mass and low-mass regime, but do not predict any brown dwarfs, whereas our simulations produce a considerable number of sub-stellar objects, which are produced by dynamical interactions (ejections). We find that these dynamical interactions also play a key role for the binary separation distribution and stellar kinematics in general. Our numerical model of star cluster formation also reproduces the observed mass dependence of multiplicity. Our multiplicity fraction estimates generally concur with the observational estimates for different spectral types. We further calculate the specific angular momentum of all the sink particles and find that the average value of $1.5 \times 10^{19}\, \mathrm{cm^2\, s^{-1}}$ is consistent with observational data. The specific angular momentum of our sink particles lies in the range typical of protostellar envelopes and binaries. We conclude that the IMF is controlled by a combination of gravity, turbulence, magnetic fields, radiation, and outflow feedback.

SIRIUS project. III. Star-by-star simulations of star cluster formation using a direct N -body integrator with stellar feedback

Abstract One of the computational challenges of cluster formation simulations is resolving individual stars and simulating massive clusters with masses of more than 104 M⊙ without gravitational softening. Combining a direct N-body code with smoothed-particle hydrodynamics (SPH) code, we have developed a new code, ASURA+BRIDGE, in which we can integrate stellar particles without softening. We add a feedback model for H ii regions into this code, in which thermal and momentum feedback is given within the Strömgren radius. We perform N-body/SPH simulations of star cluster formation. Without softening, a portion of massive stars are ejected from the forming clusters. As a result, the stellar feedback works outside the clusters. This enhances/suppresses the star formation in initially sub-virial/super-virial clouds. We find that the formed star clusters are denser than currently observed open clusters, but the mass–density relation is consistent with or even higher than that which is estimated as an initial cluster density. We also find that some clusters have multiple peaks in their stellar age distribution as a consequence of their hierarchical formation. Irrespective of the virial ratio of molecular clouds, approximately one-third of stars remain in the star clusters after gas expulsion.

Implementing primordial binaries in simulations of star cluster formation with a hybrid MHD and direct N-body method

ABSTRACT 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 magnetohydrodynamics 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 ≥ 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 semimajor 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.

Implementation of stellar heating feedback in simulations of star cluster formation: effects on the initial mass function

ABSTRACT Explaining the initial mass function (IMF) of stars is a long-standing problem in astrophysics. The number of complex mechanisms involved in the process of star cluster formation, such as turbulence, magnetic fields, and stellar feedback, make understanding and modelling the IMF a challenging task. In this paper, we aim to assert the importance of stellar heating feedback in the star cluster formation process and its effect on the shape of the IMF. We use an analytical sub-grid model to implement the radiative feedback in fully three-dimensional magnetohydrodynamical (MHD) simulations of star cluster formation, with the ultimate objective of obtaining numerical convergence on the IMF. We compare a set of MHD adaptive mesh refinement simulations with three different implementations of the heating of the gas: (1) a polytropic equation of state, (2) a spherically symmetric stellar heating feedback, and (3) our newly developed polar heating model that takes into account the geometry of the accretion disc and the resulting shielding of stellar radiation by dust. For each of the three heating models, we analyse the distribution of stellar masses formed in 10 molecular cloud simulations with different realizations of the turbulence to obtain a statistically representative IMF. We conclude that stellar heating feedback has a profound influence on the number of stars formed and plays a crucial role in controlling the IMF. We find that the simulations with the polar heating model achieve the best convergence on the observed IMF.

Modeling UV Radiation Feedback from Massive Stars. III. Escape of Radiation from Star-forming Giant Molecular Clouds

Abstract Using a suite of radiation hydrodynamic simulations of star cluster formation in turbulent clouds, we study the escape fraction of ionizing (Lyman continuum) and non-ionizing (FUV) radiation for a wide range of cloud masses and sizes. The escape fraction increases as H ii regions evolve and reaches unity within a few dynamical times. The cumulative escape fraction before the onset of the first supernova explosion is in the range 0.05–0.58; this is lower for higher initial cloud surface density, and higher for less massive and more compact clouds due to rapid destruction. Once H ii regions break out of their local environment, both ionizing and non-ionizing photons escape from clouds through fully ionized, low-density sight lines. Consequently, dust becomes the dominant absorber of ionizing radiation at late times, and the escape fraction of non-ionizing radiation is only slightly larger than that of ionizing radiation. The escape fraction is determined primarily by the mean and width σ of the optical-depth distribution in the large-scale cloud, increasing for smaller and/or larger σ. The escape fraction exceeds (sometimes by three orders of magnitude) the naive estimate due to the nonzero σ induced by turbulence. We present two simple methods to estimate, within ∼20%, the escape fraction of non-ionizing radiation using the observed dust optical depth in clouds projected on the plane of sky. We discuss implications of our results for observations, including inference of star formation rates in individual molecular clouds and accounting for diffuse ionized gas on galactic scales.

Simulating star-forming regions in spiral galaxies with AMUSE

AbstractWe present a model for hydrodynamic + N-body simulations of star cluster formation and evolution using AMUSE. Our model includes gas dynamics, star formation in regions of dense gas, stellar evolution and a galactic tidal spiral potential, thus incorporating most of the processes that play a role in the evolution of star clusters.We test our model on initial conditions of two colliding molecular clouds as well as a section of a spiral arm from a previous galaxy simulation.

The statistical properties of stars and their dependence on metallicity

We report the statistical properties of stars and brown dwarfs obtained from four radiation hydrodynamical simulations of star cluster formation, the metallicities of which span a range from 1/100 to 3 times the solar value. Unlike previous similar investigations of the effects of metallicity on stellar properties, these new calculations treat dust and gas temperatures separately and include a thermochemical model of the diffuse interstellar medium. The more advanced treatment of the interstellar medium gives rise to very different gas and dust temperature distributions in the four calculations, with lower metallicities generally resulting in higher temperatures and a delay in the onset of star formation. Despite this, once star formation begins, all four calculations produce stars at similar rates and many of the statistical properties of their stellar populations are difficult to distinguish from each other and from those of observed stellar systems. We do find, however, that the greater cooling rates at high gas densities due to the lower opacities at low metallicities increase the fragmentation on small spatial scales (disc, filament, and core fragmentation). This produces an anti-correlation between the close binary fraction of low-mass stars and metallicity similar to that which is observed, and an increase in the fraction of protostellar mergers at low metallicities. There are also indications that at lower metallicity close binaries may have lower mass ratios and the abundance of brown dwarfs to stars may increase slightly. However, these latter two effects are quite weak and need to be confirmed with larger samples.

From the top down and back up again: star cluster structure from hierarchical star formation.

Young massive star clusters spanning ~104-108M⊙ in mass have been observed to have similar surface brightness profiles. We show that recent hydrodynamical simulations of star cluster formation have also produced star clusters with this structure. We argue analytically that this type of mass distribution arises naturally in the relaxation from a hierarchically clustered distribution of stars into a monolithic star cluster through hierarchical merging. We show that initial profiles of finite maximum density will tend to produce successively shallower power-law profiles under hierarchical merging, owing to certain conservation constraints on the phase-space distribution. We perform N-body simulations of a pairwise merger of model star clusters and find that mergers readily produce the shallow surface brightness profiles observed in young massive clusters. Finally, we simulate the relaxation of a hierarchically clustered mass distribution constructed from an idealized fragmentation model. Assuming only power-law spatial and kinematic scaling relations, these numerical experiments are able to reproduce the surface density profiles of observed young massive star clusters. Thus, we bolster the physical motivation for the structure of young massive clusters within the paradigm of hierarchical star formation. This could have important implications for the structure and dynamics of nascent globular clusters.

Modeling UV Radiation Feedback from Massive Stars. II. Dispersal of Star-forming Giant Molecular Clouds by Photoionization and Radiation Pressure

Abstract UV radiation feedback from young massive stars plays a key role in the evolution of giant molecular clouds (GMCs) by photoevaporating and ejecting the surrounding gas. We conduct a suite of radiation hydrodynamic simulations of star cluster formation in marginally bound, turbulent GMCs, focusing on the effects of photoionization and radiation pressure on regulating the net star formation efficiency (SFE) and cloud lifetime. We find that the net SFE depends primarily on the initial gas surface density, Σ0, such that the SFE increases from 4% to 51% as Σ0 increases from 13 to . Cloud destruction occurs within 2–10 Myr after the onset of radiation feedback, or within 0.6–4.1 freefall times (increasing with Σ0). Photoevaporation dominates the mass loss in massive, low surface density clouds, but because most photons are absorbed in an ionization-bounded Strömgren volume, the photoevaporated gas fraction is proportional to the square root of the SFE. The measured momentum injection due to thermal and radiation pressure forces is proportional to , and the ejection of neutrals substantially contributes to the disruption of low mass and/or high surface density clouds. We present semi-analytic models for cloud dispersal mediated by photoevaporation and by dynamical mass ejection, and show that the predicted net SFE and mass loss efficiencies are consistent with the results of our numerical simulations.

On the diversity and statistical properties of protostellar discs

Abstract We present results from the first population synthesis study of protostellar discs. We analyse the evolution and properties of a large sample of protostellar discs formed in a radiation hydrodynamical simulation of star cluster formation. Due to the chaotic nature of the star formation process, we find an enormous diversity of young protostellar discs, including misaligned discs, and discs whose orientations vary with time. Star–disc interactions truncate discs and produce multiple systems. Discs may be destroyed in dynamical encounters and/or through ram-pressure stripping, but reform by later gas accretion. We quantify the distributions of disc mass and radii for protostellar ages up to ≈105 yr. For low-mass protostars, disc masses tend to increase with both age and protostellar mass. Disc radii range from of order 10 to a few hundred au, grow in size on time-scales ≲ 104 yr, and are smaller around lower mass protostars. The radial surface density profiles of isolated protostellar discs are flatter than the minimum mass solar nebula model, typically scaling as Σ ∝ r−1. Disc to protostar mass ratios rarely exceed two, with a typical range of Md/M* = 0.1–1 to ages ≲ 104 yr and decreasing thereafter. We quantify the relative orientation angles of circumstellar discs and the orbit of bound pairs of protostars, finding a preference for alignment that strengths with decreasing separation. We also investigate how the orientations of the outer parts of discs differ from the protostellar and inner disc spins for isolated protostars and pairs.