On the diversity and statistical properties of protostellar discs (article)

This is the final version of the article. Available from OUP via the DOI in this record.The dataset associated with this article is in ORE: http://hdl.handle.net/10871/31266We 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.This work was by the European Research Council under the European Commission's Seventh Framework Programme (FP7/2007-2013 Grant Agreement No. 339248). The calculation discussed in this paper was performed on the University of Exeter Supercomputer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS, and the University of Exeter, and on the DiRAC Complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility (www.dirac.ac.uk). The latter equipment is funded by BIS National E-Infrastructure capital grant ST/K000373/1 and STFC DiRAC Operations grant ST/K0003259/1. DiRAC is part of the National E-Infrastructure. The calculation was conducted as part of the award ‘The formation of stars and planets: Radiation hydrodynamical and magnetohydrodynamical simulations’ made under the European Heads of Research Councils and European Science Foundation EURYI (European Young Investigator) Awards scheme, was supported by funds from the Participating Organisations of EURYI and the EC Sixth Framework Programme

The statistical properties of stars and their dependence on metallicity (article)

This is the author accepted manuscript. The final version is available from OUP via the DOI in this recordThe dataset associated with this article is located in ORE at: https://doi.org/10.24378/exe.1123We 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.European Commissio

Sink particle radiative feedback in smoothed particle hydrodynamics models of star formation

This is the author accepted manuscript. The final version is available from Oxford University Press via the DOI in this record.We present a new method for including radiative feedback from sink particles in smoothed particle hydrodynamics simulations of low-mass star formation, and investigate its effects on the formation of small stellar groups. We find that including radiative feedback from sink particles suppresses fragmentation even further than calculations that only include radiative transfer within the gas. This reduces the star-formation rate following the formation of the initial protostars, leading to fewer objects being produced and a lower total stellar mass. The luminosities of sink particles vary due to changes in the accretion rate driven by the dynamics of the cluster gas, leading to different luminosities for protostars of similar mass. Including feedback from sinks also raises the median stellar mass. The median masses of the groups are higher than typically observed values. This may be due to the lack of dynamical interactions and ejections in small groups of protostars compared to those that occur in richer groups. We also find that the temperature distributions in our calculations are in qualitative agreement with recent observations of protostellar heating in Galactic star-forming regions.This work was supported by the European Research Coun- cil under the European Commission's Seventh Framework Programme (FP7/2007-2013 Grant Agreement No. 339248). The calculations discussed in this paper were performed on the University of Exeter Supercomputer, Isca. The rendered plots shown were produced using SPLASH (Price 2007)

The dependence of protostar formation on the geometry and strength of the initial magnetic field

Published onlineThis is the final version of the article. Available from Oxford University Press via the DOI in this record.We report results from 12 simulations of the collapse of a molecular cloud core to form one or more protostars, comprising three field strengths (mass-to-flux ratios, μ, of 5, 10 and 20) and four field geometries (with values of the angle between the field and rotation axes, ϑ, of 0°, 20°, 45° and 90°), using a smoothed particle magnetohydrodynamics method. We find that the values of both parameters have a strong effect on the resultant protostellar system and outflows. This ranges from the formation of binary systems when μ = 20 to strikingly differing outflow structures for differing values of ϑ, in particular highly suppressed outflows when ϑ = 90°. Misaligned magnetic fields can also produce warped pseudo-discs where the outer regions align perpendicular to the magnetic field but the innermost region re-orientates to be perpendicular to the rotation axis. We follow the collapse to sizes comparable to those of first cores and find that none of the outflow speeds exceed 8 km s−1. These results may place constraints on both observed protostellar outflows and also on which molecular cloud cores may eventually form either single stars or binaries: a sufficiently weak magnetic field may allow for disc fragmentation, whilst conversely the greater angular momentum transport of a strong field may inhibit disc fragmentation.BTL acknowledges support from an STFC Studentship and Long Term Attachment grant. This work was also supported by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013 Grant Agreement No. 339248). MRB's visit to Monash was funded by an International Collaboration Award from the Australian Research Council (ARC) under the Discovery Project scheme grant DP130102078. This work used the DiRAC Complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment is funded by BIS National E-Infrastructure capital grant ST/K000373/1 and STFC DiRAC Operations grant ST/K0003259/1. DiRAC is part of the National E-Infrastructure. Calculations were also performed on the University of Exeter Supercomputer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS and the University of Exeter. This work also made use of the NumPy (van der Welt, Colbert & Varoquax 2011) and Matplotlib (Hunter 2007) Python modules. Rendered plots were produced using the splash (Price 2007) visualization program

Toroidal vortices as a solution to the dust migration problem

PublishedJournal Article© 2016 The Authors.In an earlier letter, we reported that dust settling in protoplanetary discs may lead to a dynamical dust-gas instability that produces global toroidal vortices. In this Letter, we investigate the evolution of a dusty protoplanetary disc with two different dust species (1 mm and 50 cm dust grains), under the presence of the instability. We show how toroidal vortices, triggered by the interaction of mm grains with the gas, stop the radial migration of metre-sized dust, potentially offering a natural and efficient solution to the dust migration problem.The figures were created using SPLASH (Price 2007), an SPH visualization tool publicly available at http://users.monash.edu.au/∼dprice/splash. This Letter was supported by the STFC consolidated grant ST/J001627/1, and by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013 grant agreement no. 339248). This Letter used the DiRAC Complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment is funded by BIS National E-Infrastructure capital grant ST/K000373/1 and STFC DiRAC Operations grant ST/K0003259/1. DiRAC is part of the National E-Infrastructure. This Letter also used the University of Exeter Supercomputer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS and the University of Exeter

The impact of non-ideal magnetohydrodynamics on binary star formation

This is the final version of the article. Available from the publisher via the DOI in this record.We investigate the effect of non-ideal magnetohydrodynamics (MHD) on the formation of binary stars using a suite of three-dimensional smoothed particle magnetohydrodynamics simulations of the gravitational collapse of 1 M⊙, rotating, perturbed molecular-cloud cores. Alongside the role of Ohmic resistivity, ambipolar diffusion and the Hall effect, we also examine the effects of magnetic field strength, orientation and amplitude of the density per- turbation. When modelling sub-critical cores, ideal MHD models do not collapse whereas non-ideal MHD models collapse to form single protostars. In supercritical ideal MHD models, increasing the magnetic field strength or decreasing the initial-density perturbation amplitude decreases the initial binary separation. Strong magnetic fields initially perpendicular to the rotation axis suppress the formation of binaries and yield discs with magnetic fields ∼10 times stronger than if the magnetic field was initially aligned with the rotation axis. When non-ideal MHD is included, the resulting discs are larger and more massive, and the binary forms on a wider orbit. Small differences in the supercritical cores caused by non-ideal MHD effects are amplified by the binary interaction near periastron. Overall, the non-ideal effects have only a small impact on binary formation and early evolution, with the initial conditions playing the dominant role.JW and MRB acknowledge support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013 grant agreement no. 339248). JW also acknowledges support from the Australian Research Council (ARC) Discovery Projects Grant DP130102078. DJP is funded by ARC Future Fellowship FT130100034. This work was supported by resources on the gSTAR national facility at Swinburne University of Technology and by Zen. gSTAR is funded by Swinburne and the Australian Government’s Education Investment Fund. Several calculations for this paper were performed on the University of Exeter Supercomputer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS, and the University of Exeter

Photoionizing feedback in spiral arm molecular clouds

This is the author accepted manuscript. The final version is available from Oxford University Press via the DOI in this recordWe present simulations of a 500 pc2 region, containing gas of mass 4 × 106 M⊙, extracted from an entire spiral galaxy simulation, scaled up in resolution, including photoionising feedback from stars of mass > 18 M⊙. Our region is evolved for 10 Myr and shows clustered star formation along the arm generating ≈ 5000 cluster sink particles ≈ 5% of which contain at least one of the ≈ 4000 stars of mass > 18 M⊙. Photoionisation has a noticeable effect on the gas in the region, producing ionised cavities and leading to dense features at the edge of the HII regions. Compared to the no-feedback case, Photoionisation produces a larger total mass of clouds and clumps, with around twice as many such objects, which are individually smaller and more broken up. After this we see a rapid decrease in the total mass in clouds and the number of clouds. Unlike studies of isolated clouds, our simulations follow the long range effects of ionisation, with some already-dense gas, becoming compressed from multiple sides by neighbouring HII regions. This causes star formation that is both accelerated and partially displaced throughout the spiral arm with up to 30% of our cluster sink particle mass forming at distances > 5 pc from sites of sink formation in the absence of feedback. At later times, the star formation rate decreases to below that of the no-feedback case.European Union Horizon 2020European Union FP

The collapse of a molecular cloud core to stellar densities using radiation non-ideal magnetohydrodynamics (article)

This is the final version of the article. Available from Oxford University Press via the DOI in this record.The dataset associated with this article is located in ORE at: http://hdl.handle.net/10871/32503We present results from radiation non-ideal magnetohydrodynamics (MHD) calculations that follow the collapse of rotating, magnetized, molecular cloud cores to stellar densities. These are the first such calculations to include all three non-ideal effects: ambipolar diffusion, Ohmic resistivity, and the Hall effect. We employ an ionization model in which cosmic ray ionization dominates at low temperatures and thermal ionization takes over at high temperatures. We explore the effects of varying the cosmic ray ionization rate from ζcr = 10−10 to 10−16 s−1. Models with ionization rates ≳10−12 s−1 produce results that are indistinguishable from ideal MHD. Decreasing the cosmic ray ionization rate extends the lifetime of the first hydrostatic core up to a factor of 2, but the lifetimes are still substantially shorter than those obtained without magnetic fields. Outflows from the first hydrostatic core phase are launched in all models, but the outflows become broader and slower as the ionization rate is reduced. The outflow morphology following stellar core formation is complex and strongly dependent on the cosmic ray ionization rate. Calculations with high ionization rates quickly produce a fast (≈14 km s−1) bipolar outflow that is distinct from the first core outflow, but with the lowest ionization rate, a slower (≈3−4 km s−1) conical outflow develops gradually and seamlessly merges into the first core outflow.JW and MRB acknowledge support from the European Research Council under the European Commission's Seventh Framework Programme (FP7/2007- 2013 grant agreement no. 339248). DJP and JW were funded by Australian Research Council grants FT130100034 andDP130102078. The calculations for this paper were performed on the University of Exeter Supercomputer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS, and the University of Exeter. We used splash (Price 2007) for the column density figures

Dust coagulation during the early stages of star formation: molecular cloud collapse and first hydrostatic core evolution

This is the author accepted manuscript. The final version is available on open access from Oxford University Press via the DOI in this recordData availability: The data used to produce Figs. 1–9 and Figs. A1 are provided as Additional Supporting Information (see below). The SPH data files that are required to produce Figs. 10–12 and Fig. B1 are available from Bate (2022).Planet formation in protoplanetary discs requires dust grains to coagulate from the sub-micron sizes that are found in the interstellar medium into much larger objects. For the first time, we study the growth of dust grains during the earliest phases of star formation using three-dimensional hydrodynamical simulations. We begin with a typical interstellar dust grain size distribution and study dust growth during the collapse of a molecular cloud core and the evolution of the first hydrostatic core, prior to the formation of the stellar core. We examine how the dust size distribution evolves both spatially and temporarily. We find that the envelope maintains its initial population of small dust grains with little growth during these phases, except that in the inner few hundreds of au the smallest grains are depleted. However, once the first hydrostatic core forms rapid dust growth to sizes in excess of 100μm occurs within the core (before stellar core formation). Progressively larger grains are produced at smaller distances from the centre of the core. In rapidly-rotating molecular cloud cores, the `first hydrostatic core' that forms is better described as a pre-stellar disc that may be gravitationally unstable. In such cases, grain growth is more rapid in the spiral density waves leading to the larger grains being preferentially found in the spiral waves even though there is no migration of grains relative to the gas. Thus, the grain size distribution can vary substantially in the first core/pre-stellar disc even at these very early times.European CommissionNational Science Foundatio

Does turbulence determine the initial mass function?

Published onlineThis is the author accepted manuscript. The final version is available from Oxford University Press via the DOI in this record.We test the hypothesis that the initial mass function (IMF) is determined by the density probability distribution function (PDF) produced by supersonic turbulence. We compare 14 simulations of star cluster formation in 50 M molecular cloud cores where the initial turbulence contains either purely solenoidal or purely compressive modes, in each case resolving fragmentation to the opacity limit to determine the resultant IMF. We find statistically indistinguishable IMFs between the two sets of calculations, despite a factor of 2 difference in the star formation rate and in the standard deviation of log (ρ). This suggests that the density PDF, while determining the star formation rate, is not the primary driver of the IMF.We thank the anonymous referee for comments which have improved the paper. We acknowledge CPU time on gSTAR, funded by Swinburne University and the Australian Government. This project was funded via Australian Research Council Discovery Project DP130102078 and Future Fellowship FT130100034. We used SPLASH (Price 2007)