arXiv subjects

Matthew R. Bate

Publications and source records attributed to Matthew R. Bate.

At least 109 records · Page 6Linked to original sources

arXiv2005

The thermodynamics of collapsing molecular cloud cores using smoothed particle hydrodynamics with radiative transfer

We present the results of a series of calculations studying the collapse of molecular cloud cores performed using a three-dimensional smoothed particle hydr odynamics code with radiative transfer in the flux-limited diffusion approximation. The opacities and specific heat capacities are identical for each calculation. However, we find that the temperature evolution during the simulations varies significantly when starting from different initial conditions. Even spherically-symmetric clouds with different initial densities show markedly different development. We conclude that simple barotropic equations of state like those used in some previous calculations provide at best a crude approximation to the thermal behaviour of the gas. Radiative transfer is necessary to obtain accurate temperatures.

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arXiv2005

A faster algorithm for smoothed particle hydrodynamics with radiative transfer in the flux-limited diffusion approximation

We describe a new, faster implicit algorithm for solving the radiation hydrodynamics equations in the flux-limited diffusion approximation for smoothed particle hydrodynamics. This improves on the method elucidated in Whitehouse & Bate by using a Gauss-Seidel iterative method rather than iterating over the exchange of energy between pairs of particles. The new algorithm is typically many thousands of times faster than the old one, which will enable more complex problems to be solved. The new algorithm is tested using the same tests performed by Turner & Stone for ZEUS-2D, and repeated by Whitehouse & Bate.

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arXiv2005

Binary systems and stellar mergers in massive star formation

We present a model for the formation of high-mass close binary systems in the context of forming massive stars through gas accretion in the centres of stellar clusters. A low-mass wide binary evolves under mass accretion towards a high-mass close binary, attaining system masses of order 30-50 solar masses at separations of order 1 AU. The resulting high frequency of binary systems with two massive components is in agreement with observations. These systems are typically highly eccentric and may evolve to have periastron separations less than their stellar radii. Mergers of these binary systems are therefore likely and can lead to the formation of the most massive stars, circumventing the problem of radiation pressure stopping the accretion. The stellar density required to induce binary mergers is one million stars per cubic parsec, or approximately one percent that required for direct stellar collisions.

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arXiv2005

Star formation in unbound giant molecular clouds: the origin of OB associations?

We investigate the formation of star clusters in an unbound GMC, where the supporting kinetic energy is twice as large as the cloud's self-gravity. This cloud manages to form a series of star clusters and disperse, all within roughly 2 crossing times (10 Myr), supporting recent claims that star formation is a rapid process. Simple assumptions about the nature of the star formation occurring in the clusters allows us to place an estimate for the star formation efficiency at about 5 to 10 %, consistent with observations. We also propose that unbound clouds can act as a mechanism for forming OB associations. The clusters that form in the cloud behave as OB subgroups. These clusters are naturally expanding from one another due to unbound nature of the flows that create them. The properties of the cloud we present here are are consistent with those of classic OB associations.

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arXiv2004

The dependence of protoplanet migration rates on coorbital torques

We investigate the migration rates of high-mass protoplanets embedded in accretion discs via two and three-dimensional hydrodynamical simulations. The simulations follow the planet's radial motion and employ a nested-grid code that allows for high resolution close to the planet. We concentrate on the possible role of the coorbital torques in affecting migration rates. We analyse two cases: (a) a Jupiter-mass planet in a low-mass disc and (b) a Saturn-mass planet in a high-mass disc. Planet migration in case (b) is much more susceptible to coorbital torques than in case (a). We find that the coorbital torques in both cases do not depend sensitively on whether the planet is allowed to migrate through the disc or is held on a fixed orbit. We also examine the dependence of the planet's migration rate on the numerical resolution near the planet. For case (a), numerical convergence is relatively easy to obtain, even when including torques arising from deep within the planet's Hill sphere. The migration rate in this case is numerically on order of the Type II migration rate and much smaller than the Type I rate, if the disc has 0.01 solar-masses inside 26 AU. Torques from within the Hill sphere provide a substantial opposing contribution to the migration rate. In case (b), the gas mass within the Hill sphere is larger than the planet's mass and convergence is more difficult to obtain. If the torques within the Hill sphere are ignored, convergence is more easily achieved but the migration rate is artificially large. At our highest resolution, the migration rate for case (b) is much less than the Type I rate, but somewhat larger than the Type II rate.

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arXiv2004

The Origin of the Initial Mass Function and Its Dependence on the Mean Jeans Mass in Molecular Clouds

We investigate the dependence of stellar properties on the mean thermal Jeans mass in molecular clouds. We compare the results from the two largest hydrodynamical simulations of star formation to resolve the fragmentation process down to the opacity limit, the first of which was reported by Bate, Bonnell & Bromm. The initial conditions of the two calculations are identical except for the radii of the clouds, which are chosen so that the mean densities and mean thermal Jeans masses of the clouds differ by factors of nine and three, respectively. We find that the denser cloud, with the lower mean thermal Jeans mass, produces a higher proportion of brown dwarfs and has a lower characteristic (median) mass of the stars and brown dwarfs. This dependence of the initial mass function (IMF) on the density of the cloud may explain the observation that the Taurus star-forming region appears to be deficient in brown dwarfs when compared with the Orion Trapezium cluster. The new calculation also produces wide binaries (separations >20 AU), one of which is a wide binary brown dwarf system. Based on the hydrodynamical calculations, we develop a simple accretion/ejection model for the origin of the IMF. In the model, all stars and brown dwarfs begin with the same mass (set by the opacity limit for fragmentation) and grow in mass until their accretion is terminated stochastically by their ejection from the cloud through dynamically interactions. The model predicts that the main variation of the IMF in different star-forming environments should be in the location of the peak (due to variations in the mean thermal Jeans mass of the cloud) and in the substellar regime. However, the slope of the IMF at high-masses may depend on the dispersion in the accretion rates of protostars.

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arXiv2004

Smoothed particle hydrodynamics with radiative transfer in the flux-limited diffusion approximation

We describe the implementation and testing of a smoothed particle hydrodynamics (SPH) code that solves the equations of radiation hydrodynamics in the flux-limited diffusion (FLD) approximation. The SPH equations of radiation hydrodynamics for an explicit integration scheme are derived and tested. We also discuss the implementation of an implicit numerical scheme for solving the radiation equations that allows the system to be evolved using timesteps much longer than the explicit radiation timestep. The code is tested on a variety of one-dimensional radiation hydrodynamics problems including radiation propagating in an optically thin medium, optically thick and thin shocks, subcritical and supercritical radiating shocks, and a radiation dominated shock. Many of the tests were also performed by Turner and Stone (2001) to test their implementation of a FLD module for the ZEUS-2D code. The SPH code performs at least as well as the ZEUS-2D code in these tests.

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arXiv2004

Synthetic infrared images and spectral energy distributions of a young low-mass stellar cluster

We present three-dimensional Monte Carlo radiative transfer models of a very young (<10^5 years old) low mass (50 Msun) stellar cluster containing 23 stars and 27 brown dwarfs. The models use the density and the stellar mass distributions from the large-scale smoothed particle hydrodynamics (SPH) simulation of the formation of a low-mass stellar cluster by Bate, Bonnell and Bromm. We compute the spectral energy distributions of the whole cluster and the individual objects, simulated far-infrared Spitzer Space Telescope (SST) images and construct colour-colour diagrams (near-infrared HKL and SST mid-infrared bands). The presence of accretion discs around the light sources influences the morphology of the dust temperature structure on a large scale (up to a several 10^4 au). A considerable fraction of the interstellar dust is underheated compared to a model without the accretion discs because the radiation from the light sources is blocked/shadowed by the discs. The spectral energy distribution (SED) of the model cluster with accretion discs shows excess emission at lambda = 3-30 micron and lambda > 500 micron compared to that without accretion discs. Our model with accretion discs around each object shows a similar distribution of spectral index (2.2-20 micron) values (i.e. Class 0--III sources) as seen in the Rho Ophiuchus cloud. We confirm that the best diagnostics for identifying objects with accretion discs are mid-infrared (lambda = 3-10 micron) colours (e.g. SST IRAC bands) rather than HKL colours.

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arXiv2003

The hierarchical formation of a stellar cluster

Recent surveys of star forming regions have shown that most stars, and probably all massive stars, are born in dense stellar clusters. The mechanism by which a molecular cloud fragments to form several hundred to thousands of individual stars has remained elusive. Here, we use a numerical simulation to follow the fragmentation of a turbulent molecular cloud and the subsequent formation and early evolution of a stellar cluster containing more than 400 stars. We show that the stellar cluster forms through the hierarchical fragmentation of a turbulent molecular cloud. This leads to the formation of many small subclusters which interact and merge to form the final stellar cluster. The hierarchical nature of the cluster formation has serious implications in terms of the properties of the new-born stars. The higher number-density of stars in subclusters, compared to a more uniform distribution arising from a monolithic formation, results in closer and more frequent dynamical interactions. Such close interactions can truncate circumstellar discs, harden existing binaries, and potentially liberate a population of planets. We estimate that at least one-third of all stars, and most massive stars, suffer such disruptive interactions.

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arXiv2002

The Formation of Close Binary Systems by Dynamical Interactions and Orbital Decay

We present results from the first hydrodynamical star formation calculation to demonstrate that close binary stellar systems (separations $\lsim 10$ AU) need not be formed directly by fragmentation. Instead, a high frequency of close binaries can be produced through a combination of dynamical interactions in unstable multiple systems and the orbital decay of initially wider binaries. Orbital decay may occur due to gas accretion and/or the interaction of a binary with its circumbinary disc. These three mechanisms avoid the problems associated with the fragmentation of optically-thick gas to form close systems directly. They also result in a preference for close binaries to have roughly equal-mass components because dynamical exchange interactions and the accretion of gas with high specific angular momentum drive mass ratios towards unity. Furthermore, due to the importance of dynamical interactions, we find that stars with greater masses ought to have a higher frequency of close companions, and that many close binaries ought to have wide companions. These properties are in good agreement with the results of observational surveys.

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arXiv2002

The Formation of a Star Cluster: Predicting the Properties of Stars and Brown Dwarfs

We present results from the largest numerical simulation of star formation to resolve the fragmentation process down to the opacity limit. The simulation follows the collapse and fragmentation of a large-scale turbulent molecular cloud to form a stellar cluster and, simultaneously, the formation of circumstellar discs and binary stars. This large range of scales enables us to predict a wide variety of stellar properties for comparison with observations. The calculation clearly demonstrates that star formation is a highly-dynamic and chaotic process. Star-disc encounters form binaries and truncate discs. Stellar encounters disrupt bound multiple systems. The cloud produces roughly equal numbers of stars and brown dwarfs, with masses down to the opacity limit for fragmentation (~5 Jupiter masses). The initial mass function is consistent with a Salpeter slope (Gamma=-1.35) above 0.5 Msun, a roughly flat distribution (Gamma=0) in the range 0.006-0.5 Msun, and a sharp cutoff below ~0.005 Msun. This is consistent with recent observational surveys. The brown dwarfs form by the dynamical ejection of low-mass fragments from dynamically unstable multiple systems before the fragments have been able to accrete to stellar masses. Close binary systems (with separations <10 AU) are not formed by fragmentation in situ. Rather, they are produced by hardening of initially wider multiple systems through a combination of dynamical encounters, gas accretion, and/or the interaction with circumbinary and circumtriple discs. Finally, we find that the majority of circumstellar discs have radii less than 20 AU due to truncation in dynamical encounters. This is consistent with observations of the Orion Trapezium Cluster and implies that most stars and brown dwarfs do not form large planetary systems.

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arXiv2002

Interactions of High and Low-Mass Planets with Protoplanetary Disks

We present three-dimensional numerical simulations of the interaction of a circular-orbit planet with a protoplanetary disk. We calculate the flow pattern, the accretion rate, and torques on the planet. We consider planet masses ranging from 1 Earth mass to 1 Jupiter mass.

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arXiv2002

The Formation Mechanism of Brown Dwarfs

We present results from the first hydrodynamical star formation calculation to demonstrate that brown dwarfs are a natural and frequent product of the collapse and fragmentation of a turbulent molecular cloud. The brown dwarfs form via the fragmentation of dense molecular gas in unstable multiple systems and are ejected from the dense gas before they have been able to accrete to stellar masses. Thus, they can be viewed as `failed stars'. Approximately three quarters of the brown dwarfs form in gravitationally-unstable circumstellar discs while the remainder form in collapsing filaments of molecular gas. These formation mechanisms are very efficient, producing roughly the same number of brown dwarfs as stars, in agreement with recent observations. However, because close dynamical interactions are involved in their formation, we find a very low frequency of binary brown dwarf systems ($\lsim 5$%) and that those binary brown dwarf systems that do exist must be close $\lsim 10$ AU. Similarly, we find that young brown dwarfs with large circumstellar discs (radii $\gsim 10$ AU) are rare ($\approx 5$%).

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arXiv2000

Recent Advances in Binary Star Formation Using SPH

We review recent advances in the study of binary star formation that have been made using the smoothed particle hydrodynamics (SPH) technique. We discuss the importance of ensuring that the Jeans mass is always resolved during a self-gravitating SPH calculation. Even obeying this criterion, we show that it is now possible to perform calculations which follow the collapse of a molecular cloud core all the way to stellar densities. These calculations resolve 7 orders of magnitude in spatial extent and 17 orders of magnitude in density contrast. Finally, we discuss the progress that has been made in understanding the mass-ratio distributions of binary stellar systems by studying the evolution of protobinary systems as they accrete gas from their surrounding envelopes.

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arXiv2000

Predicting the Properties of Binary Stellar Systems: The Evolution of Accreting Protobinary Systems

We investigate the formation of binary stellar systems. We consider a model where a `seed' protobinary system forms, via fragmentation, within a collapsing molecular cloud core and evolves to its final mass by accreting material from an infalling gaseous envelope. This accretion alters the mass ratio and orbit of the binary, and is largely responsible for forming the circumstellar and/or circumbinary discs. Given this model for binary formation, we predict the properties of binary systems and how they depend on the initial conditions within the molecular cloud core. We predict that there should be a continuous trend such that closer binaries are more likely to have equal mass components and are more likely to have circumbinary discs than wider systems. Comparing our results to observations, we find that the observed mass-ratio distributions of binaries and the frequency of circumbinary discs as a function of separation are most easily reproduced if the progenitor molecular cloud cores have radial density profiles between uniform and 1/r (e.g. Gaussian) with near uniform-rotation. This is in good agreement with the observed properties of pre-stellar cores. Conversely, we find that the observed properties of binaries cannot be reproduced if the cloud cores are in solid-body rotation and have initial density profiles which are strongly centrally condensed. Finally, in agreement with the radial-velocity searches for extra-solar planets, we find that it is very difficult to form a brown dwarf companion to a solar-type star with a separation < 10 AU, but that the frequency of brown dwarf companions should increase with larger separations or lower mass primaries.

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arXiv1998

Collapse of a Molecular Cloud Core to Stellar Densities: The First Three-Dimensional Calculations

We present results from the first three-dimensional calculations ever to follow the collapse of a molecular cloud core (~ 10^{-18} g cm^{-3}) to stellar densities (> 0.01 g cm^{-3}). The calculations resolve structures over 7 orders of magnitude in spatial extent (~ 5000 AU - 0.1 R_\odot), and over 17 orders of magnitude in density contrast. With these calculations, we consider whether fragmentation to form a close binary stellar system can occur during the second collapse phase. We find that, if the quasistatic core that forms before the second collapse phase is dynamically unstable to the growth of non-axisymmetric perturbations, the angular momentum extracted from the central regions of the core, via gravitational torques, is sufficient to prevent fragmentation and the formation of a close binary during the subsequent second collapse.

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arXiv1998

Fragmentation of Molecular Clouds: The Initial Phase of a Stellar Cluster

The isothermal gravitational collapse and fragmentation of a region within a molecular cloud and the subsequent formation of a protostellar cluster is investigated numerically. The clump mass spectrum which forms during the fragmentation phase can be well approximated by a power law distribution dN/dM ~ M^(-1.5). In contrast, the mass spectrum of protostellar cores that form in the centers of Jeans-unstable clumps and evolve through accretion and N-body interactions is described by a log-normal distribution with a width that is in excellent agreement with observations of multiple stellar systems.

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arXiv1998

Interpreting the Mean Surface Density of Companions in Star-Forming Regions

We study the interpretation of the mean surface density of stellar companions as a function of separation (or the two point correlation function of stars) in star-forming regions. First, we consider the form of the functions for various simple stellar distributions (binaries, global density profiles, clusters, and fractals) and the effects of survey boundaries. Following this, we study the dependencies of the separation at which a transition from the binary to the large-scale clustering regime occurs. Larson (1995) found that the mean surface density of companions follows different power-law functions of separation in the two regimes. He identified the transition separation with the typical Jeans length in the molecular cloud. However, we show that this is valid only for special cases. In general, the transition separation depends on the volume density of stars, the depth of the star-forming region, the volume-filling nature of the stellar distribution, and on the parameters of the binaries. Furthermore, the transition separation evolves with time. We then apply these results to the Taurus-Auriga, Ophiuchus, and Orion Trapezium star-forming regions. We find that while the transition separation in the Taurus-Auriga star-forming region may indicate a typical Jeans length, this is not true of the Orion Trapezium Cluster. We also show that there is no evidence for sub-clustering or fractal structure in the stars of the Orion Trapezium Cluster. This is consistent with the fact that, if such structure were present when the stars formed, it would have been erased by the current age of the cluster due to the stellar velocity dispersion. [Abstract abridged]

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