arXiv subjects

Matthew R. Bate

Publications and source records attributed to Matthew R. Bate.

At least 73 records · Page 4Linked to original sources

arXiv2014

Star Cluster Formation and Feedback

Stars do not generally form in isolation. Instead, they form in clusters, and in these clustered environments newborn stars can have profound effects on one another and on their parent gas clouds. Feedback from clustered stars is almost certainly responsible for a number of otherwise puzzling facts about star formation: that it is an inefficient process that proceeds slowly when averaged over galactic scales; that most stars disperse from their birth sites and dissolve into the galactic field over timescales $\ll 1$ Gyr; and that newborn stars follow an initial mass function (IMF) with a distinct peak in the range $0.1 - 1$ $M_\odot$, rather than an IMF dominated by brown dwarfs. In this review we summarize current observational constraints and theoretical models for the complex interplay between clustered star formation and feedback.

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arXiv2013

Smoothed Particle Magnetohydrodynamics Simulations of Protostellar Jets and Turbulent Dynamos

We presents results from Smoothed Particle Magnetohydrodynamics simulations of collapsing molecular cloud cores, and dynamo amplification of the magnetic field in the presence of Mach 10 magnetised turbulence. Our star formation simulations have produced, for the first time ever, highly collimated magnetised protostellar jets from the first hydrostatic core phase. Up to 40% of the initial core mass may be ejected through this outflow. The primary difficulty in performing these simulations is maintaining the divergence free constraint of the magnetic field, and to address this issue, we have developed a new divergence cleaning method which has allowed us to stably follow the evolution of these protostellar jets for long periods. The simulations performed of supersonic MHD turbulence are able to exponentially amplify magnetic energy by up to 10 orders of magnitude via turbulent dynamo. To reduce numerical dissipation, a new shock detection algorithm is utilised which is able to track magnetic shocks throughout a large range of magnetic field strengths.

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arXiv2013

Collapse of a molecular cloud core to stellar densities: stellar core and outflow formation in radiation magnetohydrodynamics simulations

We have performed smoothed particle radiation magnetohydrodynamics (SPRMHD) simulations of the collapse of rotating, magnetised molecular cloud cores to form protostars. The calculations follow the formation and evolution of the first hydrostatic core, the collapse to form a stellar core, the launching of outflows from both the first hydrostatic core and stellar cores, and the breakout of the stellar outflow from the remnant of the first core. We investigate the roles of magnetic fields and thermal feedback on the outflow launching process, finding that both magnetic and thermal forces contribute to the launching of the stellar outflow. We also follow the stellar cores until they grow to masses of up to 20 Jupiter-masses, and determine their properties. We find that at this early stage, before fusion begins, the stellar cores have radii of $\approx 3$ R$_\odot$ with radial entropy profiles that increase outward (i.e. are convectively stable) and minimum entropies per baryon of $s/k_{\rm B} \approx 14$ in their interiors. The structure of the stellar cores is found to be insensitive to variations in the initial magnetic field strength. With reasonably strong initial magnetic fields, accretion on to the stellar cores occurs through inspiralling magnetised pseudo-discs with negligible radiative losses, as opposed to first cores which effectively radiate away the energy liberated in the accretion shocks at their surfaces. We find that magnetic field strengths of >10 kG can be implanted in stellar cores at birth.

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arXiv2012

On the convergence of the critical cooling timescale for the fragmentation of self-gravitating discs

We carry out simulations of gravitationally unstable discs using a Smoothed Particle Hydrodynamics (SPH) code and a grid-based hydrodynamics code, FARGO, to understand the previous non-convergent results reported by Meru & Bate (2011a). We obtain evidence that convergence with increasing resolution occurs with both SPH and FARGO and in both cases we find that the critical cooling timescale is larger than previously thought. We show that SPH has a first-order convergence rate while FARGO converges with a second-order rate. We show that the convergence of the critical cooling timescale for fragmentation depends largely on the numerical viscosity employed in both SPH and FARGO. With SPH, particle velocity dispersion may also play a role. We show that reducing the dissipation from the numerical viscosity leads to larger values of the critical cooling time at a given resolution. For SPH, we find that the effect of the dissipation due to the numerical viscosity is somewhat larger than had previously been appreciated. In particular, we show that using a quadratic term in the SPH artificial viscosity (beta_{SPH}) that is too low appears to lead to excess dissipation in gravitationally unstable discs, which may affect any results that sensitively depend on the thermodynamics, such as disc fragmentation. We show that the two codes converge to values of the critical cooling timescale, beta_{crit} > 20 (for a ratio of specific heats of gamma=5/3), and perhaps even as large as beta_{crit} \approx 30. These are approximately 3-5 times larger than has been found by most previous studies. This is equivalent to a maximum gravitational stress that a disc can withstand without fragmenting of alpha_{GI,crit} \approx 0.013-0.02, which is much smaller than the values typically used in the literature. It is therefore easier for self-gravitating discs to fragment than has been concluded from most past studies.

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arXiv2012

The growth and hydrodynamic collapse of a protoplanet envelope

We have conducted three-dimensional self-gravitating radiation hydrodynamical models of gas accretion onto high mass cores (15-33 Earth masses) over hundreds of orbits. Of these models, one case accretes more than a third of a Jupiter mass of gas, before eventually undergoing a hydrodynamic collapse. This collapse causes the density near the core to increase by more than an order of magnitude, and the outer envelope to evolve into a circumplanetary disc. A small reduction in the mass within the Hill radius (R_H) accompanies this collapse as a shock propagates outwards. This collapse leads to a new hydrostatic equilibrium for the protoplanetary envelope, at which point 97 per cent of the mass contained within the Hill radius is within the inner 0.03 R_H which had previously contained less than 40 per cent. Following this collapse the protoplanet resumes accretion at its prior rate. The net flow of mass towards this dense protoplanet is predominantly from high latitudes, whilst at the outer edge of the circumplanetary disc there is net outflow of gas along the midplane. We also find a turnover of gas deep within the bound envelope that may be caused by the establishment of convection cells.

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arXiv2012

On the accumulation of planetesimals near disc gaps created by protoplanets

We have performed three-dimensional two-fluid (gas-dust) hydrodynamical models of circumstellar discs with embedded protoplanets (3 - 333 M\oplu) and small solid bodies (radii 10cm to 10m). We find that high mass planets (\gtrsim Saturn mass) open sufficiently deep gaps in the gas disc such that the density maximum at the outer edge of the gap can very efficiently trap metre-sized solid bodies. This allows the accumulation of solids at the outer edge of the gap as solids from large radii spiral inwards to the trapping region. This process of accumulation occurs fastest for those bodies that spiral inwards most rapidly, typically metre-sized boulders, whilst smaller and larger objects will not migrate sufficiently rapidly in the discs lifetime to benefit from the process. Around a Jupiter mass planet we find that bound clumps of solid material, as large as several Earth masses, may form, potentially collapsing under self-gravity to form planets or planetesimals. These results are in agreement with Lyra et al. (2009), supporting their finding that the formation of a second generation of planetesimals or of terrestrial mass planets may be triggered by the presence of a high mass planet.

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arXiv2012

Collimated jets from the first core

We have performed Smoothed Particle Magnetohydrodynamics (SPMHD) simulations demonstrating the production of collimated jets during collapse of 1 solar mass molecular cloud cores to form the `first hydrostatic core' in low mass star formation. Recently a number of candidate first core objects have been observed, including L1448 IRS2E, L1451-mm and Per Bolo 58, although it is not yet clear that these are first hydrostatic cores. Recent observations of Per Bolo 58 in particular appear to show collimated, bipolar outflows which are inconsistent with previous theoretical expectations. We show that low mass first cores can indeed produce tightly collimated jets (opening angles <~ 10 degrees) with speeds of ~2-7 km/s, consistent with some of the observed candidates. We have also demonstrated, for the first time, that such phenomena can be successfully captured in SPMHD simulations.

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arXiv2011

Stellar, brown dwarf and multiple star properties from a radiation hydrodynamical simulation of star cluster formation

We report the statistical properties of stars, brown dwarfs and multiple systems obtained from the largest radiation hydrodynamical simulation of star cluster formation to date that resolves masses down to the opacity limit for fragmentation (a few Jupiter masses). The initial conditions are identical to those of previous barotropic calculations published by Bate, but this time the calculation is performed using a realistic equation of state and radiation hydrodynamics. The calculation uses sink particles to model 183 stars and brown dwarfs, including 28 binaries and 12 higher-order multiple systems, the properties of which are compared the results from observational surveys. We find that the radiation hydrodynamical/sink particle simulation reproduces many observed stellar properties very well. In particular, whereas using a barotropic equation of state produces more brown dwarfs than stars, the inclusion of radiative feedback results in a stellar mass function and a ratio of brown dwarfs to stars in good agreement with observations of Galactic star-forming regions. In addition, many of the other statistical properties of the stars and brown dwarfs are in reasonable agreement with observations, including multiplicity as a function of primary mass, the frequency of very-low-mass binaries, and general trends for the mass ratio and separation distributions of binaries. We also examine the velocity dispersion of the stars, the distributions of disc truncation radii due to dynamical interactions, and coplanarity of orbits and sink particle spins in multiple systems. Overall, the calculation produces a cluster of stars whose statistical properties are difficult to distinguish from observed systems, implying that gravity, hydrodynamics, and radiative feedback are the primary ingredients for determining the origin of the statistical properties of low-mass stars.

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arXiv2011

Collapse of a molecular cloud core to stellar densities: the formation and evolution of pre-stellar discs

We report results from radiation hydrodynamical simulations of the collapse of molecular cloud cores to form protostars. The calculations follow the formation and evolution of the first hydrostatic core/disc, the collapse to form a stellar core, and effect of stellar core formation on the surrounding disc and envelope. Past barotropic calculations have shown that rapidly-rotating first cores evolve into `pre-stellar discs' with radii up to ~100 AU that may last thousands of years before a stellar core forms. We investigate how the inclusion of a realistic equation of state and radiative transfer alters this behaviour, finding that the qualitative behaviour is similar, but that the pre-stellar discs may last 1.5-3 times longer in the more realistic calculations. The masses, radii, and lifetimes of the discs increase for initial molecular cloud cores with faster rotation rates. In the most extreme case we model, a pre-stellar disc with a mass of 0.22 Msun and a radius of ~100 AU can form in a solar-mass cloud and last several thousand years before a stellar core is formed. Such large, massive objects may be imaged using ALMA. Fragmentation of these massive discs may also provide an effective route to binary and multiple star formation, before radiative feedback from accretion onto the stellar core can inhibit fragmentation. Once collapse to form a stellar core occurs within the pre-stellar disc, the radiation hydrodynamical simulations produce qualitatively different behaviour from the barotropic calculations due to the accretion energy released. This drives a shock wave through the circumstellar disc and launches a bipolar outflow even in the absence of magnetic fields.

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arXiv2011

Migration of protoplanets with surfaces through discs with steep temperature gradients

We perform three-dimensional self-gravitating radiative transfer simulations of protoplanet migration in circumstellar discs to explore the impact upon migration of the radial temperature profiles in these discs. We model protoplanets with masses ranging between 10-100 M\bigoplus, in discs with surface density profiles of Σ \varpropto r^-1/2, and temperature profiles of the form T \varpropto r^-β, where β ranges 0-2. We find that steep (β > 1) temperature profiles lead to outward migration of low mass protoplanets in interstellar grain opacity discs, but in more optically thin discs the migration is always inwards. The trend in migration rates with changing β obtained from our models shows good agreement with those obtained using recent analytic descriptions which include consideration of the co-orbital torques and their saturation. We find that switching between two models of the protoplanet, one in which accretion acts by evacuating gas and one in which gas piles up on a surface to form an atmosphere, leads to a small shift in the migration rates. If comparing these models in discs with conditions which lead to a marginally inward migration, the small shift can lead to outward migration. However, the direction and speed of migration is dominated by disc conditions rather than by the specific prescription used to model the flow near the protoplanet.

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arXiv2010

Non-convergence of the critical cooling timescale for fragmentation of self-gravitating discs

We carry out a resolution study on the fragmentation boundary of self-gravitating discs. We perform three-dimensional Smoothed Particle Hydrodynamics (SPH) simulations of discs to determine whether the critical value of the cooling timescale in units of the orbital timescale, beta_{crit}, converges with increasing resolution. Using particle numbers ranging from 31,250 to 16 million (the highest resolution simulations to date) we do not find convergence. Instead, fragmentation occurs for longer cooling timescales as the resolution is increased. These results certainly suggest that beta_{crit} is larger than previously thought. However, the absence of convergence also questions whether or not a critical value exists. In light of these results, we caution against using cooling timescale or gravitational stress arguments to deduce whether gravitational instability may or may not have been the formation mechanism for observed planetary systems.

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arXiv2010

Non-convergence of the critical cooling timescale for fragmentation of self-gravitating discs

We carry out a resolution study on the fragmentation boundary of self-gravitating discs. We perform three-dimensional Smoothed Particle Hydrodynamics simulations of discs to determine whether the critical value of the cooling timescale in units of the orbital timescale, beta_{crit}, converges with increasing resolution. Using particle numbers ranging from 31,250 to 16 million (the highest resolution simulations to date) we do not find convergence. Instead, fragmentation occurs for longer cooling timescales as the resolution is increased. These results suggest that at the very least, the critical value of the cooling timescale is longer than previously thought. However, the absence of convergence also raises the question of whether or not a critical value exists. In light of these results, we caution against using cooling timescale or gravitational stress arguments to deduce whether gravitational instability may or may not have been the formation mechanism for observed planetary systems.

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arXiv2010

The efficiency of star formation in clustered and distributed regions

We investigate the formation of both clustered and distributed populations of young stars in a single molecular cloud. We present a numerical simulation of a 10,000 solar mass elongated, turbulent, molecular cloud and the formation of over 2500 stars. The stars form both in stellar clusters and in a distributed mode which is determined by the local gravitational binding of the cloud. A density gradient along the major axis of the cloud produces bound regions that form stellar clusters and unbound regions that form a more distributed population. The initial mass function also depends on the local gravitational binding of the cloud with bound regions forming full IMFs whereas in the unbound, distributed regions the stellar masses cluster around the local Jeans mass and lack both the high-mass and the low-mass stars. The overall efficiency of star formation is ~ 15 % in the cloud when the calculation is terminated, but varies from less than 1 % in the the regions of distributed star formation to ~ 40 % in regions containing large stellar clusters. Considering that large scale surveys are likely to catch clouds at all evolutionary stages, estimates of the (time-averaged) star formation efficiency for the giant molecular cloud reported here is only ~ 4 %. This would lead to the erroneous conclusion of 'slow' star formation when in fact it is occurring on a dynamical timescale.

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arXiv2010

On the fragmentation criteria of self-gravitating protoplanetary discs

We investigate the fragmentation criterion in massive self-gravitating discs. We present new analysis of the fragmentation conditions which we test by carrying out global three-dimensional numerical simulations. Whilst previous work has placed emphasis on the cooling timescale in units of the orbital timescale, β, we find that at a given radius the surface mass density (i.e. disc mass and profile) and star mass also play a crucial role in determining whether a disc fragments or not as well as where in the disc fragments form. We find that for shallow surface mass density profiles (p<2, where Σ\propto R^{-p}), fragments form in the outer regions of the disc. However for steep surface mass density profiles (p \gtrsim 2), fragments form in the inner regions of a disc. In addition, we also find that the critical value of the cooling timescale in units of the orbital timescale found in previous simulations is only applicable to certain disc surface mass density profiles and for particular disc radii and is not a general rule for all discs. We find an empirical fragmentation criteria between the cooling timescale in units of the orbital timescale, β, the surface mass density, the star mass and the radius.

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arXiv2010

Planet migration: self-gravitating radiation hydrodynamical models of protoplanets with surfaces

We calculate radial migration rates of protoplanets in laminar minimum mass solar nebula discs using three-dimensional self-gravitating radiation hydrodynamical (RHD) models. The protoplanets are free to migrate, whereupon their migration rates are measured. For low mass protoplanets (10-50 M_\oplus) we find increases in the migration timescales of up to an order of magnitude between locally-isothermal and RHD models. In the high-mass regime the migration rates are changed very little. These results are arrived at by calculating migration rates in locally-isothermal models, before sequentially introducing self-gravity, and radiative transfer, allowing us to isolate the effects of the additional physics. We find that using a locally-isothermal equation of state, without self-gravity, we reproduce the migration rates obtained by previous analytic and numerical models. We explore the impact of different protoplanet models, and changes to their assumed radii, upon migration. The introduction of self-gravity gives a slight reduction of the migration rates, whilst the inertial mass problem, which has been proposed for high mass protoplanets with circumplanetary discs, is reproduced. Upon introducing radiative transfer to models of low mass protoplanets (\approx 10 M_\oplus), modelled as small radius accreting point masses, we find outward migration with a rate of approximately twice the analytic inward rate. However, when modelling such a protoplanet in a more realistic manner, with a surface which enables the formation of a deep envelope, this outward migration is not seen.

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arXiv2010

Three-dimensional molecular line transfer: A simulated star-forming region

We present the first non-LTE, co-moving frame molecular line calculations of a star-forming cluster simulated using smoothed particle hydrodynamics (SPH), from which we derive high-resolution synthetic observations. We have resampled a particle representation onto an adaptive mesh and self-consistently solved the equations of statistical equilibrium in the co-moving frame, using TORUS, a three-dimensional adaptive mesh refined (AMR) radiative transfer (RT) code. We verified the applicability of the code to the conditions of the SPH simulation by testing its output against other codes. We find that the level populations obtained for optically thick and thin scenarios closely match the ensemble average of the other codes. We have used the code to obtain non-LTE level populations of multiple molecular species throughout the cluster and have created three-dimensional velocity-resolved spatial maps of the emergent intensity. Line profiles of cores traced by N2H+ (1-0) are compared to probes of low density gas, 13CO (1-0) and C18O (1-0), surrounding the cores along the line of sight. The relative differences of the line-centre velocities are shown to be small compared to the velocity dispersion, matching recent observations. We conclude that one cannot reject competitive accretion as a viable theory of star formation based on observed velocity profiles.

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arXiv2010

Stellar and brown dwarf properties from numerical simulations

We review the statistical properties of stars and brown dwarfs obtained from the first hydrodynamical simulation of star cluster formation to produce more than a thousand stars and brown dwarfs while simultaneously resolving the lowest mass brown dwarfs (those with masses set by the opacity limit for fragmentation), binaries with separations down to 1 AU, and discs with radii greater than 10 AU. In particular, we present the eccentricity distribution of the calculation's very-low-mass and brown dwarf binaries which has not been previously published.

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arXiv2010

Exploring the conditions required to form giant planets via gravitational instability in massive protoplanetary discs

We carry out global three-dimensional radiation hydrodynamical simulations of self-gravitating accretion discs to determine if, and under what conditions, a disc may fragment to form giant planets. We explore the parameter space (in terms of the disc opacity, temperature and size) and include the effect of stellar irradiation. We find that the disc opacity plays a vital role in determining whether a disc fragments. Specifically, opacities that are smaller than interstellar Rosseland mean values promote fragmentation (even at small radii, R < 25AU) since low opacities allow a disc to cool quickly. This may occur if a disc has a low metallicity or if grain growth has occurred. With specific reference to the HR 8799 planetary system, given its star is metal-poor, our results suggest that the formation of its imaged planetary system could potentially have occurred by gravitational instability. We also find that the presence of stellar irradiation generally acts to inhibit fragmentation (since the discs can only cool to the temperature defined by stellar irradiation). However, fragmentation may occur if the irradiation is sufficiently weak that it allows the disc to attain a low Toomre stability parameter.

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