arXiv subjects

Daniel J. Price

Publications and source records attributed to Daniel J. Price.

At least 181 records · Page 10Linked to original sources

arXiv2014

Dusty gas with one fluid

In this paper, we show how the two-fluid equations describing the evolution of a dust and gas mixture can be reformulated to describe a single fluid moving with the barycentric velocity of the mixture. This leads to evolution equations for the total density, momentum, the differential velocity between the dust and the gas phases and either the dust-to-gas ratio or the dust fraction. The equations are similar to the usual equations of gas dynamics, providing a convenient way to extend existing codes to simulate two-fluid mixtures without modifying the code architecture. Our approach avoids the inherent difficulties related to the standard approach where the two phases are separate and coupled via a drag term. In particular, the requirements of infinite spatial and temporal resolution as the stopping time tends to zero are no longer necessary. This means that both small and large grains can be straightforwardly treated with the same method, with no need for complicated implicit schemes. Since there is only one resolution scale the method also avoids the problem of unphysical trapping of one fluid (e.g. dust) below the resolution of the other. We also derive a simplified set of equations applicable to the case of strong drag/small grains, consisting of the standard fluid equations with a modified sound speed, plus an advection-diffusion equation for the dust-to-gas ratio. This provides a simple and fast way to evolve the mixture when the stopping time is smaller than the Courant timestep. We present a Smoothed Particle Hydrodynamics implementation in a companion paper.

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arXiv2014

Dusty gas with one fluid in smoothed particle hydrodynamics

In a companion paper we have shown how the equations describing gas and dust as two fluids coupled by a drag term can be reformulated to describe the system as a single fluid mixture. Here we present a numerical implementation of the one-fluid dusty gas algorithm using Smoothed Particle Hydrodynamics (SPH). The algorithm preserves the conservation properties of the SPH formalism. In particular, the total gas and dust mass, momentum, angular momentum and energy are all exactly conserved. Shock viscosity and conductivity terms are generalised to handle the two-phase mixture accordingly. The algorithm is benchmarked against a comprehensive suit of problems: dustybox, dustywave, dustyshock and dustyoscill, each of them addressing different properties of the method. We compare the performance of the one-fluid algorithm to the standard two-fluid approach. The one-fluid algorithm is found to solve both of the fundamental limitations of the two- fluid algorithm: it is no longer possible to concentrate dust below the resolution of the gas (they have the same resolution by definition), and the spatial resolution criterion h < csts, required in two-fluid codes to avoid over-damping of kinetic energy, is unnecessary. Implicit time stepping is straightforward. As a result, the algorithm is up to ten billion times more efficient for 3D simulations of small grains. Additional benefits include the use of half as many particles, a single kernel and fewer SPH interpolations. The only limitation is that it does not capture multi-streaming of dust in the limit of zero coupling, suggesting that in this case a hybrid approach may be required.

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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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arXiv2013

A switch to reduce resistivity in smoothed particle magnetohydrodynamics

Artificial resistivity is included in Smoothed Particle Magnetohydrodynamics simulations to capture shocks and discontinuities in the magnetic field. Here we present a new method for adapting the strength of the applied resistivity so that shocks are captured but the dissipation of the magnetic field away from shocks is minimised. Our scheme utilises the gradient of the magnetic field as a shock indicator, setting α_B = h|gradB|/|B|, such that resistivity is switched on only where strong discontinuities are present. The advantage to this approach is that the resistivity parameter does not depend on the absolute field strength. The new switch is benchmarked on a series of shock tube tests demonstrating its ability to capture shocks correctly. It is compared against a previous switch proposed by Price & Monaghan (2005), showing that it leads to lower dissipation of the field, and in particular, that it succeeds at capturing shocks in the regime where the Alfvén speed is much less than the sound speed (i.e., when the magnetic field is very weak). It is also simpler. We also demonstrate that our recent constrained divergence cleaning algorithm has no difficulty with shock tube tests, in contrast to other implementations.

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arXiv2013

Wave-like warp propagation in circumbinary discs I. Analytic theory and numerical simulations

In this paper we analyse the propagation of warps in protostellar circumbinary discs. We use these systems as a test environment in which to study warp propagation in the bending-wave regime, with the addition of an external torque due to the binary gravitational potential. In particular, we want to test the linear regime, for which an analytic theory has been developed. In order to do so, we first compute analytically the steady state shape of an inviscid disc subject to the binary torques. The steady state tilt is a monotonically increasing function of radius. In the absence of viscosity, the disc does not present any twist. Then, we compare the time-dependent evolution of the warped disc calculated via the known linearised equations both with the analytic solutions and with full 3D numerical simulations, which have been performed with the PHANTOM SPH code using 2 million particles. We find a good agreement both in the tilt and in the phase evolution for small inclinations, even at very low viscosities. Moreover, we have verified that the linearised equations are able to reproduce the diffusive behaviour when α > H/R, where α is the disc viscosity parameter. Finally, we have used the 3D simulations to explore the non-linear regime. We observe a strongly non-linear behaviour, which leads to the breaking of the disc. Then, the inner disc starts precessing with its own precessional frequency. This behaviour has already been observed with numerical simulations in accretion discs around spinning black holes. The evolution of circumstellar accretion discs strongly depends on the warp evolution. Therefore the issue explored in this paper could be of fundamental importance in order to understand the evolution of accretion discs in crowded environments, when the gravitational interaction with other stars is highly likely, and in multiple systems.

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arXiv2013

Evidence for accretion rate change during type I X-ray bursts

The standard approach for time-resolved X-ray spectral analysis of thermonuclear bursts involves subtraction of the pre-burst emission as background. This approach implicitly assumes that the persistent flux remains constant throughout the burst. We reanalyzed 332 photospheric radius expansion bursts observed from 40 sources by the Rossi X-ray Timing Explorer, introducing a multiplicative factor $f_a$ to the persistent emission contribution in our spectral fits. We found that for the majority of spectra the best-fit value of $f_a$ is significantly greater than 1, suggesting that the persistent emission typically increases during a burst. Elevated $f_a$ values were not found solely during the radius expansion interval of the burst, but were also measured in the cooling tail. The modified model results in a lower average value of the $χ^2$ fit statistic, indicating superior spectral fits, but not yet to the level of formal statistical consistency for all the spectra. We interpret the elevated $f_a$ values as an increase of the mass accretion rate onto the neutron star during the burst, likely arising from the effects of Poynting-Robertson drag on the disk material. We measured an inverse correlation of $f_a$ with the persistent flux, consistent with theoretical models of the disc response. We suggest that this modified approach may provide more accurate burst spectral parameters, as well as offering a probe of the accretion disk structure.

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arXiv2012

Hyperbolic Divergence Cleaning for SPH

We present SPH formulations of Dedner et al's hyperbolic/parabolic divergence cleaning scheme for magnetic and velocity fields. Our implementation preserves the conservation properties of SPH which is important for stability. This is achieved by deriving an energy term for the Psi field, and imposing energy conservation on the cleaning subsystem of equations. This necessitates use of conjugate operators for divB and gradPsi in the numerical equations. For both the magnetic and velocity fields, the average divergence error in the system is reduced by an order of magnitude with our cleaning algorithm. Divergence errors in SPMHD are maintained to < 1%, even for realistic 3D applications with a corresponding gain in numerical stability. Density errors for an oscillating elliptic water drop using weakly compressible SPH are reduced by a factor of two.

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arXiv2012

Constrained Hyperbolic Divergence Cleaning for Smoothed Particle Magnetohydrodynamics

We present a constrained formulation of Dedner et al's hyperbolic/parabolic divergence cleaning scheme for enforcing the \nabla\dot B = 0 constraint in Smoothed Particle Magnetohydrodynamics (SPMHD) simulations. The constraint we impose is that energy removed must either be conserved or dissipated, such that the scheme is guaranteed to decrease the overall magnetic energy. This is shown to require use of conjugate numerical operators for evaluating \nabla\dot B and \nablaψ in the SPMHD cleaning equations. The resulting scheme is shown to be stable at density jumps and free boundaries, in contrast to an earlier implementation by Price & Monaghan (2005). Optimal values of the damping parameter are found to be σ = 0.2-0.3 in 2D and σ = 0.8-1.2 in 3D. With these parameters, our constrained Hamiltonian formulation is found to provide an effective means of enforcing the divergence constraint in SPMHD, typically maintaining average values of h |\nabla\dot B| / |B| to 0.1-1%, up to an order of magnitude better than artificial resistivity without the associated dissipation in the physical field. Furthermore, when applied to realistic, 3D simulations we find an improvement of up to two orders of magnitude in momentum conservation with a corresponding improvement in numerical stability at essentially zero additional computational expense.

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arXiv2012

Response of a circumbinary accretion disc to black hole mass loss

We investigate the evolution of the surface density of a circumbinary accretion disc after the mass loss induced by the merger of two supermassive black holes. We first introduce an analytical model, under the assumption of a disc composed of test particles, to derive the surface density evolution of the disc following the mass loss. The model predicts the formation of sharp density peaks in the disc; the model also allows us to compute the typical timescale for the formation of these peaks. To test and validate the model, we run numerical simulations of the process using the Smoothed Particle Hydrodynamics (SPH) code PHANTOM, taking fluid effects into account. We find good agreement in the shape and position of the peaks between the model and the simulations. In a fluid disc, however, the epicyclic oscillations induced by the mass loss can dissipate, and only some of the predicted peaks form in the simulation. To quantify how fast this dissipation proceeds, we introduce an appropriate parameter, and we show that it is effective in explaining the differences between the analytical, collisionless model and a real fluid disc.

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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

Resolving high Reynolds numbers in SPH simulations of subsonic turbulence

Accounting for the Reynolds number is critical in numerical simulations of turbulence, particularly for subsonic flow. For Smoothed Particle Hydrodynamics (SPH) with constant artificial viscosity coefficient alpha, it is shown that the effective Reynolds number in the absence of explicit physical viscosity terms scales linearly with the Mach number - compared to mesh schemes, where the effective Reynolds number is largely independent of the flow velocity. As a result, SPH simulations with alpha=1 will have low Reynolds numbers in the subsonic regime compared to mesh codes, which may be insufficient to resolve turbulent flow. This explains the failure of Bauer and Springel (2011, arXiv:1109.4413v1) to find agreement between the moving-mesh code AREPO and the GADGET SPH code on simulations of driven, subsonic (v ~ 0.3 c_s) turbulence appropriate to the intergalactic/intracluster medium, where it was alleged that SPH is somehow fundamentally incapable of producing a Kolmogorov-like turbulent cascade. We show that turbulent flow with a Kolmogorov spectrum can be easily recovered by employing standard methods for reducing alpha away from shocks.

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arXiv2011

Dusty gas with SPH - II. Implicit timestepping and astrophysical drag regimes

In a companion paper (Laibe & Price 2011b), we have presented an algorithm for simulating two-fluid gas and dust mixtures in Smoothed Particle Hydrodynamics (SPH). In this paper, we develop an implicit timestepping method that preserves the exact conservation of the both linear and angular momentum in the underlying SPH algorithm, but unlike previous schemes, allows the iterations to converge to arbitrary accuracy and is suited to the treatment of non- linear drag regimes. The algorithm presented in Paper I is also extended to deal with realistic astrophysical drag regimes, including both linear and non-linear Epstein and Stokes drag. The scheme is benchmarked against the test suite presented in Paper I, including i) the analytic solutions of the dustybox problem and ii) solutions of the dustywave, dustyshock, dustysedov and dustydisc obtained with explicit timestepping. We find that the implicit method is 1- 10 times faster than the explicit temporal integration when the ratio r between the the timestep and the drag stopping time is 1 < r < 1000.

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arXiv2011

Dusty gas with SPH - I. Algorithm and test suite

We present a new algorithm for simulating two-fluid gas and dust mixtures in Smoothed Particle Hydrodynamics (SPH), systematically addressing a number of key issues including the generalised SPH density estimate in multi-fluid systems, the consistent treatment of variable smoothing length terms, finite particle size, time step stability, thermal coupling terms and the choice of kernel and smoothing length used in the drag operator. We find that using double-hump shaped kernels improves the accuracy of the drag interpolation by a factor of several hundred compared to the use of standard SPH bell-shaped kernels, at no additional computational expense. In order to benchmark our algorithm, we have developed a comprehensive suite of standardised, simple test problems for gas and dust mixtures: dustybox, dustywave, dustyshock, dustysedov and dustydisc, the first three of which have known analytic solutions. We present the validation of our algorithm against all of these tests. In doing so, we show that the spatial resolution criterion Δ< cs ts is a necessary condition in all gas+dust codes that becomes critical at high drag (i.e. small stopping time ts) in order to correctly predict the dynamics. Implicit timestepping and the implementation of realistic astrophysical drag regimes are addressed in a companion paper.

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arXiv2011

Smoothed Particle Hydrodynamics: Things I wish my mother taught me

I discuss the key features of Smoothed Particle Hydrodynamics (SPH) as a numerical method - in particular the key differences between SPH and more standard grid based approaches - that are important to the practitioner. These include the exact treatment of advection, the absence of intrinsic dissipation, exact conservation and more subtle properties that arise from its Hamiltonian formulation such as the existence of a minimum energy state for the particles. The implications of each of these are discussed, showing how they can be both advantages and disadvantages.

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arXiv2011

DUSTYBOX and DUSTYWAVE: Two test problems for numerical simulations of two fluid astrophysical dust-gas mixtures

In this paper we present the analytic solutions for two test problems involving two-fluid mixtures of dust and gas in an astrophysical context. The solutions provide a means of benchmarking numerical codes designed to simulate the non-linear dynamics of dusty gas. The first problem, dustybox, consists of two interpenetrating homogeneous fluids moving with relative velocity difference. We provide exact solutions to the full non-linear problem for a range of drag formulations appropriate to astrophysical fluids (i.e., various prescriptions for Epstein and Stokes drag in different regimes). The second problem, dustywave consists of the propagation of linear acoustic waves in a two-fluid gas-dust mixture. We provide the analytic solution for the case when the two fluids are interacting via a linear drag term. Both test problems are simple to set up in any numerical code and can be run with periodic boundary conditions. The solutions we derive are completely general with respect to both the dust-to-gas ratio and the amplitude of the drag coefficient. A stability analysis of waves in a gas-dust system is also presented, showing that sound waves in an astrophysical dust-gas mixture are linearly stable.

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arXiv2010

Magnetic fields and Turbulence in Star Formation using Smoothed Particle Hydrodynamics

Firstly, we give a historical overview of attempts to incorporate magnetic fields into the Smoothed Particle Hydrodynamics method by solving the equations of Magnetohydrodynamics (MHD), leading an honest assessment of the current state-of-the-art in terms of the limitations to performing realistic calculations of the star formation process. Secondly, we discuss the results of a recent comparison we have performed on simulations of driven, supersonic turbulence with SPH and Eulerian techniques. Finally we present some new results on the relationship between the density variance and the Mach number in supersonic turbulent flows, finding sigma^2_{ln rho} = ln (1 + b^2 M^2) with b=0.33 up to Mach~20, consistent with other numerical results at lower Mach number (Lemaster and Stone 2008) but inconsistent with observational constraints on sigma_rho and M in Taurus and IC5146.

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