We present a new approach to simulating mixtures of gas and dust in smoothed particle hydrodynamics (SPH). We show how the two-fluid equations can be rewritten to describe a single-fluid mixture moving with the barycentric velocity, with each particl
e carrying a dust fraction. We show how this formulation can be implemented in SPH while preserving the conservation properties (i.e. conservation of mass of each phase, momentum and energy). We also show that the method solves two key issues with the two fluid approach: it avoids over-damping of the mixture when the drag is strong and prevents a problem with dust particles becoming trapped below the resolution of the gas. We also show how the general one-fluid formulation can be simplified in the limit of strong drag (i.e. small grains) to the usual SPH equations plus a diffusion equation for the evolution of the dust fraction that can be evolved explicitly and does not require any implicit timestepping. We present tests of the simplified formulation showing that it is accurate in the small grain/strong drag limit. We discuss some of the issues we have had to solve while developing this method and finally present a preliminary application to dust settling in protoplanetary discs.
We describe a simple method for simulating the dynamics of small grains in a dusty gas, relevant to micron-sized grains in the interstellar medium and grains of centimetre size and smaller in protoplanetary discs. The method involves solving one extr
a diffusion equation for the dust fraction in addition to the usual equations of hydrodynamics. This diffusion approximation for dust is valid when the dust stopping time is smaller than the computational timestep. We present a numerical implementation using Smoothed Particle Hydrodynamics (SPH) that is conservative, accurate and fast. It does not require any implicit timestepping and can be straightforwardly ported into existing 3D codes.
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 prod
uced, 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.
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 {alpha}_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 Alfven 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.
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. Recentl
y 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.
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 Reyn
olds 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.
We introduce and test an expression for calculating the variance of a physical field in three dimensions using only information contained in the two-dimensional projection of the field. The method is general but assumes statistical isotropy. To test
the method we apply it to numerical simulations of hydrodynamic and magnetohydrodynamic turbulence in molecular clouds, and demonstrate that it can recover the 3D normalised density variance with ~10% accuracy if the assumption of isotropy is valid. We show that the assumption of isotropy breaks down at low sonic Mach number if the turbulence is sub-Alfvenic. Theoretical predictions suggest that the 3D density variance should increase proportionally to the square of the Mach number of the turbulence. Application of our method will allow this prediction to be tested observationally and therefore constrain a large body of analytic models of star formation that rely on it.
The HST ACS Coma Cluster Treasury Survey is a deep two passband imaging survey of the nearest very rich cluster of galaxies, covering a range of galaxy density environments. The imaging is complemented by a recent wide field redshift survey of the cl
uster conducted with Hectospec on the 6.5m MMT. Among the many scientific applications for this data are the search for compact galaxies. In this paper, we present the discovery of seven compact (but quite luminous) stellar systems, ranging from M32-like galaxies down to ultra-compact dwarfs (UCDs)/dwarf to globular transition objects (DGTOs). We find that all seven compact galaxies require a two-component fit to their light profile and have measured velocity dispersions that exceed those expected for typical early-type galaxies at their luminosity. From our structural parameter analysis we conclude that three of the sample should be classified as compact ellipticals or M32-like galaxies, the remaining four being less extreme systems. The three compact ellipticals are all found to have old luminosity weighted ages (> 12 Gyr), intermediate metallicities (-0.6 < [Fe/H] < -0.1) and high [Mg/Fe] (> 0.25). Our findings support a tidal stripping scenario as the formation mode of compact galaxies covering the luminosity range studied here. We speculate that at least two early-type morphologies may serve as the progenitor of compact galaxies in clusters.
We investigate the dynamics of magnetic fields in spiral galaxies by performing 3D MHD simulations of galactic discs subject to a spiral potential. Recent hydrodynamic simulations have demonstrated the formation of inter-arm spurs as well as spiral a
rm molecular clouds provided the ISM model includes a cold HI phase. We find that the main effect of adding a magnetic field to these calculations is to inhibit the formation of structure in the disc. However, provided a cold phase is included, spurs and spiral arm clumps are still present if $beta gtrsim 0.1$ in the cold gas. A caveat to two phase calculations though is that by assuming a uniform initial distribution, $beta gtrsim 10$ in the warm gas, emphasizing that models with more consistent initial conditions and thermodynamics are required. Our simulations with only warm gas do not show such structure, irrespective of the magnetic field strength. Furthermore, we find that the introduction of a cold HI phase naturally produces the observed degree of disorder in the magnetic field, which is again absent from simulations using only warm gas. Whilst the global magnetic field follows the large scale gas flow, the magnetic field also contains a substantial random component that is produced by the velocity dispersion induced in the cold gas during the passage through a spiral shock. Without any cold gas, the magnetic field in the warm phase remains relatively well ordered apart from becoming compressed in the spiral shocks. Our results provide a natural explanation for the observed high proportions of disordered magnetic field in spiral galaxies and we thus predict that the relative strengths of the random and ordered components of the magnetic field observed in spiral galaxies will depend on the dynamics of spiral shocks.
