We present Phantom, a fast, parallel, modular and low-memory smoothed particle hydrodynamics and magnetohydrodynamics code developed over the last decade for astrophysical applications in three dimensions. The code has been developed with a focus on stellar, galactic, planetary and high energy astrophysics and has already been used widely for studies of accretion discs and turbulence, from the birth of planets to how black holes accrete. Here we describe and test the core algorithms as well as modules for magnetohydrodynamics, self-gravity, sink particles, dust-gas mixtures, H2 chemistry, physical viscosity, external forces including numerous galactic potentials, Lense-Thirring precession, Poynting-Robertson drag and stochastic turbulent driving. Phantom is hereby made publicly available.

We investigate whether or not the low ionisation fractions in molecular cloud cores can solve the 'magnetic braking catastrophe', where magnetic fields prevent the formation of circumstellar discs around young stars. We perform three-dimensional smoothed particle non-ideal magnetohydrodynamics (MHD) simulations of the gravitational collapse of one solar mass molecular cloud cores, incorporating the effects of ambipolar diffusion, Ohmic resistivity and the Hall effect alongside a self-consistent calculation of the ionisation chemistry assuming 0.1µm grains. When including only ambipolar diffusion or Ohmic resistivity, discs do not form in the presence of strong magnetic fields, similar to the cases using ideal MHD. With the Hall effect included, disc formation depends on the direction of the magnetic field with respect to the rotation vector of the gas cloud. When the vectors are aligned, strong magnetic braking occurs and no disc is formed. When the vectors are anti-aligned, a disc with radius of 13 AU can form even in strong magnetic when all three non-ideal terms are present, and a disc of 38 AU can form when only the Hall effect is present; in both cases, a counter-rotating envelope forms around the first hydrostatic core. For weaker, anti-aligned fields, the Hall effect produces massive discs comparable to those produced in the absence of magnetic fields, suggesting that planet formation via gravitational instability may depend on the sign of the magnetic field in the precursor molecular cloud core.

We present hydrodynamic simulations of the common envelope binary interaction between a giant star and a compact companion carried out with the adaptive mesh refinement code enzo and the smooth particle hydrodynamics code phantom. These simulations mimic the parameters of one of the simulations by Passy et al., but assess the impact of a larger, more realistic initial orbital separation on the simulation outcome. We conclude that for both codes the post-common envelope separation is somewhat larger and the amount of unbound mass slightly greater when the initial separation is wide enough that the giant does not yet overflow or just overflows its Roche lobe. phantom has been adapted to the common envelope problem here for the first time and a full comparison with enzo is presented, including an investigation of convergence as well as energy and angular momentum conservation. We also set our simulations in the context of past simulations. This comparison reveals that it is the expansion of the giant before rapid in-spiral and not spinning up of the star that causes a larger final separation. We also suggest that the large range in unbound mass for different simulations is difficult to explain and may have something to do with simulations that are not fully converged.

drive the ultraviolet/optical variations. However, the medium energy X-ray NVA is 2-4 times that in the ultraviolet, and the single-epoch, absorption-corrected X-ray/γ-ray luminosity is only about 1/3 that of the ultraviolet/optical/infrared, suggesting that at most ∼1/3 of the total low-energy flux could be reprocessed high-energy emission.The strong wavelength dependence of the ultraviolet NVAs is consistent with an origin in an accretion disk, with the variable emission coming from the hotter inner regions and non-variable emission from the cooler outer regions. These data, when combined with the results of disk fits, indicate a boundary between these regions near a radius of order R ≈ 0.07 lt-day. No interband lag would be expected as reprocessing (and thus propagation between regions) need not occur, and the orbital time scale of ∼1 day is consistent with the observed variability time scale. However, such a model does not immediately explain the good correlation between ultraviolet and X-ray variations.

We present results from radiation non-ideal magnetohydrodynamics (MHD) calculations that follow the collapse of rotating, magnetised, 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 ionisation model in which cosmic ray ionisation dominates at low temperatures and thermal ionisation takes over at high temperatures. We explore the effects of varying the cosmic ray ionisation rate from ζ cr = 10 −10 to 10 −16 s −1 . Models with ionisation rates 10 −12 s −1 produce results that are indistinguishable from ideal MHD. Decreasing the cosmic ray ionisation rate extends the lifetime of the first hydrostatic core up to a factor of two, 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 ionisation rate is reduced. The outflow morphology following stellar core formation is complex and strongly dependent on the cosmic ray ionisation rate. Calculations with high ionisation rates quickly produce a fast (≈ 14 km s −1 ) bipolar outflow that is distinct from the first core outflow, but with the lowest ionisation rate a slower (≈ 3 − 4 km s −1 ) conical outflow develops gradually and seamlessly merges into the first core outflow.

Modelling AGN feedback in numerical simulations is both technically and theoretically challenging, with numerous approaches having been published in the literature. We present a study of five distinct approaches to modelling AGN feedback within gravitohydrodynamic simulations of major mergers of Milky Way-sized galaxies. To constrain differences to only be between AGN feedback models, all simulations start from the same initial conditions and use the same star formation algorithm. Most AGN feedback algorithms have five key aspects: the black hole accretion rate, energy feedback rate and method, particle accretion algorithm, black hole advection algorithm and black hole merger algorithm. All models follow different accretion histories, and in some cases, accretion rates differ by up to three orders of magnitude at any given time. We consider models with either thermal or kinetic feedback, with the associated energy deposited locally around the black hole. Each feedback algorithm modifies the region around the black hole to different extents, yielding gas densities and temperatures within r ∼ 200 pc that differ by up to six orders of magnitude at any given time. The particle accretion algorithms usually maintain good agreement between the total mass accreted byṀ dt and the total mass of gas particles removed from the simulation, although not all algorithms guarantee this to be true. The black hole advection algorithms dampen inappropriate dragging of the black holes by twobody interactions. Advecting the black hole a limited distance based upon local mass distributions has many desirably properties, such as avoiding large artificial jumps and allowing the possibility of the black hole remaining in a gas void. Lastly, two black holes instantly merge when given criteria are met, and we find a range of merger times for different criteria. This is important since the AGN feedback rate changes across the merger in a way that is dependent on the specific accretion algorithm used. Using the M BH -σ relation as a diagnostic of the remnants yields three models that lie within the one-sigma scatter of the observed relation and two that fall below the expected relation. The wide variation in accretion behaviours of the models reinforces the fact that there remains much to be learnt about the evolution of galactic nuclei.

The formation of a protostellar disc is a natural outcome during the star formation process. As gas in a molecular cloud core collapses under self-gravity, the angular momentum of the gas will slow its collapse on small scales and promote the formation of a protostellar disc. Although the angular momenta of dense star-forming cores remain to be fully characterized observationally, existing data indicates that typical cores have enough angular momenta to form relatively large, 100 au-scale, rotationally supported discs, as illustrated by hydrodynamic simulations. However, the molecular clouds are observed to be permeated by magnetic fields, which can in principle strongly affect the evolution of angular momentum during the core collapse through magnetic braking. Indeed, in the ideal magnetohydrodynamic (MHD) limit, magnetic braking has been shown to be so efficient as to remove essentially all of the angular momentum of the material close to the forming star such that disc formation is suppressed. This failure to produce discs in idealized cores is known as the magnetic braking catastrophe. The catastrophe must be averted in order for the all-important rotationally supported discs to appear, but when and how this happens remains debated. We review the resolutions proposed to date, with emphasis on misalignment, turbulence and especially non-ideal effects. Non-ideal MHD accounts for charged and neutral species, making it a natural extension to the ideal MHD approximation, since molecular clouds are only weakly ionized. The dissipative non-ideal effects diffuse the magnetic field to weaken it, and the dispersive term redirects the magnetic field to promote or hinder disc formation, dependent upon the magnetic geometry. When self-consistently applying non-ideal processes, rotationally supported discs of at least tens of au form, thus preventing the magnetic braking catastrophe. The non-ideal processes are sensitive to the magnetic field strength, cosmic ray ionization rate, and gas and dust grain properties, thus a complete understanding of the host molecular cloud is required. Therefore, the properties of the host molecular cloud -and especially its magnetic field -cannot be ignored when numerically modelling the formation and evolution of protostellar discs.

In partially ionised plasmas, the magnetic field can become decoupled from the neutral gas and diffuse through it in a process known as ambipolar diffusion. Although ambipolar diffusion has been implemented in several grid codes, we here provide an implementation in smoothed particle magnetohydrodynamics (SPMHD). We use the strong coupling approximation in which the ion density is negligible, allowing a single fluid approach. The equations are derived to conserve energy, and to provide a positive definite contribution to the entropy. We test the implementation in both a simple 1D SPMHD code and the fully 3D code PHANTOM. The wave damping test yields agreement within 0.03-2% of the analytical result, depending on the value of the collisional coupling constant. The oblique C-shocks test yields results that typically agree within 4% of the semi-analytical result. Our algorithm is therefore suitable for exploring the effect ambipolar diffusion has on physical processes, such as the formation of stars from molecular clouds.