Accretion Disc Particle Accretion in Major Merger Simulations

A recent approach to simulating localized feedback from active galactic nuclei by Power et al. (2011) uses an accretion disc particle to represent both the black hole and its accretion disc. We have extrapolated and adapted this approach to simulations of Milky Way-sized galaxy mergers containing black holes and explored the impact of the various parameters in this model as well as its resolution dependence. The two key parameters in the model are an effective accretion radius, which determines the radius within which gas particles are added to the accretion disc, and a viscous time-scale which determines how long it takes for material in the accretion disc to accrete on to the black hole itself. We find that there is a limited range of permitted accretion radii and viscous time-scales, with unphysical results produced outside this range. For permitted model parameters, the nuclear regions of simulations with the same resolution follow similar evolutionary paths, producing final black hole masses that are consistent within a factor of two. When comparing the resolution dependence of the model, there is a trend towards higher resolution producing slightly lower mass black holes, but values for the two resolutions studied again agree within a factor of two. We also compare these results to two other AGN feedback algorithms found in the literature. While the evolution of the systems vary, most notably the intermediate total black hole mass, the final black hole masses differ by less than a factor of five amongst all of our models, and the remnants exhibit similar structural parameters. The implication of this accretion model is that, unlike most accretion algorithms, a decoupling of the accretion rate on to the black hole and the local gas properties is permitted and obtained; this allows for black hole growth even after feedback has prevented additional accretion events on to the disc.Comment: 17 pages, accepted to MNRA

Ambipolar diffusion in smoothed particle magnetohydrodynamics

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 per cent 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 per cent 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.Comment: Accepted for publication by MNRA

AGN Feedback models: Correlations with star formation and observational implications of time evolution

We examine the correlation between the star formation rate (SFR) and black hole accretion rate (BHAR) across a suite of different AGN feedback models, using the time evolution of a merger simulation. By considering three different stages of evolution, and a distinction between the nuclear and outer regions of star formation, we consider 63 different cases. Despite many of the feedback models fitting the M-\sigma\ relationship well, there are often distinct differences in the SFR-BHAR correlations, with close to linear trends only being present after the merger. Some of the models also show evolution in the SFR-BHAR parameter space that is at times directly across the long-term averaged SFR-BHAR correlation. This suggests that the observational SFR-BHAR correlation found for ensembles of galaxies is an approximate statistical trend, as suggested by Hickox et al. Decomposing the SFR into nuclear and outer components also highlights notable differences between models and there is only modest agreement with observational studies examining this in Seyfert galaxies. For the fraction of the black hole mass growth from the merger event relative to the final black hole mass, we find as much as a factor of three variation among models. This also translates into a similar variation in the post-starburst black hole mass growth. Overall, we find that while qualitative features are often similar amongst models, precise quantitative analysis shows there can be quite distinct differences.Comment: Accepted to MNRAS. Comments welcom

Investigating prescriptions for artificial resistivity in smoothed particle magnetohydrodynamics

In numerical simulations, artificial terms are applied to the evolution equations for stability. To prove their validity, these terms are thoroughly tested in test problems where the results are well known. However, they are seldom tested in production-quality simulations at high resolution where they interact with a plethora of physical and numerical algorithms. We test three artificial resistivities in both the Orszag-Tang vortex and in a star formation simulation. From the Orszag-Tang vortex, the Price et. al. (2017) artificial resistivity is the least dissipative thus captures the density and magnetic features; in the star formation algorithm, each artificial resistivity algorithm interacts differently with the sink particle to produce various results, including gas bubbles, dense discs, and migrating sink particles. The star formation simulations suggest that it is important to rely upon physical resistivity rather than artificial resistivity for convergence.Comment: 8 pages, 7 figures. Proceedings of the "12th international SPHERIC workshop", Ourense, Spain, 13-15 June 201

The properties of clusters, and the orientation of magnetic fields relative to filaments, in magnetohydrodynamic simulations of colliding clouds

Funding: LD acknowledges funding from the European Research Council for the Horizon 2020 ERC consolida-tor grant project ICYBOB, grant number 818940.We have performed Smoothed Particle Magneto-Hydrodynamics (SPMHD) calculations of colliding clouds to investigate the formation of massive stellar clusters, adopting a timestep criterion to prevent large divergence errors. We find that magnetic fields do not impede the formation of young massive clusters (YMCs), and the development of high star formation rates, although we do see a strong dependence of our results on the direction of the magnetic field. If the field is initially perpendicular to the collision, and sufficiently strong, we find that star formation is delayed, and the morphology of the resulting clusters is significantly altered. We relate this to the large amplification of the field with this initial orientation. We also see that filaments formed with this configuration are less dense. When the field is parallel to the collision, there is much less amplification of the field, dense filaments form, and the formation of clusters is similar to the purely hydrodynamical case. Our simulations reproduce the observed tendency for magnetic fields to be aligned perpendicularly to dense filaments, and parallel to low density filaments. Overall our results are in broad agreement with past work in this area using grid codes.PostprintPeer reviewe

The impact of non-ideal magnetohydrodynamics on binary star formation

This is the final version of the article. Available from the publisher via the DOI in this record.We investigate the effect of non-ideal magnetohydrodynamics (MHD) on the formation of binary stars using a suite of three-dimensional smoothed particle magnetohydrodynamics simulations of the gravitational collapse of 1 M⊙, rotating, perturbed molecular-cloud cores. Alongside the role of Ohmic resistivity, ambipolar diffusion and the Hall effect, we also examine the effects of magnetic field strength, orientation and amplitude of the density per- turbation. When modelling sub-critical cores, ideal MHD models do not collapse whereas non-ideal MHD models collapse to form single protostars. In supercritical ideal MHD models, increasing the magnetic field strength or decreasing the initial-density perturbation amplitude decreases the initial binary separation. Strong magnetic fields initially perpendicular to the rotation axis suppress the formation of binaries and yield discs with magnetic fields ∼10 times stronger than if the magnetic field was initially aligned with the rotation axis. When non-ideal MHD is included, the resulting discs are larger and more massive, and the binary forms on a wider orbit. Small differences in the supercritical cores caused by non-ideal MHD effects are amplified by the binary interaction near periastron. Overall, the non-ideal effects have only a small impact on binary formation and early evolution, with the initial conditions playing the dominant role.JW and MRB acknowledge support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013 grant agreement no. 339248). JW also acknowledges support from the Australian Research Council (ARC) Discovery Projects Grant DP130102078. DJP is funded by ARC Future Fellowship FT130100034. This work was supported by resources on the gSTAR national facility at Swinburne University of Technology and by Zen. gSTAR is funded by Swinburne and the Australian Government’s Education Investment Fund. Several calculations for this paper were performed on the University of Exeter Supercomputer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS, and the University of Exeter

The effect of extreme ionization rates during the initial collapse of a molecular cloud core (dataset)

This is all the data created for Wurster, Bate & Price (2018b). This dataset was created using the SPHMD code Phantom, which included v1.2.1 of the NICIL library (Wurster 2016) to calculate the non-ideal MHD coefficients. The data and important files have been uploaded; the data files can be read with either Phantom, or with the graphics programme Splash. The filenames have the prefix Ionisation_. If the second component is a number or pair of number, then that file includes the data for those ionisation rates (specifically the negative of those numbers). If the second part is 'exe', then it includes the executables, graphing scripts, etc.The article associated with this dataset is located in ORE at: http://hdl.handle.net/10871/32176What cosmic ray ionization rate is required such that a non-ideal magnetohydrodynamics (MHD) simulation of a collapsing molecular cloud will follow the same evolutionary path as an ideal MHD simulation or as a purely hydrodynamics simulation? To investigate this question, we perform three-dimensional smoothed particle non-ideal MHD simulations of the gravitational collapse of rotating, one solar mass, magnetized molecular cloud cores, which include Ohmic resistivity, ambipolar diffusion, and the Hall effect. We assume a uniform grain size of ag = 0.1 μm, and our free parameter is the cosmic ray ionization rate, ζcr. We evolve our models, where possible, until they have produced a first hydrostatic core. Models with ζcr ≳ 10−13 s−1 are indistinguishable from ideal MHD models, and the evolution of the model with ζcr = 10−14 s−1 matches the evolution of the ideal MHD model within 1 per cent when considering maximum density, magnetic energy, and maximum magnetic field strength as a function of time; these results are independent of ag. Models with very low ionization rates (ζcr ≲ 10−24 s−1) are required to approach hydrodynamical collapse, and even lower ionization rates may be required for larger ag. Thus, it is possible to reproduce ideal MHD and purely hydrodynamical collapses using non-ideal MHD given an appropriate cosmic ray ionization rate. However, realistic cosmic ray ionization rates approach neither limit; thus, non-ideal MHD cannot be neglected in star formation simulations.JW and MRB acknowledge support from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007- 2013 grant agreement no. 339248). DJP received funding via Australian Research Council grants FT130100034, DP130102078, and DP180104235. This work was supported by resources on the swinSTAR national facility at Swinburne University of Technology. swinSTAR is funded by Swinburne and the Australian Government's Education Investment Fund

Can non-ideal magnetohydrodynamics solve the magnetic braking catastrophe? (dataset)

This is all the data created for Wurster, Price & Bate (2016). This dataset was created using the SPHMD code Phantom and included a precursor to the NICIL library (Wurster 2016) to calculate the non-ideal MHD coefficients. The data and important files have been uploaded; the data files can be read with either Phantom, or with the graphics programme Splash. The filenames represent the original path and the simulation, and have the prefix WPB2016_pdata_. The second component to the filename is 1e6 (models with 1e6 particles in the sphere) or 3e5 (models with 1e6 particles in the sphere) and the third component is the simulation name. Typically, the model name has the form ABC, where A=ii,ni,nim for ideal, non-ideal with Bz, non-ideal with -Bz, respectively; B=o,h,a,oha for ohmic,hall,ambipolar,ohmic+hall+ambipolar, respectively; C=B,Q,C,D,P mu0=10,7.5,5,5,hydro, respectively. Ideal runs do not have a B part to the name.We investigate whether or not the low ionization 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 ionization chemistry assuming 0.1 μm 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

The collapse of a molecular cloud core to stellar densities using radiation non-ideal magnetohydrodynamics (dataset)

This is all the data created for Wurster, Bate & Price (2018a). This dataset was created using the SPHMD code sphNH, which included v1.2.1 of the NICIL library (Wurster 2016) to calculate the non-ideal MHD coefficients. The data and important files have been uploaded; the data files can be read with either sphNG, or with the graphics programme Splash. The file are named such that number at the end of `collapse' indicates the negative of the cosmic ray ionisation rate. If this number is followed by `a` or `b', then this data set was created to reproduce data accidentally deleted from the primary set without the 'a'. If it is followed by 'imp', it uses the implicit resistivity. The subsequent two numbers are the dump numbers contained within this file. If the subsequent term is 'sup', then this is the supplementary material, including executables, plotting scripts, etc... The data for the aligned model and implicit model will be uploaded in a latter data set.The article associated with this dataset is located in ORE at: http://hdl.handle.net/10871/31265We present results from radiation non-ideal magnetohydrodynamics (MHD) calculations that follow the collapse of rotating, magnetized, 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 ionization model in which cosmic ray ionization dominates at low temperatures and thermal ionization takes over at high temperatures. We explore the effects of varying the cosmic ray ionization rate from ζcr = 10−10 to 10−16 s−1. Models with ionization rates ≳10−12 s−1 produce results that are indistinguishable from ideal MHD. Decreasing the cosmic ray ionization rate extends the lifetime of the first hydrostatic core up to a factor of 2, 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 ionization rate is reduced. The outflow morphology following stellar core formation is complex and strongly dependent on the cosmic ray ionization rate. Calculations with high ionization rates quickly produce a fast (≈14 km s−1) bipolar outflow that is distinct from the first core outflow, but with the lowest ionization rate, a slower (≈3−4 km s−1) conical outflow develops gradually and seamlessly merges into the first core outflow.JW and MRB acknowledge support from the European Research Council under the European Commission's Seventh Framework Programme (FP7/2007- 2013 grant agreement no. 339248). DJP and JW were funded by Australian Research Council grants FT130100034 andDP130102078. The calculations for this paper were performed on the University of Exeter Supercomputer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS, and the University of Exeter. We used splash (Price 2007) for the column density figures

NICIL : a stand alone library to self-consistently calculate non-ideal magnetohydrodynamic coefficients in molecular cloud cores

In this paper, we introduce Nicil: Non-Ideal magnetohydrodynamics Coefficients and Ionisation Library. Nicil is a stand-alone Fortran90 module that calculates the ionisation values and the coefficients of the non-ideal magnetohydrodynamics terms of Ohmic resistivity, the Hall effect, and ambipolar diffusion. The module is fully parameterised such that the user can decide which processes to include and decide upon the values of the free parameters, making this a versatile and customisable code. The module includes both cosmic ray and thermal ionisation; the former includes two ion species and three species of dust grains (positively charged, negatively charged, and neutral), and the latter includes five elements which can be doubly ionised. We demonstrate tests of the module, and then describe how to implement it into an existing numerical code.Publisher PDFPeer reviewe