Hall cascades versus instabilities in neutron star magnetic fields

Context. The Hall effect is an important nonlinear mechanism affecting the evolution of magnetic fields in neutron stars. Studies of the governing equation, both theoretical and numerical, have shown that the Hall effect proceeds in a turbulent cascade of energy from large to small scales. Aims. We investigate the small-scale Hall instability conjectured to exist from the linear stability analysis of Rheinhardt and Geppert. Methods. Identical linear stability analyses are performed to find a suitable background field to model Rheinhardt and Geppert’s ideas. The nonlinear evolution of this field is then modelled using a three-dimensional pseudospectral numerical MHD code. Combined with the background field, energy was injected at the ten specific eigenmodes with the greatest positive eigenvalues as inferred by the linear stability analysis. Results. Energy is transferred to different scales in the system, but not into small scales to any extent that could be interpreted as a Hall instability. Any instabilities are overwhelmed by a late-onset turbulent Hall cascade, initially avoided by the choice of background field, but soon generated by nonlinear interactions between the growing eigenmodes. The Hall cascade is shown here, and by several authors elsewhere, to be the dominant mechanism in this system

Magnetohydrodynamic simulations of mechanical stellar feedback in a sheet-like molecular cloud

We have used the adaptive-mesh-refinement hydrodynamic code, mg, to perform 3D magnetohydrodynamic simulations with self-gravity of stellar feedback in a sheet-like molecular cloud formed through the action of the thermal instability. We simulate the interaction of the mechanical energy input from a 15 star and a 40 M⊙ star into a 100 pc-diameter 17 000 M⊙ cloud with a corrugated sheet morphology that in projection appears filamentary. The stellar winds are introduced using appropriate Geneva stellar evolution models. In the 15 M⊙ star case, the wind forms a narrow bipolar cavity with minimal effect on the parent cloud. In the 40 M⊙ star case, the more powerful stellar wind creates a large cylindrical cavity through the centre of the cloud. After 12.5 and 4.97 Myr, respectively, the massive stars explode as supernovae (SNe). In the 15 M⊙ star case, the SN material and energy is primarily deposited into the molecular cloud surroundings over ∼10^5 yr before the SN remnant escapes the cloud. In the 40 M⊙ star case, a significant fraction of the SN material and energy rapidly escapes the molecular cloud along the wind cavity in a few tens of kiloyears. Both SN events compress the molecular cloud material around them to higher densities (so may trigger further star formation), and strengthen the magnetic field, typically by factors of 2–3 but up to a factor of 10. Our simulations are relevant to observations of bubbles in flattened ring-like molecular clouds and bipolar Hii regions

Hydrodynamic simulations of mechanical stellar feedback in a molecular cloud formed by thermal instability

We have used the AMR hydrodynamic code, MG, to perform 3D hydrodynamic simulations with self-gravity of stellar feedback in a spherical clumpy molecular cloud formed through the action of thermal instability. We simulate the interaction of the mechanical energy input from 15 Msun, 40 Msun, 60 Msun and 120 Msun stars into a 100 pc-diameter 16,500 Msun cloud with a roughly spherical morphology with randomly distributed high density condensations. The stellar winds are introduced using appropriate non-rotating Geneva stellar evolution models. In the 15 Msun star case, the wind has very little effect, spreading around a few neighbouring clumps before becoming overwhelmed by the cloud collapse. In contrast, in the 40 Msun, 60 Msun and 120 Msun star cases, the more powerful stellar winds create large cavities and carve channels through the cloud, breaking out into the surrounding tenuous medium during the wind phase and considerably altering the cloud structure. After 4.97 Myrs, 3.97 Myrs and 3.01 Myrs respectively, the massive stars explode as supernovae (SNe). The wind-sculpted surroundings considerably affect the evolution of these SN events as they both escape the cloud along wind-carved channels and sweep up remaining clumps of cloud/wind material. The `cloud' as a coherent structure does not survive the SN from any of these stars, but only in the 120 Msun case is the cold molecular material completely destabilised and returned to the unstable thermal phase. In the 40 Msun and 60 Msun cases, coherent clumps of cold material are ejected from the cloud by the SN, potentially capable of further star formation

Hydrodynamic simulations of mechanical stellar feedback in a molecular cloud formed by thermal instability

We have used the AMR hydrodynamic code, MG, to perform 3D hydrodynamic simulations with self-gravity of stellar feedback in a spherical clumpy molecular cloud formed through the action of thermal instability. We simulate the interaction of the mechanical energy input from 15 Msun, 40 Msun, 60 Msun and 120 Msun stars into a 100 pc-diameter 16,500 Msun cloud with a roughly spherical morphology with randomly distributed high density condensations. The stellar winds are introduced using appropriate non-rotating Geneva stellar evolution models. In the 15 Msun star case, the wind has very little effect, spreading around a few neighbouring clumps before becoming overwhelmed by the cloud collapse. In contrast, in the 40 Msun, 60 Msun and 120 Msun star cases, the more powerful stellar winds create large cavities and carve channels through the cloud, breaking out into the surrounding tenuous medium during the wind phase and considerably altering the cloud structure. After 4.97 Myrs, 3.97 Myrs and 3.01 Myrs respectively, the massive stars explode as supernovae (SNe). The wind-sculpted surroundings considerably affect the evolution of these SN events as they both escape the cloud along wind-carved channels and sweep up remaining clumps of cloud/wind material. The `cloud' as a coherent structure does not survive the SN from any of these stars, but only in the 120 Msun case is the cold molecular material completely destabilised and returned to the unstable thermal phase. In the 40 Msun and 60 Msun cases, coherent clumps of cold material are ejected from the cloud by the SN, potentially capable of further star formation

Striations, integrals, hourglasses, and collapse – thermal instability driven magnetic simulations of molecular clouds

The MHD version of the adaptive mesh refinement (AMR) code, MG, has been employed to study the interaction of thermal instability, magnetic fields, and gravity through 3D simulations of the formation of collapsing cold clumps on the scale of a few parsecs, inside a larger molecular cloud. The diffuse atomic initial condition consists of a stationary, thermally unstable, spherical cloud in pressure equilibrium with lower density surroundings and threaded by a uniform magnetic field. This cloud was seeded with 10 per cent density perturbations at the finest initial grid level around n = 1.1 cm−3 and evolved with self-gravity included from the outset. Several cloud diameters were considered (100, 200, and 400 pc) equating to several cloud masses (17 000, 136 000, and 1.1 × 106 M⊙). Low-density magnetic-field-aligned striations were observed as the clouds collapse along the field lines into disc-like structures. The induced flow along field lines leads to oscillations of the sheet about the gravitational minimum and an integral-shaped appearance. When magnetically supercritical, the clouds then collapse and generate hourglass magnetic field configurations with strongly intensified magnetic fields, reproducing observational behaviour. Resimulation of a region of the highest mass cloud at higher resolution forms gravitationally bound collapsing clumps within the sheet that contain clump-frame supersonic (M ∼ 5) and super-Alfvénic (MA ∼ 4) velocities. Observationally realistic density and velocity power spectra of the cloud and densest clump are obtained. Future work will use these realistic initial conditions to study individual star and cluster feedback

Thermal instability revisited

Field’s linear analysis of thermal instability is repeated using methods related to Whitham’s theory of wave hierarchies, which brings out the physically relevant parameters in a much clearer way than in the original analysis. It is also used for the stability of non-equilibrium states and we show that for gas cooling behind a shock, the usual analysis is only quantitatively valid for shocks that are just able to trigger a transition to the cold phase. A magnetic field can readily be included and we show that this does not change the stability criteria. By considering steady shock solutions, we show that almost all plausible initial conditions lead to a magnetically dominated state on the unstable part of the equilibrium curve. These results are used to analyse numerical calculations of perturbed steady shock solutions and of shocks interacting with a warm cloud

Comparison of Numerical Predictions with CO2 Pipeline Release Datasets of Relevance to Carbon Capture and Storage Applications

Predicting the correct multi-phase fluid flow behaviour during the discharge process in the near-field of sonic CO2 jets is of particular importance in assessing the risks associated with transport aspects of carbon capture and storage schemes, given the very different hazard profiles of CO2 in the gaseous and solid states. In this paper, we apply our state-of-the-art mathematical model implemented in an efficient computational method to available data. Compared to previous applications, an improved equation of state is used. We also compare to all the available data, rather than just subsets as previously, and demonstrate both the improved performance of the fluid flow model and the variation between the available datasets. The condensed phase fraction at the vent, puncture or rupture release point is revealed to be of key importance in understanding the near-field dispersion of sonic CO2

Validation of Turbulence Closures for the RANS Modelling of Under-expanded Fluid Releases

Presented are results from the application of a shock-capturing numerical scheme to the solution of the Favre-averaged Navier-Stokes fluid-flow equations, coupled with compressibility-corrected turbulence models. The relative performance of both a two-equation model and a Reynolds-stress transport model are evaluated in their application to the modelling of both moderately under-expanded, and highly under-expanded experimental releases. Both standard, and compressibility corrected models are investigated, and the superior predictive capabilities of the second-moment Reynolds-stress model are demonstrated

Numerical modelling of turbulent particle-laden sonic CO2 jets with experimental validation

Under-expanded particle-laden flows resulting in velocities greater than the local speed of sound are a feature of a wide number of applications in aviatic, astronautical, and process engineering scenarios including those relating to the accidental release of high-pressure fluids from reservoirs or pipelines. Such pipelines are considered to be the most likely method for transportation of captured carbon dioxide (CO2) from power plants and other industries prior to subsequent storage in carbon capture and storage (CCS) applications. Their safe operation is of paramount importance as their contents are likely to be in the region of several thousand tonnes. CO2 poses a number of dangers upon release due to its physical properties. It is a colourless and odourless asphyxiant which has a tendency to sublimation and solid formation, and is directly toxic if inhaled in air at concentrations around 5%, and likely to be fatal at concentrations around 10%. The developments presented in this paper concern the formulation of a multi-phase homogeneous discharge and dispersion model capable of predicting the near-field fluid dynamic, phase and particle behaviour of such CO2 releases, with validation against measurements of laboratory-scale jet releases of CO2 recently obtained by our group