Projects | James R. Beattie

Characterising magnetic field structure across scales - X and O point detection in three dimensions

Mon, 19 Aug 2024 00:00:00 +0000

Reconnection and dynamo are fundamentally opposite plasma processes - reconnection describing the conversion of magnetic energy density into kinetic, and dynamo conversion of kinetic energy density into magnetic. Both processes however do share a similarity in that they change the underlying topology of the magnetic field. Utilising the structure of the magnetic field via the gradient tensor of the vector potential, magnetic field itself, or current density, one can identify and characterise objects like O and X points which can be used to directly probe the local properties of a reconnecting region in a turbulent plasma, or associate global properties, like integral magnetic energy growth, with specific local regions in the plasma. In this project, we will develop a method for characterising such topologies in 2D and 3D turbulent MHD plasma, relevant to the interstellar medium, and test fundamental questions about the nature of reconnection in such a regime. This will have significant implications for understanding the very nature of MHD turbulence in our Galaxy, and the role that reconnection may play.

Developing a turbulence-regulated star formation theory in a medium with non-lognormal gas density statistics.

Mon, 19 Aug 2024 00:00:00 +0000

Star formation happens within cold molecular clouds which are subject to supersonic turbulent motions and strong magnetic fields. The gas density PDF of such a medium has been previously used to predict the star formation rate potential that a cold gas cloud has, e.g., Krumholz & McKee (2005), Federrath & Klessen (2012) and Burkhart & Mocz (2018). Critical to these theories is the lognormal gas density probability density function, which connects the underlying statistics of the medium to the star formation rate in these models. However, foundational works from Hopkins (2013a), Mocz & Burkhart (2018) and Beattie et al (2022a) indicate that (global) lognormal models violate mass conservation, and are theoretically and empirically incorrect for the gas density probability density function of a supersonic medium. In this project, we aim to utilise computational and analytical techniques to modify the Federrath & Klessen (2012)-type turbulence-regulated star formation theories to include underlying Hopkins (2013a) gas density statistics, exploring how higher-order moments of the PDF influence the theoretical star formation rate. Furthermore, we will calibrate our theoretical models with star formation rates predicted by detailed numerical star-formation simulations, which may be used directly as sub-grid star formation models in global galaxy simulations.

Exploring streaming cosmic ray propagation in zoom-in molecular cloud simulations

Mon, 19 Aug 2024 00:00:00 +0000

Cosmic rays are charged, relativistic particles that pervade the galaxy at similar total energy densities as the magnetic fields and even the kinetic turbulent energies. The most common in number density are the GeV cosmic rays, which are subject to resonant instabilities with the magnetic fields embedded in the medium that they are propagating through. The net effect of the instability is to determine the dynamics of the distribution function, making populations of relativistic particles drift at the local ion Alfven speed. This tightly couples the distribution function to the dynamical timescales of the magnetic field, and subjects the particles to the structure and statistics that govern the ion Alfven fluctuations (the ionization state, the gas density, and the magnetic field). In this project we will explore how streaming GeV particles are transported through a host of different zoom-in simulations of molecular clouds. We will use the recently developed criptic code for doing post-processed cosmic ray transport, detailed in Krumholz et al. (2022), coupled with molecular cloud simulation data from global galaxy simulations detailed in Hu et al. (2023). We will investigate how the diverse morphology of the magnetic fields and ionization state of the gas in these systems gives rise to different diffusion coefficients, which can be compared directly with observations.

Growth or decay - decaying magnetohydrodynamics meets the turbulent dynamo

Mon, 19 Aug 2024 00:00:00 +0000

The saturation of the turbulent dynamo remains a highly important, outstanding problem for all small-scale dynamo theories. Beattie, et al. (2023a) showed numerically that the saturation is completely independent of the initial magnetic field conditions, even if the magnetic field decays into the saturation, which may be present in the post-shock region of supernova remnants. The decaying magnetic field presents a novel way of understanding dynamo saturation where the mechanisms for saturation are amplified due to the strong field. Preliminary analysis shows that the decaying field finds a force-free equilibrium state and that the decay is faster than Ohmic, potentially due to reconnection. In this project we will do a detailed analysis of the decay and force-free magnetic field in high-resolution 3D simulations of decaying plasma that are being constantly injected with momentum to stir weak turbulent modes. This will provide deep insights into the nature of dynamo saturation, and the stability of force-free magnetic fields, which are important for magnetisation in the early Universe and magnetic fields around compact objects.

Investigating compressible and incompressible mode coupling in supersonic turbulent dynamos relevant to the interstellar medium

Mon, 19 Aug 2024 00:00:00 +0000

The turbulent magnetic field that is grown and maintained in our Galaxy is roughly an order of magnitude larger in strength than the ordered magnetic field. The only way to keep such a field energised is through a turbulent dynamo. Classical turbulent dynamo theory takes no account of compressibility of the plasma, however the plasma in the interstellar medium of our Galaxy is weakly-compressible and mildy-supersonic on large scales (~100pc), and highly-compressible and highly-supersonic on smaller scales (~10pc). Hence, for understanding the turbulent dynamo in our Galaxy, we must consider supersonic dynamos. Supersonic dynamos are less efficient both in growth rate and the final saturated magnetic to kinetic energy ratio compared to incompressible dynamos. A good explanation for why has not yet been made nor proven from first principles, and in fact there is reason to believe that compressible modes should enhance the dynamo through compression. To explore this question, we will utilise an advanced compressible transfer function framework outlined in Grete et al. (2017), tracking the energy fluxes in high resolution simulations, mode by mode, for all terms in the compressible / incompressible mode decomposed magnetohydrodynamic fluid equations. In particular, we will develop a better understanding for how compressible modes couple to incompressible modes (and vice versa) on various scales in the dynamo, in turn determining how compressible modes potentially inhibit dynamo action and solving this outstanding problem in compressible dynamo theory.

Kinetic helicity and chiral velocity modes in supernova driven turbulence

Mon, 19 Aug 2024 00:00:00 +0000

There is sufficient energy in supernova detonations alone to drive the turbulence in our Galaxy. However, the nature of the supernova-driven cascade, the mechanism that transports energy from the largest scales to the smallest scales, is unknown for this kind of turbulence regime, where energy flux must travel both ways because the driving happens on small scales – from large to small in a direct cascade, and from small to large in an inverse cascade. It is well known that one inverse cascade mechanism is through interacting, incompressible homochiral modes (Plunian et al. 2020; i.e., velocity modes that generate vorticity with the same handedness). In this project, we will derive a new set of energy flux transfer functions for probing the interactions between the homochiral, heterochiral and compressible modes in a turbulent plasma. We will apply them directly to high resolution supernova-driven turbulence simulations to understand how the energy cascade works in the interstellar medium of our Galaxy.

Reconstructing three-dimensional moments from anisotropic two-dimensional fields

Mon, 19 Aug 2024 00:00:00 +0000

Many astrophysical observations are intrinsically two-dimensional in position-position space (PP; e.g., a column density map). However, astrophysical plasma models are usually constructed in three-dimensions, position-position-position (PPP), so an important step to compare theory to observations is therefore being able to reconstruct the statistics of the three dimensional field from two dimensional observations. Important work from Brunt et al. (2010) showed that one could, under the assumption of isotropy, reconstruct the three-dimensional variance of a turbulent (or generally stochastic) field by using a rotational transformation of the 2D power spectrum. But in the presence of strong magnetic fields, which we find on many scales in a galaxy, isotropy is strongly violated. Hence, this project aims to utilise analytical means to generalise the Brunt et al. (2010) method to include the ability to reconstruct anisotropic fields. Furthermore, we will validate our new method on a suite of high resolution magnetohydrodynamical turbulence simulations followed by applying them dust continuum emission observations of quiescent molecular clouds.

Supersonic vortices - understanding the building blocks of supersonic, sub-Alfvenic magnetohydrodynamic turbulence

Mon, 19 Aug 2024 00:00:00 +0000

Strongly magnetised, compressible turbulence is ubiquitous in the solar wind, atmosphere of compact objects, and even cold molecular and atomic gas distributed across the Galaxy. Beattie, et al. (2020b,2022a,2022c) has shown that in this regime of turbulence the energy budget is dominated not by turbulent nor Alfvenic fluctuations, as previously assumed, but rather rigid body vortices that are self-organised into a quasi-stationary state that give rise to non-classical dissipation, non-local intermittency effects, and peculiar decay characteristics that are currently not captured by any turbulence phenomenology. By utilising both computational and analytical techniques, in this project, we aim to (1) build a vortex tracking code to use on high-resolution, three-dimensional turbulence data, so that we can extract and characterise the local dynamics that give rise to, maintain, and eventually decay these vortices; and (2) explore the stability and signature of these vortices in linear eigenmode decompositions of the turbulent plasma. These results will have fundamental repercussions for not only strongly magnetised compressible turbulence theory (e.g., residual energy theory), but also for GeV cosmic ray transport, and the measurement of interstellar magnetic fields using Davis-Chandreshkar-Fermi methods.

The secret life of over-dense regions in interstellar turbulence

Mon, 19 Aug 2024 00:00:00 +0000

The initial conditions for star formation are embedded in the fractal gas density structures produced by supersonic, magnetised turbulence. We understand in a lot of detail relations between the global statistical properties and moments of the gas density field. However, we do not understand the local properties of the densest regions, which are just as, if not more important than the global properties, for understanding the star formation process. Roberston & Goldreich (2018) demonstrated how to identify, cluster and track in time over-dense regions by using a mixture of Lagrangian and Eulerian plasma statistics, unveiling a host of important properties of the dense regions in hydrodynamical turbulence. In this project we will do the same for magnetohydrodynamical turbulence, with the student contributing to a clustering and local statistical analysis code that has already been written by Dr. James Beattie. With some further software development, we will add time tracking, and the ability to generalise this code to other interesting structures in the magnetised turbulence, such as current sheets. There will also be opportunities to do an analytical analysis of the local statistical properties, such as the density profile, of the regions as the project progresses. This project will lead to significantly better understanding of not only the initial conditions for star formation, but also the role of strong gas density fluctuations in a magnetised, turbulent medium.

The transport and flux of magnetic helicity fluctuations

Mon, 19 Aug 2024 00:00:00 +0000

Magnetic helicity describes the topological knottedness of a magnetic field, and in ideal magnetohydrodynamics, it is an invariant. It plays an important role in large-scale dynamos, and the decay of primordial magnetic fields in the early Universe, due in part to net-helicity being associated with symmetry breaking, and the helicity directly changing the decay timescale. Recent works have shown that not only is magnetic helicity an invariant, but so is the magnetic helicity correlation function, making it an even more robust invariant than previously thought. In this project we will explore the nature of the magnetic helicity flux in MHD turbulence through the use of helicity flux transfer functions. We will derive the transfer functions from the helicity evolution equation, and apply them to high resolution MHD turbulence simulation, unravelling what mechanisms give rise to the well-known inverse helicity cascade, and in turn better understanding the role of MHD turbulence in transporting helicity where it can be utilised by large-scale dynamos.