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Ian Hawke

Publications and source records attributed to Ian Hawke.

At least 19 recordsLinked to original sources
arXiv2026

RAKI: High-Order Alternative Finite Differences for General Relativistic Magnetohydrodynamics

Binary neutron star (BNS) and black hole--neutron star mergers are among the most important multimessenger sources. Observations of these events could provide valuable insights into several unresolved phenomena, ranging from the efficiency of magnetic field amplification during and after mergers to the formation of magnetars and jets. Understanding these phenomena requires accurate modelling of magnetic field evolution, which remains a challenge for state-of-the-art general relativistic magnetohydrodynamics (GRMHD) simulations. In this work, we present \texttt{RAKI} (Relativistic Astrophysics Code Implementation of the Alternative Finite Difference Approach for GRMHD), the first GRMHD code to simulate BNS mergers using high-order alternative finite-difference methods with adaptive-order WENO (AFD-WENO-AO) reconstruction and a fully non-staggered, node-centred vector-potential formulation. The code achieves up to ninth-order convergence in smooth test problems while accurately capturing discontinuities. In magnetised Tolman--Oppenheimer--Volkoff (TOV) star tests, \texttt{RAKI} retains $99.2$ per cent of the initial maximum magnetic field strength over ${\sim}2$ ms, exhibiting an order of magnitude less magnetic field loss than a reference GRMHD code at the same resolution. In BNS merger simulations, fifth-order AFD-WENO-AO reconstruction yields approximately third-order convergence of the gravitational-wave phase in both magnetised and unmagnetised models. The discrete no-monopole constraint is preserved to machine precision without staggered grids, even during BNS mergers with moving refinement regions. These results establish \texttt{RAKI} as a high-order, non-staggered GRMHD framework for accurate modelling of magnetic field evolution in neutron star mergers and its implications for multimessenger astrophysics.

astro-ph.HE↗
arXiv2026

Relativistic Plasticity

The elastic crust of a neutron star has long been established as a key player in relevant aspects of neutron star physics. However, the state-of-the-art theory of elasticity is restricted to the perturbative domain and does not account for permanent plastic deformations which should be relevant for pulsar glitches, magnetar flares, and the continuous emission of gravitational waves. Plasticity, however, is a historically challenging phenomenon to model - even in the Newtonian regime. This is owed mainly to its dissipative character and the multiscale methods required to consistently reproduce observed phenomena. In this work, we address this first challenge by making use of recent developments in the variational modelling of dissipative fluids to extend the theory of relativistic elasticity to include plastic phenomenology. The resulting theory possesses the same freedoms as the modern Newtonian formalism, while now being compatible with general relativity. The second law of thermodynamics is then used to introduce the yield criterion of plasticity theory in the relativistic setting.

gr-qc↗
arXiv2026

Simulating dust collapse: the impact of gauge choices on primordial black hole formation

We investigate why numerical relativity simulations of dust collapse in a matter-dominated era frequently fail before primordial black hole formation due to numerical limitations and inappropriate gauge choices. Using 3-dimensional fully non-linear simulations of a dust fluid, we detail the advantages of advanced numerical methods and the impact of the lapse and shift evolution equations. The challenge is twofold: 1) conventional lapse slicing evolution equations, highly effective in typical black hole simulations, must be adapted in a cosmological context. We demonstrate how different proposed lapse evolution equations perform, enabling fair comparison, and propose our own. 2) The shift evolution equation's role is to spread out the numerical grid observers for a stable simulation. However, the Gamma-driver evolution fails when confronted with shell-focussing of the dust fluid. We show how the shift damping choice depends on the resolution of the shell-focusing region, suggesting that future work should have spatially varying damping. Our improved gauge choices allow simulations to evolve significantly further and potentially reach black hole formation. The best-performing simulations reach close proximity to a black hole; however, further work on the gauge choice is required for this to be stable.

gr-qc↗
arXiv2026

An efficient approach to resistive GRMHD simulations of binary neutron star mergers

Astrophysical plasmas are often highly conducting, but finite resistivity can nevertheless influence the evolution of strongly magnetised systems. Capturing these effects in general relativistic magnetohydrodynamics is computationally challenging because high conductivity leads to stiff source terms in the evolution equations. Standard numerical approaches rely on implicit-explicit (IMEX) time integration to maintain stability, but this substantially increases the complexity and computational cost of the simulations. Building upon the previously developed Resistive Extension upGrade for Ideal MagnEtohydrodynamics (REGIME), we present a new fluid-frame formulation that simplifies the incorporation of leading-order resistive effects by avoiding matrix inversions required in previous approaches. The method is implemented in a general relativistic magnetohydrodynamics code and validated through one-dimensional current-sheet tests and simulations of isolated magnetised neutron stars and binary neutron star mergers. We find that the new formulation reproduces the expected resistive behaviour with accuracy comparable to IMEX-based methods, while substantially reducing the computational cost and complexity of the simulations. In binary neutron star mergers, finite resistivity leads to measurable differences in the post-merger gravitational-wave signal and remnant structure, showing that resistive effects can produce measurable changes in the post-merger dynamics even in the high-conductivity regime.

astro-ph.HE↗
arXiv2026

A Reproducible Black Hole-Neutron Star Merger Gallery Example for the Einstein Toolkit

Black hole-neutron star mergers are important sources of gravitational waves and potential electromagnetic counterparts, but publicly available numerical relativity configurations for these systems remain limited. In this work, we present a fully reproducible black hole-neutron star merger simulation performed exclusively with official Einstein Toolkit thorns and configured to target the detected event \texttt{GW230529}. We evolve the system at three resolutions, with finest grid spacings of $162$, $222$, and $310$~m, and assess the numerical robustness of the resulting dynamics and gravitational wave signal. The entire setup, from initial data to a parameter file with some of the analysis scripts, is publicly released as a new Einstein Toolkit gallery example and is distributed as part of the Hypatia release, establishing a reference black hole-neutron star merger configuration within the Einstein Toolkit.

astro-ph.HE↗
arXiv2026

Impact of black hole spin on low-mass black hole-neutron star mergers

The recent detection of GW230529 suggests that black hole-neutron star mergers may involve low-mass black holes, potentially producing detectable electromagnetic counterparts. Motivated by this, we perform eleven fully general-relativistic hydrodynamic simulations with and without neutrino treatment, targeting the inferred chirp mass of GW230529. We systematically vary the black hole spin from $a_{\mathrm{BH}} = 0.0$ to $0.8$ in steps of $0.1$, making this the most comprehensive study of spin effects in black hole-neutron star mergers to date. We confirm our earlier findings of fast-moving ejecta ($v \geq 0.6\,c$) in this parameter regime and demonstrate a clear spin dependence, with fast-ejecta masses reaching up to $\qty{\sim e-3}{\Mass\Sun}$ for $a_{\mathrm{BH}} = 0.8$. Most notably, we identify for the first time the presence of spiral wave-driven ejecta in black hole-neutron star mergers -- a phenomenon previously reported only in binary neutron star systems. The mass of this component grows significantly with spin, reaching levels up to $\qty{\sim 7e-3}{\Mass\Sun}$. These results establish a new spin-enhanced mechanism for powering blue kilonova emission in black hole-neutron star mergers, significantly extending the range of systems expected to produce observable electromagnetic counterparts.

astro-ph.HE↗
arXiv2025

Higher-level large-eddy filtering strategy for general relativistic fluid simulations

Nonlinear simulations of neutron star mergers are complicated by the need to represent turbulent dynamics. As we cannot (yet) perform simulations that resolve accurately both the gravitational-wave scale and the smallest scales at which magneto/hydrodynamic turbulence plays a role, we need to rely on approximations. Addressing this problem in the context of large-eddy models, we outline a coherent Lagrangian filtering framework that allows us to explore the many issues that arise, linking conceptual problems to practical implementations and the interpretation of the results. We develop understanding crucial for quantifying unavoidable uncertainties in current and future numerical relativity simulations and consider the implications for neutron-star parameter estimation and constraints on the equation of state of matter under extreme conditions.

astro-ph.HE↗
arXiv2024

Signatures of Low Mass Black Hole-Neutron Star Mergers

The recent observation of the GW230529 event indicates that black hole-neutron star binaries can contain low-mass black holes. Since lower mass systems are more favourable for tidal disruption, such events are promising candidates for multi-messenger observations. In this study, we employ five finite-temperature, composition-dependent matter equations of state and present results from ten 3D general relativistic hydrodynamic simulations for the mass ratios $q = 2.6$ and $5$. Two of these simulations target the chirp mass and effective spin parameter of the GW230529 event, while the remaining eight contain slightly higher-mass black holes, including both spinning ($a_{BH} = 0.7$) and non-spinning ($a_{BH} = 0$) models. We discuss the impact of the equation of state, spin, and mass ratio on black hole-neutron star mergers by examining both gravitational-wave and ejected matter properties. For the low-mass ratio model we do not see fast-moving ejecta for the softest equation of state model, but the stiffer model produces on the order of $10^{-6}M_\odot$ of fast-moving ejecta, expected to contribute to an electromagnetic counterpart. Notably, the high-mass ratio model produces nearly the same amount of total dynamical ejecta, but yields $52$ times more fast-moving ejecta than the low-mass ratio system. In addition, we observe that the black-hole spin tends to decrease the amount of fast-moving ejecta while increasing significantly the total ejected mass. Finally, we note that the disc mass tends to increase as the neutron star compactness decreases.

astro-ph.HE↗
arXiv2024

A dissipative extension to ideal hydrodynamics

We present a formulation of special relativistic, dissipative hydrodynamics (SRDHD) derived from the well-established Müller- Israel-Stewart (MIS) formalism using an expansion in deviations from ideal behaviour. By re-summing the non-ideal terms, our approach extends the Euler equations of motion for an ideal fluid through a series of additional source terms that capture the effects of bulk viscosity, shear viscosity and heat flux. For efficiency these additional terms are built from purely spatial derivatives of the primitive fluid variables. The series expansion is parametrized by the dissipation strength and timescale coefficients, and is therefore rapidly convergent near the ideal limit. We show, using numerical simulations, that our model reproduces the dissipative fluid behaviour of other formulations. As our formulation is designed to avoid the numerical stiffness issues that arise in the traditional MIS formalism for fast relaxation timescales, it is roughly an order of magnitude faster than standard methods near the ideal limit.

gr-qc↗
arXiv2024

Turbulence modelling in neutron star merger simulations

Observations of neutron star mergers have the potential to unveil detailed physics of matter and gravity in regimes inaccessible by other experiments. Quantitative comparisons to theory and parameter estimation require nonlinear numerical simulations. However, the detailed physics of energy and momentum transfer between different scales, and the formation and interaction of small scale structures, which can be probed by detectors, are not captured by current simulations. This is where turbulence enters neutron star modelling. This review will outline the theory and current status of turbulence modelling for relativistic neutron star merger simulations.

astro-ph.HE↗
arXiv2022

Detecting the impact of nuclear reactions on neutron star mergers through gravitational waves

Nuclear reactions may affect gravitational-wave signals from neutron-star mergers, but the impact is uncertain. In order to quantify the effect, we compare two numerical simulations representing intuitive extremes. In one case reactions happen instantaneously. In the other case, they occur on timescales much slower than the evolutionary timescale. We show that, while the differences in the two gravitational-wave signals are small, they should be detectable by third-generation observatories. To avoid systematic errors in equation of state parameters inferred from observed signals, we need to accurately implement nuclear reactions in future simulations.

astro-ph.HE↗
arXiv2021

A covariant approach to relativistic large-eddy simulations: The fibration picture

Models of turbulent flows require the resolution of a vast range of scales, from large eddies to small-scale features directly associated with dissipation. As the required resolution is not within reach of large scale numerical simulations, standard strategies involve a smoothing of the fluid dynamics, either through time averaging or spatial filtering. These strategies raise formal issues in general relativity, where the split between space and time is observer dependent. To make progress, we develop a new covariant framework for filtering/averaging based on the fibration of spacetime associated with fluid elements and the use of Fermi coordinates to facilitate a meaningful local analysis. We derive the resolved equations of motion, demonstrating how "effective" dissipative terms arise because of the coarse-graining, and paying particular attention to the thermodynamical interpretation of the resolved quantities. Finally, as the smoothing of the fluid-dynamics inevitably leads to a closure problem, we propose a new closure scheme inspired by recent progress in the modelling of dissipative relativistic fluids, and crucially, demonstrate the linear stability of the proposed model.

gr-qc↗
arXiv2021

Thermal aspects of neutron star mergers

In order to extract maximal information from neutron-star merger signals, both gravitational and electromagnetic, we need to ensure that our theoretical models/numerical simulations faithfully represent the extreme physics involved. This involves a range of issues, with the finite temperature effects regulating many of the relevant phenomena. As a step towards understanding these issues, we explore the conditions for $β$-equilibrium in neutron star matter for the densities and temperatures reached in a binary neutron star merger. Using the results from our out-of-equilibrium merger simulation, we consider how different notions of equilibrium may affect the merger dynamics, raising issues that arise when attempting to account for these conditions in future simulations. These issues are both computational and conceptual. We show that the effects lead to, in our case, a softening of the equation of state in some density regions, and to composition changes that affect processes that rely on deviation from equilibrium, such as bulk viscosity, both in terms of the magnitude and the equilibration timescales inherent to the relevant set of reactions. We also demonstrate that it is difficult to determine exactly which equilibrium conditions are relevant in which regions of the matter due to the dependence on neutrino absorption, further complicating the calculation of the reactions that work to restore the matter to equilibrium.

astro-ph.HE↗
arXiv2020

Instabilities in neutron-star postmerger remnants

Using nonlinear, fully relativistic, simulations we investigate the dynamics and gravitational-wave signature associated with instabilities in neutron star postmerger remnants. For simplified models of the remnant we establish the presence of an instability in stars with moderate $T/|W|$, the ratio between the kinetic and the gravitational potential energies. Detailed analysis of the density oscillation pattern reveals a \emph{local} instability in the inner region of the more realistic differential rotation profile. We apply Rayleigh's inflection theorem and Fjørtoft's theorem to analyze the stability criteria concluding that this \emph{inner local} instability originates from a shear instability close to the peak of the angular velocity profile, and that it later evolves into a fast-rotating m=2 oscillation pattern. We discuss the importance of the presence of a corotation point in the fluid, its connection with the shear instability, and comparisons to the Rossby wave and Papaloizou Pringle instabilities considered in the wider literature.

astro-ph.HE↗
arXiv2019

A resistive extension for ideal MHD

We present an extension to the special relativistic, ideal magnetohydrodynamics (MHD) equations, designed to capture effects due to resistivity. The extension takes the simple form of an additional source term which, when implemented numerically, is shown to emulate the behaviour produced by a fully resistive MHD description for a range of initial data. The extension is developed from first principle arguments, and thus requires no fine tuning of parameters, meaning it can be applied to a wide range of dynamical systems. Furthermore, our extension does not suffer from the same stiffness issues arising in resistive MHD, and thus can be evolved quickly using explicit methods, with performance benefits of roughly an order of magnitude compared to current methods.

physics.plasm-ph↗
arXiv2018

Resistive and multi-fluid RMHD on graphics processing units

In this work we present a proof of concept of CUDA-capable, resistive, multi-fluid models of relativistic magnetohydrodynamics (RMHD). Resistive and multi-fluid codes for simulating models of RMHD suffer from stiff source terms, so it is common to implement a set of semi-implicit time integrators to maintain numerical stability. We show, for the first time, that finite volume IMEX schemes for resistive and two-fluid models of RMHD can be accelerated by execution on graphics processing units, significantly reducing the demand set by these kinds of problems. We report parallel speed-ups of over 21$\times$ using double precision floating-point accuracy, and highlight the optimisation strategies required for these schemes, and how they differ from ideal RMHD models. The impact of these results is discussed in the context of the next-generation simulations of neutron star mergers.

physics.comp-ph↗
arXiv2015

Magnon-Driven Domain-Wall Motion with the Dzyaloshinskii-Moriya Interaction

We study domain wall (DW) motion induced by spin waves (magnons) in the presence of Dzyaloshinskii-Moriya interaction (DMI). The DMI exerts a torque on the DW when spin waves pass through the DW, and this torque represents a linear momentum exchange between the spin wave and the DW. Unlike angular momentum exchange between the DW and spin waves, linear momentum exchange leads to a rotation of the DW plane rather than a linear motion. In the presence of an effective easy plane anisotropy, this DMI induced linear momentum transfer mechanism is significantly more efficient than angular momentum transfer in moving the DW.

cond-mat.mtrl-sci↗