arXiv subjects

I. Hawke

Publications and source records attributed to I. Hawke.

At least 19 recordsLinked to original sources

arXiv2026

Action based approach to dissipative relativistic fluid systems

We develop an action principle for a relativistic two-fluid system with dissipation. The specific constituents of the model - which serves as a proof of principle - are particles and entropy. The linchpin of the action is the assertion that a given flux is dissipative if its covariant divergence is non-zero. For our model, the particle flux is taken to be conservative while the entropy flux is dissipative. This allows for a "top-down" approach where the general question is geometric. Previous work has shown that new terms (the proper time derivative of matter space "metrics") must be included in the Lagrangian in order to produce equations of motion with terms representing bulk and shear viscosity. In addition to including these terms we show that further terms - interpreted as velocities - can be included. The new action-based model recovers known relativistic formulations of the Cattaneo equation, which results in causal heat propagation. We further advance our understanding by exploring the single-fluid limit by locking the entropy four-velocity to that of the matter component. This reduces the system to a single field equation along with a constraint equation. We show that this constraint leads to a dynamical extension of the standard Tolman red-shift condition. Finally, we provide three example actions (of increasing complexity) which demonstrate that the model is able to reproduce (in the single-fluid limit) the anticipated terms from the relativistic Navier-Stokes equations. In the general case, the action based approach allows for a much richer structure, which may be relevant for realistic models of non-linear dissipative relativistic fluid systems.

gr-qc↗

arXiv2024

Problematic systematics in neutron-star merger simulations

Next-generation gravitational-wave instruments are expected to constrain the equation of state of dense nuclear matter by observing binaries involving neutron stars. We highlight a problematic systematic error in finite-temperature merger simulations, where shock heating associated with the neutron-star surface gives rise to elevated temperatures. We demonstrate the severe implications of this artificial heating by computing static and dynamical tidal parameters for neutron stars immersed in simulation temperature profiles. The induced systematic errors must be addressed if we want to build robust gravitational-wave signal models for neutron-star, or indeed neutron star-black hole, binaries.

gr-qc↗

arXiv2024

Covariant approach to relativistic large-eddy simulations: Lagrangian filtering

We present a proof-of-principle implementation of the first fully covariant filtering scheme applied to relativistic fluid turbulence. The filtering is performed with respect to special observers, identified dynamically as moving with the "bulk of the flow". This means that filtering does not depend on foliations of spacetime but rather on the intrinsic fibration traced out by the observers. The covariance of the approach means that the results may be lifted into an arbitrary, curved spacetime. This practical step follows theoretical work showing that the residuals introduced by filtering a fine-scale ideal fluid can be represented by a non-ideal fluid prescription at the coarse scale. We interpret such non-ideal terms using a simple first-order gradient model, which allows us to extract effective turbulent viscosities and conductivity. A statistical regression on these terms shows that the majority of their variation may be explained by the thermodynamic properties of the filtered fluid and invariants of its flow, such as the shear and vorticity. This serves as a validation of the method and enables us to fit a functional, power-law form for the non-ideal coefficients -- an approach that may be used practically to give a sub-grid closure model in large-eddy simulations.

astro-ph.HE↗

arXiv2023

Local magneto-shear instability in Newtonian gravity

The magneto-rotational instability (MRI) - which is due to an interplay between a sheared background and the magnetic field - is commonly considered a key ingredient for developing and sustaining turbulence in the outer envelope of binary neutron star merger remnants. To assess whether (or not) the instability is active and resolved, criteria originally derived in the accretion disk literature - thus exploiting the symmetries of such systems - are often used. In this paper we discuss the magneto-shear instability as a truly local phenomenon, relaxing common symmetry assumptions on the background on top of which the instability grows. This makes the discussion well-suited for highly dynamical environments such as binary mergers. We find that - although this is somewhat hidden in the usual derivation of the MRI dispersion relation - the instability crucially depends on the assumed symmetries. Relaxing the symmetry assumptions on the background we find that the role of the magnetic field is significantly diminished, as it affects the modes' growth but does not drive it. This suggests that we should not expect the standard instability criteria to provide a faithful indication/diagnostic of what "is actually going on" in mergers. We conclude by making contact with a suitable filtering operation, as this is key to separating background and fluctuations in highly dynamical systems.

astro-ph.HE↗

arXiv2022

Formulating bulk viscosity for neutron star simulations

In order to extract the precise physical information encoded in the gravitational and electromagnetic signals from powerful neutron-star merger events, we need to include as much of the relevant physics as possible in our numerical simulations. This presents a severe challenge, given that many of the involved parameters are poorly constrained. In this paper we focus on the role of nuclear reactions. Combining a theoretical discussion with an analysis connecting to state-of-the-art simulations, we outline multiple arguments that lead to a reactive system being described in terms of a bulk viscosity. The results demonstrate that in order to properly account for nuclear reactions, future simulations must be able to handle different regimes where rather different assumptions/approximations are appropriate. We also touch upon the link to models based on the large-eddy-strategy required to capture turbulence.

astro-ph.HE↗

arXiv2021

The physics of non-ideal general relativistic magnetohydrodynamics

We consider a framework for non-ideal magnetohydrodynamics in general relativity, paying particular attention to the physics involved. The discussion highlights the connection between the microphysics (associated with a given equation of state) and the global dynamics (from the point of view of numerical simulations), and includes a careful consideration of the assumptions that lead to ideal and resistive magnetohydrodynamics. We pay particular attention to the issue of local charge neutrality, which tends to be assumed but appears to be more involved than is generally appreciated. While we do not resolve all the involved issues, we highlight how some of the assumptions and simplifications may be tested by simulations. The final formulation is consistent, both logically and physically, preparing the ground for a new generation of models of relevant astrophysical scenarios.

astro-ph.HE↗

arXiv2018

Toward Resolved Simulations of Burning Fronts in Thermonuclear X-ray Bursts

We discuss the challenges of modeling X-ray bursts in multi-dimensions, review the different calculations done to date, and discuss our new set of ongoing simulations. We also describe algorithmic improvements that may help in the future to offset some of the expense of these simulations, and describe what may be possible with exascale computing.

astro-ph.HE↗

arXiv2018

Effects of tangential velocity in the reactive relativistic Riemann problem

Type I X-ray bursts are thermonuclear burning events which occur on the surfaces of accreting neutron stars. Burning begins in a localised spot in the star's ocean layer before propagating across the entire surface as a deflagration. On the scale of the entire star, the burning front can be thought of as discontinuity. To model this, we investigated the reactive Riemann problem for relativistic deflagrations and detonations and developed a numerical solver. Unlike for the Newtonian Riemann problem, where only the velocity perpendicular to the interface is relevant, in the relativistic case the tangential velocity becomes coupled through the Lorentz factor and can alter the waves present in the solution. We investigated whether a fast tangential velocity may be able to cause a deflagration wave to transition to a detonation. We found that such a transition is possible, but only for tangential velocities that are a significant fraction of the speed of light or for systems already on the verge of transitioning. Consequently, it is highly unlikely that this transition would occur for a burning front in a neutron star ocean without significant contributions from additional multidimensional effects.

astro-ph.HE↗

arXiv2016

A variational approach to resistive relativistic plasmas

We develop an action principle to construct the field equations for a multi-fluid system containing charge-neutral fluids, plasmas, and dissipation (via resistive interactions), by combining the standard, Maxwell action and minimal coupling of the electromagnetic field with a recently developed action for relativistic dissipative fluids. We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for both the charge-neutral fluids and currents making up the plasmas. Using basic linear algebra techniques, we show that a general "relabeling" invariance exists for the abstract matter spaces. With the field equations in place, a phenomenological model for the resistivity is developed, using as constraints charge conservation and the Second Law of Thermodynamics. A minimal model for a system of electrons, protons, and heat is developed using the Onsager procedure for incorporating dissipation.

gr-qc↗

arXiv2016

Beyond ideal magnetohydrodynamics: From fibration to 3+1 foliation

We consider a resistive multi-fluid framework from the 3+1 space-time foliation point-of-view, paying particular attention to issues relating to the use of multi-parameter equations of state and the associated inversion from evolved to primitive variables. We highlight relevant numerical issues that arise for general systems with relative flows. As an application of the new formulation, we consider a three-component system relevant for hot neutron stars. In this case we let the baryons (neutrons and protons) move together, but allow heat and electrons to exhibit relative flow. This reduces the problem to three momentum equations; overall energy-momentum conservation, a generalised Ohm's law and a heat equation. Our results provide a hierarchy of increasingly complex models and prepare the ground for new state-of-the-art simulations of relevant scenarios in relativistic astrophysics.

gr-qc↗

arXiv2016

Beyond ideal magnetohydrodynamics: Resistive, reactive and relativistic plasmas

We develop a new framework for the modelling of charged fluid dynamics in general relativity. The model, which builds on a recently developed variational multi-fluid model for dissipative fluids, accounts for relevant effects like the inertia of both charge currents and heat and, for mature systems, the decoupling of superfluid components. We discuss how the model compares to standard relativistic magnetohydronamics and consider the connection between the fluid dynamics, the microphysics and the underlying equation of state. As illustrations of the formalism, we consider three distinct two-fluid models describing i) an Ohm's law for resistive charged flows, ii) a relativistic heat equation, and iii) an equation representing the momentum of a decoupled superfluid component. As a more complex example, we also formulate a three-fluid model which demonstrates the thermo-electric effect. This framework allows us to model neutron stars (and related systems) at a hierarchy of increasingly complex levels, and should enable us to make progress on a range of exciting problems in astrophysics and cosmology.

gr-qc↗

arXiv2013

The nonlinear development of the relativistic two-stream instability

The two-stream instability has been mooted as an explanation for a range of astrophysical applications from GRBs and pulsar glitches to cosmology. Using the first nonlinear numerical simulations of relativistic multi-species hydrodynamics we show that the onset and initial growth of the instability is very well described by linear perturbation theory. In the later stages the linear and nonlinear description match only qualitatively, and the instability does not saturate even in the nonlinear case by purely ideal hydrodynamic effects.

gr-qc↗

arXiv2012

Scientific Objectives of Einstein Telescope

The advanced interferometer network will herald a new era in observational astronomy. There is a very strong science case to go beyond the advanced detector network and build detectors that operate in a frequency range from 1 Hz-10 kHz, with sensitivity a factor ten better in amplitude. Such detectors will be able to probe a range of topics in nuclear physics, astronomy, cosmology and fundamental physics, providing insights into many unsolved problems in these areas.

gr-qc↗

arXiv2011

Crustal failure during binary inspiral

We present the first fully relativistic calculations of the crustal strain induced in a neutron star by a binary companion at the late stages of inspiral, employing realistic equations of state for the fluid core and the solid crust. We show that while the deep crust is likely to fail only shortly before coalescence, there is a large variation in elastic strain, with the outermost layers failing relatively early on in the inspiral. We discuss the significance of the results for both electromagnetic and gravitational-wave astronomy.

astro-ph.SR↗

arXiv2011

Tidal deformations of neutron stars: The role of stratification and elasticity

We discuss the response of neutron stars to the tidal interaction in a compact binary system, as encoded in the Love number associated with the induced deformation. This problem is of interest for gravitational-wave astronomy as there may be a detectable imprint on the signal from the late stages of binary coalescence. Previous work has focussed on simple barotropic neutron star models, providing an understanding of the role of the stellar compactness and overall density profile. We add realism to the discussion by developing the framework required to model stars with varying composition and an elastic crust. These effects are not expected to be significant for the next generation of detectors but it is nevertheless useful to be able to quantify them. Our results show that (perhaps surprisingly) internal stratification has no impact whatsoever on the Love number. We also show that crust elasticity provides a (predictably) small correction to existing models.

astro-ph.SR↗

arXiv2010

Dynamics and Gravitational Wave Signature of Collapsar Formation

We perform 3+1 general relativistic simulations of rotating core collapse in the context of the collapsar model for long gamma-ray bursts. We employ a realistic progenitor, rotation based on results of stellar evolution calculations, and a simplified equation of state. Our simulations track self-consistently collapse, bounce, the postbounce phase, black hole formation, and the subsequent early hyperaccretion phase. We extract gravitational waves from the spacetime curvature and identify a unique gravitational wave signature associated with the early phase of collapsar formation.

astro-ph.HE↗

arXiv2009

Numerical simulations of interfaces in relativistic hydrodynamics

We consider models of relativistic matter containing sharp interfaces across which the matter model changes. These models will be relevant for neutron stars with crusts, phase transitions, or for viscous boundaries where the length scale is too short to be modelled smoothly. In particular we look at numerical techniques that allow us to evolve stable interfaces, for the interfaces to merge, and for strong waves and shocks to interact with the interfaces. We test these techniques for ideal hydrodynamics in special and general relativity for simple equations of state, finding that simple level set-based methods extend well to relativistic hydrodynamics.

gr-qc↗

arXiv2009

Oscillations of rapidly rotating stratified neutron stars

We use time-evolutions of the linear perturbation equations to study the oscillations of rapidly rotating neutrons stars. Our models account for the buoyancy due to composition gradients and we study, for the first time, the nature of the resultant g-modes in a fast spinning star. We provide detailed comparisons of non-stratified and stratified models. This leads to an improved understanding of the relationship between the inertial modes of a non-stratified star and the g-modes of a stratified system. In particular, we demonstrate that each g-mode becomes rotation-dominated, i.e. approaches a particular inertial mode, as the rotation rate of the star is increased. We also discuss issues relating to the gravitational-wave driven instability of the various classes of oscillation modes.

astro-ph↗