arXiv subjects

Toby S. Wood

Publications and source records attributed to Toby S. Wood.

At least 19 recordsLinked to original sources

arXiv2025

Vortex Avalanches and Collective Motion in Neutron Stars

We simulate the dynamics of about 600 quantum vortices in a spinning-down cylindrical container using a Gross--Pitaevskii model. For the first time, we find convincing spatial-temporal evidence of avalanching behaviour resulting from vortex depinning and collective motion. During a typical avalanche, about 10 to 20 vortices exit the container in a short period, producing a glitch in the superfluid angular momentum and a localised void in the vorticity. After the glitch, vortices continue to depin and circulate around the vorticity void in a similar manner to that seen in previous point-vortex simulations. We present evidence of collective vortex motion throughout this avalanche process. We also show that the effective Magnus force can be used to predict when and where avalanches will occur. Lastly, we comment on the challenge of extrapolating these results to conditions in real neutron stars, which contain many orders of magnitude more vortices.

astro-ph.HE↗

arXiv2024

Shear-driven magnetic buoyancy in the solar tachocline: Dependence of the mean electromotive force on diffusivity and latitude

The details of the dynamo process that is responsible for driving the solar magnetic activity cycle are still not fully understood. In particular, whilst differential rotation provides a plausible mechanism for the regeneration of the toroidal (azimuthal) component of the large-scale magnetic field, there is ongoing debate regarding the process that is responsible for regenerating the Sun's large-scale poloidal field. Our aim is to demonstrate that magnetic buoyancy, in the presence of rotation, is capable of producing the necessary regenerative effect. Building upon our previous work, we carry out numerical simulations of a local Cartesian model of the tachocline, consisting of a rotating, fully compressible, electrically conducting fluid with a forced shear flow. An initially weak, vertical magnetic field is sheared into a strong, horizontal magnetic layer that becomes subject to magnetic buoyancy instability. By increasing the Prandtl number we lessen the back reaction of the Lorentz force onto the shear flow, maintaining stronger shear and a more intense magnetic layer. This in turn leads to a more vigorous instability and a much stronger mean electromotive force, which has the potential to significantly influence the evolution of the mean magnetic field. These results are only weakly dependent upon the inclination of the rotation vector, i.e. the latitude of the local Cartesian model. Although further work is needed to confirm this, these results suggest that magnetic buoyancy in the tachocline is a viable poloidal field regeneration mechanism for the solar dynamo.

astro-ph.SR↗

arXiv2024

Stratified Resistive Tearing Instability

Resistive tearing instabilities are common in fluids that are highly electrically conductive and carry strong currents. We determine the effect of stable stratification on the tearing instability under the Boussinesq approximation. Our results generalise previous work that considered only specific parameter regimes, and we show that the length scale of the fastest growing mode depends non-monotonically on the stratification strength. We confirm our analytical results by solving the linearised equations numerically, and we discuss whether the instability could operate in the solar tachocline.

physics.flu-dyn↗

arXiv2023

Vortex depinning in a two-dimensional superfluid

We employ the Gross--Pitaevskii theory to model a quantized vortex depinning from a small obstacle in a two-dimensional superfluid due to an imposed background superfluid flow. We find that, when the flow's velocity exceeds a critical value, the vortex drifts orthogonally to the flow before subsequently moving parallel to it away from the pinning site. The motion of the vortex around the pinning site is also accompanied by an emission of a spiral-shaped sound pulse. Through simulations, we present a phase diagram of the critical flow velocity for vortex depinning together with an empirical formula that illustrates how the critical velocity increases with the height and width of the pinning site. By employing a variety of choices of initial and boundary conditions, we are able to obtain lower and upper bounds on the critical velocity and demonstrate the robustness of these results.

cond-mat.quant-gas↗

arXiv2023

Shear-driven magnetic buoyancy in the solar tachocline: The mean electromotive force due to rotation

The leading theoretical paradigm for the Sun's magnetic cycle is an $αω$-dynamo process, in which a combination of differential rotation and turbulent, helical flows produces a large-scale magnetic field that reverses every 11 years. Most $αω$ solar dynamo models rely on differential rotation in the solar tachocline to generate a strong toroidal field. The most problematic part of such models is then the production of the large-scale poloidal field, via a process known as the $α$-effect. Whilst this is usually attributed to small-scale convective motions under the influence of rotation, the efficiency of this regenerative process has been called into question by some numerical simulations. Motivated by likely conditions within the tachocline, the aim of this paper is to investigate an alternative mechanism for the poloidal field regeneration, namely the magnetic buoyancy instability in a shear-generated, rotating magnetic layer. We use a local, fully compressible model in which an imposed vertical shear winds up an initially vertical magnetic field. The field ultimately becomes buoyantly unstable, and we measure the resulting mean electromotive force (EMF). For sufficiently rapid rotation, we find that a significant component of the mean EMF is aligned with the direction of the mean magnetic field, which is the characteristic feature of the classical $αω$-dynamo model. Our results therefore suggest that magnetic buoyancy could contribute directly to the generation of large-scale poloidal field in the Sun.

astro-ph.SR↗

arXiv2022

Validity of sound-proof approximations for magnetic buoyancy

The presence of acoustic waves in models of compressible flows can present complications for analytical and numerical analysis. Therefore, several methods have been developed to filter out these waves, leading to various "sound-proof" models, including the Boussinesq, anelastic and pseudo-incompressible models. We assess the validity of each of these approximate models for describing magnetic buoyancy in the context of the solar interior. A general sound-proof model is introduced and compared to the fully compressible system in a number of asymptotic regimes, including both non-rotating and rotating cases. We obtain specific constraints that must be satisfied in order that the model captures the leading-order behaviour of the fully compressible system. We then discuss which of the existing sound-proof models satisfy these constraints, and in what parameter regimes. We also present a variational derivation of the pseudo-incompressible MHD model, demonstrating its underlying Hamiltonian structure.

physics.flu-dyn↗

arXiv2022

Three-Dimensional Magnetothermal Simulations of Magnetar Outbursts

The defining trait of magnetars, the most strongly magnetized neutron stars (NSs), is their transient activity in the X/$γ$-bands. In particular, many of them undergo phases of enhanced emission, the so-called outbursts, during which the luminosity rises by a factor $\sim$10$-$1000 in a few hours to then decay over months/years. Outbursts often exhibit a thermal spectrum, associated with the appearance of hotter regions on the surface of the star, which subsequently change in shape and cool down. Here we simulate the unfolding of a sudden, localized heat injection in the external crust of a NS with a 3D magneto-thermal evolution code, finding that this can reproduce the main features of magnetar outbursts. A full 3D treatment allows us to study for the first time the inherently asymmetric hot-spots which appear on the surface of the star as the result of the injection and to follow the evolution of their temperature and shape. We investigate the effects produced by different physical conditions in the heated region, highlighting in particular how the geometry of the magnetic field plays a key role in determining the properties of the event.

astro-ph.HE↗

arXiv2021

X-ray Emission from Isolated Neutron Stars revisited: 3D magnetothermal simulations

X-ray emission from the surface of isolated neutron stars (NSs) has been now observed in a variety of sources. The ubiquitous presence of pulsations clearly indicates that thermal photons either come from a limited area, possibly heated by some external mechanism, or from the entire (cooling) surface but with an inhomogeneous temperature distribution. In a NS the thermal map is shaped by the magnetic field topology, since heat flows in the crust mostly along the magnetic field lines. Self-consistent surface thermal maps can hence be produced by simulating the coupled magnetic and thermal evolution of the star. We compute the evolution of the neutron star crust in three dimensions for different initial configurations of the magnetic field and use the ensuing thermal surface maps to derive the spectrum and the pulse profile as seen by an observer at infinity, accounting for general-relativistic effects. In particular, we compare cases with a high degree of symmetry with inherently 3D ones, obtained by adding a quadrupole to the initial dipolar field. Axially symmetric fields result in rather small pulsed fractions ($\lesssim 5\%$), while more complex configurations produce higher pulsed fractions, up to $\sim25\%$. We find that the spectral properties of our axisymmetric model are close to those of the bright isolated NS RX~J1856.5-3754 at an evolutionary time comparable with the inferred dynamical age of the source.

astro-ph.HE↗

arXiv2021

Superconducting phases in a two-component microscale model of neutron star cores

We identify the possible ground states for a mixture of two superfluid condensates (one neutral, the other electrically charged) using a phenomenological Ginzburg-Landau model. While this framework is applicable to any interacting condensed-matter mixture of a charged and a neutral component, we focus on nuclear matter in neutron star cores, where proton and neutron condensates are coupled via non-dissipative entrainment. We employ the Skyrme interaction to determine the neutron star's equilibrium composition, and hence obtain realistic coefficients for our Ginzburg-Landau model at each depth within the star's core. We then use the Ginzburg-Landau model to determine the ground state in the presence of a magnetic field. In this way, we obtain superconducting phase diagrams for six representative Skyrme models, revealing the microphysical magnetic flux distribution throughout the neutron star core. The phase diagrams are rather complex and the locations of most of the phase transitions can only be determined through numerical calculations. Nonetheless, we find that for all equations of state considered in this work, much of the outer core exhibits type-1.5 superconductivity, rather than type-II superconductivity as is generally assumed. For local magnetic field strengths $\lesssim 10^{14} \, {\rm G}$, the magnetic flux is distributed inhomogeneously, with bundles of magnetic fluxtubes separated by flux-free Meissner regions. We provide an approximate criterion to determine the transition between this type-1.5 phase and the type-I region in the inner core.

cond-mat.supr-con↗

arXiv2021

3D Magneto-thermal Simulations of Tangled Crustal Magnetic Field in Central Compact Objects

Central compact objects are young neutron stars emitting thermal X-rays with bolometric luminosities $L_X$ in the range $10^{32}$-$10^{34}$ erg/s. Gourgouliatos, Hollerbach and Igoshev recently suggested that peculiar emission properties of central compact objects can be explained by tangled magnetic field configurations formed in a stochastic dynamo during the proto-neutron star stage. In this case the magnetic field consists of multiple small-scale components with negligible contribution of global dipolar field. We study numerically three-dimensional magneto-thermal evolution of tangled crustal magnetic fields in neutron stars. We find that all configurations produce complicated surface thermal patterns which consist of multiple small hot regions located at significant separations from each other. The configurations with initial magnetic energy of $2.5-10\times 10^{47}$ erg have temperatures of hot regions that reach $\approx 0.2$ keV, to be compared with the bulk temperature of $\approx 0.1$ keV in our simulations with no cooling. A factor of two in temperature is also seen in observations of central compact objects. The hot spots produce periodic modulations in light curve with typical amplitudes of $\leq 9-11$ %. Therefore, the tangled magnetic field configuration can explain thermal emission properties of some central compact objects.

astro-ph.HE↗

arXiv2020

3D modelling of magneto-thermal evolution of neutron stars: method and test cases

Neutron stars harbour extremely strong magnetic fields within their solid outer crust. The topology of this field strongly influences the surface temperature distribution, and hence the star's observational properties. In this work, we present the first realistic simulations of the coupled crustal magneto-thermal evolution of isolated neutron stars in three dimensions with account for neutrino emission, obtained with the pseudo-spectral code Parody. We investigate both the secular evolution, especially in connection with the onset of instabilities during the Hall phase, and the short-term evolution following episodes of localised energy injection. Simulations show that a resistive tearing instability develops in about a Hall time if the initial toroidal field exceeds ~$10^{15}$ G. This leads to crustal failures because of the huge magnetic stresses coupled with the local temperature enhancement produced by dissipation. Localised heat deposition in the crust results in the appearance of hot spots on the star surface which can exhibit a variety of patterns. Since the transport properties are strongly influenced by the magnetic field, the hot regions tend to drift away and get deformed following the magnetic field lines while cooling. The shapes obtained with our simulations are reminiscent of those recently derived from NICER X-ray observations of the millisecond pulsar PSR J0030+0451.

astro-ph.HE↗

arXiv2020

On the saturation mechanism of the fluctuation dynamo at ${\text{Pr}_\mathrm{M}} \ge 1$

The presence of magnetic fields in many astrophysical objects is due to dynamo action, whereby a part of the kinetic energy is converted into magnetic energy. A turbulent dynamo that produces magnetic field structures on the same scale as the turbulent flow is known as the fluctuation dynamo. We use numerical simulations to explore the nonlinear, statistically steady state of the fluctuation dynamo in driven turbulence. We demonstrate that as the magnetic field growth saturates, its amplification and diffusion are both affected by the back-reaction of the Lorentz force upon the flow. The amplification of the magnetic field is reduced due to stronger alignment between the velocity field, magnetic field, and electric current density. Furthermore, we confirm that the amplification decreases due to a weaker stretching of the magnetic field lines. The enhancement in diffusion relative to the field line stretching is quantified by a decrease in the computed local value of the magnetic Reynolds number. Using the Minkowski functionals, we quantify the shape of the magnetic structures produced by the dynamo as magnetic filaments and ribbons in both kinematic and saturated dynamos and derive the scalings of the typical length, width, and thickness of the magnetic structures with the magnetic Reynolds number. We show that all three of these magnetic length scales increase as the dynamo saturates. The magnetic intermittency, strong in the kinematic dynamo (where the magnetic field strength grows exponentially) persists in the statistically steady state, but intense magnetic filaments and ribbons are more volume-filling.

astro-ph.GA↗

arXiv2018

On energy equipartition between cosmic rays and magnetic fields

Interpretations of synchrotron observations often assume a tight correlation between magnetic and cosmic ray energy densities. We examine this assumption using both test-particle simulations of cosmic rays and MHD simulations which include cosmic rays as a diffusive fluid. We find no spatial correlation between the cosmic rays and magnetic field energy densities at turbulent scales. Moreover, the cosmic ray number density and magnetic field energy density are statistically independent. Nevertheless, the cosmic ray spatial distribution is highly inhomogeneous, especially at low energies because the particles are trapped between random magnetic mirrors. These results can significantly change the interpretation of synchrotron observations and thus our understanding of the strength and structure of magnetic fields in the Milky Way and nearby spiral galaxies.

astro-ph.GA↗

arXiv2018

A self-consistent model of the solar tachocline

We present a local but fully nonlinear model of the solar tachocline, using three-dimensional direct numerical simulations. The tachocline forms naturally as a statistically steady balance between Coriolis, pressure, buoyancy and Lorentz forces beneath a turbulent convection zone. Uniform rotation is maintained in the radiation zone by a primordial magnetic field, which is confined by meridional flows in the tachocline and convection zone. Such balanced dynamics has previously been found in idealised laminar models, but never in fully self-consistent numerical simulations.

astro-ph.SR↗

arXiv2017

Relative distribution of cosmic rays and magnetic fields

Synchrotron radiation from cosmic rays is a key observational probe of the galactic magnetic field. Interpreting synchrotron emission data requires knowledge of the cosmic ray number density, which is often assumed to be in energy equipartition (or otherwise tightly correlated) with the magnetic field energy. However, there is no compelling observational or theoretical reason to expect such tight correlation to hold across all scales. We use test particle simulations, tracing the propagation of charged particles (protons) through a random magnetic field, to study the cosmic ray distribution at scales comparable to the correlation scale of the turbulent flow in the interstellar medium ($\simeq 100\,{\rm pc}$ in spiral galaxies). In these simulations, we find that there is no spatial correlation between the cosmic ray number density and the magnetic field energy density. In fact, their distributions are approximately statistically independent. We find that low-energy cosmic rays can become trapped between magnetic mirrors, whose location depends more on the structure of the field lines than on the field strength.

astro-ph.GA↗

arXiv2015

Three-dimensional simulations of the magnetic stress in a neutron star crust

We present the first fully self-consistent three-dimensional model of a neutron star's magnetic field, generated by electric currents in the star's crust via the Hall effect. We find that the global-scale field converges to a Hall-attractor state, as seen in recent axisymmetric models, but that small-scale features in the magnetic field survive even on much longer timescales. These small-scale features propagate toward the dipole equator, where the crustal electric currents organize themselves into a strong equatorial jet. By calculating the distribution of magnetic stresses in the crust, we predict that neutron stars with fields stronger than $10^{14}$G can still be subject to starquakes more than $10^5$yr after their formation.

astro-ph.SR↗

arXiv2015

Transport by meridional circulations in solar-type stars

Transport by meridional flows has significant consequences for stellar evolution, but is difficult to capture in global-scale numerical simulations because of the wide range of timescales involved. Stellar evolution models therefore usually adopt parameterizations for such transport based on idealized laminar or mean-field models. Unfortunately, recent attempts to model this transport in global simulations have produced results that are not consistent with any of these idealized models. In an effort to explain the discrepancies between global simulations and idealized models, we here use three-dimensional local Cartesian simulations of compressible convection to study the efficiency of transport by meridional flows below a convection zone in several parameter regimes of relevance to the Sun and solar-type stars. In these local simulations we are able to establish the correct ordering of dynamical timescales, although the separation of the timescales remains unrealistic. We find that, even though the generation of internal waves by convective overshoot produces a high degree of time dependence in the meridional flow field, the mean flow has the qualitative behavior predicted by laminar, "balanced" models. In particular, we observe a progressive deepening, or "burrowing", of the mean circulation if the local Eddington-Sweet timescale is shorter than the viscous diffusion timescale. Such burrowing is a robust prediction of laminar models in this parameter regime, but has never been observed in any previous numerical simulation. We argue that previous simulations therefore underestimate the transport by meridional flows.

astro-ph.SR↗

arXiv2015

A new model for mixing by double-diffusive convection (semi-convection). II. The transport of heat and composition through layers

Regions of stellar and planetary interiors that are unstable according to the Schwarzschild criterion, but stable according to the Ledoux criterion, are subject to a form of oscillatory double-diffusive (ODD) convection often called "semi-convection". In this series of papers, we use an extensive suite of three-dimensional (3D) numerical simulations to quantify the transport of heat and composition by ODD convection, and ultimately propose a new 1D prescription that can be used in stellar and planetary structure and evolution models. The first paper in this series demonstrated that under certain conditions ODD convection spontaneously transitions from an initially homogeneously turbulent state into a staircase of convective layers, which results in a substantial increase in the transport of heat and composition. Here, we present simulations of ODD convection in this layered regime, we describe the dynamical behavior of the layers, and we derive empirical scaling laws for the transport through layered convection.

astro-ph.SR↗