Hall Drift Research Articles

Hall effect in protostellar disc formation and evolution

ABSTRACT The Hall effect is recently shown to be efficient in magnetized dense molecular cores and could lead to a bimodal formation of rotationally supported discs (RSDs) in the first core phase. However, how such Hall dominated systems evolve in the protostellar accretion phase remains unclear. We carry out 2D axisymmetric simulations including Hall effect and ohmic dissipation, with realistic magnetic diffusivities computed from our equilibrium chemical network. We find that Hall effect only becomes efficient when the large population of very small grains (VSGs: ≲100 Å) is removed from the standard Mathis–Rumpl–Nordsieck size distribution. With such an enhanced Hall effect, however, the bimodality of disc formation does not continue into the main accretion phase. The outer part of the initial ∼40 au disc formed in the anti-aligned configuration ($\boldsymbol {\Omega \cdot B}\lt 0$) flattens into a thin rotationally supported Hall current sheet as Hall effect moves the poloidal magnetic field radially inward relative to matter, leaving only the inner ≲10–20 au RSD. In the aligned configuration ($\boldsymbol {\Omega \cdot B}\gt 0$), disc formation is suppressed initially but a counter-rotating disc forms subsequently due to efficient azimuthal Hall drift. The counter-rotating disc first grows to ∼30 au as Hall effect moves the magnetic field radially outward, but only the inner ≲10 au RSD is long lived like in the anti-aligned case. Besides removing VSGs, cosmic ray ionization rate should be below a few 10−16 s−1 for Hall effect to be efficient in disc formation. We conclude that Hall effect produces small ≲10–20 au discs regardless of the polarity of the magnetic field, and that radially outward diffusion of magnetic fields remains crucial for disc formation and growth.

Young magnetars with fracturing crusts as fast radio burst repeaters

AbstractFast radio bursts are millisecond-duration radio pulses of extragalactic origin. A recent statistical analysis has found that the burst energetics of the repeating source FRB 121102 follow a power law, with an exponent that is curiously consistent with the Gutenberg–Richter law for earthquakes. This hints that repeat bursters may be compact objects undergoing violent tectonic activity. For young magnetars, possessing crustal magnetic fields which are both strong (B ≳ 1015 G) and highly multipolar, Hall drift can instigate significant field rearrangements even on ≲ century long time-scales. This reconfiguration generates zones of magnetic stress throughout the outer layers of the star, potentially strong enough to facilitate frequent crustal failures. In this paper, assuming a quake scenario, we show how the crustal field evolution, which determines the resulting fracture geometries, can be tied to burst properties. Highly anisotropic stresses are generated by the rapid evolution of multipolar fields, implying that small, localized cracks can occur sporadically throughout the crust during the Hall evolution. Each of these shallow fractures may release bursts of energy, consistent in magnitude with those seen in the repeating sources FRB 121102 and FRB 180814.J0422+73.

Stability of a force‐free Hall equilibrium and release of magnetic energy

Conservation of magnetic helicity by the Hall drift does not prevent Hall instability of helical fields. This conclusion follows from stability analysis of a force‐free spatially periodic Hall equilibrium. The growth rates of the instability scale as σ ∝ B3/4η1/4 with the field strength B and magnetic diffusivity η and can be large compared to the rate of resistive decay of the background field. The instability deviates the magnetic field from the force‐free configuration. The unstable eigenmodes include a fine spatial structure that evolves into current sheets at the nonlinear stage of the instability. The instability catalyzes the resistive release of magnetic energy. The energy is released in a sequence of spikes, every spike emits several percent of the total energy. A numerically defined scaling for the energy released in a single spike permits an extrapolation to astrophysically relevant values of the Hall number. The instability can be relevant to magnetic energy release in a neutron star crust and, possibly, in stellar coronae.

Local semi-analytic models of magnetic flux transport in protoplanetary discs

Abstract The evolution of a large-scale poloidal magnetic field in an accretion disc is an important problem because it determines the launching of winds and the feasibility of the magnetorotational instability to generate turbulence or channel flows. Recent studies, both semi-analytical calculations and numerical simulations, have highlighted the crucial role non-ideal magnetohydrodynamic effects (Ohmic resistivity, Hall drift, and ambipolar diffusion), relevant in the protoplanetary disc context, might play in magnetic flux evolution in the disc. We investigate the flux transport in discs through the use of two 1D semi-analytic models in the vertical direction, exploring regimes where different physical source terms and effects dominate. The governing equations for both models are derived by performing an asymptotic expansion in the limit of a thin disc, with the different regimes isolated through setting the relative order of the leading terms between variables. Flux transport rates and vertical structure profiles are calculated for a range of diffusivities and disc magnetizations. We found that Ohmic and ambipolar diffusivities drive radially outward flux transport with an outwardly inclined field. A wind outflow drives inward flux transport, which is significantly enhanced in the presence of Hall drift in the positive polarity case, $\eta _\mathrm{ H} (\boldsymbol{B}_\mathrm{ z} \cdot \boldsymbol{\Omega }) \gt 0$, an effect which has only been briefly noted before. Coupled only with outward inclination, the Hall effect reduces the flux transport given by a background Ohmic and/or ambipolar diffusivity, but drives no flux transport when it is the only non-ideal effect present.

Magnetic-field evolution in a plastically failing neutron-star crust

Under normal conditions in a neutron-star crust, ions are locked in place in the crustal lattice and only electrons are mobile, and magnetic-field evolution is thus directly related to the electron velocity. The evolution, however, builds magnetic stresses that can become sufficiently large for the crust to exceed its elastic limit, and to flow plastically. We consider the nature of this plastic flow and the back-reaction on the crustal magnetic field evolution. We formulate a plane-parallel model for the local failure, showing that surface motions are inevitable once the crust yields, in the absence of extra dissipative mechanisms. We perform numerical evolutions of the crustal magnetic field under the joint effect of Hall drift and Ohmic decay, tracking the build-up of magnetic stresses, and diagnosing crustal failure with the von Mises criterion. Beyond this point we solve for the coupled evolution of the plastic velocity and magnetic field. Our results suggest that to have a coexistence of a magnetar corona with small-scale magnetic features, the viscosity of the plastic flow must be roughly $10^{36}-10^{37}\ \textrm{g cm}^{-1}\textrm{s}^{-1}$. We find significant motion at the surface at a rate of $10-100$ centimetres per year, and that the localised magnetic field is weaker than in evolutions without plastic flow. We discuss astrophysical implications, and how our local simulations could be used to build a global model of field evolution in the neutron-star crust.

Numerical study of azimuthal sheath structure and asymmetric anomalous erosion in a stationary plasma thruster

The influence of the azimuthal electron drift on anomalous erosion and the sheath profile in a stationary plasma thruster (SPT) is analysed in this article. It is found that the anomalous erosion has a self-organized structure, which is formed by the interaction between the plasma and the ceramic walls. In order to interpret the mechanism of the azimuthal erosion structure, a particle in cell (PIC) model is developed to simulate the azimuthal sheath. The results show that the electron azimuthal Hall drift due to crossed electric and magnetic field plays a key role in the azimuthal erosion evolution process. Electron Hall drift can generate an asymmetric sheath structure and induce azimuthal sheath oscillation. Furthermore, an asymmetric sheath caused by the integrated effect of the azimuthal irregular wall structure and azimuthal Hall drift will result in the azimuthal movement of ions. Based on the sheath simulated results, an erosion model is used to simulate the azimuthal erosion evolution. An asymmetric erosion profile caused by the azimuthal asymmetric ion sputtering is found.

Investigations of the Ohmic Decay and the Soft X-Ray Emission of the High-braking-index Pulsar PSR J1640−4631

The young pulsar PSR J1640−4631 is the first pulsar reported with a high braking index, n = 3.15 ± 0.03, and has attracted extensive attention. In this work, by inputting the equation of state, we obtain two typical and feasible ranges of the electrical conductivity in the crust of PSR J1640−4631. Then, by considering the effects of general relativity, we formulate the induction equation and use it to investigate the decay of crustal magnetic fields within two scenarios: pure Ohmic decay, and the combination of Ohmic decay and Hall drift. In the former scenario, we calculate the current magnetic field decay rates as dBp/dt ∼ (0.78–1.00) × 107 G yr−1 and dBt/dt ∼ (0.82–1.05) × 108 G yr−1 for the poloidal and toroidal parts, respectively, and estimate the current magnetic energy decay rate as LB ∼ (0.95–1.22) × 1032 erg s−1. In the latter scenario, the combination of Ohmic decay and Hall drift accelerates the decay of magnetic fields, and we calculate the current magnetic field decay rates as dBp/dt ∼ (1.26–1.47) × 107 G yr−1, and dBt/dt ∼ (1.32–1.54) × 108 G yr−1 for the poloidal and toroidal parts, respectively, and estimate the current magnetic energy decay rate as LB ∼ (1.86–2.18) × 1032 erg s−1. It is found that the recalculated value of the braking index n of the star is lower than its observed value, which implies that other factors influence the spin-down evolution. The current magnetic energy decay rates calculated in both scenarios are far less than the isotropic soft X-ray luminosity obtained from Chandra+NuStar telescopes. The observed soft X-ray flux in the (2–10) keV band is FX ∼ 1.8(4) × 10−13 erg cm−2 s−1, which corresponds to a high surface temperature, T ∼ 1.54(6) × 106 K. The observed X-ray flux of the star could be caused by the decay of a multipolar magnetic field near the pole, which is strong enough to activate the slot-gap mechanism. The high surface temperature of the star is attributed either to magnetic spot formation or thermoplastic wave heating due to the decay of the toroidal field near the pole. Our results could be useful in interpreting the high soft X-ray flux from high magnetic field pulsars.

Conductivity of neutron star crust under superhigh magnetic fields and Ohmic decay of toroidal magnetic field of magnetar

<sec>Magnetar is a kind of pulsar powered by magnetic field energy. Part of the X-ray luminosities of magnetars in quiescence have a thermal origin and can be fitted by a blackbody spectrum with temperature <i>kT</i> ～ 0.2－0.6 keV, much higher than the typical values for rotation-powered pulsars. The observation and theoretical study of magnetar are one of hot topics in the field of pulsar research. The activity and emission characteristics of magnetar can be attributed to internal superhigh magnetic field. According to the work of WGW19 and combining with the equation of state, we first calculate the electric conductivity of the crust under a strong magnetic field, and then calculate the toroidal magnetic field decay rate and magnetic energy decay rate by using an eigenvalue equation of toroidal magnetic field decay and considering the effect of general relativity. We reinvestigate the <i>L</i><sub>X</sub>-<i>L</i><sub>rot</sub> relationship of 22 magnetars with persistent soft X-ray luminosities and obtain two new fitting formulas on <i>L</i><sub>X</sub>-<i>L</i><sub>rot</sub>. We find that for the magnetars with <i>L</i><sub>X</sub> < <i>L</i><sub>rot</sub>, the soft X-ray radiations may originate from their rotational energy loss rate, or from magneto-sphere flow and particle wind heating. For the magnetars with <i>L</i><sub>X</sub> > <i>L</i><sub>rot</sub>, the Ohmic decay of crustal toroidal magnetic fields can provide their observed isotropic soft X-ray radiation and maintain higher thermal temperature.</sec><sec>As for the initial dipole magnetic fields of magnetars, we mainly refer to the rersearch by Viganò et al. (Viganò D, Rea N, Pons J A, Perna R, Aguilera D N, Miralles J A 2013 <i>Mon. Not. R. Astron. Soc.</i> <b>434</b> 123), because they first proposed the up-dated neutron star magneto-thermal evolution model, which can successfully explain the X-ray radiation and cooling mechanism of young pulsars including magnetars and high-magnetic field pulsars. Objectively speaking, as to the decay of toroidal magnetic fields, there are some differences between our theoretical calculations of magnetic energy release rates and the actual situation of magnetic field decay in magnetars, this is because the estimate of initial dipolar magnetic field, true age and the thickness of inner crust of a magnetar are somewhat uncertain. In addition, due to the interstellar-medium’s absorptions to soft X-ray and the uncertainties of distance estimations, the observed soft X-ray luminosities of magnetars have certain deviations. With the continuous improvement of observation, equipment and methods, as well as the in-depth development of theoretical research, our model will be further improved, and the theoretical results are better accordant with the high-energy observation of magnetars.</sec><sec>We also discuss other possible anisotropy origins of soft X-ray fluxes of magnetars, such as the formation of magnetic spots and thermoplastic flow wave heating in the polar cap. Although anisotropic heating mechanisms are different from Ohmic decay, all of them require that there exist strong toroidal magnetic fields inside a magnetar. However, the anisotropic heating mechanisms require higher toroidal multipole fields inside a magnetar (such as magnetic octupole field) and are related to complex Hall drift: these may be our research subjects in the future.</sec>

Simulations of Secondary Farley‐Buneman Instability Driven by a Kilometer‐Scale Primary Wave: Anomalous Transport and Formation of Flat‐Topped Electric Fields

AbstractSince the 1950s, high frequency and very high frequency radars near the magnetic equator have frequently detected strong echoes caused ultimately by the Farley‐Buneman instability (FBI) and the gradient drift instability (GDI). In the 1980s, coordinated rocket and radar campaigns made the astonishing observation of flat‐topped electric fields coincident with both meter‐scale irregularities and the passage of kilometer‐scale waves. The GDI in the daytime E region produces kilometer‐scale primary waves with polarization electric fields large enough to drive meter‐scale secondary FBI waves. The meter‐scale waves propagate nearly vertically along the large‐scale troughs and crests and act as VHF tracers for the large‐scale dynamics. This work presents a set of hybrid numerical simulations of secondary FBIs, driven by a primary kilometer‐scale GDI‐like wave. Meter‐scale density irregularities develop in the crest and trough of the kilometer‐scale wave, where the total electric field exceeds the FBI threshold, and propagate at an angle near the direction of total Hall drift determined by the combined electric fields. The meter‐scale irregularities transport plasma across the magnetic field, producing flat‐topped electric fields similar to those observed in rocket data and reducing the large‐scale wave electric field to just above the FBI threshold value. The self‐consistent reduction in driving electric field helps explain why echoes from the FBI propagate near the plasma acoustic speed.

Effect of magnetic field directionality on discharging characteristics of Hall effect thruster with azimuthal diversion rail

The structure of an azimuthal diversion rail causes the neutral gas in the Hall effect thruster to possess a certain circumferential velocity. Two different directions of the magnetic field can be formed in the discharge channel, where the direction of the magnetic field depends on the direction of the excitation current. The aim of this work is to study the effect of magnetic field directionality on the discharging characteristics of a Hall effect thruster with an azimuthal diversion rail. The experimental results demonstrate that a change in the magnetic field direction corresponds to a change in the electronic Hall drift direction. When the electronic Hall drift direction is opposite to the circumferential velocity of the neutral gas, its thrust, specific impulse, and efficiency are higher than the case in which the electronic Hall drift direction is in the same direction as that of the circumferential velocity of neutral gas. The increase in performances is due to the increase in the propellant utilization. The reasons for the increase in the propellant utilization are explained. The experimental result provides a guide for the selection of the direction of excitation current of the Hall effect thruster with an azimuthal diversion rail.

Theoretical analysis of Hall factor and hole mobility in p-type 4H-SiC considering anisotropic valence band structure

The temperature dependencies of hole density and hole mobility of p-type 4H-SiC obtained by Hall effect measurement were theoretically analyzed taking account of its anisotropic valence band structure. The experimental Hall factor, which was derived from the ratio of theoretical hole density to experimental Hall hole density, was reproduced by theoretical Hall factor computed using the valence band structure and relaxation times of scattering mechanisms. The product of the theoretical Hall factor and drift mobility computed by the same transport model agreed well with the experimental Hall mobility. Based on analyses of the results, it was revealed that the temperature dependence of Hall factor can be explained by considering the anisotropic valence band structure along with consideration of anisotropic relaxation times. The contribution of each scattering mechanism was also discussed, and empirical formulas for Hall and drift mobilities are presented.

Magnetic field evolution of neutron stars – I. Basic formalism, numerical techniques and first results

In this work we explore the evolution of magnetic fields inside strongly magnetized neutron stars in axisymmetry. We model numerically the coupled field evolution in the core and the crust. Our code models the Hall drift and Ohmic effects in the crust, the back-reaction on the field from magnetically-induced elastic deformation of the crust, the magnetic twist exchange between the crust and the core, and the drift of superconducting flux tubes inside the core. The correct hydromagnetic equilibrium is enforced in the core. We find that i) The Hall attractor found by Gourgouliatos and Cumming in the crust exists also for configurations when the B-field penetrates into the core. However, the evolution timescale for the core-penetrating fields is dramatically different than that of the fields confined to the crust. ii) The combination of Jones' flux tube drift and Ohmic dissipation in the crust can deplete the pulsar magnetic fields on the timescale of $150$ Myr if the crust is hot ($T\sim2\times10^8$ K), but acts on much slower timescales for cold neutron stars, such as recycled pulsars ($\sim 1.8 $ Gyr, depending on impurity levels). iii) The outward motion of superfluid vortices during the rapid spin-down of a young highly magnetized pulsar, can result in a partial expulsion of flux from the core when $B\lesssim 10^{13}$ G. However for $B\gtrsim2\times 10^{13}$ G, the combination of a stronger magnetic field and a longer spin period implies that the core field cannot be expelled.

Stabilizing effect of resistivity towards ELM-free H-mode discharge in lithium-conditioned NSTX

Linear stability analysis of the national spherical torus experiment (NSTX) Li-conditioned ELM-free H-mode equilibria is carried out in the context of the extended magneto-hydrodynamic (MHD) model in NIMROD. The purpose is to investigate the physical cause behind edge localized mode (ELM) suppression in experiment after the Li-coating of the divertor and the first wall of the NSTX tokamak. Besides ideal MHD modeling, including finite-Larmor radius effect and two-fluid Hall and electron diamagnetic drift contributions, a non-ideal resistivity model is employed, taking into account the increase of Zeff after Li-conditioning in ELM-free H-mode. Unlike an earlier conclusion from an eigenvalue code analysis of these equilibria, NIMROD results find that after reduced recycling from divertor plates, profile modification is necessary but insufficient to explain the mechanism behind complete ELMs suppression in ideal two-fluid MHD. After considering the higher plasma resistivity due to higher Zeff, the complete stabilization could be explained. A thorough analysis of both pre-lithium ELMy and with-lithium ELM-free cases using ideal and non-ideal MHD models is presented, after accurately including a vacuum-like cold halo region in NIMROD to investigate ELMs.

Global simulations of protoplanetary disks with net magnetic flux

The planet-forming region of protoplanetary disks is cold, dense, and therefore weakly ionized. For this reason, magnetohydrodynamic (MHD) turbulence is thought to be mostly absent, and another mechanism has to be found to explain gas accretion. It has been proposed that magnetized winds, launched from the ionized disk surface, could drive accretion in the presence of a large-scale magnetic field. The efficiency and the impact of these surface winds on the disk structure is still highly uncertain. We present the first global simulations of a weakly ionized disk that exhibits large-scale magnetized winds. We also study the impact of self-organization, which was previously demonstrated only in non-stratified models. We perform numerical simulations of stratified disks with the PLUTO code. We compute the ionization fraction dynamically, and account for all three non-ideal MHD effects: ohmic and ambipolar diffusions, and the Hall drift. Simplified heating and cooling due to non-thermal radiation is also taken into account in the disk atmosphere. We find that disks can be accreting or not, depending on the configuration of the large-scale magnetic field. Magnetothermal winds, driven both by magnetic acceleration and heating of the atmosphere, are obtained in the accreting case. In some cases, these winds are asymmetric, ejecting predominantly on one side of the disk. The wind mass loss rate depends primarily on the average ratio of magnetic to thermal pressure in the disk midplane. The non-accreting case is characterized by a meridional circulation, with accretion layers at the disk surface and decretion in the midplane. Finally, we observe self-organization, resulting in axisymmetric rings of density and associated pressure "bumps". The underlying mechanism and its impact on observable structures are discussed.

Hall Effect–Mediated Magnetic Flux Transport in Protoplanetary Disks

Abstract The global evolution of protoplanetary disks (PPDs) has recently been shown to be largely controlled by the amount of poloidal magnetic flux threading the disk. The amount of magnetic flux must also coevolve with the disk, as a result of magnetic flux transport, a process that is poorly understood. In weakly ionized gas as in PPDs, magnetic flux is largely frozen in the electron fluid, except when resistivity is large. When the disk is largely laminar, we show that the relative drift between the electrons and ions (the Hall drift), and the ions and neutral fluids (ambipolar drift) can play a dominant role on the transport of magnetic flux. Using two-dimensional simulations that incorporate the Hall effect and ambipolar diffusion (AD) with prescribed diffusivities, we show that when large-scale poloidal field is aligned with disk rotation, the Hall effect rapidly drags magnetic flux inward at the midplane region, while it slowly pushes flux outward above/below the midplane. This leads to a highly radially elongated field configuration as a global manifestation of the Hall-shear instability. This field configuration further promotes rapid outward flux transport by AD at the midplane, leading to instability saturation. In quasi-steady state, magnetic flux is transported outward at approximately the same rate at all heights, and the rate is comparable to the Hall-free case. For anti-aligned field polarity, the Hall effect consistently transports magnetic flux outward, leading to a largely vertical field configuration in the midplane region. The field lines in the upper layer first bend radially inward and then outward to launch a disk wind. Overall, the net rate of outward flux transport is about twice as fast as that of the aligned case. In addition, the rate of flux transport increases with increasing disk magnetization. The absolute rate of transport is sensitive to disk microphysics, which remains to be explored in future studies.

On the structure and statistical theory of turbulence of extended magnetohydrodynamics

Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties of XMHD turbulence, and to compare them against their ideal MHD counterparts. For instance, the helicity flux transfer rates for XMHD are computed, and Liouville’s theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known ideal MHD inverse cascade of magnetic helicity. After a similar analysis is conducted for XMHD by inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the Hall MHD range—this is shown to be consistent with previous results in the literature. In contrast, in the inertial MHD range, viz at scales smaller than the electron skin depth, all spectral quantities are expected to undergo direct cascading. The consequences and relevance of our results in space and astrophysical plasmas are also briefly discussed.

MAGNETAR HEATING

ABSTRACT We examine four candidate mechanisms that could explain the high surface temperatures of magnetars. (1) Heat flux from the liquid core heated by ambipolar diffusion. It could sustain the observed surface luminosity erg s−1 if core heating offsets neutrino cooling at a temperature K. This scenario is viable if the core magnetic field exceeds 1016 G and the heat-blanketing envelope of the magnetar has a light-element composition. However, we find that the lifetime of such a hot core should be shorter than the typical observed lifetime of magnetars. (2) Mechanical dissipation in the solid crust. This heating can be quasi-steady, powered by gradual (or frequent) crustal yielding to magnetic stresses. We show that it obeys a strong upper limit. As long as the crustal stresses are fostered by the field evolution in the core or Hall drift in the crust, mechanical heating is insufficient to sustain persistent erg s−1. The surface luminosity is increased in an alternative scenario of mechanical deformations triggered by external magnetospheric flares. (3) Ohmic dissipation in the crust, in volume or current sheets. This mechanism is inefficient because of the high conductivity of the crust. Only extreme magnetic configurations with crustal fields G varying on a 100 meter scale could provide erg s−1. (4) Bombardment of the stellar surface by particles accelerated in the magnetosphere. This mechanism produces hot spots on magnetars. Observations of transient magnetars show evidence of external heating.

EXTENDED MHD TURBULENCE AND ITS APPLICATIONS TO THE SOLAR WIND

ABSTRACT Extended MHD is a one-fluid model that incorporates two-fluid effects such as electron inertia and the Hall drift. This model is used to construct fully nonlinear Alfvénic wave solutions, and thereby derive the kinetic and magnetic spectra by resorting to a Kolmogorov-like hypothesis based on the constant cascading rates of the energy and generalized helicities of this model. The magnetic and kinetic spectra are derived in the ideal , Hall , and electron inertia regimes; k is the wavenumber and is the skin depth of species “s.” In the Hall regime, it is shown that the emergent results are fully consistent with previous numerical and analytical studies, especially in the context of the solar wind. The focus is primarily on the electron inertia regime, where magnetic energy spectra with power-law indexes of and are always recovered. The latter, in particular, is quite close to recent observational evidence from the solar wind with a potential slope of approximately −4 in this regime. It is thus plausible that these spectra may constitute a part of the (extended) inertial range, as opposed to the standard “dissipation” range paradigm.

Resistive tearing instability in electron MHD: application to neutron star crusts

We study a resistive tearing instability developing in a system evolving through the combined effect of Hall drift in the Electron-MHD limit and Ohmic dissipation. We explore first the exponential growth of the instability in the linear case and we find the fastest growing mode, the corresponding eigenvalues and dispersion relation. The instability growth rate scales as $\gamma \propto B^{2/3} \sigma^{-1/3}$ where $B$ is the magnetic field and $\sigma$ the electrical conductivity. We confirm the development of the tearing resistive instability in the fully non-linear case, in a plane parallel configuration where the magnetic field polarity reverses, through simulations of systems initiating in Hall equilibrium with some superimposed perturbation. Following a transient phase, during which there is some minor rearrangement of the magnetic field, the perturbation grows exponentially. Once the instability is fully developed the magnetic field forms the characteristic islands and X-type reconnection points, where Ohmic decay is enhanced. We discuss the implications of this instability for the local magnetic field evolution in neutron stars' crusts, proposing that it can contribute to heating near the surface of the star, as suggested by models of magnetar post-burst cooling. In particular, we find that a current sheet a few meters thick, covering as little as $1\%$ of the total surface can provide $10^{42}~$erg in thermal energy within a few days. We briefly discuss applications of this instability in other systems where the Hall effect operates such as protoplanetary discs and space plasmas.

MAGNETAR FIELD EVOLUTION AND CRUSTAL PLASTICITY

ABSTRACT The activity of magnetars is believed to be powered by colossal magnetic energy reservoirs. We sketch an evolutionary picture in which internal field evolution in magnetars generates a twisted corona, from which energy may be released suddenly in a single giant flare, or more gradually through smaller outbursts and persistent emission. Given the ages of magnetars and the energy of their giant flares, we suggest that their evolution is driven by a novel mechanism: magnetic flux transport/decay due to persistent plastic flow in the crust, which would invalidate the common assumption that the crustal lattice is static and evolves only under Hall drift and Ohmic decay. We estimate the field strength required to induce plastic flow as a function of crustal depth, and the viscosity of the plastic phase. The star’s superconducting core may also play a role in magnetar field evolution, depending on the star’s spindown history and how rotational vortices and magnetic fluxtubes interact.