Hall cascades versus instabilities in neutron star magnetic fields

Context. The Hall effect is an important nonlinear mechanism affecting the evolution of magnetic fields in neutron stars. Studies of the governing equation, both theoretical and numerical, have shown that the Hall effect proceeds in a turbulent cascade of energy from large to small scales. Aims. We investigate the small-scale Hall instability conjectured to exist from the linear stability analysis of Rheinhardt and Geppert. Methods. Identical linear stability analyses are performed to find a suitable background field to model Rheinhardt and Geppert’s ideas. The nonlinear evolution of this field is then modelled using a three-dimensional pseudospectral numerical MHD code. Combined with the background field, energy was injected at the ten specific eigenmodes with the greatest positive eigenvalues as inferred by the linear stability analysis. Results. Energy is transferred to different scales in the system, but not into small scales to any extent that could be interpreted as a Hall instability. Any instabilities are overwhelmed by a late-onset turbulent Hall cascade, initially avoided by the choice of background field, but soon generated by nonlinear interactions between the growing eigenmodes. The Hall cascade is shown here, and by several authors elsewhere, to be the dominant mechanism in this system

Magnetic spherical Couette flow in linear combinations of axial and dipolar fields

We present axisymmetric numerical calculations of the fluid flow induced in a spherical shell with inner sphere rotating and outer sphere stationary. A magnetic field is also imposed, consisting of particular linear combinations of axial and dipolar fields, chosen to make $B_r=0$ at either the outer sphere, or the inner, or in between. This leads to the formation of Shercliff shear layers at these particular locations. We then consider the effect of increasingly large inertial effects, and show that an outer Shercliff layer is eventually de-stabilized, an inner Shercliff layer appears to remain stable, and an in-between Shercliff layer is almost completely disrupted even before the onset of time-dependence, which does eventually occur though

Instabilities of Shercliffe and Stewartson layers in spherical Couette flow

We explore numerically the flow induced in a spherical shell by differentially rotating the inner and outer spheres. The fluid is also taken to be electrically conducting (in the low magnetic Reynolds number limit), and a magnetic field is imposed parallel to the axis of rotation. If the outer sphere is stationary, the magnetic field induces a Shercliffe layer on the tangent cylinder, the cylinder just touching the inner sphere and parallel to the field. If the magnetic field is absent, but a strong overall rotation is present, Coriolis effects induce a Stewartson layer on the tangent cylinder. The nonaxisymmetric instabilities of both types of layer separately have been studied before; here, we consider the two cases side by side, as well as the mixed case, and investigate how magnetic and rotational effects interact. We find that if the differential rotation and the overall rotation are in the same direction, the overall rotation may have a destabilizing influence, whereas if the differential rotation and the overall rotation are in the opposite direction, the overall rotation always has a stabilizing influence

Tidally driven dynamos in a rotating sphere

Large-scale planetary or stellar magnetic fields generated by a dynamo effect are mostly attributed to flows forced by buoyancy forces in electrically conducting fluid layers. However, these large-scale fields may also be controlled by tides, as previously suggested for the star $\tau$-boo, Mars or the Early Moon. By simulating a small local patch of a rotating fluid, \cite{Barker2014} have recently shown that tides can drive small-scale dynamos by exciting a hydrodynamic instability, the so-called elliptical (or tidal) instability. By performing global magnetohydrodynamic simulations of a rotating spherical fluid body, we investigate if this instability can also drive the observed large-scale magnetic fields. We are thus interested by the dynamo threshold and the generated magnetic field in order to test if such a mechanism is relevant for planets and stars. Rather than solving the problem in a geometry deformed by tides, we consider a spherical fluid body and add a body force to mimic the tidal deformation in the bulk of the fluid. This allows us to use an efficient spectral code to solve the magnetohydrodynamic problem. We first compare the hydrodynamic results with theoretical asymptotic results, and numerical results obtained in a truely deformed ellipsoid, which confirms the presence of the elliptical instability. We then perform magnetohydrodynamic simulations, and investigate the dynamo capability of the flow. Kinematic and self-consistent dynamos are finally simulated, showing that the elliptical instability is capable of generating dipole dominated large-scale magnetic field in global simulations of a fluid rotating sphere.Comment: Astrophysical Journal Letters In press, (accepted) (2014) (accepted

Forward and inverse cascades in decaying two-dimensional electron magnetohydrodynamic turbulence

Electron magnetohydrodynamic (EMHD) turbulence in two dimensions is studied via high-resolution numerical simulations with a normal diffusivity. The resulting energy spectra asymptotically approach a $k^{-5/2}$ law with increasing $R_B$, the ratio of the nonlinear to linear timescales in the governing equation. No evidence is found of a dissipative cutoff, consistent with non-local spectral energy transfer. Dissipative cutoffs found in previous studies are explained as artificial effects of hyperdiffusivity. Relatively stationary structures are found to develop in time, rather than the variability found in ordinary or MHD turbulence. Further, EMHD turbulence displays scale-dependent anisotropy with reduced energy transfer in the direction parallel to the uniform background field, consistent with previous studies. Finally, the governing equation is found to yield an inverse cascade, at least partially transferring magnetic energy from small to large scales.Comment: 16 pages, 6 figures, accepted by Physics of Plasmas. For high resolution figures, please visit the PoP website or contact C.Warein

An unstable superfluid Stewartson layer in a differentially rotating neutron star

Experimental and numerical evidence is reviewed for the existence of a Stewartson layer in spherical Couette flow at small Ekman and Rossby numbers (\Ek \lsim 10^{-3}, \Ro \lsim 10^{-2}), the relevant hydrodynamic regime in the superfluid outer core of a neutron star. Numerical simulations of a superfluid Stewartson layer are presented for the first time, showing how the layer is disrupted by nonaxisymmetric instabilities. The unstable ranges of \Ek and \Ro are compared with estimates of these quantities in radio pulsars that exhibit glitches. It is found that glitching pulsars lie on the stable side of the instability boundary, allowing differential rotation to build up before a glitch.Comment: 4 pages, 3 figures. Accepted for publication in ApJ Letter

Information length as a new diagnostic of stochastic resonance

Stochastic resonance is a subtle, yet powerful phenomenon in which noise plays an interesting role of amplifying a signal instead of attenuating it. It has attracted great attention with a vast number of applications in physics, chemistry, biology, etc. Popular measures to study stochastic resonance include signal-to-noise ratios, residence time distributions, and different information theoretic measures. Here, we show that the information length provides a novel method to capture stochastic resonance. The information length measures the total number of statistically different states along the path of a system. Specifically, we consider the classical double-well model of stochastic resonance in which a particle in a potential V ( x , t ) = [ - x 2 / 2 + x 4 / 4 - A sin ( ω t ) x ] is subject to an additional stochastic forcing that causes it to occasionally jump between the two wells at x ≈ ± 1 . We present direct numerical solutions of the Fokker–Planck equation for the probability density function p ( x , t ) for ω = 10 - 2 to 10 - 6 , and A ∈ [ 0 , 0 . 2 ] and show that the information length shows a very clear signal of the resonance. That is, stochastic resonance is reflected in the total number of different statistical states that a system passes through