Geodynamo alpha-effect derived from box simulations of rotating magnetoconvection

The equations for fully compressible rotating magnetoconvection are numerically solved in a Cartesian box assuming conditions roughly suitable for the geodynamo. The mean electromotive force describing the generation of mean magnetic flux by convective turbulence in the rotating fluid is directly calculated from the simulations, and the corresponding alpha-coefficients are derived. Due to the very weak density stratification the alpha-effect changes its sign in the middle of the box. It is positive at the top and negative at the bottom of the convection zone. For strong magnetic fields we also find a clear downward advection of the mean magnetic field. Both of the simulated effects have been predicted by quasi-linear computations (Soward, 1979; Kitchatinov and Ruediger, 1992). Finally, the possible connection of the obtained profiles of the EMF with mean-field models of oscillating alpha^2-dynamos is discussed.Comment: 17 pages, 9 figures, submitted to Phys. Earth Planet. Inte

Spot-like Structures of Neutron Star Surface Magnetic Fields

There is growing evidence, based on both X-ray and radio observations of isolated neutron stars, that besides the large--scale (dipolar) magnetic field, which determines the pulsar spin--down behaviour, small--scale poloidal field components are present, which have surface strengths one to two orders of magnitude larger than the dipolar component. We argue in this paper that the Hall--effect can be an efficient process in producing such small--scale field structures just above the neutron star surface. It is shown that due to a Hall--drift induced instability, poloidal magnetic field structures can be generated from strong subsurface toroidal fields, which are the result of either a dynamo or a thermoelectric instability acting at early times of a neutron star's life. The geometrical structure of these small--scale surface anomalies of the magnetic field resembles that of some types of ``star--spots''. The magnetic field strength and the length--scales are comparable with values that can be derived from various observations.Comment: 4 pages, 2 figures, accepted by Astronomy & Astrophysics Letters; language improved, 2nd para of Sect. 3 change

The Occurrence of the Hall--Instability in Crusts of Isolated Neutron Stars

In former papers we showed that during the decay of a neutron star's magnetic field under the influence of the Hall--drift, an unstable rise of small--scale field structures at the expense of the large--scale background field may happen. This linear stability analysis was based on the assumption of a uniform density throughout the neutron star crust, whereas in reality the density and all transport coefficients vary by many orders of magnitude. Here, we extend the investigation of the Hall--drift induced instability by considering realistic profiles of density and chemical composition, as well as background fields with more justified radial profiles. Two neutron star models are considered differing primarily in the assumption on the core matter equation of state. For their cooling history and radial profiles of density and composition we use known results to infer the conductivity profiles. These were fed into linear calculations of a dipolar field decay starting from various initial configurations. At different stages of the decay, snapshots of the magnetic fields at the equator were taken to yield background field profiles for the stability analysis. The main result is that the Hall instability may really occur in neutron star crusts. Characteristic growth times are in the order of \lesssim 10^4 ... 10^6 yrs depending on cooling age and background field strength. The influence of the equation of state and of the initial field configuration is discussed.Comment: 16 pages, 16 figures, PS, submitted to A&A. Justification/discussion slightly changed/extended in replying to the referee. Changes on p. 3, 11, 13, framed by XXX mark

Time-dependent probability density function in cubic stochastic processes

We report time-dependent Probability Density Functions (PDFs) for a nonlinear stochastic process with a cubic force by novel analytical and computational studies. Analytically, a transition probability is formulated by using a path integral and is computed by the saddle-point solution (instanton method) and a new nonlinear transformation of time. The predicted PDF p(x, t) is in general given as a time integral and useful PDFs with explicit dependence on x and t are presented in certain limits (e.g. in the short and long time limits). Numerical simulations of the FokkerPlanck equation provide exact time evolution of the PDFs and confirm analytical predictions in the limit of weak noise. In particular, we show that non-equilibrium PDFs behave drastically differently from the stationary PDFs in regards to the asymmetry (skewness) and kurtosis. Specifically, while stationary PDFs are symmetric, transient PDFs are skewed; transient PDFs are much broader than stationary PDFs, with the kurtosis larger and smaller than 3, respectively. We elucidate the effect of nonlinear interaction on the strong fluctuations and intermittency in relaxation process

Turning Points in the Evolution of Isolated Neutron Stars' Magnetic Fields

During the life of isolated neutron stars (NSs) their magnetic field passes through a variety of evolutionary phases. Depending on its strength and structure and on the physical state of the NS (e.g. cooling, rotation), the field looks qualitatively and quantitatively different after each of these phases. Three of them, the phase of MHD instabilities immediately after NS's birth, the phase of fallback which may take place hours to months after NS's birth, and the phase when strong temperature gradients may drive thermoelectric instabilities, are concentrated in a period lasting from the end of the proto--NS phase until 100, perhaps 1000 years, when the NS has become almost isothermal. The further evolution of the magnetic field proceeds in general inconspicuous since the star is in isolation. However, as soon as the product of Larmor frequency and electron relaxation time, the so-called magnetization parameter, locally and/or temporally considerably exceeds unity, phases, also unstable ones, of dramatic changes of the field structure and magnitude can appear. An overview is given about that field evolution phases, the outcome of which makes a qualitative decision regarding the further evolution of the magnetic field and its host NS.Comment: References updated, typos correcte

Magnetic field dissipation in neutron star crusts: from magnetars to isolated neutron stars

We study the non--linear evolution of magnetic fields in neutron star crusts with special attention to the influence of the Hall drift. Our goal is to understand the conditions for fast dissipation due to the Hall term in the induction equation. We study the interplay of Ohmic dissipation and Hall drift in order to find a timescale for the overall crustal field decay. We solve numerically the Hall induction equation by means of a hybrid method (spectral in angles but finite differences in the radial coordinate). The microphysical input consists of the most modern available crustal equation of state, composition and electrical conductivities. We present the first long term simulations of the non--linear magnetic field evolution in realistic neutron star crusts with a stratified electron number density and temperature dependent conductivity. We show that Hall drift influenced Ohmic dissipation takes place in neutron star crusts on a timescale of 1 Myr. When the initial magnetic field has magnetar strength, the fast Hall drift results in an initial rapid dissipation stage that lasts 10-50 kyr. The interplay of the Hall drift with the temporal variation and spatial gradient of conductivity tends to favor the displacement of toroidal fields toward the inner crust, where stable configurations can last for 1 Myr. We show that the thermally emitting isolated neutron stars, as the Magnificent Seven, are very likely descendants of neutron stars born as magnetars.Comment: 14 pages, 10 figure

Strongly magnetized pulsars: explosive events and evolution

Well before the radio discovery of pulsars offered the first observational confirmation for their existence (Hewish et al., 1968), it had been suggested that neutron stars might be endowed with very strong magnetic fields of $10^{10}$-$10^{14}$G (Hoyle et al., 1964; Pacini, 1967). It is because of their magnetic fields that these otherwise small ed inert, cooling dead stars emit radio pulses and shine in various part of the electromagnetic spectrum. But the presence of a strong magnetic field has more subtle and sometimes dramatic consequences: In the last decades of observations indeed, evidence mounted that it is likely the magnetic field that makes of an isolated neutron star what it is among the different observational manifestations in which they come. The contribution of the magnetic field to the energy budget of the neutron star can be comparable or even exceed the available kinetic energy. The most magnetised neutron stars in particular, the magnetars, exhibit an amazing assortment of explosive events, underlining the importance of their magnetic field in their lives. In this chapter we review the recent observational and theoretical achievements, which not only confirmed the importance of the magnetic field in the evolution of neutron stars, but also provide a promising unification scheme for the different observational manifestations in which they appear. We focus on the role of their magnetic field as an energy source behind their persistent emission, but also its critical role in explosive events.Comment: Review commissioned for publication in the White Book of "NewCompStar" European COST Action MP1304, 43 pages, 8 figure

A comparison of no-slip, stress-free and inviscid models of rapidly rotating fluid in a spherical shell

We investigate how the choice of either no-slip or stress-free boundary conditions affects numerical models of rapidly rotating flow in Earth's core by computing solutions of the weakly-viscous magnetostrophic equations within a spherical shell, driven by a prescribed body force. For non-axisymmetric solutions, we show that models with either choice of boundary condition have thin boundary layers of depth E^(1/2), where E is the Ekman number, and a free-stream flow that converges to the formally inviscid solution. At Earth-like values of viscosity, the boundary layer thickness is approximately 1m, for either choice of condition. In contrast, the axisymmetric flows depend crucially on the choice of boundary condition, in both their structure and magnitude (either E^(-1/2) or E^(-1)). These very large zonal flows arise from requiring viscosity to balance residual axisymmetric torques. We demonstrate that switching the mechanical boundary conditions can cause a distinct change of structure of the flow, including a sign-change close to the equator, even at asymptotically low viscosity. Thus implementation of stress-free boundary conditions, compared with no-slip conditions, may yield qualitatively different dynamics in weakly-viscous magnetostrophic models of Earth's core. We further show that convergence of the free-stream flow to its asymptotic structure requires E ≤10^(-5)

What should be known prior to performing EUS exams? (Part II)

In "What should be known prior to performing EUS exams, Part I," the authors discussed the need for clinical information and whether other imaging modalities are required before embarking EUS examinations. Herewith, we present part II which addresses some (technical) controversies how EUS is performed and discuss from different points of view providing the relevant evidence as available. (1) Does equipment design influence the complication rate? (2) Should we have a standardized screen orientation? (3) Radial EUS versus longitudinal (linear) EUS. (4) Should we search for incidental findings using EUS