Pulsar timing irregularities and the imprint of magnetic field evolution

Context. The rotational evolution of isolated neutron stars is dominated by the magnetic field anchored to the solid crust of the star. Assuming that the core field evolves on much longer timescales, the crustal field evolves mainly though Ohmic dissipation and the Hall drift, and it may be subject to relatively rapid changes with remarkable effects on the observed timing properties. Aims. We investigate whether changes of the magnetic field structure and strength during the star evolution may have observable consequences in the braking index n. This is the most sensitive quantity to reflect small variations of the timing properties that are caused by magnetic field rearrangements. Methods. We performed axisymmetric, long-term simulations of the magneto-thermal evolution of neutron stars with state-of-the-art microphysical inputs to calculate the evolution of the braking index. Relatively rapid magnetic field modifications can be expected only in the crust of neutron stars, where we focus our study. Results. We find that the effect of the magnetic field evolution on the braking index can be divided into three qualitatively different stages depending on the age and the internal temperature: a first stage that may be different for standard pulsars (with n ~ 3) or low field neutron stars that accreted fallback matter during the supernova explosion (systematically n < 3); in a second stage, the evolution is governed by almost pure Ohmic field decay, and a braking index n > 3 is expected; in the third stage, at late times, when the interior temperature has dropped to very low values, Hall oscillatory modes in the neutron star crust result in braking indices of a high absolute value and both positive and negative signs. Conclusions. Current magneto-thermal evolution models predict a large contribution to the timing noise and, in particular, to the braking index, from temporal variations of the magnetic field. Models with strong (≳ 1014 G) multipolar or toroidal components, even with a weak (~1012 G) dipolar field are consistent with the observed trend of the timing properties.

The influence of magnetic field geometry on magnetars X-ray spectra

Nowadays, the analysis of the X-ray spectra of magnetically powered neutron stars or magnetars is one of the most valuable tools to gain insight into the physical processes occurring in their interiors and magnetospheres. In particular, the magnetospheric plasma leaves a strong imprint on the observed X-ray spectrum by means of Compton up-scattering of the thermal radiation coming from the star surface. Motivated by the increased quality of the observational data, much theoretical work has been devoted to develop Monte Carlo (MC) codes that incorporate the effects of resonant Compton scattering (RCS) in the modeling of radiative transfer of photons through the magnetosphere. The two key ingredients in this simulations are the kinetic plasma properties and the magnetic field (MF) configuration. The MF geometry is expected to be complex, but up to now only mathematically simple solutions (self-similar solutions) have been employed. In this work, we discuss the effects of new, more realistic, MF geometries on synthetic spectra. We use new force-free solutions [14] in a previously developed MC code [9] to assess the influence of MF geometry on the emerging spectra. Our main result is that the shape of the final spectrum is mostly sensitive to uncertain parameters of the magnetospheric plasma, but the MF geometry plays an important role on the angle-dependence of the spectra.

Modelling of the surface emission of the low magnetic field magnetar SGR 0418+5729

We perform a detailed modelling of the post-outburst surface emission of the low magnetic field magnetar SGR 0418+5729. The dipolar magnetic field of this source, B=6×1012G estimated from its spin-down rate, is in the observed range of magnetic fields for normal pulsars. The source is further characterized by a high pulse fraction and a single-peak profile. Using synthetic temperature distribution profiles, and fully accounting for the general-relativistic effects of light deflection and gravitational redshift, we generate synthetic X-ray spectra and pulse profiles that we fit to the observations. We find that asymmetric and symmetric surface temperature distributions can reproduce equally well the observed pulse profiles and spectra of SGR 0418. None the less, the modelling allows us to place constraints on the system geometry (i.e. the angles ψ and ξ that the rotation axis makes with the line of sight and the dipolar axis, respectively), as well as on the spot size and temperature contrast on the neutron star surface. After performing an analysis iterating between the pulse profile and spectra, as done in similar previous works, we further employed, for the first time in this context, a Markov-Chain Monte Carlo approach to extract constraints on the model parameters from the pulse profiles and spectra, simultaneously. We find that, to reproduce the observed spectrum and flux modulation: (a) the angles must be restricted to 65° ≲ ψ + ξ ≲ 125° or 235° ≲ ψ + ξ ≲ 295°; (b) the temperature contrast between the poles and the equator must be at least a factor of ∼6, and (c) the size of the hottest region ranges between 0.2 and 0.7 km (including uncertainties on the source distance). Lastly, we interpret our findings within the context of internal and external heating models.

Simulated magnetic field expulsion in neutron star cores

The study of long-term evolution of neutron star (NS) magnetic fields is key to understanding the rich diversity of NS observations, and to unifying their nature despite the different emission mechanisms and observed properties. Such studies in principle permit a deeper understanding of the most important parameters driving their apparent variety, e.g. radio pulsars, magnetars, X-ray dim isolated NSs, gamma-ray pulsars. We describe, for the first time, the results from self-consistent magnetothermal simulations considering not only the effects of the Hall-driven field dissipation in the crust, but also adding a complete set of proposed driving forces in a superconducting core. We emphasize how each of these core-field processes drive magnetic evolution and affect observables, and show that when all forces are considered together in vectorial form, the net expulsion of core magnetic flux is negligible, and will have no observable effect in the crust (consequently in the observed surface emission) on megayear time-scales. Our new simulations suggest that strong magnetic fields in NS cores (and the signatures on the NS surface) will persist long after the crustal magnetic field has evolved and decayed, due to the weak combined effects of dissipation and expulsion in the stellar core.

Magnetic resonance imaging of the manipulation of a chemical wave using an inhomogeneous magnetic field

The effects of applied magnetic fields on the traveling wave formed by the reaction of (ethylenediaminetetraacetato)cobalt(II) (Co(II)EDTA2-) and hydrogen peroxide have been studied using magnetic resonance imaging (MRI). It was found that the wave could be manipulated by applying pulsed magnetic field gradients to a sample contained in a vertical cylindrical tube in the 7.0 T magnetic field of the spectrometer. Transverse field gradients decelerated the propagation of the wave down the high-field side of the tube and accelerated it down the low-field side. This control of the wave propagation eventually promoted the formation of a finger on the low-field side of the tube and allowed the wave to be maneuvered within the sample tube. The origin of these effects is rationalized by considering the Maxwell stress arising from the combined homogeneous and inhomogeneous magnetic fields and the magnetic susceptibility gradient across the wave front.

Dynamics of cholesteric liquid crystals in the presence of a random magnetic field:stochastic dynamics of cholesteric liquid crystal

Based on dynamic renormalization group techniques, this letter analyzes the effects of external stochastic perturbations on the dynamical properties of cholesteric liquid crystals, studied in presence of a random magnetic field. Our analysis quantifies the nature of the temperature dependence of the dynamics; the results also highlight a hitherto unexplored regime in cholesteric liquid crystal dynamics. We show that stochastic fluctuations drive the system to a second-ordered Kosterlitz-Thouless phase transition point, eventually leading to a Kardar-Parisi-Zhang (KPZ) universality class. The results go beyond quasi-first order mean-field theories, and provides the first theoretical understanding of a KPZ phase in distorted nematic liquid crystal dynamics.

Numerical Investigation of the Effect of Magnetic Field on Natural Convection in a Curved-Shape Enclosure

This investigation reports the magnetic field effect on natural convection heat transfer in a curved-shape enclosure. The numerical investigation is carried out using the control volume-based-finite element method (CVFEM). The numerical investigations are performed for various values of Hartmann number and Rayleigh number. The obtained results are depicted in terms of streamlines and isotherms which show the significant effects of Hartmann number on the fluid flow and temperature distribution inside the enclosure. Also, it was found that the Nusselt number decreases with an increase in the Hartmann number.

Studies of turbulent flows in continuous casting of steel with and without magnetic field

This thesis develops and tests various transient and steady-state computational models such as direct numerical simulation (DNS), large eddy simulation (LES), filtered unsteady Reynolds-averaged Navier-Stokes (URANS) and steady Reynolds-averaged Navier-Stokes (RANS) with and without magnetic field to investigate turbulent flows in canonical as well as in the nozzle and mold geometries of the continuous casting process. The direct numerical simulations are first performed in channel, square and 2:1 aspect rectangular ducts to investigate the effect of magnetic field on turbulent flows. The rectangular duct is a more practical geometry for continuous casting nozzle and mold and has the option of applying magnetic field either perpendicular to broader side or shorter side. This work forms the part of a graphic processing unit (GPU) based CFD code (CU-FLOW) development for magnetohydrodynamic (MHD) turbulent flows. The DNS results revealed interesting effects of the magnetic field and its orientation on primary, secondary flows (instantaneous and mean), Reynolds stresses, turbulent kinetic energy (TKE) budgets, momentum budgets and frictional losses, besides providing DNS database for two-wall bounded square and rectangular duct MHD turbulent flows. Further, the low- and high-Reynolds number RANS models (k-ε and Reynolds stress models) are developed and tested with DNS databases for channel and square duct flows with and without magnetic field. The MHD sink terms in k- and ε-equations are implemented as proposed by Kenjereš and Hanjalić using a user defined function (UDF) in FLUENT. This work revealed varying accuracies of different RANS models at different levels. This work is useful for industry to understand the accuracies of these models, including continuous casting. After realizing the accuracy and computational cost of RANS models, the steady-state k-ε model is then combined with the particle image velocimetry (PIV) and impeller probe velocity measurements in a 1/3rd scale water model to study the flow quality coming out of the well- and mountain-bottom nozzles and the effect of stopper-rod misalignment on fluid flow. The mountain-bottom nozzle was found more prone to the longtime asymmetries and higher surface velocities. The left misalignment of stopper gave higher surface velocity on the right leading to significantly large number of vortices forming behind the nozzle on the left. Later, the transient and steady-state models such as LES, filtered URANS and steady RANS models are combined with ultrasonic Doppler velocimetry (UDV) measurements in a GaInSn model of typical continuous casting process. LES-CU-LOW is the fastest and the most accurate model owing to much finer mesh and a smaller timestep. This work provided a good understanding on the performance of these models. The behavior of instantaneous flows, Reynolds stresses and proper orthogonal decomposition (POD) analysis quantified the nozzle bottom swirl and its importance on the turbulent flow in the mold. Afterwards, the aforementioned work in GaInSn model is extended with electromagnetic braking (EMBr) to help optimize a ruler-type brake and its location for the continuous casting process. The magnetic field suppressed turbulence and promoted vortical structures with their axis aligned with the magnetic field suggesting tendency towards 2-d turbulence. The stronger magnetic field at the nozzle well and around the jet region created large scale and lower frequency flow behavior by suppressing nozzle bottom swirl and its front-back alternation. Based on this work, it is advised to avoid stronger magnetic field around jet and nozzle bottom to get more stable and less defect prone flow.

Double diffusive magneto-convection fluid flow in a strong cross magnetic field with uniform surface heat and mass flux

In this study, magnetohydrodynamic natural convection boundary layer flow of an electrically conducting and viscous incompressible fluid along a heated vertical flat plate with uniform heat and mass flux in the presence of strong cross magnetic field has been investigated. For smooth integrations the boundary layer equations are transformed in to a convenient dimensionless form by using stream function formulation as well as the free variable formulation. The nonsimilar parabolic partial differential equations are integrated numerically for Pr ≪1 that is appropriate for liquid metals against the local Hartmann parameter ξ . Further, asymptotic solutions are obtained near the leading edge using regular perturbation method for smaller values of ξ . Solutions for values of ξ ≫ 1 are also obtained by employing the matched asymptotic technique. The results obtained for small, large and all ξ regimes are examined in terms of shear stress, τw, rate of heat transfer, qw, and rate of mass transfer, mw, for important physical parameter. Attention has been given to the influence of Schmidt number, Sc, buoyancy ratio parameter, N and local Hartmann parameter, ξ on velocity, temperature and concentration distributions and noted that velocity and temperature of the fluid achieve their asymptotic profiles for Sc ≥ 10:0.

Natural convection flow in a strong cross magnetic field with radiation

The problem of MHD natural convection boundary layer flow of an electrically conducting and optically dense gray viscous fluid along a heated vertical plate is analyzed in the presence of strong cross magnetic field with radiative heat transfer. In the analysis radiative heat flux is considered by adopting optically thick radiation limit. Attempt is made to obtain the solutions valid for liquid metals by taking Pr≪1. Boundary layer equations are transformed in to a convenient dimensionless form by using stream function formulation (SFF) and primitive variable formulation (PVF). Non-similar equations obtained from SFF are then simulated by implicit finite difference (Keller-box) method whereas parabolic partial differential equations obtained from PVF are integrated numerically by hiring direct finite difference method over the entire range of local Hartmann parameter, $xi$ . Further, asymptotic solutions are also obtained for large and small values of local Hartmann parameter $xi$ . A favorable agreement is found between the results for small, large and all values of $xi$ . Numerical results are also demonstrated graphically by showing the effect of various physical parameters on shear stress, rate of heat transfer, velocity and temperature.

Electron transport across magnetic field in low-temperature plasmas : an alternative approach for obtaining evidence of Bohm mechanism

A comparative study involving both experimental and numerical investigations was made to resolve a long-standing problem of understanding electron conductivity mechanism across magnetic field in low-temperature plasmas. We have calculated the plasma parameters from experimentally obtained electric field distribution, and then made a 'back' comparison with the distributions of electron energy and plasma density obtained in the experiment. This approach significantly reduces an influence of the assumption about particular phenomenology of the electron conductivity in plasma. The results of the experiment and calculations made by this technique have showed that the classical conductivity is not capable of providing realistic total current and electron energy, whereas the phenomenological anomalous Bohm mobility has demonstrated a very good agreement with the experiment. These results provide an evidence in favor of the Bohm conductivity, thus making it possible to clarify this pressing long-living question about the main driving mechanism responsible for the electron transport in low-temperature plasmas.

Bats respond to polarity of a magnetic field

Bats have been shown to use information from the Earth's magnetic field during orientation. However, the mechanism underlying this ability remains unknown. In this study we investigated whether bats possess a polarity- or inclination-based compass that could be used in orientation. We monitored the hanging position of adult Nyctalus plancyi in the laboratory in the presence of an induced magnetic field of twice Earth-strength. When under the influence of a normally aligned induced field the bats showed a significant preference for hanging at the northern end of their roosting basket. When the vertical component of the field was reversed, the bats remained at the northern end of the basket. However, when the horizontal component of the field was reversed, the bats changed their positions and hung at the southern end of the basket. Based on these results, we conclude that N. plancyi, unlike all other non-mammalian vertebrates tested to date, uses a polarity-based compass during orientation in the roost, and that the same compass is also likely to underlie bats' long-distance navigation abilities.