General relativistic models for rotating magnetized neutron stars in conformally flat spacetime

The extraordinary energetic activity of magnetars is usually explained in terms of dissipation of a huge internal magnetic field of the order of $10^{15-16}$G. How such a strong magnetic field can originate during the formation of a neutron star is still subject of active research. An important role can be played by fast rotation: if magnetars are born as millisecond rotators dynamo mechanisms may efficiently amplify the magnetic field inherited from the progenitor star during the collapse. In this case, the combination of rapid rotation and strong magnetic field determine the right physical condition not only for the development of a powerful jet driven explosion, manifesting as a gamma ray burst, but also for a copious gravitational waves emission. Strong magnetic fields are indeed able to induce substantial quadrupolar deformations in the star. In this paper we analyze the joint effect of rotation and magnetization on the structure of a polytropic and axisymmetric neutron star, within the ideal magneto-hydrodynamic regime. We will consider either purely toroidal or purely poloidal magnetic field geometries. Through the sampling of a large parameter space, we generalize previous results in literature, inferring new quantitative relations that allow for a parametrization of the induced deformation, that takes into account also the effects due to the stellar compactness and the current distribution. Finally, in the case of purely poloidal field, we also discuss how different prescriptions on the surface charge distribution (a gauge freedom) modify the properties of the surrounding electrosphere and its physical implications.Comment: 25 pages, 17 figures, 6 tables, accepted for publication in MNRA

Axisymmetric equilibrium models for magnetized neutron stars in General Relativity under the Conformally Flat Condition

Extremely magnetized neutron stars with magnetic fields as strong as $\sim 10^{15-16}$ G, or magnetars, have received considerable attention in the last decade due to their identification as a plausible source for Soft Gamma Repeaters and Anomalous X-ray Pulsars. Moreover, this class of compact objects has been proposed as a possible engine capable of powering both Long and Short Gamma-Ray Bursts, if the rotation period in their formation stage is short enough (~1 ms). Such strong fields are expected to induce substantial deformations of the star and thus to produce the emission of gravitational waves. Here we investigate, by means of numerical modeling, axisymmetric static equilibria of polytropic and strongly magnetized stars in full general relativity, within the ideal magneto-hydrodynamic regime. The eXtended Conformally Flat Condition (XCFC) for the metric is assumed, allowing us to employ the techniques introduced for the X-ECHO code [Bucciantini & Del Zanna, 2011, Astron. Astrophys. 528, A101], proven to be accurate, efficient, and stable. The updated XNS code for magnetized neutron star equilibria is made publicly available for the community (see www.arcetri.astro.it/science/ahead/XNS). Several sequences of models are here retrieved, from the purely toroidal (resolving a controversy in the literature) or poloidal cases, to the so-called twisted torus mixed configurations, expected to be dynamically stable, which are solved for the first time in the non-perturbative regime.Comment: 24 pages, 22 figures, 5 table

Modeling the structure of magnetic fields in Neutron Stars: from the interior to the magnetosphere

The phenomenology of the emission of pulsars and magnetars depends dramatically on the structure and properties of their magnetic field. In particular it is believed that the outbursting and flaring activity observed in AXPs and SRGs is strongly related to their internal magnetic field. Recent observations have moreover shown that charges are present in their magnetospheres supporting the idea that their magnetic field is tightly twisted in the vicinity of the star. In principle these objects offer a unique opportunity to investigate physics in a regime beyond what can be obtained in the laboratory. We will discuss the properties of equilibrium models of magnetized neutron stars, and we will show how internal and external currents can be related. These magnetic field configurations will be discussed considering also their stability, relevant for their origin and possibly connected to events like SNe and GRBs. We will also show what kind of deformations they induce in the star, that could lead to emission of gravitational waves. In the case of a twisted magnetosphere we will show how the amount of twist regulates their general topology. A general formalism based on the simultaneous numerical solution of the general relativistic Grad-Shafranov equation and Einstein equations will be presented.Comment: 9 pages, 3 figures, Proceedings of the 10th International Conference on Numerical Modeling of Space Plasma Flows, 8-12 June 2015, Avignon, Franc

The role of currents distribution in general relativistic equilibria of magnetized neutron stars

Magnetic fields play a critical role in the phenomenology of neutron stars. There is virtually no observable aspect which is not governed by them. Despite this, only recently efforts have been done to model magnetic fields in the correct general relativistic regime, characteristic of these compact objects. In this work we present, for the first time a comprehensive and detailed parameter study, in general relativity, of the role that the current distribution, and the related magnetic field structure, have in determining the precise structure of neutron stars. In particular, we show how the presence of localized currents can modify the field strength at the stellar surface, and we look for general trends, both in terms of energetic properties, and magnetic field configurations. Here we verify that, among other things, for a large class of different current distributions the resulting magnetic configurations are always dominated by the poloidal component of the current.Comment: 14 pages, 13 figures, accepted for publication in MNRA

A Constrained Transport Method for the Solution of the Resistive Relativistic MHD Equations

We describe a novel Godunov-type numerical method for solving the equations of resistive relativistic magnetohydrodynamics. In the proposed approach, the spatial components of both magnetic and electric fields are located at zone interfaces and are evolved using the constrained transport formalism. Direct application of Stokes' theorem to Faraday's and Ampere's laws ensures that the resulting discretization is divergence-free for the magnetic field and charge-conserving for the electric field. Hydrodynamic variables retain, instead, the usual zone-centred representation commonly adopted in finite-volume schemes. Temporal discretization is based on Runge-Kutta implicit-explicit (IMEX) schemes in order to resolve the temporal scale disparity introduced by the stiff source term in Ampere's law. The implicit step is accomplished by means of an improved and more efficient Newton-Broyden multidimensional root-finding algorithm. The explicit step relies on a multidimensional Riemann solver to compute the line-averaged electric and magnetic fields at zone edges and it employs a one-dimensional Riemann solver at zone interfaces to update zone-centred hydrodynamic quantities. For the latter, we introduce a five-wave solver based on the frozen limit of the relaxation system whereby the solution to the Riemann problem can be decomposed into an outer Maxwell solver and an inner hydrodynamic solver. A number of numerical benchmarks demonstrate that our method is superior in stability and robustness to the more popular charge-conserving divergence cleaning approach where both primary electric and magnetic fields are zone-centered. In addition, the employment of a less diffusive Riemann solver noticeably improves the accuracy of the computations.Comment: 25 pages, 14 figure

Thermal structure of hot non-flaring corona from Hinode/EIS

In previous studies a very hot plasma component has been diagnosed in solar active regions through the images in three different narrow-band channels of SDO/AIA. This diagnostic from EUV imaging data has also been supported by the matching morphology of the emission in the hot Ca XVII line, as observed with Hinode/EIS. This evidence is debated because of unknown distribution of the emission measure along the line of sight. Here we investigate in detail the thermal distribution of one of such regions using EUV spectroscopic data. In an active region observed with SDO/AIA, Hinode/EIS and XRT, we select a subregion with a very hot plasma component and another cooler one for comparison. The average spectrum is extracted for both, and 14 intense lines are selected for analysis, that probe the 5.5 < log T < 7 temperature range uniformly. From these lines the emission measure distributions are reconstructed with the MCMC method. Results are cross-checked with comparison of the two subregions, with a different inversion method, with the morphology of the images, and with the addition of fluxes measured with from narrow and broad-band imagers. We find that, whereas the cool region has a flat and featureless distribution that drops at temperature log T >= 6.3, the distribution of the hot region shows a well-defined peak at log T = 6.6 and gradually decreasing trends on both sides, thus supporting the very hot nature of the hot component diagnosed with imagers. The other cross-checks are consistent with this result. This study provides a completion of the analysis of active region components, and the resulting scenario supports the presence of a minor very hot plasma component in the core, with temperatures log T > 6.6.Comment: 12 pages, 8 figures, accepted for publicatio

Multi-D magnetohydrodynamic modelling of pulsar wind nebulae: recent progress and open questions

In the last decade, the relativistic magnetohydrodynamic (MHD) modelling of pulsar wind nebulae, and of the Crab nebula in particular, has been highly successful, with many of the observed dynamical and emission properties reproduced down to the finest detail. Here, we critically discuss the results of some of the most recent studies: namely the investigation of the origin of the radio emitting particles and the quest for the acceleration sites of particles of different energies along the termination shock, by using wisps motion as a diagnostic tool; the study of the magnetic dissipation process in high magnetization nebulae by means of new long-term three-dimensional simulations of the pulsar wind nebula evolution; the investigation of the relativistic tearing instability in thinning current sheets, leading to fast reconnection events that might be at the origin of the Crab nebula gamma-ray flares.Comment: 30 pages, 12 figure

Sub-structure formation in starless cores

Motivated by recent observational searches of sub-structure in starless molecular cloud cores, we investigate the evolution of density perturbations on scales smaller than the Jeans length embedded in contracting isothermal clouds, adopting the same formalism developed for the expanding Universe and the solar wind. We find that initially small amplitude, Jeans-stable perturbations (propagating as sound waves in the absence of a magnetic field), are amplified adiabatically during the contraction, approximately conserving the wave action density, until they either become nonlinear and steepen into shocks at a time $t_{\rm nl}$, or become gravitationally unstable when the Jeans length decreases below the scale of the perturbations at a time $t_{\rm gr}$. We evaluate analytically the time $t_{\rm nl}$ at which the perturbations enter the non-linear stage using a Burgers' equation approach, and we verify numerically that this time marks the beginning of the phase of rapid dissipation of the kinetic energy of the perturbations. We then show that for typical values of the rms Mach number in molecular cloud cores, $t_{\rm nl}$ is smaller than $t_{\rm gr}$, and therefore density perturbations likely dissipate before becoming gravitational unstable. Solenoidal modes grow at a faster rate than compressible modes, and may eventually promote fragmentation through the formation of vortical structures.Comment: 8 pages, 4 figure