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L'odierna Psichiatria Forense italiana non può dimenticare le sue origini legate alla Medicina Legale, quale modello fondativo e strutturale. La realtà odierna, però, è caratterizzata da un rilevante iato culturale ed organizzativo che separa norme, forse troppo radicali, e risorse, strutturalmente carenti. Tutto ciò si traduce spesso in percorsi articolati ma di grande difficoltà, se non impossibili, soprattutto qualora la formazione in ambito psichiatrico non preveda un percorso strutturato che renda idonei gli specialisti all'impiego degli strumenti dell'arte forense. Il panorama internazionale è di difficile confronto per una questione ontologica correlata sostanzialmente alle differenze legali e dell'iter giudiziario, ma sicuramente può essere da spunto per pensare all'opportunità di un riconoscimento di specifici requisiti in ambito forense. Stante la persistenza di modelli talvolta arcaici e di pratiche non di rado obsolete per quanto attiene alla realtà contemporanea in ambito forense, si rende necessario attualizzare i modelli didattici della disciplina, così da poter chiedere al legislatore anche una riforma dei parametri valutativi e del contesto di riferimento dove si opera. Ciò renderebbe il lavoro peritale maggiormente qualificato e degno di essere identificato e riconosciuto come parte integrante di una Psichiatria contemporanea, ovvero una rielaborazione culturale e didattica in grado di allargare gli orizzonti di una disciplina certamente nobile.giustificazione del minore, ma di responsabilizzazione dell'adulto e di inquadramento contestualizzante. In tale contesto la chiave di lettura della Criminologia, opportunamente corredata in specie in presenza di casi di disagio psichico dal contributo interpretativo della Psichiatria forense, può costituire uno strumento operativo di rilevanza centrale in prospettiva sia trattamentale che preventiva.

Neutron stars cool down during their lifetime through the combination of neutrino emission from the interior and photon cooling from the surface. Strongly magnetised neutron stars, called magnetars, are no exception, but the effect of their strong fields adds further complexities to the cooling theory. Besides other factors, modelling the outermost hundred meters (the envelope) plays a crucial role in predicting their surface temperatures. In this letter, we revisit the influence of envelopes on the cooling properties of neutron stars, with special focus on the critical effects of the magnetic field. We explore how our understanding of the relation between the internal and surface temperatures has evolved over the past two decades, and how different assumptions about the neutron star envelope and field topology lead to radically different conclusions on the surface temperature and its cooling with age. In particular, we find that relatively old magnetars with core-threading magnetic fields are actually much cooler than a rotation-powered pulsar of the same age. This is at variance with what is typically observed in crustal-confined models. Our results have important implications for the estimates of the X-ray luminosities of aged magnetars, and the subsequent population study of the different neutron star classes., Comment: 5 pages, 4 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Society

While predominantly dipolar, large-scale magnetic fields are usually assumed in most studies involving neutron stars, there are multiple observational, theoretical hints and numerical simulations highlightening the importance of non-dipolar components. I review here the most important observational facts and numerical studies pointing towards the existence of magnetospheric currents and internal small-scale structures, arising from multipoles of poloidal and toroidal fields. This holds for all neutron star stages: at birth, during their lifetime and after a merger.

The detection of a binary neutron star merger in 2017 through both gravitational waves and electromagnetic emission opened a new era of multimessenger astronomy. The understanding of the magnetic field amplification triggered by the Kelvin-Helmholtz instability during the merger is still a numerically unresolved problem because of the relevant small scales involved. One of the uncertainties comes from the simplifications usually assumed in the initial magnetic topology of merging neutron stars. We perform high-resolution, convergent large-eddy simulations of binary neutron star mergers, following the newly formed remnant for up to $30$ milliseconds. Here we specifically focus on the comparison between simulations with different initial magnetic configurations, going beyond the widespread-used aligned dipole confined within each star. The results obtained show that the initial topology is quickly forgotten, in a timescale of few miliseconds after the merger. Moreover, at the end of the simulations, the average intensity ($B\sim 10^{16}$ G) and the spectral distribution of magnetic energy over spatial scales barely depend on the initial configuration. This is expected due to the small-scale efficient dynamo involved, and thus it holds as long as: (i) the initial large-scale magnetic field is not unrealistically high (as often imposed in mergers studies); (ii) the turbulent instability is numerically (at least partially) resolved, so that the amplified magnetic energy is distributed across a wide range of scales and becomes orders-of-magnitude larger than the initial one., Comment: 8 pages, 5 figures

The period and the period derivative of a pulsar are critical magnitudes for defining the properties of the magnetospheric size and plasma dynamics. The pulsar light cylinder, the magnetic field intensity nearby it, and the curvature radius all depend on these timing properties, and shape the observed high-energy synchro-curvature emission. Therefore, the radiative properties of pulsars are inextricably linked to them. This fact poses the question of how well does a given pulsar's spectral energy distribution embed information of the timing parameters, and if so, whether we can deduce them if they have not been measured directly. This is relevant to possibly constrain the timing properties of potential pulsar candidates among unidentified γ-ray sources. We consider well-measured pulsar spectra blinding us from the knowledge of their timing properties, and address this question by using our radiative synchro-curvature model that was proven able to fit the observed spectra of the pulsar population. We find that in the majority of the cases studied (8 out of 13), the spin period is constrained within a range of about 1 order of magnitude, within which the real period lies. In the other cases, there is degeneracy and no period range can be constrained. This can be used to facilitate the blind search of pulsed signals., This work has been supported by the grants PID2021-124581OB-I00, PGC2018-095512-B-I00 as well as the Spanish program Unidad de Excelencia "Mara de Maeztu" CEX2020-001058-M. D.I.P. has been supported by CSIC program JAE-ICU. D.F.T. also acknowledges USTC and the Chinese Academy of Sciences Presidential Fellowship Initiative 2021VMA0001. D.V. is funded by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (ERC Starting Grant IMAGINE, No. 948582).

In this work, we introduce the use of the differential geometry Frenet-Serret equations to describe a magnetic line in a pulsar magnetosphere. These equations, which need to be solved numerically, fix the magnetic line in terms of their tangent, normal, and binormal vectors at each position, given assumptions on the radius of curvature and torsion. Once the representation of the magnetic line is defined, we provide the relevant set of transformations between reference frames; the ultimate aim is to express the map of the emission directions in the star co-rotating frame. In this frame, an emission map can be directly read as a light curve seen by observers located at a certain fixed angle with respect to the rotational axis. We provide a detailed step-by-step numerical recipe to obtain the emission map for a given emission process, and give a set of simplified benchmark tests. Key to our approach is that it offers a setting to achieve an effective description of the system's geometry {\it together} with the radiation spectrum. This allows to compute multi-frequency light curves produced by a specific radiation process (and not just geometry) in the pulsar magnetosphere, and intimately relates with averaged observables such as the spectral energy distribution., Comment: Accepted for publication in MNRAS

On a magnetar’s surface, magnetic fields can create permanent sunspot-like structures. Accounting for heat diffusion and magnetic evolution in a magnetar’s crust in the latest simulations improves agreement with observations.

Magnetic fields are expected to play a key role in the dynamics and the ejection mechanisms that accompany the merger of two neutron stars. General relativistic magnetohydrodynamic (MHD) simulations offer a unique opportunity to unravel the details of the ongoing physical processes. Nevertheless, current numerical studies are severely limited by the fact that any affordable resolution remains insufficient to fully capture the small-scale dynamo, initially triggered by the Kelvin-Helmholtz instability, and later sourced by several MHD processes involving differential rotation. Here, we alleviate this limitation by using explicit large-eddy simulations, a technique where the unresolved dynamics occurring at the subgrid scales (SGS) is modeled by extra terms, which are functions of the resolved fields and their derivatives. The combination of high-order numerical schemes, high resolutions, and the gradient SGS model allow us to capture the small-scale dynamos produced during the binary neutron star mergers, as shown in previous works. Here, we follow the first 50 milliseconds after the merger and, for the first time, we find numerical convergence on the magnetic field amplification, in terms of integrated energy and spectral distribution over spatial scales. Among other results, we find that the average intensity of the magnetic field in the remnant saturates at ∼1016 G around 5 ms after the merger. After 20-30 ms, both toroidal and poloidal magnetic field components grow continuously, fed by the winding mechanism that provides a slow inverse cascade, i.e., gradually transferring kinetic into magnetic energy. We find no clear hints for magnetorotational instabilities and no significant impact of the magnetic field on the redistribution of angular momentum in the remnant in our simulations, probably due to the very turbulent and dynamical topology of the magnetic field at all stages, with small-scale components largely dominating over the large-scale ones. Although the magnetic field grows near the rotation axis of the remnant, longer large-eddy simulations are necessary to further investigate the formation of large-scale, helical structures close to the rotational axis, which could be associated to jet formation., This work was supported by European Union FEDER funds, the Ministry of Science, Innovation and Universities and the Spanish Agencia Estatal de Investigación Grant No. PID2019–110301 GB-I00. R. C. acknowledges support from the Project No. PRIN-INAF 2019 “Short gamma-ray burst jets from binary neutron star mergers.” JVK kindly acknowledges the CARIPARO Foundation for funding his Ph.D. fellowship within the Ph.D. School in Physics at the University of Padova. DV is funded by the European Research Council (ERC) Starting Grant IMAGINE (Grant Agreement No. [948582]) under the European Union’s Horizon 2020 research and innovation programme.

arXiv:2010.00617v1, The activity of magnetars is powered by their intense and dynamic magnetic fields and has been proposed as the trigger to extragalactic fast radio bursts. Here we estimate the frequency of crustal failures in young magnetars, by computing the magnetic stresses in detailed magnetothermal simulations including Hall drift and ohmic dissipation. The initial internal topology at birth is poorly known but is likely to be much more complex than a dipole. Thus, we explore a wide range of initial configurations, finding that the expected rate of crustal failures varies by orders of magnitude depending on the initial magnetic configuration. Our results show that this rate scales with the crustal magnetic energy, rather than with the often used surface value of the dipolar component related to the spin-down torque. The estimated frequency of crustal failures for a given dipolar component can vary by orders of magnitude for different initial conditions, depending on how much magnetic energy is distributed in the crustal nondipolar components, likely dominant in newborn magnetars. The quantitative reliability of the expected event rate could be improved by a better treatment of the magnetic evolution in the core and the elastic/plastic crustal response, not included here. Regardless of that, our results are useful inputs in modeling the outburst rate of young Galactic magnetars, and their relation with the fast radio bursts in our and other galaxies., CD, DV, NR and AGG are supported by the ERC Consolidator Grant “MAGNESIA” (nr.817661) and acknowledge funding from grants SGR2017-1383 and PGC2018-095512-BI00. JAP acknowledges support by the Generalitat Valenciana (PROMETEO/2019/071) and by AEI grant PGC2018-095984-B-I00. RP acknowledges support from NSF award AST-1616157. We acknowledge support from the PHAROS COST Action (CA16214).

Magnetohydrodynamics (MHD) turbulence is likely to play an important role in several astrophysical scenarios, where the magnetic Reynolds is very large. Numerically, these cases can be studied efficiently by means of large-eddy simulations, in which the computational resources are used to evolve the system only up to a finite grid size. The resolution is not fine enough to capture all the relevant small-scale physics at play, which is instead effectively modeled by a set of additional terms in the evolution equations, dubbed as subgrid-scale model. Here we extend such approach, commonly used in nonrelativistic/nonmagnetic/incompressible fluid dynamics, to any general set of equation written in conservative form. We apply the so-called gradient model, giving recipes for these general balance-law systems, including the relevant case in which a nontrivial inversion of conserved to primitive fields is needed. In particular, we focus on the relativistic compressible ideal MHD scenario, by providing for the first time and for any equation of state, all the additional nontrivial subgrid-scale terms. As an application, we consider box simulations of the relativistic Kelvin-Helmholtz instability, which is also the first mechanism responsible for the magnetic field amplification in binary neutron star mergers and cannot be captured by the finest grid and longest simulations available (currently and in the near future). We numerically assess the performance of our model, by comparing it to the residuals coming from the filtering of high-resolution simulations. We find that the model can fit very well the residuals coming from filtering simulations with a resolution a few times higher. The application shown here explicitly considers the Minkovski metric, but it can be directly extended to general relativity, thus settling the basis to implement for the first time the gradient subgrid model in a general relativistic magnetohydrodynamics (GRMHD) binary merger large-eddy simulations. Our results suggest that this approach will be potentially able to unveil much better the small-scale dynamics achievable of full GRMHD simulations, or equivalently, to obtain the same results but saving a considerable amount of computational time.

In several relativistic astrophysics scenarios, the understanding of the rich magnetohydrodynamics is hampered by the limitations set by the achievable numerical resolution. In these cases, it is a tremendous challenge to accurately simulate numerically all the relevant scales. We present how to study such systems by using large eddy simulations with a self-consistent subgrid-scale gradient model that we generalized to the special relativistic case in a previous work and now extend to the general relativistic case. Adapted from nonrelativistic scenarios, the so-called gradient model allows us to capture part of the effects of the hidden dynamics on the resolved scales, by means of a physically agnostic, mathematically based Taylor expansion of the nonlinear terms in the conservative evolution equations’ fluxes. One of the main applications is the binary neutron star mergers, where the collision excites a nontrivial amplification at small spatial scales. Motivated by this scenario, we assess the validity of this approach in bounding-box simulations of the magnetic Kelvin-Helmholtz instability. Several resolutions and a broad range of scenarios are considered in order to carefully test the performance of the model under three crucial aspects: (i) highly curved backgrounds, (ii) jumps on the fluid density profiles, and (iii) strong shocks. The results suggest that our extension of the gradient subgrid-scale model to general relativistic magnetohydrodynamics is a promising approach for studying binary neutron star mergers and other relevant astrophysical scenarios., We acknowledge support from Spanish Ministry of Economy and Competitiveness Grants No. FPA2013-41042-P and No. AYA2016-80289-P (AEI/FEDER, UE). C. P. also acknowledges support from the Spanish Ministry of Education and Science through a Ramon y Cajal grant. D. V. is supported by the ERC Consolidator Grant “MAGNESIA” (No. 817661). We thankfully acknowledge the computer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center, with the time granted through the 17th PRACE regular call (project Tier-0 GEEFBNSM, Principal Investigator (P. I.) C. P.) and the RES calls AECT-2018-1-0005 (P. I. D. V.), AECT-2019-1-0007 (P. I. D. V.).

arXiv:2004.04083v2, The magnetar Swift J1818.0–1607 was discovered in 2020 March when Swift detected a 9 ms hard X-ray burst and a long-lived outburst. Prompt X-ray observations revealed a spin period of 1.36 s, soon confirmed by the discovery of radio pulsations. We report here on the analysis of the Swift burst and follow-up X-ray and radio observations. The burst average luminosity was Lburst ~ 2 × 1039 erg s−1 (at 4.8 kpc). Simultaneous observations with XMM-Newton and NuSTAR three days after the burst provided a source spectrum well fit by an absorbed blackbody (${N}_{{\rm{H}}}$ = (1.13 ± 0.03) × 1023 cm−2 and kT = 1.16 ± 0.03 keV) plus a power law (Γ = 0.0 ± 1.3) in the 1–20 keV band, with a luminosity of ~8 × 1034 erg s−1, dominated by the blackbody emission. From our timing analysis, we derive a dipolar magnetic field B ~ 7 × 1014 G, spin-down luminosity ${\dot{E}}_{\mathrm{rot}}\sim 1.4\times {10}^{36}$ erg s−1, and characteristic age of 240 yr, the shortest currently known. Archival observations led to an upper limit on the quiescent luminosity, We acknowledge the support of the PHAROS COST Action (CA16214). NR, AB, DV, CD, MR, AGG and VG are supported by the ERC Consolidator Grant “MAGNESIA” (nr.817661) and acknowledge funding from grants SGR2017-1383 and PGC2018-095512-BI00. AB and FCZ are also supported by a Juan de la Cierva fellowship. GLI, SM, AT, and RT acknowledge financial support from the Italian MIUR through PRIN grant 2017LJ39LM. AP, AR, MB and LS acknowledge funding from the grant “iPeska” (INAF PRIN-SKA/CTA; PI Possenti). LS acknowledges funding from ASI-INAF agreements 2017-14-H.O and I/037/12/0.

The magnetar SGR J1745-2900, discovered at a distance of parsecs from the Milky Way central black hole, Sagittarius A, represents the closest pulsar to a supermassive black hole ever detected. Furthermore, its intriguing radio emission has been used to study the environment of the black hole, as well as to derive a precise position and proper motion for this object. The discovery of SGR J1745-2900 has led to interesting debates about the number, age, and nature of pulsars expected in the Galactic center region. In this work, we present extensive X-ray monitoring of the outburst of SGR J1745-2900 using the Chandra X-ray Observatory, the only instrument with the spatial resolution to distinguish the magnetar from the supermassive black hole (2.″4 angular distance). It was monitored from its outburst onset in 2013 April until 2019 August, collecting more than 50 Chandra observations for a total of more than 2.3 Ms of data. Soon after the outburst onset, the magnetar emission settled onto a purely thermal emission state that cooled from a temperature of about 0.9-0.6 keV over 6 yr. The pulsar timing properties showed at least two changes in the period derivative, increasing by a factor of about 4 during the outburst decay. We find that the long-term properties of this outburst challenge current models for the magnetar outbursts., N.R., D.V., and A.B. are supported by the H2020 ERC Consolidator Grant “MAGNESIA” under grant agreement No. 817661 (PI: Rea). N.R., F.C.Z., D.V., A.B., and D.F.T. also acknowledge support from grants SGR2017-1383 and PGC2018-095512-BI00. F.C.Z. is supported by a Juan de la Cierva fellowship. A.P. acknowledges financial support from grants ASI/INAF I/037/12/0, ASI/INAF 2017-14- H.0 (PI: Belloni) and from INAF grant “Sostegno alla ricerca scientifica main streams dell’INAF,” Presidential Decree 43/2018 (PI: Belloni). D.H. acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant, the Fonds de recherche du Québec–Nature et Technologies (FRQNT) Nouveaux Chercheurs program, and the Canadian Institute for Advanced Research (CIFAR). G.L.I., S.M., and R.T. have been partially supported by PRIN-MIUR 2017. J.A.P. acknowledges support by the Generalitat Valenciana (PROMETEO/2019/071) and by Agencia Estatal de Investigación (PGC2018-095984- B-I00). G.P. is supported by the H2020 ERC Consolidator Grant “Hot Milk” under grant agreement No. 865637. L.S. acknowledges financial contributions from ASI-INAF agreements 2017-14-H.O and I/037/12/0 and from “iPeska” research grant (PI: Andrea Possenti) funded under the INAF call PRIN-SKA/CTA (resolution 70/2016). We acknowledge support from the PHAROS COST Action (CA16214). This article is based on data obtained with the Chandra X-ray Observatory, and on software and tools provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. We thank the referee for useful suggestions. We are grateful to Giovanni Fazio, Joseph Hora, Gordon Garmire, and Steven Willner, and their proposal co-Is, for sharing their data.

The strong magnetic field of neutron stars is intimately coupled to the observed temperature and spectral properties, as well as to the observed timing properties (distribution of spin periods and period derivatives). Thus, a proper theoretical and numerical study of the magnetic field evolution equations, supplemented with detailed calculations of microphysical properties (heat and electrical conductivity, neutrino emission rates) is crucial to understand how the strength and topology of the magnetic field vary as a function of age, which in turn is the key to decipher the physical processes behind the varied neutron star phenomenology. In this review, we go through the basic theory describing the magneto-thermal evolution models of neutron stars, focusing on numerical techniques, and providing a battery of benchmark tests to be used as a reference for present and future code developments. We summarize well-known results from axisymmetric cases, give a new look at the latest 3D advances, and present an overview of the expectations for the field in the coming years., Comment: Accepted for Living Reviews in Computational Astrophysics. 64 pages, 20 figures

We apply a synchro-curvature spectral emission model based on characterizing the dynamics of magnetospheric particles to fit the phase-average spectra of the most extended database for the non-thermal spectra of pulsars. We consider 36 pulsars with well-determined non-thermal spectra from X-rays to gamma-rays. The sample includes Crab and Crab twin, for which the spectra extends even to the optical/ultraviolet and infrared energies. We find that the model --with just three physical parameters and a global scaling-- can fit the observations well across eight orders of magnitude for 18 of the 36 pulsars studied. Additionally, we find a set of 8 pulsars for which the model still provides arguably good fits and another set of 10 pulsars for which the model fails in reproducing the spectra. We discuss why, propose and provide physical interpretations for a simple model extension (related to the geometry of the accelerating system with regards to the observer) that allows dealing with all such cases, ultimately providing very good fits for all pulsars. The extended model is still austere, adding only two additional parameters to the former set, of the same kind of the ones previously used. We use these fits to discuss issues going from the observed spectral origin, to the extent of the dominance of synchrotron or curvature regimes, the use of a model as predictor for searching new non-thermal pulsars starting from gamma-ray surveys, and how the model offers a setting where phase shifts between X-ray and gamma-ray light curves would naturally arise., 20 pages, 15 figures, 2 tables. Accepted for publication in MNRAS on August 14

In this letter, we present the first 3D force-free general relativity simulations of the magnetosphere dynamics related to the magnetar outburst/flare phenomenology. Starting from an initial dipole configuration, we adiabatically increase the helicity by twisting the footprints of a spot on the stellar surface and follow the succession of quasi-equilibrium states until a critical twist is reached. Twisting beyond that point triggers instabilities that results in the rapid expansion of magnetic field lines, followed by reconnection, as observed in previous axi-symmetric simulations. If the injection of magnetic helicity goes on, the process is recurrent, periodically releasing a similar amount of energy, of the order of a few % of the total magnetic energy. From our current distribution, we estimate the local temperature assuming that dissipation occurs mainly in the highly resistive outermost layer of the neutron star. We find that the temperature smoothly increases with injected twist, being larger for spots located in the tropical regions than in polar regions, and rather independent of their sizes. After the injection of helicity ceases, the magnetosphere relaxes to a new stable state, in which the persistent currents maintain the footprints area slightly hotter than before the onset of the instability., 6 pages, 5 figures

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 neutron stars, gamma-ray pulsars. We describe, for the first time, the results from self-consistent magneto-thermal simulations considering not only the effects of the Hall-driven field dissipation in the crust, but 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., 15 pages, 11 figures, accepted by MNRAS

Performing accurate large eddy simulations in compressible, turbulent magnetohydrodynamics is more challenging than in non-magnetized fluids due to the complex interplay between kinetic, magnetic and internal energy at different scales. Here we extend the sub-grid-scale gradient model, so far used in the momentum and induction equations, to account also for the unresolved scales in the energy evolution equation of a compressible ideal MHD fluid with a generic equation of state. We assess the model by considering box simulations of the turbulence triggered across a shear layer by the Kelvin-Helmholtz instability, testing cases where the small-scale dynamics cannot be fully captured by the resolution considered, such that the efficiency of the simulated dynamo effect depends on the resolution employed. This lack of numerical convergence is actually a currently common issue in several astrophysical problems, where the integral and fastest-growing-instability scales are too far apart to be fully covered numerically. We perform a-priori and a-posteriori tests of the extended gradient model. In the former, we find that, for many different initial conditions and resolutions, the gradient model outperforms other commonly used models in terms of correlation with the residuals coming from the filtering of a high-resolution run. In the second test, we show how a low-resolution run with the gradient model is able to quantitatively reproduce the evolution of the magnetic energy (the integrated value and the spectral distribution) coming from higher-resolution runs. This extension is the first step towards the implementation in relativistic magnetohydrodynamics., Comment: 25 pages, 23 figures, 2 tables. Submitted as a first revision

In the interior of neutron stars, the induction equation regulates the long-term evolution of the magnetic fields by means of resistivity, Hall dynamics and ambipolar diffusion. Despite the apparent simplicity and compactness of the equation, the dynamics it describes is not trivial and its understanding relies on accurate numerical simulations. While a few works in 2D have reached a mature stage and a consensus on the general dynamics at least for some simple initial data, only few attempts have been performed in 3D, due to the computational costs and the need for a proper numerical treatment of the intrinsic non-linearity of the equation. Here, we carefully analyze the general induction equation, studying its characteristic structure, and we present a new Cartesian 3D code, generated by the user-friendly, publicly available {\em Simflowny} platform. The code uses high-order numerical schemes for the time and spatial discretization, and relies on the highly-scalable {\em SAMRAI} architecture for the adaptive mesh refinement. We present the application of the code to several benchmark tests, showing the high order of convergence and accuracy achieved and the capabilities in terms of magnetic shock resolution and three-dimensionality. This paper paves the way for the applications to a realistic, 3D long-term evolution of neutron stars interior and, possibly, of other astrophysical sources., Comment: 23 pages, 13 figures. In press

En este documento se trata el tema de la electrificacion de aldeas rurales en paises en desarrollo donde se utilizan sistemas de energia sostenible. El estudio de factibilidad de electrificacion rural se realiza utilizando el Modelo de Optimizacion Hibrido para Electric Renewable PRO (HOMER PRO). El software de modelado de energia HOMER PRO es de optimizacion, mejorado por el Laboratorio Nacional de Energia Renovable de Estados Unidos. Ayuda en el diseno, la comparacion y la optimizacion de tecnologias de generacion de energia. En este trabajo, se presentan y analizan dos casos de electrificacion rural mediante el uso de HOMER PRO. Se aplican criterios de evaluacion tecnica y economica para estudiar la viabilidad de una microhidroelectrica en El Diptamo (Honduras), asi como de una planta hibrida compuesta de matrices de modulos fotovoltaicos, generadores diesel y baterias de flujo, en una pequena isla ubicada en el lago Victoria. Para ambos casos, mostramos los resultados de los estudios de las cargas diarias y anuales, de los recursos disponibles en el area y la evaluacion economica de la configuracion de las plantas elegidas.

One of the most important predictions of any gap model for pulsar magnetospheres is the predicted $\gamma$-ray spectra. In the outer gap model, the properties of the synchro-curvature radiation are sensitive to many parameters, whose realistic ranges have been studied in detail in an accompanying paper. There we demonstrated that the uncertainty in the radius of curvature, the magnetic field geometry, and the X-ray surface flux may affect by orders of magnitude the predicted flux and spectral peak in the $\gamma$-ray regime. Here, we present a systematic, numerical study of the impact of the different parameters on the particle dynamics along the gap and calculate the emitted synchro-curvature radiation along the trajectory. By integrating the emitted radiation along the gap and convolving it with a parametrized particle distribution, we discuss how the comparison with the wealth of {\em Fermi}-LAT data can be used to constrain the applicability of the model. The resulting spectra show very different energy peaks, fluxes and shapes, qualitatively matching the great variety of the observed {\em Fermi}-LAT pulsars. In particular, if we see a large fraction of photons emitted from the initial part of the trajectory, we show that the spectra will be flatter at the low-energy {\it Fermi}-LAT regime (100 MeV -- 1 GeV). This provides a solution for such observed flat spectra, while still maintain synchro-curvature radiation as the origin of these photons., Comment: 9 pages, 6 figures, 1 table. Accepted for pubblication in MNRAS main journal. References updated

Rural electrification in remote areas of developing countries has several challenges which hinders energy access to the population. For instance the extension of the national grid to provide electricity in these areas is largely not viable. The Kenyan government has put a target to achieve universal energy access by the year 2020. In order to realize this objective, focus is being shifted to establishing off-grid power stations in rural areas.Among rural areas to be electrified, Habaswein is a settlement in Kenya's North Eastern region without connection to the National Power Grid where Kenya Power installed a stand alone hybrid mini-grid.Based on field observations, power generation data analysis, evaluation of the potential energy resource and simulations, this research intends to evaluate the performance of the Habaswein mini-grid and optimize the existing hybrid generation system to enhance its reliability and reduce the operation costs.The result will be a suggestion of how Kenyan rural areas could be sustainably electrified by using renewable energy based off-grid power stations. It will contribute to bridge the research gap currently existing on that area, and it will be a vital tool to researchers, implementers and the policy makers in energy sector.

We consider the fundamental problem of charged particles moving along and around a curved magnetic field line, revising the synchro-curvature radiation formulae introduced by Cheng and Zhang (1996). We provide more compact expressions to evaluate the spectrum emitted by a single particle, identifying the key parameter that controls the transition between the curvature-dominated and the synchrotron-dominated regime. This parameter depends on the local radius of curvature of the magnetic field line, the gyration radius, and the pitch angle. We numerically solve the equations of motion for the emitting particle by considering self-consistently the radiative losses, and provide the radiated spectrum produced by a particle when an electric acceleration is balanced by its radiative losses, as it is assumed to happen in the outer gaps of pulsar's magnetospheres. We compute the average spectrum radiated throughout the particle trajectory finding that the slope of the spectrum before the peak depends on the location and size of the emission region. We show how this effect could then lead to a variety of synchro-curvature spectra. Our results reinforce the idea that the purely synchrotron or curvature losses are, in general, inadequate to describe the radiative reaction on the particle motion, and the spectrum of emitted photons. Finally, we discuss the applicability of these calculations to different astrophysical scenarios., 9 pages, 5 figures, 2 tables. Accepted for publication in MNRAS main journal. References updated

The magnetic field strength at birth is arguably one of the most important properties to determine the evolutionary path of a neutron star. Objects with very high fields, collectively known as magnetars, are characterized by high X-ray quiescent luminosities, occurrence of outbursts, and, for some of them, sporadic giant flares. While the magnetic field strength is believed to drive their collective behaviour, however, the diversity of their properties, and, especially, the observation of magnetar-like bursts from “low-field” pulsars, has been a theoretical puzzle. In this review, we discuss results of long-term simulations following the coupled evolution of the X-ray luminosity and the timing properties for a large, homogeneous sample of X-ray emitting isolated neutron stars, accounting for a range of initial magnetic field strengths, envelope compositions, and neutron star masses. In addition, by following the evolution of magnetic stresses within the neutron star crust, we can also relate the observed magnetar phenomenology to the physical properties of neutron stars, and in particular to their age and magnetic field strength and topology. The dichotomy of “high-B” field pulsars versus magnetars is naturally explained, and occasional outbursts from old, low B-field neutron stars are predicted. We conclude by speculating on the fate of old magnetars, and by presenting observational diagnostics of the neutron star crustal field topology. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We present a long-term phase-coherent timing analysis and pulse-phase resolved spectroscopy for the two outbursts observed from the transient anomalous X-ray pulsar CXOU J164710.2-45521. For the first outburst we used 11 Chandra and XMM-Newton observations between September 2006 to August 2009, the longest baseline yet for this source. We obtain a coherent timing solution with $P=10.61065583(4)$ s, $\dot{P} = 9.72(1) \times 10^{-13}\;$s s$^{-1}$ and $\ddot{P} = -1.05(5)\times10^{-20}\; $s s$^{-2}$. Under the standard assumptions this implies a surface dipolar magnetic field of $\sim 10^{14}$ G, confirming this source as a standard-$B$ magnetar. We also study the evolution of the pulse profile (shape, intensity and pulsed fraction) as a function of time and energy. Using the phase-coherent timing solution we perform a phase-resolved spectroscopy analysis, following the spectral evolution of pulse-phase features, which hints at the physical processes taking place on the star. The results are discussed from the perspective of magneto-thermal evolution models and the untwisting magnetosphere model. Finally, we present similar analysis for the second, less intense, 2011 outburst. For the timing analysis we used Swift data together with 2 XMM-Newton and Chandra pointings. The results inferred for both outbursts are compared and briefly discussed in a more general framework., Comment: 13 pages, 14 figures

The thermal X-ray spectra of several isolated neutron stars display deviations from a pure blackbody. The accurate physical interpretation of these spectral features bears profound implications for our understanding of the atmospheric composition, magnetic field strength and topology, and equation of state of dense matter. With specific details varying from source to source, common explanations for the features have ranged from atomic transitions in the magnetized atmospheres or condensed surface, to cyclotron lines generated in a hot ionized layer near the surface. Here we quantitatively evaluate the X-ray spectral distortions induced by inhomogeneous temperature distributions of the neutron star surface. To this aim, we explore several surface temperature distributions, we simulate their corresponding general relativistic X-ray spectra (assuming an isotropic, blackbody emission), and fit the latter with a single blackbody model. We find that, in some cases, the presence of a spurious 'spectral line' is required at a high significance level in order to obtain statistically acceptable fits, with central energy and equivalent width similar to the values typically observed. We also perform a fit to a specific object, RX J0806.4-4123, finding several surface temperature distributions able to model the observed spectrum. The explored effect is unlikely to work in all sources with detected lines, but in some cases it can indeed be responsible for the appearance of such lines. Our results enforce the idea that surface temperature anisotropy can be an important factor that should be considered and explored also in combination with more sophisticated emission models like atmospheres., 11 pages, 7 figures; accepted for publication in MNRAS

The tremendous challenge of comparing our theoretical models with the gravitational-wave observations in the new era of multimessenger astronomy requires accurate and fast numerical simulations of complicated physical systems described by the Einstein and the matter equations. These requirements can only be satisfied if the simulations can be parallelized efficiently on a large number of processors and advanced computational strategies are adopted. To achieve this goal we have developed Simflowny, an open platform for scientific dynamical models which automatically generates parallel code for different simulation frameworks, allowing the use of HPC infrastructures to non-specialist scientists. One of these frameworks is SAMRAI, a mature patch-based structured adaptive mesh refinement infrastructure, capable of reaching exascale in some specific problems. Here we present the numerical techniques that we have implemented on this framework by using Simflowny in order to perform fast, efficient, accurate and highly-scalable simulations. These techniques involve high-order schemes for smooth and non-smooth solutions, Adaptive Mesh Refinement with arbitrary resolution ratios and an optimal strategy for the sub-cycling in time. We validate the automatically generated codes for the SAMRAI infrastructure with some simple test examples (i.e. wave equation and Newtonian MHD) and finally with the Einstein equations.

$\gamma$-ray radiation from pulsars is usually thought to be mostly produced by the synchro-curvature losses of accelerated particles. Here we present a systematic study of all currently reported, good-quality Fermi-LAT pulsar spectral data. We do so by applying a model which follows the particle dynamics and consistently computes the emission of synchro-curvature radiation. By fitting observational data on a case by case basis, we are able to obtain constraints about the parallel electric field, the typical lengthscale over which particles emit the bulk of the detected radiation, and the number of involved particles. The model copes well with data of several dozens of millisecond and young pulsars. By correlating the inferred model parameters with the observed timing properties, some trends are discovered. First, a non-negligible part of the radiation comes from the loss of perpendicular momentum soon after pair creation. Second, the electric field strongly correlates with both the inverse of the emission lengthscale and the magnetic field at light cylinder, thus ruling out models with high-energy photon production close to the surface. These correlations unify young and millisecond pulsars under the same physical scenario, and predict that magnetars are intrinsically $\gamma$-ray quiet via syncrhro-curvature processes, since magnetospheric particles are not accelerated enough to emit a detectable $\gamma$-ray flux., Comment: Accepted for publication in MNRAS main journal. 25 pages, 4 tables, 16 figures

In 2013 April a new magnetar, SGR 1745-2900, was discovered as it entered an outburst, at only 2.4 arcsec angular distance from the supermassive black hole at the Centre of the Milky Way, Sagittarius A*. SGR 1745-2900 has a surface dipolar magnetic field of ~ 2x10^{14} G, and it is the neutron star closest to a black hole ever observed. The new source was detected both in the radio and X-ray bands, with a peak X-ray luminosity L_X ~ 5x10^{35} erg s^{-1}. Here we report on the long-term Chandra (25 observations) and XMM-Newton (8 observations) X-ray monitoring campaign of SGR 1745-2900, from the onset of the outburst in April 2013 until September 2014. This unprecedented dataset allows us to refine the timing properties of the source, as well as to study the outburst spectral evolution as a function of time and rotational phase. Our timing analysis confirms the increase in the spin period derivative by a factor of ~2 around June 2013, and reveals that a further increase occurred between 2013 Oct 30 and 2014 Feb 21. We find that the period derivative changed from 6.6x10^{-12} s s^{-1} to 3.3x10^{-11} s s^{-1} in 1.5 yr. On the other hand, this magnetar shows a slow flux decay compared to other magnetars and a rather inefficient surface cooling. In particular, starquake-induced crustal cooling models alone have difficulty in explaining the high luminosity of the source for the first ~200 days of its outburst, and additional heating of the star surface from currents flowing in a twisted magnetic bundle is probably playing an important role in the outburst evolution., Comment: 16 pages, 12 figures; accepted for publication on MNRAS

$\gamma$-ray spectra of pulsars have been mostly studied in a phenomenological way, by fitting them to a cut-off power-law function. Here, we analyze a model where pulsed emission comes from synchro-curvature processes in a gap. We calculate the variation of kinetic energy of magnetospheric particles along the gap and the associated radiated spectra, considering an effective particle distribution. We fit the phase-averaged and phase-resolved Fermi-LAT spectra of the three brightest gamma-ray pulsars: Geminga, Crab, and Vela, and constrain the three free parameters we leave free in the model. Our best-fit models well reproduce the observed data, apart from residuals above a few GeV in some cases, range for which the inverse Compton scattering likely becomes the dominant mechanism. In any case, the flat slope at low-energy (< GeV) seen by Fermi-LAT both in the phase-averaged and phase-resolved spectra of most pulsars, including the ones we studied, requires that most of the detected radiation below ~ GeV is produced during the beginning of the particle trajectories, when radiation mostly come from the loss of perpendicular momentum., Comment: 11 pages, 9 figures, 2 tables. Published in MNRAS main journal

Population synthesis studies constitute a powerful method to reconstruct the birth distribution of periods and magnetic fields of the pulsar population. When this method is applied to populations in different wavelengths, it can break the degeneracy in the inferred properties of initial distributions that arises from single-band studies. In this context, we extend previous works to include $X$-ray thermal emitting pulsars within the same evolutionary model as radio-pulsars. We find that the cumulative distribution of the number of X-ray pulsars can be well reproduced by several models that, simultaneously, reproduce the characteristics of the radio-pulsar distribution. However, even considering the most favourable magneto-thermal evolution models with fast field decay, log-normal distributions of the initial magnetic field over-predict the number of visible sources with periods longer than 12 s. We then show that the problem can be solved with different distributions of magnetic field, such as a truncated log-normal distribution, or a binormal distribution with two distinct populations. We use the observational lack of isolated NSs with spin periods P>12 s to establish an upper limit to the fraction of magnetars born with B > 10^{15} G (less than 1\%). As future detections keep increasing the magnetar and high-B pulsar statistics, our approach can be used to establish a severe constraint on the maximum magnetic field at birth of NSs., 12 pages, 11 figures, 5 tables

According to the partially screened gap scenario, an efficient electron-positron pair creation, a general precondition of radio-pulsar activity, relies on the existence of magnetic spots, i.e., local concentrations of strong and small scale magnetic field structures at the surface of neutron stars. They have a strong impact on the surface temperature, which is potentially observable. Here we reinforce the idea that such magnetic spots can be formed by extracting magnetic energy from the toroidal field that resides in deep crustal layers, via Hall drift. We study and discuss the magneto-thermal evolution of qualitatively different neutron star models and initial magnetic field configurations that lead to the creation of magnetic spots. We find that magnetic spots can be created on a timescale of $10^4$ years with magnetic field strengths $\gtrsim 5\times 10^{13}$ G, provided almost the whole magnetic energy is stored in its toroidal component, and that the conductivity in the inner crust is not too large. The lifetime of the magnetic spots is at least $\sim$one million of years, being longer if the initial field permeates both core and crust., Comment: Accepted by M.N.R.A.S

We revisit the population synthesis of isolated radio-pulsars incorporating recent advances on the evolution of the magnetic field and the angle between the magnetic and rotational axes from new simulations of the magneto-thermal evolution and magnetosphere models, respectively. An interesting novelty in our approach is that we do not assume the existence of a death line. We discuss regions in parameter space that are more consistent with the observational data. In particular, we find that any broad distribution of birth spin periods with $P_0\lesssim 0.5$ s can fit the data, and that if the alignment angle is allowed to vary consistently with the torque model, realistic magnetospheric models are favoured compared to models with classical magneto-dipolar radiation losses. Assuming that the initial magnetic field is given by a lognormal distribution, our optimal model has mean strength $\langle\log B_0{\rm [G]}\rangle \approx 13.0-13.2$ with width $\sigma (\log B_0) = 0.6-0.7$. However, there are strong correlations between parameters. This degeneracy in the parameter space can be broken by an independent estimate of the pulsar birth rate or by future studies correlating this information with the population in other observational bands (X-rays and $\gamma$-rays)., Comment: 10 pages, 9 figures, submitted and accepted to MNRAS, comments welcome

We report on the quiescent state of the Soft Gamma Repeater SGR 0501+4516 observed by XMM-Newton on 2009 August 30. The source exhibits an absorbed flux ~75 times lower than that measured at the peak of the 2008 outburst, and a rather soft spectrum, with the same value of the blackbody temperature observed with ROSAT back in 1992. This new observation is put into the context of all existing X-ray data since its discovery in August 2008, allowing us to complete the study of the timing and spectral evolution of the source from outburst until its quiescent state. The set of deep XMM-Newton observations performed during the few-years timescale of its outburst allows us to monitor the spectral characteristics of this magnetar as a function of its rotational period, and their evolution along these years. After the first ~10 days, the initially hot and bright surface spot progressively cooled down during the decay. We discuss the behaviour of this magnetar in the context of its simulated secular evolution, inferring a plausible dipolar field at birth of 3x10^14 G, and a current (magneto-thermal) age of ~10 kyr., Comment: 9 pages, 11 figures, accepted by MNRAS

The popular outer gap model of magnetospheric emission from pulsars has been widely applied to explain the properties observed in $\gamma$-rays. However, its quantitative predictions rely on a number of approximations and assumptions that are usually overlooked. Here we examine them, reviewing the main ingredients entering in the model, evaluating their range of uncertainties. Usually, in the quantitative applications of the model, key parameters like the radius of curvature and the energies of the interacting photons are taken to be a fixed, single value. Instead, here we explore their realistic ranges, and the impact of these on the consistency of the model itself. We conclude that the popular evaluation of the trans-field size of the gap as a function of period and period derivative, is unreliable and affected by a huge dispersion. Last, the exploration of the possible values for the radius of curvature, the local magnetic field and other quantities deserve more attention for quantitative applications of the outer gap model, like the calculation of $\gamma$-ray spectra, which is the subject of an accompanying paper., Comment: 19 pages, 5 figures, 3 tables. Accepted for pubblication in MNRAS main journal. References updated

The lack of X-ray pulsars with spin periods > 12 s raises the question of where the population of evolved high magnetic field neutron stars has gone. Unlike canonical radio pulsars, X-ray pulsars are not subject to physical limits to the emission mechanism nor observational biases against the detection of sources with longer periods. Here we show that a highly resistive layer in the innermost part of the crust of neutron stars naturally limits the spin period to a maximum value of about 10-20 s. This highly resistive layer is expected if the inner crust is amorphous and heterogeneous in nuclear charge, possibly due to the existence of a nuclear pasta phase. Our findings suggest that the maximum period of isolated X-ray pulsars can be the first observational evidence of an amorphous inner crust, which properties can be further constrained by future X-ray timing missions combined with more detailed models., 18 pages (4 in the Nature format) and 3 figures

Observations of magnetars and some of the high magnetic field pulsars have shown that their thermal luminosity is systematically higher than that of classical radio-pulsars, thus confirming the idea that magnetic fields are involved in their X-ray emission. Here we present the results of 2D simulations of the fully-coupled evolution of temperature and magnetic field in neutron stars, including the state-of-the-art kinetic coefficients and, for the first time, the important effect of the Hall term. After gathering and thoroughly re-analysing in a consistent way all the best available data on isolated, thermally emitting neutron stars, we compare our theoretical models to a data sample of 40 sources. We find that our evolutionary models can explain the phenomenological diversity of magnetars, high-B radio-pulsars, and isolated nearby neutron stars by only varying their initial magnetic field, mass and envelope composition. Nearly all sources appear to follow the expectations of the standard theoretical models. Finally, we discuss the expected outburst rates and the evolutionary links between different classes. Our results constitute a major step towards the grand unification of the isolated neutron star zoo., 21 pages, 11 figures, MNRAS accepted

We report on the long term X-ray monitoring of the outburst decay of the low magnetic field magnetar SGR 0418+5729, using all the available X-ray data obtained with RXTE, SWIFT, Chandra, and XMM-Newton observations, from the discovery of the source in June 2009, up to August 2012. The timing analysis allowed us to obtain the first measurement of the period derivative of SGR 0418+5729: \dot{P}=4(1)x10^{-15} s/s, significant at ~3.5 sigma confidence level. This leads to a surface dipolar magnetic field of B_dip ~6x 10^{12} G. This measurement confirms SGR 0418+5729 as the lowest magnetic field magnetar. Following the flux and spectral evolution from the beginning of the outburst up to ~1200 days, we observe a gradual cooling of the tiny hot spot responsible for the X-ray emission, from a temperature of ~0.9 to 0.3 keV. Simultaneously, the X-ray flux decreased by about 3 orders of magnitude: from about 1.4x10^{-11} to 1.2x10^{-14} erg/s/cm^2 . Deep radio, millimeter, optical and gamma-ray observations did not detect the source counterpart, implying stringent limits on its multi-band emission, as well as constraints on the presence of a fossil disk. By modeling the magneto-thermal secular evolution of SGR 0418+5729, we infer a realistic age of ~550 kyr, and a dipolar magnetic field at birth of ~10^{14} G. The outburst characteristics suggest the presence of a thin twisted bundle with a small heated spot at its base. The bundle untwisted in the first few months following the outburst, while the hot spot decreases in temperature and size. We estimate the outburst rate of low magnetic field magnetars to be about one per year per galaxy, and we briefly discuss the consequences of such result in several other astrophysical contexts., Comment: ApJ in press (15 pages, 11 figures)

Isolated neutron stars (NSs) show a bewildering variety of astrophysical manifestations, presumably shaped by the magnetic field strength and topology at birth. Here, using state-of-the art calculations of the coupled magnetic and thermal evolution of NSs, we compute the thermal spectra and pulse profiles expected for a variety of initial magnetic field configurations. In particular, we contrast models with purely poloidal magnetic fields to models dominated by a strong internal toroidal component. We find that, while the former displays double peaked profiles and very low pulsed fractions, in the latter, the anisotropy in the surface temperature produced by the toroidal field often results in a single pulse profile, with pulsed fractions that can exceed the 50-60% level even for perfectly isotropic local emission. We further use our theoretical results to generate simulated "observed" spectra, and show that blackbody (BB) fits result in inferred radii that can be significantly smaller than the actual NS radius, even as low as ~ 1-2 km for old NSs with strong internal toroidal fields and a high absorption column density along their line of sight. We compute the size of the inferred BB radius for a few representative magnetic field configurations, NS ages, and magnitudes of the column density. Our theoretical results are of direct relevance to the interpretation of X-ray observations of isolated NSs, as well as to the constraints on the equation of state of dense matter through radius measurements., 12 pages, 7 figures, accepted to MNRAS

(Abridged) 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. We investigate whether changes of the magnetic field structure and strength during the star evolution may have observable consequences in the braking index, which is the most sensitive quantity to reflect small variations of the timing properties that are caused by magnetic field rearrangements. By performing axisymmetric, long-term simulations of the magneto-thermal evolution of neutron stars with state-of-the-art microphysical inputs, 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 n3 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 high absolute value and both positive and negative signs. Models with strong (1e14 G) multipolar or toroidal components, even with a weak (~1e12 G) dipolar field are consistent with the observed trend of the timing properties., 7 pages, 5 figures, accepted for publication in Astronomy & Astrophysics (submitted July 24, 2012)