This is a White Paper in support of the mission concept of the Large Observatory for X-ray Timing (LOFT), proposed as a medium-sized ESA mission. We discuss the potential of LOFT for the study of magnetospheres of isolated neutron stars. For a summary, we refer to the paper.
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 rela
tivistic 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.
Soft Gamma-Ray Repeaters and Anomalous X-Ray Pulsars are extreme manifestations of the most magnetized neutron stars: magnetars. The phenomenology of their emission and spectral properties strongly support the idea that the magnetospheres of these as
trophysical objects are tightly twisted in the vicinity of the star. Previous studies on equilibrium configurations have so far focused on either the internal or the external magnetic field configuration, without considering a real coupling between the two fields. Here we investigate numerical equilibrium models of magnetized neutron stars endowed with a confined twisted magnetosphere, solving the general relativistic Grad-Shafranov equation both in the interior and in the exterior of the compact object. A comprehensive study of the parameters space is provided to investigate the effects of different current distributions on the overall magnetic field structure.
We present a new numerical code, X-ECHO, for general relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes. This is aimed at studying astrophysical situations where strong gravity and magnetic fields are both supposed to play an important
role, such as for the evolution of magnetized neutron stars or for the gravitational collapse of the magnetized rotating cores of massive stars, which is the astrophysical scenario believed to eventually lead to (long) GRB events. The code is based on the extension of the Eulerian conservative high-order (ECHO) scheme [Del Zanna et al., A&A 473, 11 (2007)] for GRMHD, here coupled to a novel solver for the Einstein equations in the extended conformally flat condition (XCFC). We fully exploit the 3+1 Eulerian formalism, so that all the equations are written in terms of familiar 3D vectors and tensors alone, we adopt spherical coordinates for the conformal background metric, and we consider axisymmetric spacetimes and fluid configurations. The GRMHD conservation laws are solved by means of shock-capturing methods within a finite-difference discretization, whereas, on the same numerical grid, the Einstein elliptic equations are treated by resorting to spherical harmonics decomposition and solved, for each harmonic, by inverting band diagonal matrices. As a side product, we build and make available to the community a code to produce GRMHD axisymmetric equilibria for polytropic relativistic stars in the presence of differential rotation and a purely toroidal magnetic field. This uses the same XCFC metric solver of the main code and has been named XNS. Both XNS and the full X-ECHO codes are validated through several tests of astrophysical interest.
Pulsar Wind Nebulae (PWNe) are bubbles or relativistic plasma that form when the pulsar wind is confined by the SNR or the ISM. Recent observations have shown a richness of emission features that has driven a renewed interest in the theoretical model
ing of these objects. In recent years a MHD paradigm has been developed, capable of reproducing almost all of the observed properties of PWNe, shedding new light on many old issues. Given that PWNe are perhaps the nearest systems where processes related to relativistic dynamics can be investigated with high accuracy, a reliable model of their behavior is paramount for a correct understanding of high energy astrophysics in general. I will review the present status of MHD models: what are the key ingredients, their successes, and open questions that still need further investigation.
We present a new model for the spectral evolution of Pulsar Wind Nebulae inside Supernova Remnants. The model couples the long-term dynamics of these systems, as derived in the 1-D approximation, with a 1-zone description of the spectral evolution of
the emitting plasma. Our goal is to provide a simplified theoretical description that can be used as a tool to put constraints on unknown properties of PWN-SNR systems: a piece of work that is preliminary to any more accurate and sophisticated modeling. In the present paper we apply the newly developed model to a few objects of different ages and luminosities. We find that an injection spectrum in the form of a broken-power law gives a satisfactory description of the emission for all the systems we consider. More surprisingly, we also find that the intrinsic spectral break turns out to be at a similar energy for all sources, in spite of the differences mentioned above. We discuss the implications of our findings on the workings of pulsar magnetospheres, pair multiplicity and on the particle acceleration mechanism(s) that might be at work at the pulsar wind termination shock.
We use ideal axisymmetric relativistic magnetohydrodynamic simulations to calculate the spindown of a newly formed millisecond, B ~ 10^{15} G, magnetar and its interaction with the surrounding stellar envelope during a core-collapse supernova (SN) ex
plosion. The mass, angular momentum, and rotational energy lost by the neutron star are determined self-consistently given the thermal properties of the cooling neutron stars atmosphere and the winds interaction with the surrounding star. The magnetar drives a relativistic magnetized wind into a cavity created by the outgoing SN shock. For high spindown powers (~ 10^{51}-10^{52} ergs/s), the magnetar wind is super-fast at almost all latitudes, while for lower spindown powers (~ 10^{50} erg/s), the wind is sub-fast but still super-Alfvenic. In all cases, the rates at which the neutron star loses mass, angular momentum, and energy are very similar to the corresponding free wind values (<~ 30% differences), in spite of the causal contact between the neutron star and the stellar envelope. In addition, in all cases that we consider, the magnetar drives a collimated (~5-10 deg.) relativistic jet out along the rotation axis of the star. Nearly all of the spindown power of the neutron star escapes via this polar jet, rather than being transferred to the more spherical SN explosion. The properties of this relativistic jet and its expected late-time evolution in the magnetar model are broadly consistent with observations of long duration gamma-ray bursts (GRBs) and their associated broad-lined Type Ic SN.
We model the interaction between the wind from a newly formed rapidly rotating magnetar and the surrounding progenitor. In the first few seconds after core collapse the magnetar inflates a bubble of plasma and magnetic fields behind the supernova sho
ck, which expands asymmetrically because of the pinching effect of the toroidal magnetic field, as in PWNe, even if the host star is spherically symmetric. The degree of asymmetry depends on the ratio of the magnetic energy to the total energy in the bubble. We assume that the wind by newly formed magnetars inflating these bubbles is more magnetized than for PWNe. We show that for a magnetic to total power supplied by the central magnetar $sim 0.1$ the bubble expands relatively spherically while for values greater than 0.3, most of the pressure in the bubble is exerted close to the rotation axis, driving a collimated outflow out through the host star. This can account for the collimation inferred from observations of long-duration gamma-ray bursts (GRBs). Given that the wind magnetization increases in time, we thus suggest that the magnetar-driven bubble initially expands relatively spherically (enhancing the energy of the associated supernova) while at late times it becomes progressivelymore collimated (producing the GRB). Similar processes may operate in more modestly rotating neutron stars to produce asymmetric supernovae and lower energy transients such as X-ray flashes.
We present time-dependent axisymmetric magnetohydrodynamic simulations of the interaction of a relativistic magnetized wind produced by a proto-magnetar with a surrounding stellar envelope, in the first $sim 10$ seconds after core collapse. We inject
a super-magnetosonic wind with $dot E = 10^{51}$ ergs s$^{-1}$ into a cavity created by an outgoing supernova shock. A strong toroidal magnetic field builds up in the bubble of plasma and magnetic field that is at first inertially confined by the progenitor star. This drives a jet out along the polar axis of the star, even though the star and the magnetar wind are each spherically symmetric. The jet has the properties needed to produce a long-duration gamma-ray burst (GRB). At $sim 5$ s after core bounce, the jet has escaped the host star and the Lorentz factor of the material in the jet at large radii $sim 10^{11}$ cm is similar to that in the magnetar wind near the source. Most of the spindown power of the central magnetar escapes via the relativistic jet. There are fluctuations in the Lorentz factor and energy flux in the jet on $sim 0.01-0.1$ second timescale. These may contribute to variability in GRB emission (e.g., via internal shocks).
We model the interaction between the wind from a newly formed rapidly rotating magnetar and the surrounding supernova shock and host star. The dynamics is modeled using the two-dimensional, axisymmetric thin-shell equations. In the first ~10-100 seco
nds after core collapse the magnetar inflates a bubble of plasma and magnetic fields behind the supernova shock. The bubble expands asymmetrically because of the pinching effect of the toroidal magnetic field, just as in the analogous problem of the evolution of pulsar wind nebulae. The degree of asymmetry depends on E_mag/E_tot. The correct value of E_mag/E_tot is uncertain because of uncertainties in the conversion of magnetic energy into kinetic energy at large radii in relativistic winds; we argue, however, that bubbles inflated by newly formed magnetars are likely to be significantly more magnetized than their pulsar counterparts. We show that for a ratio of magnetic to total power supplied by the central magnetar L_mag/L_tot ~ 0.1 the bubble expands relatively spherically. For L_mag/L_tot ~ 0.3, however, most of the pressure in the bubble is exerted close to the rotation axis, driving a collimated outflow out through the host star. This can account for the collimation inferred from observations of long-duration gamma-ray bursts (GRBs). Outflows from magnetars become increasingly magnetically dominated at late times, due to the decrease in neutrino-driven mass loss as the young neutron star cools. We thus suggest that the magnetar-driven bubble initially expands relatively spherically, enhancing the energy of the associated supernova, while at late times it becomes progressively more collimated, producing the GRB.
