Neutron Star Magnetosphere Research Articles

The force-free twisted magnetosphere of a neutron star

We present a detailed analysis of the properties of twisted, force-free magnetospheres of non-rotating neutron stars, which are of interest in the modelling of magnetar properties and evolution. In our models the magnetic field smoothly matches to a current-free (vacuum) solution at some large external radius, and they are specifically built to avoid pathological surface currents at any of the interfaces. By exploring a large range of parameters, we find a few remarkable general trends. We find that the total dipolar moment can be increased by up to $40\%$ with respect to a vacuum model with the same surface magnetic field, due to the contribution of magnetospheric currents to the global magnetic field. Thus, estimates of the surface magnetic field based on the large-scale dipolar braking torque are slightly overestimating the surface value by the same amount. Consistently, there is a moderate increase in the total energy of the model with respect to the vacuum solution of up to $25\%$, which would be the available energy budget in the event of a fast, global magnetospheric reorganization commonly associated with magnetar flares. We have also found the interesting result of the existence of a critical twist ($\varphi_{\rm max} \lesssim 1.5$ rad), beyond which we cannot find any more numerical solutions. Combining the models considered in this paper with the evolution of the interior of neutron stars will allow us to study the influence of the magnetosphere on the long-term magnetic, thermal, and rotational evolution.

QPO frequency derivative–frequency correlation indicates non-Keplerian boundary layer with a maximum in rotation rate

Abstract The correlation between the frequency and the absolute value of the frequency derivative of the kilohertz quasi-periodic oscillations (QPOs) observed for the first time from 4U 1636-53 is a simple consequence and indicator of the existence of a non-Keplerian rotation rate in the accretion disc boundary layer. This Letter interprets the observed correlation, showing that the observations provide strong evidence in support of the fundamental assumption of disc accretion models around slow rotators, that the boundary layer matches the Keplerian disc to the neutron star magnetosphere.

HOW ELSE CAN WE DETECT FAST RADIO BURSTS?

ABSTRACT We discuss possible electromagnetic signals accompanying Fast Radio Bursts (FRBs) that are expected in the scenario where FRBs originate in neutron star magnetospheres. For models involving Crab-like giant pulses, no appreciable contemporaneous emission is expected at other wavelengths. However, magnetar giant flares, driven by the reconfiguration of the magnetosphere, can produce both contemporaneous bursts at other wavelengths as well as afterglow-like emission. We conclude that the best chances are: (i) prompt short GRB-like emission, (ii) a contemporaneous optical flash that can reach naked eye peak luminosity (but only for a few milliseconds), and (iii) a high-energy afterglow emission. Case (i) could be tested by coordinated radio and high-energy experiments. Case (ii) could be seen in a coordinated radio-optical surveys, e.g., by the Palomar Transient Factory in a 60 s frame as a transient object of m = 15–20 mag with an expected optical detection rate of about 0.1 hr−1, an order of magnitude higher than in radio. Shallow, but large-area sky surveys such as ASAS-SN and EVRYSCOPE could also detect prompt optical flashes from the more powerful Lorimer-burst clones. The best constraints on the optical to radio power for this kind of emission could be provided by future observations with facilities like Large Synoptic Survey Telescope. Case (iii) might be seen in relatively rare cases that the relativistically ejected magnetic blob is moving along the line of sight.

Fluctuating neutron star magnetosphere: braking indices of eight pulsars, frequency second derivatives of 222 pulsars and 15 magnetars

Eight pulsars have low braking indices, which challenge the magnetic dipole braking of pulsars. 222 pulsars and 15 magnetars have abnormal distribution of frequency second derivatives, which also make contradiction with classical understanding. How neutron star magnetospheric activities affect these two phenomena are investigated by using the wind braking model of pulsars. It is based on the observational evidence that pulsar timing is correlated with emission and both aspects reflect the magnetospheric activities. Fluctuations are unavoidable for a physical neutron star magnetosphere. Young pulsars have meaningful braking indices, while old pulsars' and magnetars' fluctuation item dominates their frequency second derivatives. It can explain both the braking index and frequency second derivative of pulsars uniformly. The braking indices of eight pulsars are the combined effect of magnetic dipole radiation and particle wind. During the life time of a pulsar, its braking index will evolve from three to one. Pulsars with low braking index may put strong constraint on the particle acceleration process in the neutron star magnetosphere. The effect of pulsar death should be considered during the long term rotational evolution of pulsars. An equation like the Langevin equation for Brownian motion was derived for pulsar spin-down. The fluctuation in the neutron star magnetosphere can be either periodic or random, which result in anomalous frequency second derivative and they have similar results. The magnetospheric activities of magnetars are always stronger than those of normal pulsars.

On propagation of photons in a magnetized medium

AbstractThe aim of this work is to solve the dispersion relations near the first excitation threshold of a photon propagating along a magnetic field in the strong field limit. We have calculated the time damping of the photon in two particular cases: the degenerate gas as well as the diluted gas limit, both being important from the astro‐physical point of view. In particular, the diluted gas limit could describe the magnetosphere of neutron stars. The solutions have been used to obtain a finite quantum Faraday angle in both limits. A resonant behavior for the Faraday angle is also obtained. To reproduce the semi‐classical result for the Faraday rotation angle, the weak field limit is considered. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Gamma-ray pulsars: A gold mine

The most energetic neutron stars, powered by their rotation, are capable of producing pulsed radiation from the radio up to gamma rays with nearly TeV energies. These pulsars are part of the universe of energetic and powerful particle accelerators, using their uniquely fast rotation and formidable magnetic fields to accelerate particles to ultra-relativistic speed. The extreme properties of these stars provide an excellent testing ground, beyond Earth experience, for nuclear, gravitational, and quantum-electrodynamical physics. A wealth of gamma-ray pulsars has recently been discovered with the Fermi Gamma-Ray Space Telescope. The energetic gamma rays enable us to probe the magnetospheres of neutron stars and particle acceleration in this exotic environment. We review the latest developments in this field, beginning with a brief overview of the properties and mysteries of rotation-powered pulsars, and then discussing gamma-ray observations and magnetospheric models in more detail.

A 3+1 formalism for quantum electrodynamical corrections to Maxwell equations in general relativity

Magnetized neutron stars constitute a special class of compact objects harbouring gravitational fields that deviate strongly from the Newtonian weak field limit. Moreover strong electromagnetic fields anchored into the star give rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). Electromagnetic fields close to or above the critical value of BQ = 4.4 × 10 9 T are probably present in some pulsars and for most of the magnetars. To account properly for emission emanating from the neutron star surface like for instance thermal radiation and its polarization properties, it is important to include general relativistic (GR) effects simultaneously with non-linear electrodynamics. This can be achieved through a 3+1 formalism known in general relativity and that incorporates QED perturbations to Maxwell equations. Starting from the lowest order corrections to the Lagrangian for the electromagnetic field, as given for instance by Born-Infeld or Euler-Heisenberg theory, we derive the non-linear Maxwell equations in general relativity including quantum vacuum effects. We also derive a prescription for the force-free limit and show that these equations can be solved with classical finite volume methods for hyperbolic conservation laws. It is therefore straightforward to include general relativity and quantum electrodynamics in the description of neutron star magnetospheres by using standard classical numerical techniques borrowed from Maxwell and Newton theory. As an application, we show that spin-down luminosity corrections associated to QED effects are negligible with respect to GR corrections.

A PROPELLER MODEL FOR THE SUB-LUMINOUS STATE OF THE TRANSITIONAL MILLISECOND PULSAR PSR J1023+0038

The discovery of millisecond pulsars switching between states powered either by the rotation of their magnetic field or by the accretion of matter, has recently proved the tight link shared by millisecond radio pulsars and neutron stars in low-mass X-ray binaries. Transitional millisecond pulsars also show an enigmatic intermediate state in which the neutron star is surrounded by an accretion disk, it emits coherent X-ray pulsations, but is sub-luminous in X-rays with respect to accreting neutron stars, and is brighter in gamma-rays than millisecond pulsars in the rotation-powered state. Here, we model the X-ray and gamma-ray emission observed from PSR J1023+0038 in such a state based on the assumption that most of the disk in-flow is propelled away by the rapidly rotating neutron star magnetosphere, and that electrons can be accelerated to energies of a few GeV at the turbulent disk-magnetosphere boundary. We show that the synchrotron and self-synchrotron Compton emission coming from such a region, together with the hard disk emission typical of low states of accreting compact objects, is able to explain the radiation observed i n the X-ray and gamma-ray band. The average emission observed from PSR J1023+0038 is modelled by a disk in-flow with a rate of 1‐3 × 10 −11 M⊙ yr −1 , truncated at a radius ranging between 30 and 45 km, compatible with the hypothesis of a propelling magnetosphere. We compare the results we obtained with models that rather assume that a rotation-powered pulsar is turned on, showing how the spin down power released in similar scenarios is hardly able to account for the magnitude of the observed emission. Subject headings: accretion, accretion disks ‐ magnetic fields ‐ gamma rays: st ars ‐ pulsars: individual (PSR J1023+0038)

An analysis of magnetic field and magnetosphere of neutron star under effect of a shock wave

We consider a model of magnetosphere of a neutron star subjected to a strong shock wave from supernova explosion. In this model a form of magnetosphere’s boundary is determined from the condition of equilibrium between external gas pressure behind the shock and interior magnetic pressure. The field of neutron star is approximated as a point magnetic dipole. The magnetic field is assumed to be potential in circumstellar space. In magnetotail there is a reconnecting current layer, which accumulates an excess magnetic energy. The model under consideration is reduced to consequent solution of two Riemann–Hilbert problems. The obtained analytic solution of the both problems, in particular, shows the presence of reverse current in the current layer. The solution has importance for possibility estimation of directional relativistic plasma jets and impulse bursts of gamma-impulses or hard radiation of other kinds.

MAPPING THE SURFACE OF THE MAGNETAR 1E 1048.1–5937 IN OUTBURST AND QUIESCENCE THROUGH PHASE-RESOLVED X-RAY SPECTROSCOPY

We model the pulse profiles and the phase resolved spectra of the anomalous X-ray pulsar 1E 1048.1-5937 obtained with XMM-Newton to map its surface temperature distribution during an active and a quiescent epoch. We develop and apply a model that takes into account the relevant physical and geometrical effects on the neutron star surface, magnetosphere, and spacetime. Using this model, we determine the observables at infinity as a function of pulse phase for different numbers and sizes of hot spots on the surface. We show that the pulse profiles extracted from both observations can be modeled with a single hot spot and an antipodal cool component. The size of the hot spot changes from $\approx 80^{\circ}$ in 2007, 3 months after the onset of a dramatic flux increase, to $\approx 30^{\circ}$ during the quiescent observation in 2011, when the pulsed fraction returned to the pre-outburst $\approx$ 65\% level. For the 2007 observation, we also find that a model consisting of a single 0.4 keV hot spot with a magnetic field strength of $1.8 \times 10^{14}$ G accounts for the spectra obtained at three different pulse phases but under predicts the flux at the pulse minimum, where the contribution to the emission from the cooler component is non-negligible. The inferred temperature of the spot stays approximately constant between different pulse phases, in agreement with a uniform temperature, single hot spot model. These results suggest that the emitting area grows significantly during outbursts but returns to its persistent and significantly smaller size within a few year timescale.

X-ray coherent pulsations during a sub-luminous accretion disc state of the transitional millisecond pulsar XSS J12270−4859

Abstract We present the first detection of X-ray coherent pulsations from the transitional millisecond pulsar XSS J12270−4859, while it was in a sub-luminous accretion disc state characterized by a 0.5–10 keV luminosity of 5 × 1033 erg s−1 (assuming a distance of 1.4 kpc). Pulsations were observed by XMM–Newton at an rms amplitude of (7.7 ± 0.5) per cent with a second harmonic stronger than the fundamental frequency, and were detected when the source is neither flaring nor dipping. The most likely interpretation of this detection is that matter from the accretion disc was channelled by the neutron star magnetosphere and accreted on to its polar caps. According to standard disc accretion theory, for pulsations to be observed the mass inflow rate in the disc was likely larger than the amount of plasma actually reaching the neutron star surface; an outflow launched by the fast rotating magnetosphere then probably took place, in agreement with the observed broad-band spectral energy distribution. We also report about the non-detection of X-ray pulsations during a recent observation performed while the source behaved as a rotationally-powered radio pulsar.

General relativistic monopole magnetosphere of neutron stars: a pseudo-spectral discontinuous Galerkin approach

The close vicinity of neutron stars remains poorly constrained by observations. Although plenty of data are available for the peculiar class of pulsars we are still unable to deduce the underlying plasma distribution in their magnetosphere. In the present paper, we try to unravel the magnetospheric structure starting from basic physics principles and reasonable assumptions about the magnetosphere. Beginning with the monopole force-free case, we compute accurate general-relativistic solutions for the electromagnetic field around a slowly rotating magnetized neutron star. Moreover, here we address this problem by including the important effect of plasma screening. This is achieved by solving the time-dependent Maxwell equations in a curved space-time following the 3+1~formalism. We improved our previous numerical code based on pseudo-spectral methods in order to allow for possible discontinuities in the solution. Our algorithm based on a multi-domain decomposition of the simulation box belongs to the discontinuous Galerkin finite element methods. We performed several sets of simulations to look for the general-relativistic force-free monopole and split monopole solutions. Results show that our code is extremely powerful in handling extended domains of hundredth of light-cylinder radii~$\rlight$. The code has been validated against known exact analytical monopole solutions in flat space-time. We also present semi-analytical calculations for the general-relativistic vacuum monopole.

THREE-DIMENSIONAL NON-VACUUM PULSAR OUTER-GAP MODEL: LOCALIZED ACCELERATION ELECTRIC FIELD IN THE HIGHER ALTITUDES

We investigate the particle accelerator that arises in a rotating neutron-star magnetosphere. Solving the Poisson equation for the electro-static potential, the Boltzmann equations for relativistic electrons and positrons, and the radiative transfer equation simultaneously, we demonstrate that the electric field is substantially screened along the magnetic field lines by the pairs that are created and separated within the accelerator. As a result, the magnetic-field-aligned electric field is localized in the higher altitudes near the light cylinder and efficiently accelerates the positrons created in the lower altitudes outwards but not the electrons inwards. The resulting photon flux becomes predominantly outwards, leading to typical double-peak light curves, which are commonly observed from many high-energy pulsars.

Six faint gamma-ray pulsars seen with theFermiLarge Area Telescope

Context: GeV gamma-ray pulsations from over 140 pulsars have been characterized using the Fermi Large Area Telescope, enabling improved understanding of the emission regions within the neutron star magnetospheres, and the contributions of pulsars to high energy electrons and diffuse gamma rays in the Milky Way. The first gamma-ray pulsars to be detected were the most intense and/or those with narrow pulses. Aims: As the Fermi mission progresses, progressively fainter objects can be studied. In addition to more distant pulsars (thus probing a larger volume of the Galaxy), or ones in high background regions (thus improving the sampling uniformity across the Galactic plane), we detect pulsars with broader pulses or lower luminosity. Adding pulsars to our catalog with inclination angles that are rare in the observed sample, and/or with lower spindown power, will reduce the bias in the currently known gamma-ray pulsar population. Methods: We use rotation ephemerides derived from radio observations to phase-fold gamma rays recorded by the Fermi Large Area Telescope, to then determine the pulse profile properties. Spectral analysis provides the luminosities and, when the signal-to-noise ratio allows, the cutoff energies. We constrain the pulsar distances by different means in order to minimize the luminosity uncertainties. Results: We present six new gamma-ray pulsars with an eclectic mix of properties. Three are young, and three are recycled. They include the farthest, the lowest power, two of the highest duty-cycle pulsars seen, and only the fourth young gamma-ray pulsar with a radio interpulse. We discuss the biases existing in the current gamma-ray pulsar catalog, and steps to be taken to mitigate the bias.

HST optical polarimetry of the Vela pulsar and nebula

Polarisation measurements of pulsars offer an unique insight into the geometry of the emission regions in the neutron star magnetosphere. Therefore, they provide observational constraints on the different models proposed for the pulsar emission mechanisms. Optical polarisation data of the Vela pulsar was obtained from the {\em Hubble Space Telescope} ({\em HST}) archive. The data, obtained in two filters (F606W; central wavelength = 590.70 nm, and F550M; central wavelength = 558.15 nm), consists of a series of observations of the pulsar taken with the {\em HST}/Advanced Camera for Surveys (ACS) and covers a time span of 5 days. This data have been used to carry out the first high-spatial resolution and multi-epoch study of the polarisation of the pulsar. We produced polarisation vector maps of the region surrounding the pulsar and measured the degree of linear polarisation (P.D.) and the position angle (P.A.) of the pulsar's integrated pulse beam. %This yielded We obtained $\rm P.D.=8.1\%\pm0.7\%$ and $\rm P.A.=146.3\degr\pm2.4\degr$, averaged over the time span covered by these observations. These results not only confirm those originally obtained by \citeauthor{Wagner00} and \citeauthor{Mignani07}, both using the Very Large Telescope (VLT), but are of greater precision. Furthermore, we confirm that the P.A. of the pulsar polarisation vector is aligned with the direction of the pulsar proper-motion. The pulsar wind nebula (PWN) is undetected in polarised light as is the case in unpolarised light, down to a flux limit of 26.8 magnitudes arcsec$^{-2}$.

Compton scattering in strong magnetic fields: Spin-dependent influences at the cyclotron resonance

The quantum electrodynamical (QED) process of Compton scattering in strong magnetic fields is commonly invoked in atmospheric and inner magnetospheric models of x-ray and soft gamma-ray emission in high-field pulsars and magnetars. A major influence of the field is to introduce resonances at the cyclotron frequency and its harmonics, where the incoming photon accesses thresholds for the creation of virtual electrons or positrons in intermediate states with excited Landau levels. At these resonances, the effective cross section typically exceeds the classical Thomson value by over 2 orders of magnitude. Near and above the quantum critical magnetic field of 44.13 TeraGauss, relativistic corrections must be incorporated when computing this cross section. This paper presents formalism for the QED magnetic Compton differential cross section valid for both subcritical and supercritical fields, yet restricted to scattered photons that are below pair creation threshold. Calculations are developed for the particular case of photons initially propagating along the field, mathematically simple specializations that are germane to interactions involving relativistic electrons frequently found in neutron star magnetospheres. This exposition of relativistic, quantum, magnetic Compton cross sections treats electron spin dependence fully, since this is a critical feature for describing the finite decay lifetimes of the intermediate states. The formalism employs both the Johnson and Lippmann (JL) wave functions and the Sokolov and Ternov (ST) electron eigenfunctions of the magnetic Dirac equation. The ST states are formally correct for self-consistently treating spin-dependent effects that are so important in the resonances. Relatively compact analytic forms for the cross sections are presented that will prove useful for astrophysical modelers.

Self-organized criticality in a spherically closed cellular automaton: Modeling soft gamma repeater bursts driven by magnetic reconnection

A new cellular automaton (CA) model is presented for the self-organized criticality (SOC) in recurrent bursts of soft gamma repeaters (SGRs), which are interpreted as avalanches of reconnection in the magnetosphere of neutron stars. The nodes of a regular dodecahedron and a truncated icosahedron are adopted as spherically closed grids enclosing a neutron star. It is found that the system enters the SOC state if there are sites where the expectation value of the added perturbation is nonzero. The energy distributions of SOC avalanches in CA simulations are described by a power law with a cutoff, which is consistent with the observations of SGR 1806-20 and SGR 1900+14. The power-law index is not universal and depends on the amplitude of the perturbation. This result shows that the SOC of SGRs can be illustrated not only by the crust quake model but also by the magnetic reconnection model.

Does a strong particle accelerator arise very close to the light cylinder in a pulsar magnetosphere?

Abstract We examine if an efficient particle acceleration takes place by a magnetic-field-aligned electric field near the light cylinder in a rotating neutron star magnetosphere. Constructing the electric current density with the actual motion of collisionless plasmas, we express the rotationally induced Goldreich–Julian charge density as a function of position. It is demonstrated that the ‘light cylinder gap’, which emits very high energy photons via curvature process by virtue of a strong magnetic-field-aligned electric field very close to the light cylinder, will not arise in an actual pulsar magnetosphere.

A year in the life of the low-mass X-ray transient Aql X-1

The Swift satellite monitored the quiescence of the low-mass X-ray binary transient Aql X-1 on a weekly basis during the March-November 2012 interval. A total of 42 observations were carried out in the soft X-ray (0.3-10 keV) band with the X-ray Telescope on board Swift. We investigated the X-ray variability properties of Aql X-1 during quiescence by tracking luminosity variations and characterising them with a detailed spectral analysis. The source is highly variable in this phase and two bright flares were detected, with peak luminosities of ~4x10^{34} erg s^{-1} (0.3-10 keV). Quiescent X-ray spectra require both a soft thermal component below ~2 keV and a hard component (a power law tail) above ~2 keV. Changes in the power law normalisation alone can account for the overall observed variability. Therefore, based on our data set, the quiescent X-ray emission of Aql X-1 is consistent with the cooling of the neutron star core and with mechanisms involving the accretion of matter onto the neutron star surface or magnetosphere.

The Magnetospheres of (Accreting) Neutron Stars

I give an overview of the most important observational tools to study the magnetospheres of accreting neutron stars, with a focus on accreting neutron stars in high mass X-ray binary systems. Topics covered are the different types of accretion onto neutron stars and the structure of the accretion column, and how models for these can be tested with observations.