The bottom magnetic field and magnetosphere evolution of neutron star in low-mass X-ray binary

The accretion-induced neutron star (NS) magnetic field evolution is studied through considering the accretion flow to drag the field lines aside and dilute the polar-field strength, and as a result the equatorial field strength increases, which is buried inside the crust on account of the accretion-induced global compression of star crust. The main conclusions of model are as follows: (i) the polar field decays with increase in the accreted mass; (ii) the bottom magnetic field strength of about 10⁸ G can occur when the NS magnetosphere radius approaches the star radius, and it depends on the accretion rate as     ; and (iii) the NS magnetosphere radius decreases with accretion until it reaches the star radius, and its evolution is little influenced by the initial field and the accretion rate after accreting  ∼0.01 M_⊙  , which implies that the magnetosphere radii of NSs in low-mass X-ray binaries would be homogeneous if they accreted the comparable masses. As an extension, the physical effects of the possible strong magnetic zone in the X-ray NSs and recycled pulsars are discussed. Moreover, the strong magnetic fields in the binary pulsars PSR 1831−00 and PSR 1718−19 after accreting about  0.5 M_⊙  in the binary-accretion phase,  8.7 × 10¹⁰  and  1.28 × 10¹² G  , respectively, can be explained through considering the incomplete frozen flow in the polar zone. As an expectation of the model, the existence of the low magnetic field  (∼3 × 10⁷ G)  NSs or millisecond pulsars is suggested.     

Constraining the geometry of the neutron star RX J1856.5−3754

RX J1856.5−3754 is one of the brightest, nearby isolated neutron stars (NSs), and considerable observational resources have been devoted to its study. In previous work, we found that our latest models of a magnetic, hydrogen atmosphere match well the entire spectrum, from X-rays to optical (with best-fitting NS radius   R ≈ 14  km, gravitational redshift   z _g∼ 0.2  , and magnetic field   B ≈ 4 × 10¹²  G). A remaining puzzle is the non-detection of rotational modulation of the X-ray emission, despite extensive searches. The situation changed recently with XMM–Newton observations that uncovered 7-s pulsations at the     level. By comparing the predictions of our model (which includes simple dipolar-like surface distributions of magnetic field and temperature) with the observed brightness variations, we are able to constrain the geometry of RX J1856.5−3754, with one angle <6° and the other angle     , though the solutions are not definitive, given the observational and model uncertainties. These angles indicate a close alignment between the rotation and the magnetic axes or between the rotation axis and the observer. We discuss our results in the context of RX J1856.5−3754 being a normal radio pulsar and a candidate for observation by future X-ray polarization missions such as Constellation-X or XEUS .     

Early evolution of newly born magnetars with a strong toroidal field

We present a state-of-the-art scenario for newly born magnetars as strong sources of gravitational waves (GWs) in the early days after formation. We address several aspects of the astrophysics of rapidly rotating, ultra-magnetized neutron stars (NSs), including early cooling before transition to superfluidity, the effects of the magnetic field on the equilibrium shape of NSs, the internal dynamical state of a fully degenerate, oblique rotator and the strength of the electromagnetic torque on the newly born NS. We show that our scenario is consistent with recent studies of supernova remnant surrounding Anomalous X-ray Pulsars (AXPs) and Soft Gamma-Ray Repeaters (SGRs) in the Galaxy that constrains the electromagnetic energy input from the central NS to be  ≤ 10⁵¹  erg. We further show that if this condition is met, then the GW signal from such sources is potentially detectable with the forthcoming generation of GW detectors up to Virgo cluster distances where an event rate ∼1 yr⁻¹ can be estimated. Finally, we point out that the decay of an internal magnetic field in the 10¹⁶ G range couples strongly with the NS cooling at very early stages, thus significantly slowing down both processes: the field can remain this strong for at least 10³ yr, during which the core temperature stays higher than several times 10⁸ K.     

What is the nature of RX J0720.4–3125?

RX J0720.4–3125 has recently been identified as a pulsating soft X-ray source in the ROSAT all-sky survey with a period of 8.391 s. Its spectrum is well characterized by a blackbody with a temperature of 8 × 10⁵ K. We propose that the radiation from this object is thermal emission from a cooling neutron star. For this blackbody temperature we can obtain a robust estimate of the object's age of ∼ 3 × 10⁵ yr, yielding a polar field ∼ 10¹⁴ G for magnetic dipole spin-down and a value of P compatible with current observations.     

Magnetic hydrogen atmosphere models and the neutron star RX J1856.5–3754

RX J1856.5−3754 is one of the brightest nearby isolated neutron stars (INSs), and considerable observational resources have been devoted to it. However, current models are unable to satisfactorily explain the data. We show that our latest models of a thin, magnetic, partially ionized hydrogen atmosphere on top of a condensed surface can fit the entire spectrum, from X-rays to optical, of RX J1856.5−3754, within the uncertainties. In our simplest model, the best-fitting parameters are an interstellar column density   N _H≈ 1 × 10²⁰ cm⁻²  and an emitting area with   R ^∞≈ 17 km  (assuming a distance to RX J1856.5−3754 of 140 pc), temperature   T ^∞≈ 4.3 × 10⁵ K  , gravitational redshift   z _g ∼ 0.22  , atmospheric hydrogen column   y _H≈ 1 g cm⁻²  , and magnetic field   B ≈ (3–4) × 10¹² G  ; the values for the temperature and magnetic field indicate an effective average over the surface. We also calculate a more realistic model, which accounts for magnetic field and temperature variations over the NS surface as well as general relativistic effects, to determine pulsations; we find that there exist viewing geometries that produce pulsations near the currently observed limits. The origin of the thin atmospheres required to fit the data is an important question, and we briefly discuss mechanisms for producing these atmospheres. Our model thus represents the most self-consistent picture to date for explaining all the observations of RX J1856.5−3754.     

Collapse and fragmentation of rotating magnetized clouds – I. Magnetic flux–spin relation

We discuss the evolution of the magnetic flux density and angular velocity in a molecular cloud core, on the basis of three-dimensional numerical simulations, in which a rotating magnetized cloud fragments and collapses to form a very dense optically thick core of  >5 × 10¹⁰ cm⁻³  . As the density increases towards the formation of the optically thick core, the magnetic flux density and angular velocity converge towards a single relationship between the two quantities. If the core is magnetically dominated its magnetic flux density approaches  1.5( n /5 × 10¹⁰ cm⁻³)^1/2 mG  , while if the core is rotationally dominated the angular velocity approaches  2.57 × 10⁻³ ( n /5 × 10¹⁰ cm⁻³)^1/2 yr⁻¹  , where n is the density of the gas. We also find that the ratio of the angular velocity to the magnetic flux density remains nearly constant until the density exceeds  5 × 10¹⁰ cm⁻³  . Fragmentation of the very dense core and emergence of outflows from fragments will be shown in the subsequent paper.     

Magnetized relativistic jets and long-duration GRBs from magnetar spin-down during core-collapse supernovae

We use ideal axisymmetric relativistic magnetohydrodynamic simulations to calculate the spin-down of a newly formed millisecond,   B ∼ 10¹⁵ G  , magnetar and its interaction with the surrounding stellar envelope during a core-collapse supernova (SN) explosion. The mass, angular momentum and rotational energy lost by the neutron star are determined self-consistently given the thermal properties of the cooling neutron star's atmosphere and the wind's interaction with the surrounding star. The magnetar drives a relativistic magnetized wind into a cavity created by the outgoing SN shock. For high spin-down powers  (∼10⁵¹–10⁵² erg s⁻¹)  , the magnetar wind is superfast at almost all latitudes, while for lower spin-down powers  (∼10⁵⁰ erg s⁻¹)  , the wind is subfast but still super-Alfvénic. 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 per cent 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°)  relativistic jet out along the rotation axis of the star. Nearly all of the spin-down 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.     

Atmospheres and spectra of strongly magnetized neutron stars

We construct atmosphere models for strongly magnetized neutron stars with surface fields     and effective temperatures     . The atmospheres directly determine the characteristics of thermal emission from isolated neutron stars, including radio pulsars, soft gamma-ray repeaters, and anomalous X-ray pulsars. In our models, the atmosphere is composed of pure hydrogen or helium and is assumed to be fully ionized. The radiative opacities include free–free absorption and scattering by both electrons and ions computed for the two photon polarization modes in the magnetized electron–ion plasma. Since the radiation emerges from deep layers in the atmosphere with     , plasma effects can significantly modify the photon opacities by changing the properties of the polarization modes. In the case where the magnetic field and the surface normal are parallel, we solve the full, angle-dependent, coupled radiative transfer equations for both polarization modes. We also construct atmosphere models for general field orientations based on the diffusion approximation of the transport equations and compare the results with models based on full radiative transport. In general, the emergent thermal radiation exhibits significant deviation from blackbody, with harder spectra at high energies. The spectra also show a broad feature     around the ion cyclotron resonance     , where Z and A are the atomic charge and atomic mass of the ion, respectively; this feature is particularly pronounced when     . Detection of the resonance feature would provide a direct measurement of the surface magnetic fields on magnetars.     

The effect of the neutron-star crust on the evolution of a core magnetic field

We consider the expulsion of the magnetic field from the super-conducting core of a neutron star and its subsequent decay in the crust. Particular attention is paid to a strong feedback of the distortion of magnetic field lines in the crust on the expulsion of the flux from the core. This causes a considerable delay in the core flux expulsion if the initial field strength is larger than 10¹¹ G. It is shown that the hypothesis on the magnetic field expulsion induced by the neutron-star spin-down is adequate only for a relatively weak initial magnetic field B ≈10¹¹ G. The expulsion time-scale depends not only on the conductivity of the crust, but also on the initial magnetic field strength itself. Our model of the field evolution naturally explains the existence of the residual magnetic field of neutron stars. Its strength is correlated with the impurity concentration in neutron-star crusts and anticorrelated with the initial field strengths.     

One-dimensional electric field structure of an outer gap accelerator – I. γ-ray production resulting from curvature radiation

We study the structure of a stationary and axisymmetric charge-deficient region (or potential gap) in the outer magnetosphere of a spinning neutron star. Assuming the existence of global current flow patterns in the magnetosphere, the charge depletion causes a large electric field along the magnetic field lines. This longitudinal electric field accelerates migratory electrons and/or positrons to ultrarelativistic energies. These relativistic electrons/positrons radiate γ -ray photons by curvature radiation. These γ -rays, in turn, produce yet more radiating particles by colliding with ambient X-ray photons, leading to a pair production cascade in the gap. The replenished charges partially screen the longitudinal electric field, which is self-consistently solved together with the distribution of e^± and γ -ray photons. We find the voltage drop in the gap as a function of the soft photon luminosity. It is demonstrated that the voltage drop is less than 3×10¹³ V when the background X-ray radiation is as luminous as Vela . However, this value increases with decreasing X-ray luminosity and attains 3×10¹⁵ V when the X-ray luminosity is as low as L _X=10³¹ erg s⁻¹.     

Magnetic activity in stellar merger products

We study the expected X-ray luminosity of stellar merger products several years after merger. The X-ray emission is assumed to result from magnetic activity. The extended envelope of the merger product possesses a large convective region and it is expected to rotate fast. The rotation and convection might give rise to an efficient dynamo operation; therefore we expect strong magnetic activity. Using well-known relations connecting magnetic activity and X-ray luminosity in other types of magnetically active stars, we estimate that the strong X-ray luminosity will start several years after merger, will reach a maximum of L _x∼ 3 × 10³⁰ erg s⁻¹, and will slowly decline on a time-scale of ∼100 yr. We predict that X-ray emission from V838 Mon which erupted in 2002 will be detected in 2008 with 20 h of observation.     

Continuous frequency spectrum of the global hydromagnetic oscillations of a magnetically confined mountain on an accreting neutron star

We compute the continuous part of the ideal-magnetohydrodynamic (ideal-MHD) frequency spectrum of a polar mountain produced by magnetic burial on an accreting neutron star. Applying the formalism developed by Hellsten & Spies, extended to include gravity, we solve the singular eigenvalue problem subject to line-tying boundary conditions. This spectrum divides into an Alfvén part and a cusp part. The eigenfunctions are chirped and anharmonic with an exponential envelope, and the eigenfrequencies cover the whole spectrum above a minimum ω_low. For equilibria with accreted mass  1.2 × 10⁻⁶≲ M _a/M_⊙≲ 1.7 × 10⁻⁴  and surface magnetic fields  10¹¹≲ B _*/G ≲ 10¹³, ω_low  is approximately independent of   B _*  , and increases with M _a. The results are consistent with the Alfvén spectrum excited in numerical simulations with the zeus-mp solver. The spectrum is modified substantially by the Coriolis force in neutron stars spinning faster than ∼100 Hz. The implications for gravitational-wave searches for low-mass X-ray binaries are considered briefly.     

Almost analytic models of ultramagnetized neutron star envelopes

Recent ROSAT measurements show that the X-ray emission from isolated neutron stars is modulated at the stellar rotation period. To interpret these measurements, one needs precise calculations of the heat transfer through the thin insulating envelopes of neutron stars. We present nearly analytic models of the thermal structure of the envelopes of ultramagnetized neutron stars. Specifically, we examine the limit in which only the ground Landau level is filled. We use the models to estimate the amplitude of modulation expected from non-uniformities in the surface temperatures of strongly magnetized neutron stars. In addition, we estimate cooling rates for stars with fields B  ∼ 10¹⁵ − 10¹⁶ G, which are relevant to models that invoke 'magnetars' to account for soft γ-ray emission from some repeating sources.     

A large-scale survey of X-ray filaments in the Galactic Centre

We present a catalogue of 17 filamentary X-ray features located within a  68 × 34  arcmin²  view centred on the Galactic Centre region from images taken by Chandra . These features are described by their morphological and spectral properties. Many of the X-ray features have non-thermal spectra that are well fitted by an absorbed power law. Of the 17 features, we find six that have not been previously detected, four of which are outside the immediate  20 × 20  arcmin²  area centred on the Galactic Centre. Seven of the 17 identified filaments have morphological and spectral properties expected for pulsar wind nebulae (PWNe) with X-ray luminosities of  5 × 10³²  to 10³⁴ erg s⁻¹ in the 2.0–10.0 keV band and photon indices in the range of  Γ= 1.1  to 1.9. In one feature, we suggest the strong neutral Fe Kα emission line to be a possible indicator for past activity of Sgr A*. For G359.942−0.03, a particular filament of interest, we propose the model of a ram pressure confined stellar wind bubble from a massive star to account for the morphology, spectral shape and 6.7 keV He-like Fe emission detected. We also present a piecewise spectral analysis on two features of interest, G0.13−0.11 and G359.89−0.08, to further examine their physical interpretations. This analysis favours the PWN scenario for these features.     

The strong magnetic fields of the X-ray pulsars Hercules X-1 and 4U 1626–67 and their evolutionary scenarios

We consider the magnetic and spin evolution of the X-ray binary pulsars Her X-1 and 4U 1626–67, assuming that their magnetic fields are of crustal origin. We adopt the standard evolutionary model which implies that the neutron star passes through several phases in a binary system ('isolated pulsar' – propeller – wind accretion – Roche lobe overflow). In the framework of the model under consideration, the strong magnetic fields of relatively old pulsars like Her X-1 and 4U 1626–67 can naturally be understood if, at their birth, they had a sufficiently strong magnetic field, ∼3 × 10¹³ G, comparable to the maximal field observed in radio pulsars.     

Indirect imaging of the accretion stream in eclipsing polars – II. HU Aquarii

We apply our technique for indirect imaging of the accretion stream to the polar HU Aquarii, using eclipse profiles observed when the system was in a high accretion state. The accretion stream is relatively luminous, contributing as much as the accretion region on the white dwarf, or more, to the overall system brightness. We model the eclipse profiles using a model stream consisting of a ballistic trajectory from the L1 point followed by a magnetically channelled trajectory that follows a dipole field line out of the orbital plane. We perform model fits using two geometries: a stream that accretes on to both footpoints of the field line, and a stream that accretes only on to the footpoint of the field line above the orbital plane. The stream images indicate that the distribution of emission along the stream is not a simple function of the radial distance from the white dwarf. The stream is redirected by the magnetic field of the white dwarf at a distance 1.0–1.3×10¹⁰ cm from the white dwarf; this implies a mass transfer rate in the range 8–76×10¹⁶ g s⁻¹. The absorption dips in the light curve indicate that the magnetically entrained part of the stream moves from 42° to 48° from the line of centres over the three nights of observation. This is in close agreement with the results of the one-footpoint models, suggesting that this is the more appropriate geometry for these data. The stream images show that, in almost all sections of the stream, the flux peaks in B and is successively fainter in U , V and R .     

Multidimensional thermal structure of magnetized neutron star envelopes

Recently launched X-ray telescopes have discovered several candidate isolated neutron stars. The thermal radiation from these objects may potentially constrain our understanding of nuclear physics in a realm inaccessible to terrestrial experiments. To translate the observed fluxes from neutron stars into constraints, one needs precise calculations of the heat transfer through the thin insulating envelopes of neutron stars. We describe models of the thermal structure of the envelopes of neutron stars with magnetic fields up to 10¹⁴ G. Unlike earlier work, we infer the properties of envelope models in two dimensions and precisely account for the quantization of the electron phase-space. Both dipole and uniformly magnetized envelopes are considered.     

Resistive relaxation of a magnetically confined mountain on an accreting neutron star

Three-dimensional numerical magnetohydrodynamic (MHD) simulations are performed to investigate how a magnetically confined mountain on an accreting neutron star relaxes resistively. No evidence is found for non-ideal MHD instabilities on a short time-scale, such as the resistive ballooning mode or the tearing mode. Instead, the mountain relaxes gradually as matter is transported across magnetic surfaces on the diffusion time-scale, which evaluates to  τ_I∼ 10⁵–10⁸ yr  (depending on the conductivity of the neutron star crust) for an accreted mass of   M _a= 1.2 × 10⁻⁴ M_⊙  . The magnetic dipole moment simultaneously re-emerges as the screening currents dissipate over  τ_I  . For non-axisymmetric mountains, ohmic dissipation tends to restore axisymmetry by magnetic reconnection at a filamentary neutral sheet in the equatorial plane. Ideal-MHD oscillations on the Alfvén time-scale, which can be excited by external influences, such as variations in the accretion torque, compress the magnetic field and hence decrease  τ_I  by one order of magnitude relative to its standard value (as computed for the static configuration). The implications of long-lived mountains for gravitational wave emission from low-mass X-ray binaries are briefly explored.     

Radiative transitions of the helium atom in highly magnetized neutron star atmospheres

Recent observations of thermally emitting isolated neutron stars revealed spectral features that could be interpreted as radiative transitions of He in a magnetized neutron star atmosphere. We present Hartree–Fock calculations of the polarization-dependent photoionization cross-sections of the He atom in strong magnetic fields ranging from 10¹² to 10¹⁴ G. Convenient fitting formulae for the cross-sections are given along with the related oscillator strengths for various bound–bound transitions. The effects of finite nucleus mass on the radiative absorption cross-sections are examined using perturbation theory.     

The very flat radio–millimetre spectrum of Cygnus X-1

We present almost-simultaneous detections of Cygnus X-1 in the radio and mm regimes, obtained during the low/hard X-ray state. The source displays a flat spectrum between 2 and 220 GHz, with a spectral index | α |0.15 (3 σ ). There is no evidence for either a low- or high-frequency cut-off, but in the mid-infrared (∼30 μm) thermal emission from the OB-type companion star becomes dominant. The integrated luminosity of this flat-spectrum emission in quiescence is 2×10³¹ erg s⁻¹ (2×10²⁴ W). Assuming the emission originates in a jet for which non-radiative (e.g. adiabatic expansion) losses dominate, this is a very conservative lower limit on the power required to maintain the jet. A comparison with Cyg X-3 and GRS 1915+105, the other X-ray binaries for which a flat spectrum at shorter than cm wavelengths has been observed, shows that the jet in Cyg X-1 is significantly less luminous and less variable, and is probably our best example to date of a continuous, steady, outflow from an X-ray binary. The emissive mechanism responsible for such a flat spectral component remains uncertain. Specifically, we note that the radio–mm spectra observed from these X-ray binaries are much flatter than those of the 'flat-spectrum' AGN, and that existing models of synchrotron emission from partially self-absorbed radio cores, which predict a high-frequency cut-off in the mm regime, are not directly applicable.