Gamma-ray lines, electron-positron annihilation, and possible radio emission in X-ray pulsars

Cyclotron resonance scattering features are observed in the spectra of some X-ray pulsars and show significant changes in the line energy with the pulsar luminosity. In a case of bright sources, the line centroid energy is anti-correlated with the luminosity. Such a behaviour is often associated with the onset and growth of the accretion column, which is believed to be the origin of the observed emission and the cyclotron lines. However, this scenario inevitably implies large gradient of the magnetic field strength within the line-forming region, and it makes the formation of the observed line-like features problematic. Moreover, the observed variation of the cyclotron line energy is much smaller than could be anticipated for the corresponding luminosity changes. We argue that a more physically realistic situation is that the cyclotron line forms when the radiation emitted by the accretion column is reflected from the neutron star surface. The idea is based on the facts that a substantial part of column luminosity is intercepted by the neutron star surface and the reflected radiation should contain absorption features. The reflection model is developed and applied to explain the observed variations of the cyclotron line energy in a bright X-ray pulsar V 0332+53 over a wide range of luminosities.

Cyclotron resonance scattering features observed in the spectra of some X-ray pulsars show significant changes of the line energy with the pulsar luminosity. At high luminosities, these variations are often associated with the onset and growth of the accretion column, which is believed to be the origin of the observed emission and of the cyclotron lines. However, this scenario inevitably implies large gradient of the magnetic field strength within the line-forming region, which makes the formation of the observed line-like features problematic. Moreover, the observed variation of the cyclotron line energy is much smaller than could be anticipated for the corresponding luminosity changes. We argue here that a more physically realistic situation is that the cyclotron line forms when the radiation emitted by the accretion column is reflected from the neutron star surface, where the gradient of the magnetic field strength is significantly smaller. We develop here the reflection model and apply it to explain the observed variations of the cyclotron line energy in a bright X-ray pulsar V 0332+53 over a wide range of luminosities.

The spectral flux is calculated for x-ray emission from a rotating neutron star uniformly heated over its surface (T = 10 /sup 80/K) and having a strong dipolar magnetic field (B = 5 x 10/sup 12/ G at the pole). It is shown that because of the strong anisotropy of the local intensity and its dependence on the magnetic field, the flux in the photon energy interval E approx. 2-70 keV varies over time with the period of rotation, that is, a star such as this manifests itself as an x-ray pulsar. The amplitude of the variations and the shape of the brightness curves are strongly dependent on the energy. The spectrum of the flux contains two emission cyclotron features. Their position, like the shape of the continuum, depends on the phase of the rotation. The results obtained demonstrate the possibility of models or x-ray pulsars in which the radiating (hot) regions are not localized around the magnetic poles, but occupy a large part of the surface of a neutron star.

Context. Accretion onto magnetic neutron stars results in X-ray spectra that often exhibit a cyclotron resonance scattering feature (CRSF) and, sometimes, higher harmonics of it. Two places are suspect for the formation of a CRSF: the surface of the neutron star and the radiative shock in the accretion column. Aims. Here we explore the first possibility: reflection at the neutron-star surface of the continuum produced at the radiative shock. It has been proposed that for high-luminosity sources, as the luminosity increases, the height of the radiative shock increases, thus a larger polar area is illuminated, and as a consequence the energy of the CRSF decreases because the dipole magnetic field decreases by a factor of two from the pole to the equator. This model has been specifically proposed to explain the observed anticorrelation of the cyclotron line energy and luminosity of the high-luminosity source V 0332+53. Methods. We used a Monte Carlo code to compute the reflected spectrum from the atmosphere of a magnetic neutron star, when the incident spectrum is a power-law one. We restricted ourselves to cyclotron energies ≪mec2 and used polarization-dependent scattering cross sections, allowing for polarization mode change. Results. As expected, a prominent CRSF is produced in the reflected spectra if the incident photons are in a pencil beam, which hits the neutron-star surface at a point with a well-defined magnetic field strength. However, the incident beam from the radiative shock has a finite width and thus various magnetic field strengths are sampled. As a result of overlap, the reflected spectra have a CRSF, which is close to that produced at the magnetic pole, independent of the height of the radiative shock. Conclusions. Reflection at the surface of a magnetic neutron star cannot explain the observed decrease in the CRSF energy with luminosity in the high-luminosity X-ray pulsar V 0332+53. In addition, it produces absorption lines much shallower than the observed ones.

Recently it was pointed out by Shabad and Usov that in the vicinity of pulsars high-energy photons can be captured by the strong magnetic field without creating pairs. We have reconsidered this process and find that the captured photon is transformed into bound positronium. This positronium can be ionized by the intense electric fields present in the polar cap region, or by thermal radiation from the neutron star surface, whereby the free electrons and positrons are regained that are urgently required for the models of pulsar radio emission.

Isolated Neutron Stars: From the Surface to the Interior

Context: Very high magnetic fields at the surface of neutron stars or in the accretion disk of black holes inhibit the production of jets. Aims: We quantify here the magnetic field strength for jet formation. Methods: By using the Alfven Radius, R_A, we study what we call {\it the basic condition}, R_A/R_*=1 or R_A/R_{LSO}=1 (LSO, last stable orbit), in its dependency on the magnetic field strength and the mass accretion rate, and we analyse these results in 3-D and 2-D plots in the case of neutron star and black hole accretor systems, respectively. For this purpose, we did a systematic search of all available observational data for magnetic field strength and the mass accretion rate. Results: The association of a classical X-ray pulsar (i.e. B ~10^{12} G) with jets is excluded even if accreting at the Eddington critical rate. Z-sources may develop jets for B \simlt 10^{8.2} G, whereas Atoll-sources are potential sources of jets if B \simlt 10^{7.7} G. It is not ruled out that a millisecond X-ray pulsar could develop jets, at least for those sources where B \simlt 10^{7.5} G. In this case the millisecond X-ray pulsar could switch to a microquasar phase during its maximum accretion rate. For stellar-mass black hole X-ray binaries, the condition is that B \simlt 1.35 x 10^8 G and B \simlt 5 x 10^8 G at the last stable orbit for a Schwarzschild and a Kerr black hole, respectively. For active galactic nuclei (AGNs), it reaches B \simlt 10^{5.9} G for each kind of black hole. These theoretical results are in complete agreement with available observational data.

The luminosity of X-ray pulsars powered by accretion on to magnetized neutron stars covers a wide range over a few orders of magnitude. The brightest X-ray pulsars recently discovered as pulsating ultraluminous X-ray sources reach accretion luminosity above $10^{40}\, {\rm erg\ \rm s^{-1}}$ which exceeds the Eddington value more than by a factor of 10. Most of the energy is released within small regions in the vicinity of magnetic poles of accreting neutron star - in accretion columns. Because of the extreme energy release within small volume accretion columns of bright X-ray pulsars are one of the hottest places in the Universe, where the internal temperature can exceed 100 keV. Under these conditions, the processes of creation and annihilation of electron-positron pairs can be influential but have been largely neglected in theoretical models of accretion columns. In this Letter, we investigate properties of a gas of electron--positron pairs under physical conditions typical for accretion columns. We argue that the process of pair creation can crucially influence both the dynamics of the accretion process and internal structure of accretion column limiting its internal temperature, dropping the local Eddington flux and increasing the gas pressure.

Context.X-ray pulsars are binary systems which consist of a neutron star in orbit with a mass donor (companion). In these systems the neutron accretes matter from the companion star, which creates accretion columns or hot spots on the neutron star surface and gives rise to pulsations in the X-ray light curve. The pulse profiles carry information about the accretion and magnetic field geometry. Here we present a study and classification of energy-resolved pulse profiles of a sample of X-ray pulsars, focusing on high-mass X-ray binaries.Aims.Our goal is to perform a classification of X-ray pulsars based on their observed pulse profiles and look for correlations between this classification and their principle physical observables. The analysis pipeline is available online.Methods.We analysed the pulse profiles of a sample of X-ray pulsars using data obtained with the X-ray Multi-Mirror Mission (XMM-Newton) and the Nuclear Spectroscopic Telescope Array (NuSTAR). We fitted the energy-resolved pulse profiles with a Fourier series of up to five harmonics. We then used the energy evolution of the different Fourier components to classify the pulse profiles into groups. We investigated relationships between the pulse profile properties and other observables of the systems (e.g. orbital period, magnetic field strength, and luminosity) to study the extreme physics of these systems.Results.The sources were divided into three groups using a classification based on the shape, the dominance of the fitted Fourier harmonics, and their respective evolution with energy. We do not find a conclusive correlation between the pulse profile shapes or groups and other parameters of the systems. However, a weak trend was found when comparing our classification to the sources’ locations in the spin period-orbital period diagram. Further studies are required to confirm this trend.Conclusions.Despite the large variety of pulse profiles of the X-ray pulsars, we found that with our approach clear categories emerge which we use to classify their behaviour as a function of energy. As we do not find a clear relationship between our classification scheme and other parameters, like the luminosity, the magnetic field strength, or the orbital and spin periods, we conclude that X-ray pulse profiles are influenced by other hidden variables.

The luminosity of X-ray pulsars is their key parameter determining the geometry and physical conditions of the accretion flow both on the spatial scales of a binary system and on much smaller scales of emitting regions located close to the stellar surface. Traditionally, the luminosity of X-ray pulsars is estimated out of the X-ray energy flux averaged over the pulsed period and the estimated distance to the source. Due to the anisotropy of X-ray emission, the luminosity estimated on the base of the observed pulse profile can differ from the actual one. Super-cw2ritical X-ray pulsars with accretion columns are of particular interest because the X-ray flux from columns is a matter of strong gravitational lensing by a neutron star. Using toy model of an accretion column, we simulate beam patterns in super-critical X-ray pulsars, construct theoretical pulse profiles for different geometries and mutual orientations of pulsars and distant observers and show that despite strong light bending, the typical deviation of the apparent luminosity from the actual one is $\sim 20~{{\ \rm per \, cent}}$ only, and in $\sim 90~{{\ \rm per \, cent}}$ of cases, the apparent luminosity 0.8L ≲ Lapp ≲ 1.25L. However, the shape of the pulse profiles is strongly affected by the geometry of the emitting region. We show that the appearance and growth of accretion columns tend to be accompanied by an increase of observed pulsed fraction, which is in agreement with the recent observations of bright X-ray transients.

Extreme accretion in X-ray pulsars (XRPs) results in radiation-driven outflows launched from the inner parts of the accretion disc. The outflows affect the apparent luminosity of the XRPs and their pulsations through the geometrical beaming. We model processes of geometrical beaming and pulse formation using Monte Carlo simulations. We confirm our earlier statement that strong amplification of luminosity due to the collimation of X-ray photons is inconsistent with a large pulsed fraction. Accounting for relativistic aberration due to possibly high outflow velocity (∼0.2c) does not affect this conclusion. We demonstrate that the beaming causes phase lags of pulsations. Within the opening angle of the accretion cavity formed by the outflows, phase lags tend to be sensitive to observers viewing angles. Variations in outflow geometry and corresponding changes of the phase lags might influence the detectability of pulsation in bright X-ray pulsars and ULXs. We speculate that the strong geometrical beaming is associated with large radiation pressure on the walls of accretion cavity due to multiple photons reflections. We expect that the mass-loss rate limits geometrical beaming: strong beaming becomes possible only under sufficiently large fractional mass-loss rate from the disc.

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.

We investigate self-consistent particle acceleration near a pulsar polar cap (PC) by the electrostatic field due to the effect of inertial frame dragging. Test particles gain energy from the electric field parallel to the open magnetic field lines and lose energy by both curvature radiation (CR) and resonant and non-resonant inverse Compton scattering (ICS) with soft thermal X-rays from the neutron star (NS) surface. Gamma-rays radiated by electrons accelerated from the stellar surface produce pairs in the strong magnetic field, which screen the electric field beyond a pair formation front (PFF). Some of the created positrons can be accelerated back toward the surface and produce gamma-rays and pairs that create another PFF above the surface. We find that ICS photons control PFF formation near the surface, but due to the different angles at which the electron and positron scatter the soft photons, positron initiated cascades develop above the surface and screen the accelerating electric field. Stable acceleration from the NS surface is therefore not possible in the presence of dominant ICS energy losses. However, we find that stable acceleration zones may occur at some distance above the surface, where CR dominates the electron and positron energy losses, and there is up-down symmetry between the electron and positron PFFs. We examine the dependence of CR-controlled acceleration zone voltage, width and height above the surface on parameters of the pulsar and its soft X-ray emission. For most pulsars, we find that acceleration will start at a height of 0.5 - 1 stellar radii above the NS surface.

Only three of the dozen central compact objects (CCOs) in supernova remnants (SNRs) show thermal X-ray pulsations due to nonuniform surface temperature (hot spots). The absence of X-ray pulsations from several unpulsed CCOs has motivated suggestions that they have uniform-temperature carbon atmospheres (UTCAs), which adequately fit their spectra with appropriate neutron star (NS) surface areas. This is in contrast to the two-temperature blackbody or hydrogen atmospheres that also fit well. Here we investigate the applicability of UTCAs to CCOs. We show the following: (i) The phase-averaged spectra of the three pulsed CCOs can also be fitted with a UTCA of the appropriate NS area, despite pulsed CCOs manifestly having nonuniform surface temperature. A good spectral fit is therefore not strong support for the UTCA model of unpulsed CCOs. (ii) An improved spectrum of one unpulsed CCO, previously analyzed with a UTCA, does not allow an acceptable fit. (iii) For two unpulsed CCOs, the UTCA does not allow a distance compatible with the SNR distance. These results imply that, in general, CCOs must have hot, localized regions on the NS surface. We derive new X-ray pulse modulation upper limits on the unpulsed CCOs, and constrain their hot spot sizes and locations. We develop an alternative model that accounts for both the pulsed and unpulsed CCOs: a range of angles between hot spot and rotation axes consistent with an exponential distribution with scale factor λ ∼ 20°. We discuss the physical mechanisms that could produce such small angles and small hot spots.

The spectra of many X-ray pulsars show, in addition to a power law, a low-energy component that has often been modeled as a blackbody with kT ~ 0.1 keV. However the physical origin of this soft excess has remained a mystery. We examine a sample of well-studied, bright X-ray pulsars, which have been observed using ROSAT, ASCA, Ginga, RXTE, BeppoSAX, Chandra, and XMM-Newton. In particular we consider the Magellanic Cloud pulsars SMC X-1, LMC X-4, XTE J0111.2-7317, and RX J0059.2-7138 and the Galactic sources Her X-1, 4U 1626-67, Cen X-3, and Vela X-1. We show that the soft excess is a very common if not ubiquitous feature intrinsic to X-ray pulsars. We evaluate several possible mechanisms for the soft emission, using theoretical arguments as well as observational clues such as spectral shapes, eclipses, pulsations of the soft component, and superorbital modulation of the source flux. We find that reprocessing of hard X-rays from the neutron star by the inner region of the accretion disk is the only process that can explain the soft excess in all the pulsars with Lx > 10^38 ergs/s. Other mechanisms, such as emission from diffuse gas in the system, are important in less luminous objects.