Hard Tail Research Articles

THE COMPLETE SPECTRUM OF THE NEUTRON STAR X-RAY BINARY 4U 0614+091

We observed the neutron star (NS) ultra-compact X-ray binary 4U0614+091 quasi-simultaneously in the radio band (VLA), mid-IR/IR (Spitzer/MIPS and IRAC), near-IR/optical (SMARTS), optical-UV (Swift/UVOT), soft and hard X-rays (Swift/XRT and RXTE). The source was steadily in its `hard state'. We detected the source in the whole range, for the first time in the radio band at 4.86 and 8.46 GHz and in the mid-IR at 24 um, up to 100 keV. The optically thick synchrotron spectrum of the jet is consistent with being flat from the radio to the mid-IR band. The flat jet spectrum breaks in the range (1-4)x10^(13) Hz to an optically-thin power-law synchrotron spectrum with spectral index ~-0.5. These observations allow us to estimate a lower limit on the jet radiative power of ~3x10^(32) erg/s and a total jet power Lj~10^(34) u_(0.05)^(-1) Ec^(0.53) erg/s (where Ec is the high-energy cutoff of the synchrotron spectrum in eV and u_(0.05) is the radiative efficiency in units of 0.05). The contemporaneous detection of the optically thin part of the compact jet and the X-ray tail above 30 keV allows us to assess the contribution of the jet to the hard X-ray tail by synchrotron self-Compton (SSC) processes. We conclude that, for realistic jet size, boosting, viewing angle and energy partition, the SSC emission alone, from the post-shock, accelerated, non-thermal population in the jet, is not a viable mechanism to explain the observed hard X-ray tail of the neutron star 4U0614+091.

A FURTHER DROP INTO QUIESCENCE BY THE ECLIPSING NEUTRON STAR 4U 2129+47

The low mass X-ray binary 4U 2129+47 was discovered during a previous X-ray outburst phase and was classified as an accretion disk corona source. A 1% delay between two mid-eclipse epochs measured ~22 days apart was reported from two XMM-Newton observations taken in 2005, providing support to the previous suggestion that 4U 2129+47 might be in a hierarchical triple system. In this work we present timing and spectral analysis of three recent XMM-Newton observations of 4U 2129+47, carried out between November 2007 and January 2008. We found that absent the two 2005 XMM-Newton observations, all other observations are consistent with a linear ephemeris with a constant period of 18857.63s; however, we confirm the time delay reported for the two 2005 XMM-Newton observations. Compared to a Chandra observation taken in 2000, these new observations also confirm the disappearance of the sinusoidal modulation of the lightcurve as reported from two 2005 XMM-Newton observations. We further show that, compared to the Chandra observation, all of the XMM-Newton observations have 40% lower 0.5--2 keV absorbed fluxes, and the most recent XMM-Newton observations have a combined 2--6 keV flux that is nearly 80% lower. Taken as a whole, the timing results support the hypothesis that the system is in a hierarchical triple system (with a third body period of at least 175 days). The spectral results raise the question of whether the drop in soft X-ray flux is solely attributable to the loss of the hard X-ray tail (which might be related to the loss of sinusoidal orbital modulation), or is indicative of further cooling of the quiescent neutron star after cessation of residual, low-level accretion.

DEEPXMM-NEWTONSPECTROSCOPIC AND TIMING OBSERVATIONS OF THE ISOLATED RADIO MILLISECOND PULSAR PSR J0030+0451

We present deep XMM-Newton European Photon Imaging Camera spectroscopic and timing X-ray observations of the nearby solitary radio millisecond pulsar, PSR J0030+0451. Its emission spectrum in the 0.1–10 keV range is found to be remarkably similar to that of the nearest and best-studied millisecond pulsar, PSR J0437–4715, being well described by a predominantly thermal two-temperature model plus a faint hard tail evident above ∼2 keV. The pulsed emission in the 0.3–2 keV band is characterized by two broad pulses with pulsed fraction ∼60%–70%, consistent with a mostly thermal origin of the X-rays only if the surface polar cap radiation is from a light-element atmosphere. Modeling of the thermal pulses permits us to place constraints on the neutron star radius of R > 10.7 (95% confidence) and R > 10.4 km (at 99.9% confidence) for M = 1.4 M☉.

Chandra and Swift observations of the quasi-persistent neutron star transient EXO 0748—676 back to quiescence

Abstract The quasi-persistent neutron star X-ray transient and eclipsing binary EXO 0748−676 recently started the transition to quiescence following an accretion outburst that lasted more than 24 years. We report on two Chandra and 12 Swift observations performed within five months after the end of the outburst. The Chandra spectrum is composed of a soft, thermal component that fits to a neutron star atmosphere model with kT∞∼ 0.12keV, joined by a hard power-law tail that contributes ∼20 per cent of the total 0.5–10 keV unabsorbed flux. The combined Chandra/Swift data set reveals a relatively hot and luminous quiescent system with a temperature of kT∞∼ 0.11–0.13keV and a bolometric thermal luminosity of ∼8.1 × 1033–1.6 × 1034(d/7.4kpc)2ergs −1. We discuss our results in the context of cooling neutron star models.

Topology of magnetars external field - I. Axially symmetric fields

There is an increasing theoretical and observational evidence that the external magnetic field of magnetars may contain a toroidal component, likely of the same order of the poloidal one. Such 'twisted magnetospheres' are threaded by currents flowing along the closed field lines which can efficiently interact with soft thermal photons via resonant cyclotron scatterings (RCS). Actually, RCS spectral models proved quite successful in explaining the persistent ∼1-10 keV emission from the magnetar candidates, the soft γ-ray repeaters (SGRs) and the anomalous X-ray pulsars (AXPs). Moreover, it has been proposed that, in the presence of highly relativistic electrons, the same process can give rise to the observed hard X-ray spectral tails extending up to ∼200 keV. Spectral calculations have been restricted up to now to the case of a globally twisted dipolar magnetosphere, although there are indications that the twist may be confined only to a portion of the magnetosphere, and/or that the large-scale field is more complex than a simple dipole. In this paper, we investigate multipolar, force-free magnetospheres of ultramagnetized neutron stars. We first discuss a general method to generate multipolar solutions of the Grad-Schliiter-Shafranov (GSS) equation, and analyse in detail dipolar, quadrupolar and octupolar fields. The spectra and lightcurves for these multipolar, globally twisted fields are then computed using a Monte Carlo code and compared with those of a purely dipolar configuration. Finally, the phase-resolved spectra and energy-dependent lightcurves obtained with a simple model of a locally sheared field are confronted with the International Gamma-Ray Astrophysics Laboratory (INTEGRAL) observations of the AXPs 1RXS J1708-4009 and 4U 0142+61. Results support a picture in which the field in these two sources is not globally twisted.

A classification of the X-ray and radio states of Cyg X-3 and their long-term correlations

We present a detailed classification of the X-ray states of Cyg X-3 based on the spectral shape and a new classification of the radio states based on the long-term correlated behaviour of the radio and soft X-ray light curves. We find a sequence of correlations, starting with a positive correlation between the radio and soft X-ray fluxes in the hard spectral state, changing to a negative one at the transition to soft spectral states. The temporal evolution can be in either direction on that sequence, unless the source goes into a very weak radio state, from which it can return only following a major radio flare. The flare decline is via relatively bright radio states, which results in a hysteresis loop on the flux-flux diagram. We also study the hard X-ray light curve, and find its overall anticorrelation with the soft X-rays. During major radio flares, the radio flux responds exponentially to the level of a hard X-ray high-energy tail. We also specify the detailed correspondence between the radio states and the X-ray spectral states. We compare our results to those of black-hole and neutron-star binaries. Except for the effect of strong absorption and the energy of the high-energy break in the hard state, the X-ray spectral states of Cyg X-3 closely correspond to the canonical X-ray states of black-hole binaries. Also, the radio/X-ray correlation closely corresponds to that found in black-hole binaries, but it significantly differs from that in neutron-star binaries. Overall, our results strongly support the presence of a black hole in Cyg X-3.

Robust fuzzy clustering using mixtures of Student’s- t distributions

In this paper, we propose a robust fuzzy clustering algorithm, based on a fuzzy treatment of finite mixtures of multivariate Student’s- t distributions, using the fuzzy c-means (FCM) algorithm. As we experimentally demonstrate, the proposed algorithm, by incorporating the assumptions about the probabilistic nature of the clusters being dirived into the fuzzy clustering procedure, allows for the exploitation of the hard tails of the multivariate Student’s- t distribution, to obtain a robust to outliers fuzzy clustering algorithm, offering increased clustering performance comparing to existing FCM-based algorithms. Our experimental results prove that the proposed fuzzy treatment of finite mixtures of Student’s- t distributions is more effective comparing to their statistical treatments using EM-type algorithms, while imposing comparable computational loads.

X-ray spectra from magnetar candidates - II. Resonant cross-sections for electron-photon scattering in the relativistic regime

Recent models of spectral formation in magnetars called renewed attention on electron–photon scattering in the presence of ultrastrong magnetic fields. Investigations presented so far mainly focused on mildly relativistic particles and magnetic scattering was treated in the non-relativistic (Thomson) limit. This allows for consistent spectral calculations up to a few tens of keV, but becomes inadequate in modelling the hard tails (≲200 keV) detected by INTEGRAL from magnetar sources. In this paper, the second in a series devoted to model the X-/soft γ-ray persistent spectrum of magnetar candidates, we present explicit, relatively simple expressions for the magnetic Compton cross-section at resonance which account for Landau–Raman scattering up to the second Landau level. No assumption is made on the magnetic field strength. We find that sensible departures from the Thomson regime can be already present at B∼ 5 × 1012 G. The form of the magnetic cross-section we derived can be easily implemented in Monte Carlo transfer codes and a direct application to magnetar spectral calculations will be presented in a forthcoming study.

X-ray spectra from magnetar candidates – I. Monte Carlo simulations in the non-relativistic regime

The anomalous X-ray pulsars (AXPs) and soft γ -repeaters (SGRs) are peculiar high-energy sources believed to host a magnetar, an ultramagnetized neutron star with surface magnetic field in the petagauss range. Their persistent, soft X-ray emission exhibits a two component spectrum, usually modelled by the superposition of a blackbody and a power-law tail. It has been suggested that the ∼1‐10 keV spectrum of AXPs/SGRs forms as the thermal photons emitted by the cooling star surface traverse the magnetosphere. Magnetar magnetospheres are, in fact, likely different from those of ordinary radio pulsars, since the external magnetic field may acquire a toroidal component as a consequence of the deformation of the star crust induced by the superstrong interior field. In a twisted magnetosphere, the supporting currents can provide a large optical depth to resonant cyclotron scattering. The thermal spectrum emitted by the star surface will be then distorted because primary photons gain energy in the repeated scatterings with the flowing charges, and this may provide a natural explanation for the observed spectra. In this paper we present 3D Monte Carlo simulations of photon propagation in a twisted magnetosphere. Our model is based on a simplified treatment of the charge carrier velocity distribution which however accounts for the particle collective motion, in addition to the thermal one. The present treatment is restricted to conservative (Thomson) scattering in the electron rest frame. The code, none the less, is completely general and inclusion of the relativistic quantum electrodynamical resonant cross-section, which is required in the modelling of the hard (∼20‐200 keV) spectral tails observed in the magnetar candidates, is under way. The properties of emerging spectra have been assessed under different conditions, by exploring the model parameter space, including effects arising from the viewing geometry. Monte Carlo runs have been collected into a spectral archive which has then been implemented in the X-ray fitting package XSPEC. Two tabulated XSPEC spectral models, with and without viewing angles, have been produced and applied to the 0.1‐10 keV XMM‐Newton EPIC-pn spectrum of the AXP CXOU J1647−4552.

Suzaku Detection of Extended/Diffuse Hard X-Ray Emission from the Galactic Center

Abstract Five on-plane regions within $\pm$0.8D of the galactic center were observed with the Hard X-ray Detector (HXD) and the X-ray Imaging Spectrometer (XIS) aboard Suzaku. From all regions, significant hard X-ray emission was detected with HXD-PIN up to 40keV, in addition to the extended plasma emission which is dominant in the XIS band. The hard X-ray signals are inferred to come primarily from a spatially extended source, rather than from a small number of bright discrete objects. Contributions to the HXD data from catalogued X-ray sources, typically brighter than 1mCrab, were estimated and removed using information from Suzaku and other satellites. Even after this removal, the hard X-ray signals remained significant, exhibiting a typical 12-40keV surface brightness of 4$\times$10$^{-10}$ergcm$^{-2}$s$^{-1}$deg$^{-2}$ and power-law-like spectra with a photon index of 1.8. Combined fittings to the XIS and HXD-PIN spectra confirm that a separate hard tail component is superposed onto the hot thermal emission, confirming a previous report based on the XIS data. Over the 5-40keV band, the hard tail is spectrally approximated by a power law of photon index $\sim$2, but better by those with somewhat convex shapes. Possible origins of the extended hard X-ray emission are discussed.

Timing and Spectral Properties of the Accreting Millisecond Pulsar SWIFT J1756.9−2508

SWIFT J1756.9-2508 is one of the few accreting millisecond pulsars (AMPs) discovered to date. We report here the results of our analysis of its aperiodic X-ray variability, as measured with the Rossi X-Ray Timing Explorer during the 2007 outburst of the source. We detect strong (~35%) flat-topped broadband noise throughout the outburst with low characteristic frequencies (~0.1 Hz). This makes SWIFT J1756.9-2508 similar to the rest of AMPs and to other low-luminosity accreting neutron stars when they are in their hard states, and enables us to classify this AMP as an atoll source in the extreme island state. We also find a hard tail in its energy spectrum extending up to 100 keV, fully consistent with such source and state classification.

Linking Jet Emission, X‐Ray States, and Hard X‐Ray Tails in the Neutron Star X‐Ray Binary GX 17 \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $+$ \end{document} 2

We present the results of simultaneous radio (VLA) and X-ray (RXTE) observations of the Z-type neutron star X-ray binary GX 17+2. The aim is to assess the coupling between X-ray and radio properties throughout its three rapidly variable X-ray states and during the time-resolved transitions. These observations allow us, for the first time, to investigate quantitatively the possible relations between the radio emission and the presence of hard X-ray tails and the X-ray state of the source. The observations reveal (1) a coupling between the radio jet emission and the X-ray state of the source, that is, the position in the X-ray hardness-intensity diagram (HID); (2) a coupling between the presence of a hard X-ray tail and the position in the HID, qualitatively similar to that found for the radio emission; (3) an indication of a quantitative positive correlation between the radio flux density and the X-ray flux in the hard tail power-law component; (4) evidence for the formation of a radio jet associated with the flaring branch-to-normal branch X-ray state transition; and (5) that the radio flux density of the newly formed jet stabilizes when the normal-branch oscillation (NBO) in the X-ray power spectrum stabilizes its characteristic frequency, suggesting a possible relation between X-ray variability associated with the NBO and jet formation. We discuss our results in the context of jet models.

The 1–200 keV X‐Ray Spectrum of NGC 2992 and NGC 3081

The Seyfert 2 galaxies NGC 2992 and NGC 3081 have been observed by INTEGRAL and Swift. We report the results and a comparison of the spectrum above 10 keV based on INTEGRAL IBIS/ISGRI, Swift/BAT, and BeppoSAX/PDS. A spectrum can be extracted in the X-ray energy band ranging from 1 up to 200 keV. Although NGC 2992 shows a complex spectrum below 10 keV, the hard tail observed by various missions exhibits a slope of Γ = 2, independent of the flux level during the observation. No cut-off is detectable up to the detection limit around 200 keV. In addition, NGC 3081 is detected in the INTEGRAL and Swift observation and also shows an unbroken Γ = 1.8 spectrum up to 150 keV. These two Seyfert galaxies give further evidence that a high-energy cut-off in the hard X-ray spectra is often located at energies EC 100 keV. In NGC 2992 a constant spectral shape is observed over a hard X-ray luminosity variation by a factor of 11. This might indicate that the physical conditions of the emitting hot plasma are constant, while the amount of plasma varies, due to long-term flaring activity.

BeppoSAX observation of 4U 1705-44: detection of hard X-ray emission in the soft state

Context. 4U 1705-44 is one of the best-studied type I X-ray burster and atoll sources. Aims. Since it covers a wide range in luminosity (from a few to 50 × 10 36 erg s −1 ) and shows clear spectral state transitions, it represents a good laboratory for testing the accretion models proposed for atoll sources. Methods. We analyzed the energy spectrum accumulated with BeppoSAX observations (43.5 ks) in August 2000 when the source was in a soft spectral state. Results. The continuum of the wide-band energy spectrum is well-described by the sum of a blackbody (kTbb ∼ 0.56 keV) and a Comptonized component (seed-photon temperature kTW ∼ 1 keV, electron temperature kTe ∼ 2.7 keV, and optical depth τ ∼ 11). A hard tail was detected at energies above ∼25 keV. The latter can be modeled by a power law having a photon index ∼2.9, which contributes ∼11% of the total flux in the range 0.1–200 keV. A broad emission line, possibly from a relativistic accretion disk, models the feature in the Fe K line region of the spectrum. Conclusions. This is the first time that a high-energy tail has been observed during a soft state of the source.

The Hard X‐Ray Tails in Neutron Star Low‐Mass X‐Ray Binaries:BeppoSAXObservations and Possible Theoretical Explanation of the Case of GX 17 \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $+$ \end{document} 2

We report results of a new spectral analysis of two BeppoSAX observations of the Z source GX 17+2. In one of the two observations the source exhibits a powerlaw-like hard (> 30 keV) X-ray tail which was described in a previous work by a hybrid Comptonization model. Recent high-energy observations with INTEGRAL of a sample of Low Mass X-Ray Binaries including both Z and atoll classes have shown that bulk (dynamical) Comptonization of soft photons can be a possible alternative mechanism for producing hard X-ray tails in such systems. We start from the INTEGRAL results and we exploit the broad-band capability of BeppoSAX to better investigate the physical processes at work. We use GX 17+2 as a representative case. Moreover, we suggest that weakening (or disappearance) of the hard X-ray tail can be explained by increasing radiation pressure originated at the surface of the neutron star (NS). As a result the high radiation pressure stops the bulk inflow and consequently this radiation feedback of the NS surface leads to quenching the bulk Comptonization.

Is the Lack of Pulsations in Low‐Mass X‐Ray Binaries due to Comptonizing Coronae?

The spin periods of the neutron stars in most Low Mass X-ray Binary (LMXB) systems still remain undetected. One of the models to explain the absence of coherent pulsations has been the suppression of the beamed signal by Compton scattering of X-ray photons by electrons in a surrounding corona. We point out that simultaneously with wiping out the pulsation signal, such a corona will upscatter (pulsating or not) X-ray emission originating at and/or near the surface of the neutron star leading to appearance of a hard tail of Comptonized radiation in the source spectrum. We analyze the hard X-ray spectra of a selected set of LMXBs and demonstrate that the optical depth of the corona is not likely to be large enough to cause the pulsations to disappear.

Suzaku Spectroscopic Study of Hard X-Ray Emission in the Arches Cluster

We present the results of a Suzaku study of the Arches cluster in the Galactic center region. A high signal-to-noise ratio spectrum in the 3–12 keV band was obtained with the X-ray Imaging Spectrometer (XIS) onboard the Suzaku observatory. We found that the spectrum consists of a thermal plasma, a hard power-law tail, and two Gaussian line components. The plasma component with a temperature of $\sim 2.2 \,\mathrm{keV}$ is established from the presence of Ca XIX and Fe XXV $\mathrm{K}\alpha$ lines as well as absence of the Fe XXVI $\mathrm{K}\alpha$ line. The two Gaussian lines represent the $\mathrm{K}\alpha$ and $\mathrm{K}\beta$ lines from iron at lower ionization stages at $\sim 6.4$ and $\sim 7.1 \,\mathrm{keV}$. Both the line centers and the intensity ratio of these two lines are consistent with neutral iron. The hard power-law tail with a photon index of $\sim 0.7$ was found to have no pronounced iron K edge feature. Compared with the published Chandra spectra constructed separately for point-like and diffuse emission, we conclude that the thermal component is from an ensemble of point-like sources plus thermal diffuse emission concentrated at the cluster center, while the Gaussian and the hard tail components are from non-thermal diffuse emission extended in a larger scale. In band-limited images of the XIS field, the distribution of the 7.5–10.0 keV emission resembles that of the 6.4 keV emission, including local excess at the Arches cluster. This strongly suggests that the power-law emission is related to the 6.4 and 7.1 keV lines in the underlying physics. We discuss two ideas to explain both the hard continuum and the lines: (1) X-ray photoionization that produces fluorescence lines and the Thomson scattering continuum and (2) non-thermal electron impact ionization of iron atoms and bremsstrahlung continuum. However, whichever scenario is adopted, the photon or particle flux from the Arches cluster is too low to account for the observed lines and continuum intensity.

A Joint Suzaku and Chandra Spectroscopy Study of Hard X-Ray Emission from the Arches Cluster

We present the results of a joint Suzaku and Chandra X-ray spectroscopic study of the Arches cluster in the Galactic center region. The superb spectroscopic performance of XIS on-board Suzaku brought a tight constraint of the spectrum of the Arches X-rays. We found that the spectrum consists of a thermal plasma, a hard power-law tail, and two Gaussian components. The plasma component with a temperature of ∼2.2 keV is established from highly ionized Ca XIX and Fe XXV Kα emission lines as well as the lack of Fe XXVI Kα line. The two Gaussian lines represent the Kα and Kβ lines from iron at lower ionization stages at ∼6.4 keV and ∼7.1 keV. Both the line centers and the intensity ratio of these two lines are consistent with the neutral iron. The hard power-law tail with a photon index of ∼0.7 was found to have no pronounced iron K edge feature. In comparison with ACIS spectra constructed separately for point-like and diffuse emission by using the unprecedented spatial capability of Chandra, we conclude that the thermal component is from the ensemble of point-like sources plus thermal diffuse emission concentrated at the cluster center, while the Gaussian and the hard tail components are from the non-thermal diffuse emission extended in a larger scale. In the band-limited images of the XIS field, the distribution of the 7.5– 10.0 keV emission resembles that of the 6.4 keV emission, including the local excess at the Arches cluster. This strongly suggests that the power-law emission is related to the 6.4 and 7.1 keV lines in the underlying physics. The full discussion can be found in Tsujimoto et al. [M. Tsujimoto, Y. Hyodo and K. Koyama, Publ. Astron. Soc. Jpn. 59 (2007), S229]. For point-like X-ray emission, three Arches sources are exceptionally bright among cluster members. The brightest spectrum of them requires two temperature plasma with an extinction of 2×10 23 cm −2 . The estimated hard-band luminosity of ≈10 35 erg s −1 ,w hich is brighter than any known stellar sources in our Galaxy, might be a consequence of colliding

Nonthermal Hard X-Ray Excess in the Coma Cluster: Resolving the Discrepancy between the Results of Different PDS Data Analyses

The detection of a nonthermal excess in the Coma Cluster spectrum by two BeppoSAX observations analyzed with the XAS package (Fusco-Femiano et al.) has been disavowed by an analysis (Rossetti & Molendi) performed with a different software package (SAXDAS) for the extraction of the spectrum. To resolve this discrepancy we reanalyze the PDS data considering the same software used by Rossetti & Molendi. A correct selection of the data and the exclusion of contaminating sources in the background determination show that the SAXDAS analysis also reports a nonthermal excess with respect to the thermal emission at about the same confidence level of that obtained with the XAS package (~4.8 σ). In addition, we report the lack of the systematic errors investigated by Rossetti & Molendi and Nevalainen et al., taking into account the whole sample of the PDS observations off the Galactic plane, as already shown in our data analysis of Abell 2256 (Fusco-Femiano, Landi, & Orlandini). All this eliminates any ambiguity and confirms the presence of a hard tail in the spectrum of the Coma Cluster.

Atmosphere models of magnetized neutron stars: QED effects, radiation spectra and polarization signals

Observations of surface emission from isolated neutron stars (NSs) provide unique challenges to theoretical modelling of radiative transfer in magnetized NS atmospheres. Recent work has demonstrated the critical role of vacuum polarization effects in determining NS spectra and polarization signals, in particular the conversion of photon modes (due to the 'vacuum resonance' between plasma and vacuum polarization) propagating in the density gradient of the NS atmosphere. Previous NS atmosphere models incorporated the mode conversion effect approximately, relying on transfer equations for the photon modes. Such treatments are inadequate near the vacuum resonance, particularly for magnetic field strengths around B ∼ B l ≃ 7 × 10 13 G, where the vacuum resonance occurs near the photosphere. In this paper, we provide an accurate treatment of the mode conversion effect in magnetized NS atmosphere models, employing both the modal radiative transfer equations coupled with an accurate mode conversion probability at the vacuum resonance, and the full evolution equations for the photon Stokes parameters. In doing so, we are able to quantitatively calculate the effects of vacuum polarization on atmosphere structure, emission spectra and beam patterns, and polarizations for the entire range of magnetic field strengths, B = 10 12 -10 15 G. In agreement with previous works, we find that for NSs with magnetic field strength B ≥ 2B l , vacuum polarization reduces the widths of spectral features, and softens the hard spectral tail typical of magnetized atmosphere models. For B ≤ B l /2, vacuum polarization does not change the emission spectra, but can significantly affect the polarization signals. Our new, accurate treatment of vacuum polarization is particularly important for quantitative modelling of NS atmospheres with 'intermediate' magnetic fields, B ≃ (0.5-2) B l . We provide fitting formulae for the temperature profiles for a suite of NS atmosphere models with different field strengths, effective temperatures and chemical compositions (ionized H or He). These analytical profiles are useful for direct modelling of various observed properties of NS surface emission. As an example, we calculate the observed intensity and polarization light curves from a rotating NS hotspot, taking into account the evolution of photon polarization in the magnetosphere. We show that vacuum polarization induces a unique energy-dependent linear polarization signature, and that circular polarization can be generated in the magnetosphere of rapidly rotating NSs. We discuss the implications of our results to recent observations of thermally emitting isolated NSs and magnetars, as well as the prospects of future spectral and polarization observations.