Vacuum polarization alters the spectra of accreting X-ray pulsars

It is a common belief that for magnetic fields typical for accreting neutron stars in High-Mass X-ray Binaries vacuum polarization only affects the propagation of polarized emission in the neutron star magnetosphere. We show that vacuum resonances can significantly alter the emission from the poles of accreting neutron stars. The effect is similar to vacuum polarization in the atmospheres of isolated neutron stars and can result in suppression of the continuum and the cyclotron lines. It is enhanced by magnetic Comptonization in the hot plasma and proximity to the electron cyclotron resonance. We present several models to illustrate the vacuum polarization effect for various optically thick media and discuss how the choice of polarization modes affects the properties of the emergent radiation by simulating polarized energy- and angle-dependent radiative transfer. Polarization effects, including vacuum polarization, crucially alter the emission properties. Together with strongly angle- and energy- dependent magnetic Comptonization, they result in a complex spectral shape, which can be described by dips and humps on top of a power-law-like continuum with high-energy cutoff. These effects provide a possible explanation for the common necessity of additional broad Gaussian components and two-component Comptonization models that are used to describe spectra of accreting X-ray pulsars. We also demonstrate the character of depolarization introduced by the radiation field's propagation inside the inhomogeneous emission region.Comment: 4 pages, 6 figures, accepted for publication in A&A Letter

Cyclotron resonant scattering feature simulations. I. Thermally averaged cyclotron scattering cross sections, mean free photon-path tables, and electron momentum sampling

Electron cyclotron resonant scattering features (CRSFs) are observed as absorption-like lines in the spectra of X-ray pulsars. A significant fraction of the computing time for Monte Carlo simulations of these quantum mechanical features is spent on the calculation of the mean free path for each individual photon before scattering, since it involves a complex numerical integration over the scattering cross section and the (thermal) velocity distribution of the scattering electrons. We aim to numerically calculate interpolation tables which can be used in CRSF simulations to sample the mean free path of the scattering photon and the momentum of the scattering electron. The tables also contain all the information required for sampling the scattering electron's final spin. The tables were calculated using an adaptive Simpson integration scheme. The energy and angle grids were refined until a prescribed accuracy is reached. The tables are used by our simulation code to produce artificial CRSF spectra. The electron momenta sampled during these simulations were analyzed and justified using theoretically determined boundaries. We present a complete set of tables suited for mean free path calculations of Monte Carlo simulations of the cyclotron scattering process for conditions expected in typical X-ray pulsar accretion columns (0.01<B/B_{crit}<=0.12, where B_{crit}=4.413x10^{13} G and 3keV<=kT<15keV). The sampling of the tables is chosen such that the results have an estimated relative error of at most 1/15 for all points in the grid. The tables are available online at http://www.sternwarte.uni-erlangen.de/research/cyclo.Comment: A&A, in pres

Luminosity-dependent changes of the cyclotron line energy and spectral hardness in Cepheus X-4

Context. X-ray spectra of accreting pulsars are generally observed to vary with their X-ray luminosity. In particular, the hardness of the X-ray continuum is found to depend on luminosity. In a few sources, the correlation between the energy of the cyclotron resonance scattering feature (CRSF) and the luminosity is clear. Different types (signs) of the correlation are believed to reflect different accretion modes. Aims. We analyse two NuSTAR observations of the transient accreting pulsar Cep X-4 during its 2014 outburst. Our analysis is focused on a detailed investigation of the dependence of the CRSF energy and of the spectral hardness on X-ray luminosity, especially on short timescales. Methods. To investigate the spectral changes as a function of luminosity within each of the two observations, we used the intrinsic variability of the source on the timescale of individual pulse cycles (tens of seconds), the so-called pulse-to-pulse variability. Results. We find that the NuSTAR spectrum of Cep X-4 contains two CRSFs: the fundamental line at ~30 keV and its harmonic at ~55 keV. We find for the first time that the energy of the fundamental CRSF increases and the continuum becomes harder with increasing X-ray luminosity not only between the two observations, that is, on the long timescale, but also within an individual observation, on the timescale of a few tens of seconds. We investigate these dependencies in detail including their non-linearity. We discuss a possible physical interpretation of the observed behaviour in the frame of a simple one-dimensional model of the polar emitting region with a collisionless shock formed in the infalling plasma near the neutron star surface. With this model, we are able to reproduce the observed variations of the continuum hardness ratio and of the CRSF energy with luminosity

NuSTAR observation of GRO J1744-28 at low mass accretion rate

We present the spectral analysis of the LMXB GRO J1744-28 using $\sim$29 ks of NuSTAR data taken in 2017 February at a low luminosity of $3.2\times 10^{36}$ erg/s (3-50 keV). The continuum spectrum is modeled with an absorbed power-law with exponential cut-off, and an additional iron line component. We find no obvious indications for a CRSF and therefore perform a detailed cyclotron line search using statistical methods on the pulse phase-averaged as well as phase-resolved spectra. The previously detected Type II X-ray bursts are absent. Clear pulsations at a period of 2.141124(9) Hz are detected. The pulse profile shows an indication of a secondary peak, which was not seen at higher flux. The 4$\sigma$ upper limit for the strength of a CRSF in the 3-20 keV band is 0.07 keV, lower than the strength of the line found at higher luminosity. The detection of pulsations shows that the source did not enter the "propeller" regime, even though the source flux of $4.15\times 10^{-10}$ erg/cm$^{2}$/s was almost one order of magnitude below the threshold for the propeller regime claimed in previous studies on this source. The transition into the propeller regime in GRO J1744-28 must therefore be below a luminosity of $3.2\times 10^{36}$ erg/s, which implies a surface magnetic field $\lesssim 2.9\times 10^{11}$ G and mass accretion rate $\lesssim 1.7\times 10^{16}$ g/s. A change of the CRSF depth as function of luminosity is not unexpected and has been observed in other sources. This result possibly implies a change in emission geometry as function of mass accretion rate to reduce the depth of the line below our detection limit

X-ray emission from magnetized neutron star atmospheres at low mass accretion rates. I. Phase-averaged spectrum

Recent observations of X-ray pulsars at low luminosities allow, for the first time, to compare theoretical models for the emission from highly magnetized neutron star atmospheres at low mass accretion rates ($\dot{M} \lesssim 10^{15}$ g s$^{-1}$) with the broadband X-ray data. The purpose of this paper is to investigate the spectral formation in the neutron star atmosphere at low $\dot{M}$ and to conduct a parameter study of physical properties of the emitting region. We obtain the structure of the static atmosphere, assuming that Coulomb collisions are the dominant deceleration process. The upper part of the atmosphere is strongly heated by the braking plasma, reaching temperatures of 30-40 keV, while its denser isothermal interior is much cooler (~2 keV). We numerically solve the polarized radiative transfer in the atmosphere with magnetic Compton scattering, free-free processes, and non-thermal cyclotron emission due to possible collisional excitations of electrons. The strongly polarized emitted spectrum has a double-hump shape that is observed in low-luminosity X-ray pulsars. A low-energy "thermal" component is dominated by extraordinary photons that can leave the atmosphere from deeper layers due to their long mean free path at soft energies. We find that a high-energy component is formed due to resonant Comptonization in the heated non-isothermal part of the atmosphere even in the absence of collisional excitations. The latter, however, affect the ratio of the two components. A strong cyclotron line originates from the optically thin, uppermost zone. A fit of the model to NuSTAR and Swift/XRT observations of GX 304-1 provides an accurate description of the data with reasonable parameters. The model can thus reproduce the characteristic double-hump spectrum observed in low-luminosity X-ray pulsars and provides insights into spectral formation.Comment: 18 pages, 10 figures, A&A accepte

The giant outburst of 4U 0115+634 in 2011 with Suzaku and RXTE - Minimizing cyclotron line biases

We present an analysis of X-ray spectra of the high-mass X-ray binary 4U 0115+634 as observed with Suzaku and RXTE in 2011 July, during the fading phase of a giant X-ray outburst. We used a continuum model consisting of an absorbed cutoff power law and an ad hoc Gaussian emission feature centered around 8.5 keV, which we attribute to cyclotron emission. Our results are consistent with a fundamental cyclotron absorption line centered at ∼10.2 keV for all observed flux ranges. At the same time we rule out significant influence of the 8.5 kev Gaussian on the parameters of the cyclotron resonant scattering feature, which are not consistent with the cyclotron line energies or the depths of previously reported flux-dependent descriptions. We also show that some continuum models can lead to artificial line-like residuals in the analyzed spectra, which are then misinterpreted as unphysically strong cyclotron lines. Specifically, our results do not support the existence of a previously claimed additional cyclotron feature at ∼15 keV. Apart from these features, we find for the first time evidence for a He-like Fe XXV emission line at ∼6.7 keV and weak H-like Fe XXVI emission close to ∼7.0 keV.We acknowledge funding by the European Space Agency under contract number C4000115860/15/NL/IB, by the Bundesministerium für Wirtschaft und Technologie under Deutsches Zentrum für Luft- und Raumfahrt grants 50OR0808, 50OR0905, 50OR1113, and 50OR1207, and by the Deutscher Akademischer Austauschdienst. MTW is supported by the NASA Astrophysical Data Analysis Program and the Chief of Naval Research. VG is supported through the Margarethe von Wrangell fellowship by the ESF and the Ministry of Science, Research and the Arts Baden-Württemberg. SMN and JMT acknowledge Spanish Ministerio de Ciencia, Tecnología e Innovación (MICINN) through the grant ESP2016-76683-C3-1-R and ESP2017-85691-P, respectively

Luminosity-dependent changes of the cyclotron line energy and spectral hardness in Cepheus X-4

Context. X-ray spectra of accreting pulsars are generally observed to vary with their X-ray luminosity. In particular, the hardness of the X-ray continuum is found to depend on luminosity. In a few sources, the correlation between the energy of the cyclotron resonance scattering feature (CRSF) and the luminosity is clear. Different types (signs) of the correlation are believed to reflect different accretion modes. Aims. We analyse two NuSTAR observations of the transient accreting pulsar Cep X-4 during its 2014 outburst. Our analysis is focused on a detailed investigation of the dependence of the CRSF energy and of the spectral hardness on X-ray luminosity, especially on short timescales. Methods. To investigate the spectral changes as a function of luminosity within each of the two observations, we used the intrinsic variability of the source on the timescale of individual pulse cycles (tens of seconds), the so-called pulse-to-pulse variability. Results. We find that the NuSTAR spectrum of Cep X-4 contains two CRSFs: the fundamental line at ~30 keV and its harmonic at ~55 keV. We find for the first time that the energy of the fundamental CRSF increases and the continuum becomes harder with increasing X-ray luminosity not only between the two observations, that is, on the long timescale, but also within an individual observation, on the timescale of a few tens of seconds. We investigate these dependencies in detail including their non-linearity. We discuss a possible physical interpretation of the observed behaviour in the frame of a simple one-dimensional model of the polar emitting region with a collisionless shock formed in the infalling plasma near the neutron star surface. With this model, we are able to reproduce the observed variations of the continuum hardness ratio and of the CRSF energy with luminosity

Luminosity-dependent Changes of the Cyclotron Line Energy and Spectral Hardness in Cepheus X-4

Context. X-ray spectra of accreting pulsars are generally observed to vary with their X-ray luminosity. In particular, the hardness of the X-ray continuum is found to depend on luminosity. In a few sources, the correlation between the energy of the cyclotron resonance scattering feature (CRSF) and the luminosity is clear. Different types (signs) of the correlation are believed to reflect different accretion modes. Aims. We analyse two NuSTAR observations of the transient accreting pulsar Cep X-4 during its 2014 outburst. Our analysis is focused on a detailed investigation of the dependence of the CRSF energy and of the spectral hardness on X-ray luminosity, especially on short timescales. Methods. To investigate the spectral changes as a function of luminosity within each of the two observations, we used the intrinsic variability of the source on the timescale of individual pulse cycles (tens of seconds), the so-called pulse-to-pulse variability. Results. We find that the NuSTAR spectrum of Cep X-4 contains two CRSFs: the fundamental line at ~30 keV and its harmonic at ~55 keV. We find for the first time that the energy of the fundamental CRSF increases and the continuum becomes harder with increasing X-ray luminosity not only between the two observations, that is, on the long timescale, but also within an individual observation, on the timescale of a few tens of seconds. We investigate these dependencies in detail including their non-linearity. We discuss a possible physical interpretation of the observed behaviour in the frame of a simple one-dimensional model of the polar emitting region with a collisionless shock formed in the infalling plasma near the neutron star surface. With this model, we are able to reproduce the observed variations of the continuum hardness ratio and of the CRSF energy with luminosity

Continuum, cyclotron line, and absorption variability in the high-mass X-ray binary Vela X-1

Because of its complex clumpy wind, prominent cyclotron resonant scattering features, intrinsic variability and convenient physical parameters (close distance, high inclination, small orbital separation) which facilitate the observation and analysis of the system, Vela X-1 is one of the key systems to understand accretion processes in high-mass X-ray binaries on all scales. We revisit Vela X-1 with two new observations taken with NuSTAR at orbital phases ~0.68-0.78 and ~0.36-0.52 which show a plethora of variability and allow us to study the accretion geometry and stellar wind properties of the system. We follow the evolution of spectral parameters down to the pulse period time-scale using a partially covered powerlaw continuum with a Fermi-Dirac cut-off to model the continuum and local absorption. We could confirm anti-correlations between the photon index and the luminosity and, for low fluxes, between the folding energy and the luminosity, implying a change of properties in the Comptonising plasma. We could not confirm a previously seen correlation between the cyclotron line energy and the luminosity of the source in the overall observation, but we observed a drop in the cyclotron line energy following a strong flare. We see strong variability in absorption between the two observations and within one observation (for the ~0.36-0.52 orbital phases) that can be explained by the presence of a large-scale structure, such as accretion- and photoionisation wakes in the system and our variable line of sight through this structure.Comment: 18 pages, 13 figures, A&A accepte

X-ray emission from magnetized neutron star atmospheres at low mass-accretion rates: I. Phase-averaged spectrum

Recent observations of X-ray pulsars at low luminosities allow, for the first time, the comparison of theoretical models of the emission from highly magnetized neutron star atmospheres at low mass-accretion rates (M ≤ 1015 g s-1) with the broadband X-ray data. The purpose of this paper is to investigate spectral formation in the neutron star atmosphere at low á¹€ and to conduct a parameter study of the physical properties of the emitting region. We obtain the structure of the static atmosphere, assuming that Coulomb collisions are the dominant deceleration process. The upper part of the atmosphere is strongly heated by the braking plasma, reaching temperatures of 30-40 keV, while its denser isothermal interior is much cooler (∼2 keV). We numerically solve the polarized radiative transfer in the atmosphere with magnetic Compton scattering, free-free processes, and nonthermal cyclotron emission due to possible collisional excitations of electrons. The strongly polarized emitted spectrum has a double-hump shape that is observed in low-luminosity X-ray pulsars. A low-energy "thermal"component is dominated by extraordinary photons that can leave the atmosphere from deeper layers because of their long mean free path at soft energies. We find that a high-energy component is formed because of resonant Comptonization in the heated nonisothermal part of the atmosphere even in the absence of collisional excitations. However, these latter, if present, affect the ratio of the two components. A strong cyclotron line originates from the optically thin, uppermost zone. A fit of the model to NuSTAR and Swift/XRT observations of GX 304-1 provides an accurate description of the data with reasonable parameters. The model can thus reproduce the characteristic double-hump spectrum observed in low-luminosity X-ray pulsars and provides insights into spectral formation