Using RXTE/ASM archival data, we investigate the behaviour of the spectral hardness ratio as a function of X-ray luminosity in a sample of six transient X-ray pulsars (EXO 2030+375, GX 304-1, 4U 0115+63, V 0332+63, A 0535+26 and MXB 0656-072). In all sources we find that the spectral hardness ratio defined as F 5−12keV /F 1.33−3keV increases with the ASM flux (1.33-12 keV) at low luminosities and then saturates or even slightly decreases above some critical X-ray luminosity falling into the range ∼ (3 − 7) × 10 37 erg s −1 . Two-dimensional structure of accretion columns in the radiation-diffusion limit is calculated for two possible geometries (filled and hollow cylinder) for mass accretion ratesṀ ranging from 10 17 to 1.2×10 18 g s −1 . The observed spectral behaviour in the transient X-ray pulsars with increasinġ M can be reproduced by a Compton saturated sidewall emission from optically thick magnetized accretion columns with taking into account the emission reflected from the neutron star atmosphere. AtṀ above some critical valueṀ cr ∼ (6 − 8) × 10 17 g s −1 , the hight of the column becomes such that the contribution of the reflected component to the total emission starts decreasing, which leads to the saturation and even slight decrease of the spectral hardness. Hollow-cylinder columns have a smaller height than the filled-cylinder ones, and the contribution of the reflected component in the total emission does not virtually change withṀ (and hence the hardness of the continuum monotonically increases) up to higher mass accretion rates thanṀ cr for the filled columns.

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.

The RXTE observed four outbursts of the accreting X-ray binary transient source, GX 304−1 in 2010 and 2011. We present results of detailed 3−100 keV spectral analysis of 69 separate observations, and report a positive correlation between cyclotron line parameters, as well as other spectral parameters, with power law flux. The cyclotron line energy, width and depth versus flux, and thus luminosity, correlations show a flattening of the relationships with increasing luminosity, which are well described by quasi-spherical or disk accretion that yield the surface magnetic field to be ∼60 keV. Since HEXTE cluster A was fixed aligned with the PCA field of view and cluster B was fixed viewing a background region 1.5 degrees off of the source direction during these observations near the end of the RXTE mission, the cluster A background was estimated from cluster B events using HEXTEBACKEST. This made possible the detection of the ∼55 keV cyclotron line and an accurate measurement of the continuum. Correlations of all spectral parameters with the primary 2−10 keV power law flux reveal it to be the primary driver of the spectral shape. The accretion is found to be in the collisionless shock braking regime.

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 (Ṁ ≲ 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 Ṁ 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.

The paper presents the results of three-dimensional modelling of the structure and the emission of accretion columns formed above the surface of accreting strongly magnetized neutron stars under the circumstances when a pressure of the photons, generated in the column base is enough to determine the dynamics of the accretion plasma flow. On the foundation of numerical radiation hydrodynamic simulations, several three-dimensional models of accretion column are constructed. The first group of the models contains spatially three-dimensional columns. The corresponding calculations give the distributions of the radiation flux over the sidewalls of the columns which do not have an axial symmetry. The second group includes the self-consistent modelling of spectral radiative transfer and two-dimensional spatial structure of the column, with both thermal and bulk Comptonization are taked into account. The changes in the structure of the column and the shape of X-ray continuum are investigated depending on physical parameters of the model.